I  PRESENTED  BY 


Please 

handle  this  volume 

with  care. 

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Libraries,  Storrs 


530 
G  i^ 


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iM 


BOOK    530. G  15    c.  1 

GANOT    #    ELEMENTARY    TREATISE    ON 

PHYSICS 


3  T153  00126307  6 


GANOT'S     PHYSICS. 


Sixth    Edition,  with   34  pages  of  new  matter,   2   Plates, 

518  Woodcuts,  and  an  Appendix  of  Questions. 

Crown  8vo.  "js.  6d. 

NATURAL    PHILOSOPHY 

FOR  GENERAL  READERS  AND  YOUNG  PERSONS. 

A  Course  of  Physics  divested  of  Mathematical  Formula;, 
expressed  in  the  language  of  daily  life. 

Translated    and    Edited    from  Ganot's  Cmirs  Elcmentaire  de 
Physiqzic,  by  E.  Atkinson,  Ph.D.  F.C.S. 

London  :   LONGMANS,  GREEN,  &   CO. 


"^ 


^> 


9d7(^ 


ELEMENTARY      TREATISE 


PHYSICS  '' 


EXPERIMENTAL     AND     APPLIED 

FOR     THE     USE     OF    COLLEGES    AND    SCHOOLS. 
TRANSLATED   AND   EDITED   FROM 

GANOT'S    ELEMENTS     DE     PHYSIQUE 

(with  the  Author's   saiiction) 
BY 

E.  ATKINSON,  Ph.D.,  F.C.S. 

LATE      PROFESSOR      OF      EXPERIMENTAL      SCIENCE      IN      THE      STAFF      COLLEGE. 

®;i^irte£nt^  (SMtioit,  rjfrisfb  Hnl»  enlargeb. 

ILLUSTRATED  by  g  COLOURED   PLATES  and  MAPS  and  987   WOODCUTS. 


NEW     YORK  : 
WILLIAM     WOOD     AND     CO.,     PUBLISHERS, 

56  &  58  lafayette  place. 
i8qo. 


,.-^p#^ 


CONTENTS. 


BOOK    I. 
ON    MATTER,   FORCE,   AND    MOTION. 


Errata 

Pages  494  and  513,  Figs.  451  and  480  should  be  interchanged 

Ganot's  Physics. 
iV.      rK.urii.Kij.ii-D   1 -r-v^uj^ij-iiv    IV. 

BOOK   III. 
ON     LIQUIDS. 

I.  Hydrostatics  .  .  .  '  •  •  •  •  .86 
II.     Capillarity,  Endosmose,  Effusion,  and  Absorption     .  .114 

III.     Hydrodynamics         .......       127 

BOOK   IV. 
ON     GASES. 

I.     Properties  of  Gases.     Atmosphere.     Barometers         .  .136 

II.  Measurement  of  the  Elastic  Force  of  Gases  .  .  -157 

III.  Pressure  on  Bodies  in  Air.     Balloons    .  .  .  -173 

IV.  Apparatus  which  depend  on  the  Properties  of  Air  .  .       178 


CONTENTS. 


BOOK   I. 
ON    MATTER,   FORCE,   AND    MOTION. 

CHAPTER  PAGE 

I.     General  Principles  .......  i 

II.     General  Properties  of  Bodies      .....  4 

III.     On  Force,  Equilibrium,  and  Motion       .  .  ,  .11 

BOOK   11. 

ON  GRAVITATION  AND  MOLECULAR  ATTRACTION. 

I.     Gravity,  Centre  of  Gravity,  the  Balance        .  .  .54 

II.     Laws  of  Falling  Bodies.    Intensity  of  Terrestrial  Gravity. 

The  Pendulum    .......        63 

III.  Molecular  Forces    .......        73 

IV.  Properties  peculiar  to  Solids       .....         77 

BOOK   III. 

ON     LIQUIDS. 

I.     Hydrostatics  .  .  .  '  .  .  .  .  .86 

II.     Capillarity,  Endosmose,  Effusion,  and  Absorption    .  .114 


III.     Hydrodynamics 


II.     Measurement  of  the  Elastic  Force  of  Gases  . 
III.     Pressure  on  Bodies  in  Air.     Balloons   . 


127 


BOOK    IV. 
ON     GASES. 
I.     Properties  of  Gases.     Atmosphere.     Barometers         .  .       136 


157 
173 


IV.     Apparatus  which  depend  on  the  Properties  of  Air  .  .178 


Contents. 


BOOK   V. 


ON     SOUND. 

CHAPTER 

I.  Production,  Propagation,  and  Reflection  of  Sound 

II.  Measurement  of  the  Number  of  Vibrations  . 

III.  The  Physical  Theory  of  Music  .... 

IV.  Vibrations  of  Stretched  Strings,  and  of  Columns  of  Air 
V.  Vibrations  of  Rods,  Plates,  and  Membranes  . 

VT.     Graphical  Method  of  Studying  Vibratory  Motions 


PAGE 

199 

2X8 

224 
241 
255 
259 


BOOK   VI. 

ON      HEAT. 


I.  Preliminary  Ideas.     Thermometers 

II.  Expansion  of  Solids 

III.  Expansion  of  Liquids 

IV.  Expansion  and  Density  of  Gases 
V.  Changes  of  Condition.     Vapours 

VI.  Hygrometry 

VII.  Conductivity  of  Solids,  Liquids,  and 

VIII.  Radiation  of  Heat 

IX.  Calorimetry 

X.  Steam  Engines 

XI.  Sources  of  Heat  and  Cold 

XII.  Mechanical  Equivalent  of  Heat 


Gases 


272 
287 

295 

302 

311 

365 

375 
3S3 
422 
442 
457 
474 


BOOK  VII. 
ON     LIGHT. 


I.  Transmission,  Velocity,  and  Intensity  of  Light 

II.  Reflection  of  Light.     Mirrors  . 

III.  Single  Refraction.     Lenses 

IV.  Dispersion  and  Achromatism 

V.  Optical  Instruments         .... 

VI.  The  Eye  considered  as  an  Optical  Instrument 

VII.  Sources  of  Light.     Phosphorescence    . 

VIII.  Double  Refraction.     Interference.     Polarisation 


4S1 
494 
512 

535 
560 
587 
607 
6x1 


ADVERTISEMENT 

TO 

THE     THIRTEENTH      EDITION. 


In  the  present  edition  the  additions  made  have  increased  by  about 
fifty-one  pages  the  size  of  the  work  as  it  stood  in  the  last  edition. 
The  new  matter  contains  also  fifty-seven  additional  illustrations. 

I  have  to  express  my  acknowledgments  to  Dr.  G.  H.  Johnson  for 
his  kindness  in  revising  the  chapter  on  the  Eye. 

I  am  further  indebted  to  Mr.  F.  C.  Poynder  for  having  called  my 
attention  to  a  number  of  errata. 

The    continued   favour  with  which   the   work  has   been   received, 

as   a   Text-book  for   Colleges   and   Schools,  and   also  as   a   book  of 

reference   for   the   general  reader,  renders  any  apology  for  omissions 

perhaps   unnecessary  ;    it   may,   however,    be   as   well   once  more   to 

point   out  that   the   book   is   intended   to   be   a   general  Elementary 

Treatise  on.  Physics,  and  that,  while  it  accordingly  aims  at  giving  an 

account  of  the  most  important  facts  and  general  laws  of  all  branches 

of  Physics,  an  attempt  to  treat  completely  and  exhaustively  of  any  one 

branch  would  both  be  inconsistent  with  the  general  plan  of  the  book 

and  impossible  within  the  available  space. 

E.  ATKINSON. 

PORTESBERY    HiLL,    CaMBERLEY  :     Dcc.    1889. 


EXTRACT  FROM  ADVERTISEMENT  TO    THE 
TWELFTH  EDITION. 

Some  alterations  have  been  made  in  Book  I. :  in  making  these  I 
have  availed  myself  of  an  introductory  chapter  which  Prof  Nipher,  of 
the  University  of  Missouri,  prepared  for  the  use  of  his  classes,  and 
which  he  kindly  placed  at  my  disposal. 

E.  A. 


TRANSLATORS  PREFACE   TO  FIRST  EDITION. 

The  Elements  de  Physique  of  Professor  Ganot,  of  which  the  present 
work  is  a  translation,  has  acquired  a  high  reputation  as  an  Introduction 
to  Physical  Science.  In  France  it  has  passed  through  Nine  large 
editions  in  little  more  than  as  many  years,  and  it  has  been  translated 
into  German  and  Spanish. 

This  reputation  it  doubtless  owes  to  the  clearness  and  conciseness 
with  which  the  principal  physical  laws  and  phenomena  are  explained, 
to  its  methodical  arrangement,  and  to  the  excellence  of  its  illustrations. 
In  undertaking  a  translation,  I  was  influenced  by  the  favourable  opinion 
which  a  previous  use  of  it  in  teaching  had  enabled  me  to  form. 

I  found  that  its  principal  defect  consisted  in  its  too  close  adaptation 
to  the  French  systems  of  instruction ;  and  accordingly,  my  chief  labour, 
beyond  that  of  mere  translation,  has  been  expended  in  making  such 
alterations  and  additions  as  might  render  it  more  useful  to  the  English 
student. 

I  have  retained  throughout  the  use  of  the  Centigrade  thermometer, 
and  in  some  cases  have  expressed  the  smaller  linear  measures  on  the 
metrical  system.  These  systems  are  now  everywhere  gaining  ground, 
and  an  apology  is  scarcely  needed  for  an  innovation  which  may  help  to 
familiarise  the  English  student  with  their  use  in  the  perusal  of  the  larger 
and  more  complete  works  on  Physical  Science  to  which  this  work  may 
serve  as  an  introduction. 

E.    A. 
Royal  Military  College,   Sandhurst  : 


LIST  OF  TABLES. 


Absorbing  powers       .        .        .     394 
Absorption  of  gases       .  .      166,  170 

heat  by  gases  .  .     410 

liquids  .     404 

vapours         .     406 

various  bodies 

405,411 
Atmosphere,  composition  of  .         .      139 


Barometric  variations 

Boiling  points 

Breaking  weight  of  substances 

Capillarity  in  barometers  . 
Capillary,  constant 
Combustion,  heat  of 
Conducting   powers    of    solids   for 
heat 

liquids  for  heat 

Conductors  of  electricity 

Densities  of  gases 


vapours 


Density  of  water  . 
Diamagnetism 
Diathermanous  power 
Diffusion  of  solutions 

,,        of  heat  . 
Dulong  and  Petit's  law 


Elasticity. 
Electrical  conductivity  . 
Electricity,  positive  and  negative 
Electromotive    force    of    different 
elements  .... 

series     . 

Endosmotic  equivalents 
Expansion,  coefficients  of  solids  290. 

liquids 

gases 

Eye,  dimensions  of 

refractive  indices  of  media  of 

Freezing  mixtures 
Fusing  points  of  bodies 


150 
333 

«3 

148 
122 
465 

377 
380 
390 

310 
364 
301 

950 
404 
126 
408 
432 

79 
926 

693 

787 

775 
124 
),  291 
298 
306 
590 
590 

320 
3" 


l-AGE 

Glaisher's  factors       .         .         -371 
Gravity,  force  of,  at  various  places        69 

Hardness,  scale  of      .         .         .84 


Latent  heat,  of  evaporation  .  341 
fusion          .  .437 

Magnetic  declination .         .  .     658 

inclination .         .  .     664 

Molecular  velocity  of  gases    .  ,     275 

Radiating  powers  .  .  395,  402 
Radiation  of  powders  .  .  .  414 
Reflecting  powers  .  .  .  393 
Refraction,  angle  of  double  .  .616 
Refractive  indices  .  .  .  5-2 
of  media  of  eye    .      590 


Sound,  transmission  of,  in  tubes 
Specific  gravity  of  liquids 
solids 


[08 


heat  of  solids  and  liquids  430,  431 

gases       ._  _      .         .     434 

inductive  capacities  ,  .      716 

striking  distance        .         .      757 


Tangent  galvanometer  and  volta- 
meter, comparison  between 
Temperatures,  various  remarkable . 

at  different  latitudes  . 

thermal  springs 

measurement  of 


Tension  of  aqueous  vapour     .     325. 

vapours  of  liquids 

Thermo-electric  series  . 


Undulations,  length  of 

Velocity  of  sound  in  gases 

liquids 

rock 

solids 

Vibrations  of  musical  scale 


833 
286 
984 
986 
307 
329 
330 
911 

6x1 

208 
210 
212 
211 

225 


LIST  OF  PLATES  AND  MAPS. 

Table  of  Spectra Fyontispieu 

Coloured  Rings  produced  by  Polarised  Light  in  Double  Refract- 
ing Crystals To  face  p.  636 

Isogonic  Lines  for  the  Year  1882 ,,         659 

IsocLiNic  Lines  for  the  Year  1882 ,,         664 

IsoDYNAMic  Lines  for  the  Year  1882 ,,         067 

Aurora  Borealis ,,       1029 

Isothermal  Lines  for  the  Year    ......  ,,       1031 

Isothermal  Lines  for  January ,,       1032 

Isothermal  Lines  for  July ,,       1034 


Mini 


iiliiiiilii 

Millimetres 


Square 
Centi- 


13 


15 

Centimetres 


The  area  of  the  figure  within  the  heavy  lines  is 
that  of  a  square  decimetre.  A  cube,  one  of  whose 
sides  is  this  area,  is  a  cubic  decimetre  or  litre.  A 
htre  of  water  at  the  temperature  of  4°  C.  weighs  a 
kilogramme.  A  litre  of  air  at  0°  C.  and  760™" 
pressure  weighs  1*2 93  gramme. 

A  Htre  is  i-'jdp'nt ;  a  pint  is  0*568  of  a  htre. 

The  smaller  figures  in  dotted  lines  represent  the 
areas  of  a  square  centimetre  and  of  a  square  inch. 

A  cubic  centimetre  of  water  at  4°  C.  weighs  a 
oramme. 


Square  Inch 


Inches  Feet 

Millimetre    .....  o'o3937  o"oo328i 

Centimetre       .....  o'3937i  o'o328ig 

Decimetre     .....  3'937o8  o"328o90 

Metre 39 '37079  3  ■280899 

Kilometre 3937070000  328o'899i67 

A  Hectare  or  10,000  square  metres  is  equal  to  2'47ii4  acres,  each  of  which  is  43,560 
square  feet.  A  kilometre  is  o-62i4  of  a  statute  mile.  A  statute  mile  is  i '609  kilometre. 
A  knot  (in  telegraphy)  is  2,029  yards  or  i'iS28  statute  mile. 

Measures  of  Capacity. 

Cubic  Feet 

Cubic  Inches  1,728  c.  in.  =  1  c.  ft. 

Cubic  centimetre  or  millimetre     .  o'o6io3  o'oooo35 

Litre  or  cubic  decimetre  .         .     .         61 '02705  o'C353i7 

Kilolitre  or  cubic  metre         .         .  6i,o27'o5i52  35'3i658i 

Measures  of  Weight. 

Avoirdupois  Pounds 
English  Grains  of  7,000  grains 

Milligramme o"oi543  o"ooooo22 

Gramme i5'4323S  o'oo22046 

Kilogramme 15, 432 '34880  2 '2046213 

I  grain  =  0*064799  gramme  ;  i  pound  avoirdupois  is  o'4S3593  kilogramme. 


Contents, 


BOOK  VIII. 
ON    MAGNETISM. 

CHAPTER 

I.  Properties  of  Magnets     .... 

II.  Terrestrial  Magnetism.     Compasses 

III.  Laws  of  Magnetic  Attraction  and  Repulsion 

IV,  Processes  of  Magnetisation 


PAGE 

649 
656 
669 

677 


BOOK   IX. 

ON    FRICTIONAL   ELECTRICITY. 

I.     Fundamental  Principles  ......      688 

II.     Quantitative  Laws  of  Electrical  Action       .  .  .      696 

III.  Action  of  Electrified  Bodies  on  Bodies  in  the  Natural 

State.     Induced  Electricity.     Electrical  Machines    .       709 

IV.  Condensation  or  Accumulatio-n  of  Electricity        .  .       737 

BOOK   X. 

ON    DYNAMICAL   ELECTRICITY. 


I. 
IL 

in. 

IV. 


VI. 

VIL 

VIIL 

IX. 

X. 


Voltaic  Pile.     Its  Modifications 
Detection  and  Measurement  of  Voltaic  Currents  . 
Effects  of  the  Current  ..... 
Electrodynamics.     Attraction  and  Repulsion  of  Currents 

BY  Currents     ...... 

Magnetisation    by   Currents.      Electromagnets.      Electric 

Telegraphs   ...... 

Voltaic  Induction  ..... 

Optical  Effects  of  Powerful  Magnets.     Diamagnetism 
Thermo-electric  Currents  .... 

Determination  of  Electrical  Constants 

Animal  Electricity  ..... 


Elementary  Outlines  of  Meteorology  and  Climatology 
Problems  and  Examples  in  Physics 


770 
790 


844 

S62 
8S7 
944 
952 
965 
942 

993 
1039 


INDEX 


1063 


ELEMENTARY    TREATISE 

ON 

PHYSICS. 

BOOK    I. 

ON    MATTER,    FORCE,   AND    MOTION. 
CHAPTER    I. 

GENEKAL    PRINCIPLES. 

1.  Object  Of  Physics. — The  object  of  Physics  is  the  study  of  the  phe- 
nomena presented  to  us  by  bodies.  It  should,  however,  be  added,  that 
changes  in  the  nature  of  the  body  itself,  such  as  the  decomposition  of  one 
body  into  others,  are  phenomena  whose  study  forms  the  more  immediate 
object  oi  clicmistry. 

2.  Matter. — That  which  possesses  the  properties  whose  existence  is 
revealed  to  us  by  our  senses,  we  call  matter  or  substance. 

All  substances  at  present  known  to  us  may  be  considered  as  chemical 
combinations  of  sixty-seven  elementary  or  simple  substances.  This  number, 
however,  may  hereafter  be  diminished  or  increased  by  the  discovery  of  some 
more  powerful  means  of  chemical  analysis  than  we  at  present  possess. 

3.  Atoms,  molecules. — From  various  properties  of  bodies,  we  conclude 
that  the  matter  of  which  they  are  formed  is  not  perfectly  continuous,  but 
consists  of  an  aggregate  of  an  immense  number  of  exceedingly  small  por- 
tions or  atoms  of  matter.  These  atoms  cannot  be  divided  physically  ;  they 
are  retained  side  by  side,  without  touching  each  other,  being  separated  by 
distances  which  are  great  in  comparison  with  their  supposed  dimensions. 

A  group  of  two  or  more  atoms  forms  a  molecule.,  so  that  a  body  may  be 
considered  as  an  aggregate  of  very  small  molecules,  and  these  again  as 
aggregates  of  still  smaller  atoms.  The  smallest  masses  of  matter  we  e\'er 
obtain  artificially  are  particles^  and  not  molecules  or  atoms.  Molecules 
retain  their  position  in  virtue  of  the  action  of  certain  forces  called  molecular 
forces. 

From  considerations  based  upon  various  physical  phenomena  Sir  W, 
Thomson  has  calculated    that    in  ordinary  solids  and  liquids,  the  average 


2  On  Matter,  Force,  and  Motion.  [3- 

distance  between  contiguous  molecules  is  less  than  the  one  hundred-millionth 
but  greater  than  the  one  two  thousand-millionth  of  a  centimetre. 

To  form  an  idea  of  the  degree  of  the  size  of  the  molecules,  Sir  W. 
Thomson  gives  this  illustration  : — '  Imagine  a  drop  of  rain,  or  a  glass  sphere 
the  size  of  a  pea,  magnified  to  the  size  of  the  earth,  the  molecules  in  it  being 
increased  in  the  same  proportion.  The  structure  of  the  mass  would  then  be 
coarser  than  that  of  a  heap  of  fine  shot,  but  probably  not  so  coarse  as  that 
of  a  heap  of  cricket-balls.' 

The  number  of  molecules  of  gas  in  a  cubic  centimetre  of  air  is  calculated 
at  twenty-one  trillions. 

By  dissolving  in  alcohol  a  known  weight  of  fuchsine,  and  diluting  the 
liquid,  it  was  observed  that  a  solution  containing  not  more  than  0-00000002 
of  a  gramme  in  one  cubic  centimetre  had  still  a  distinct  colour  ;  that  is,  that 
a  weight  of  not  more  than  the  ^^-;-millionth  of  a  gramme  can  be  perceived  by 
the  naked  eye.  As  the  molecular  weight  of  this  substance  is  2,1)1  times  that 
of  hydrogen,  it  follows  that  the  weight  of  an  atom  of  hydrogen  cannot  be 
greater  than  the  one  20,000-millionth  of  a  gramme. 

Loschmidt  gives  the  diameter  of  the  molecules  of  hydrogen  at  0-00000004 
of  a  centimetre  ;  and  according  to  Mousson  and  Quincke  the  diameter  of 
the  sphere  within  which  one  molecule  can  act  upon  an  adjacent  one,  or 
what  is  called  the  radius  of  molecular  action,  is  between  the  0-00003  and 
0-00004  of  a  millimetre,  and  is  therefore  from  5  to  10  times  less  than  the 
wave-length  of  light. 

4.  Molecular  state  of  bodies. — With  respect  to  the  molecules  of  bodies, 
three  different  stages  of  aggregation  present  themseh'es. 

First,  the  solid  state,  as  observed  in  wood,  stone,  metals,  &c.,  at  the 
ordinary  temperature.  The  distinctive  character  of  this  state  is,  that  the 
relative  position  of  the  molecules  of  the  bodies  is  fixed  and  cannot  be 
changed  without  the  expenditure  of  more  or  less  force.  Solid  bodies  tend, 
therefore,  to  retain  whatever  form  may  have  been  given  to  them  by  nature  or 
by  art. 

Secondly,  the  liquid  state,  as  observed  in  water,  alcohol,  oil,  &c.  Here 
the  relative  position  of  the  molecules  is  no  longer  fixed,  the  molecules  glide 
past  each  other  with  the  greatest  ease,  and  the  body  assumes  with  readiness 
the  form  of  any  vessel  in  w  hich  it  may  be  placed. 

Thirdly,  the  gaseous  state,  as  in  air  and  in  hydrogen.  In  gases  the 
mobility  of  the  molecules  is  still  greater  than  in  liquids  ;  but  the  distinctive 
character  of  a  gas  is  its  incessant  struggle  to  occupy  a  greater  space,  in  con- 
sequence of  which  a  gas  has  neither  an  independent  form  nor  an  independent 
volume,  for  this  depends  upon  the  pressure  to  which  it  is  subject. 

The  general  \(tx\\\  fluid  \-i  applied  to  both  liquids  and  gases. 

Most  simple  bodies,  and  many  compound  ones,  may  be  made  to  pass 
successively  through  all  the  three  states.  Water  presents  the  most  familiar 
example  of  this.  Sulphur,  iodine,  mercury,  phosphorus,  and  zinc  are  other 
instances. 

5.  Physical  phenomena,  la-ws,  and  theories. — E\  ery  change  which 
can  happen  to  a  body,  actual  alteration  of  its  chemical  constitution  being  ex- 
cepted, may  be  regarded  as  ?^  physical  phenomenon.  The  fall  of  a  stone,  the 
vibration  of  a  string,  and  the  sound  which  accompanies  it,  the  attraction  of 


-6]  Physical  Agents.  3 

light  particles  by  a  rod  of  sealing-wax  which  has  been  rubbed  by  flannel, 
the  rippling  of  the  surface  of  a  lake,  and  the  freezing  of  water,  are  examples 
of  such  phenomena. 

K  physical  law  is  the  constant  relation  which  exists  between  any  pheno- 
menon and  its  cause.  As  an  example,  we  have  the  phenomenon  of  the 
diminution  of  the  volume  of  a  gas  by  the  application  of  pressure  ;  the  cor- 
responding law  has  been  discovered,  and  is  expressed  by  saying  that  tlie 
volume  of  a  gas  is  inversely  proportional  to  the  pressure. 

In  order  to  explain  the  cause  of  whole  classes  of  phenomena,  suppositions, 
■or  hypotheses.,  are  made  use  of.  The  utility  and  probability  of  an  hypothesis 
or  theory  are  the  greater  the  simpler  it  is,  and  the  more  varied  and  numerous 
are  the  phenomena  which  are  explained  by  it  ;  that  is  to  say,  are  brought 
into  regular  causal  connection  among  themselves  and  with  other  natural 
phenomena.  Thus  the  adoption  of  the  undulatory  theory  of  Hght  is  justified 
by  the  simple  and  unconstrained  explanation  it  gives  of  all  luminous  pheno- 
mena, and  by  the  connection  it  reveals  with  the  phenomena  of  heat. 

6.  Physical  agrents. —  In  our  attempts  to  ascend  from  a  phenomenon  to 
its  cause,  we  assume  the  existence  oi physical  agents,  or  ?tatural  forces  SLCimg 
upon  matter ;  as  examples  of  such  we  have  gravitation,  heat,  light,  magnet- 
ism, and  electricity. 

Since  these  physical  agents  are  disclosed  to  us  only  by  their  effects,  their 
intimate  nature  is  completely  unknown.  In  the  present  state  of  science,  we 
cannot  say  w^hether  they  are  properties  inherent  in  matter,  or  whether  they 
result  from  movements  impressed  on  the  mass  of  subtile  and  imponderable 
forms  of  matter  diffused  through  the  universe.  The  latter  hypothesis  is,  how- 
ever, generally  admitted.  This  being  so,  it  may  be  further  asked,  are  there 
several  distinct  forms  of  imponderable  matter,  or  are  they  in  reality  but  one 
and  the  same  ?  As  the  physical  sciences  extend  their  limits,  the  opinion 
tends  to  prevail  that  there  is  a  subtile,  imponderable,  and  eminently  elastic 
fluid  called  the  ether  distributed  through  the  entire  universe  ;  it  pervades 
the  mass  of  all  bodies,  the  densest  and  most  opaque,  as  well  as  the  lightest 
or  the  most  transparent.  It  is  also  considered  that  the  ultimate  particles  of 
which  matter  is  made  up  are  capable  of  definite  motions  varying  in  character 
and  velocity,  and  which  can  be  communicated  to  the  ether.  A  motion  of  a 
particular  kind  communicated  to  the  ether  can  give  rise  to  the  phenomenon 
of  heat  ;  a  motion  of  the  same  kind,  but  of  greater  velocity,  produces  light  ; 
and  it  may  be  that  a  motion  different  in  form  or  in  character  is  the  cause  of 
electricity.  Not  merely  do  the  atoms  of  bodies  communicate  motion  to  the 
atoms  of  the  ether,  but  this  latter  can  impart  it  to  the  former.  Thus  the 
atoms  of  bodies  are  at  once  the  sources  and  the  recipients  of  the  motion. 
All  physical  phenomena,  referred  thus  to  a  single  cause,  are  but  transforma- 
tions of  motion. 


On  Matter,  Force,  and  Motion. 


CHAPTER   II. 

GENERAL   PROPERTIES   OF   BODIES. 

7.  Different  kinds  of  properties. — By  the  term  properties,  as  applied 
to  bodies,  we  understand  the  different  ways  in  which  bodies  present  them- 
selves to  our  senses.  We  distinguish  general  from  specific  properties.  The 
former  are  shared  by  all  bodies,  and  amongst  them  the  most  important  are 
impenetrability,  extension,  divisibility,  porosity,  compressibility,  elasticity,^ 
mobility,  and  inertia. 

Specific  properties  are  such  as  are  observed  in  certain  bodies  only,  or  in 
certain  states  of  these  bodies  ;  such  are  solidity,  fluidity,  tenacity,  ductility, 
malleability,  hardness,  transparency,  colour,  &c. 

With  respect  to  the  above  general  properties,  impenetrability  and  exten- 
sion might,  perhaps,  be  more  aptly  termed  essential  attributes  of  matter, 
since  they  suffice  to  define  it  ;  while  divisibility,  porosity,  compressibility, 
and  elasticity  do  not  apply  to  atoms,  but  only  to  bodies  or  aggregates  of 
atoms  (3). 

8.  Impenetrability. — Impenetrability  is  the  property  in  virtue  of  which 
two  portions  of  matter  cannot  at  the  same  time  occupy  the  same  portion  of 
space.  Thus,  when  a  stone  is  placed  in  a  vessel  of  water  the  volume  of  the 
water  rises  by  an  amount  depending  on  the  volume  of  the  stone  ;  this  method, 
indeed,  is  used  to  determine  the  bulk  of  irregularly  shaped  bodies  by  means 
of  graduated  measures. 

Strictly  speaking,  this  property  applies  only  to  the  atoms  of  a  body.  In 
many  phenomena  bodies  appear  to  penetrate  each  other  ;  thus,  the  volume 
of  a  compound  body  is  always  less  than  the  sum  of  the  volumes  of  its  con- 
stituents ;  for  instance,  the  volume  of  a  mixture  of  water  and  sulphuric  acid, 
or  of  water  and  alcohol,  is  less  than  the  sum  of  the  volumes  before  mixture. 
In  all  these  cases,  however,  the  penetration  is  merely  apparent,  and  arises 
from  the  fact  that  in  every  body  there  are  interstices,  or  spaces  unoccupied 
by  matter  (13). 

9.  Extension. — Extension  or  magnitude  is  the  property  in  virtue  of  which 
every  body  occupies  a  limited  portion  of  space. 

Many  instruments  have  been  invented  for  measuring  linear  extension  or 
lengths  with  great  precision.  Two  of  these,  the  vernier  and  micrometer 
screw,  on  account  of  their  great  utility,  deserve  to  be  here  mentioned. 

10.  Vernier. — The  vernier  forms  a  necessary  part  of  all  instruments 
where  lengths  or  angles  have  to  be  estimated  with  precision  ;  it  derives  its 
name  from  its  inventor,  a  French  mathematician,  who  died  in  1637,  and 
consists  essentially  of  a  short  graduated  scale,  ab  (fig.  i),  which  is  made  to 


-11]  Micrometer  Screw.  5 

slide  along  a  fixed  scale,  AB,  so  that  the  graduations  of  both  may  be  com- 
pared with  each  other.  The  fixed  scale  AB,  being  divided  into  equal  parts, 
the  whole  length  of  the  vernier,  ab,  may  be  taken  equal  to  nine  of  those  parts, 
and  is  itself  divided  into  ten  equal  parts.  Each  of  the  parts  of  the  vernier, 
ab,  will  then  be  less  than  a  part  of  the  scale  by  one  tenth  of  the  latter. 

This  being  granted,  in  order  to  measure  the  length  of  any  object,  ;//;/,  let 
us  suppose  that  the  latter,  when  placed  as  in  the  figure,  has  a  length  greater 
than  four  but  less  than  five  parts  of  the  fixed  scale.  In  order  to  determine 
by  what  fraction  of  a  part  /nn  exceeds  four,  one  of  the  ends,  a,  of  the  vernier, 
ab,  is  placed  in  contact  with  one  extremity  of  the  object,  7nn,  and  the 
division  on  the  vernier  is  sought  which  coincides  with  a  division  on  the 
scale  AB.  In  the  figure  this  coincidence  occurs  at  the  eighth  division  of 
the  vernier,  counting  from  the  end,  ti,  and  indicates  that  the  fraction  to  be 
measured  is  equal  to  y^  of  a  part  of  the  scale,  AB.  In  fact,  each  of  the 
parts  of  the  vernier  being  less  than  a  part  of  the  scale  by  ~  of  the  latter,  it 
is  clear  that  on  proceeding  towards  the  left  from  the  point  of  coincidence 
the    divisions  of  the  vernier  are  respectively  one,  two,    three,  &c.  tenths 


i 


^^ 


Fig.  I. 

behind  the  divisions  of  the  scale  ;  so  that  the  end,  n,  of  the  object  (that  is  to 
say,  the  eighth  division  of  the  vernier)  is  ~  behind  the  division  4  on  the 
scale  ;  in  other  words,  the  length  of  mft  is  equal  to  4^*^  of  the  parts  into 
which  the  scale  AB  is  divided.  Consequently  if  the  scale  AB  were  divided 
into  inches,  the  length  of  nm  would  be  4/^  =  4|  inches.  The  divisions  on 
the  scale  remaining  the  same,  it  would  be  necessary  to  increase  the  length 
of  the  vernier  in  order  to  measure  the  length  inn  more  accurately.  For 
instance,  if  the  length  of  the  vernier  were  equal  to  nineteen  of  the  parts  on 
the  scale,  and  this  length  were  divided  into  twenty  equal  parts,  the  length  nui 
could  be  determined  to  the  twentieth  of  a  part  on  the  scale,  and  so  on.  In 
instruments  like  the  theodolite,  intended  for  measuring  angles,  the  scale  and 
vernier  have  a  circular  form,  and  the  latter  usually  carries  a  magnifier  in 
order  to  determine  with  greater  precision  the  coincident  divisions  of  vernier 
and  scale. 

II.  micrometer  screw. — Another  useful  little  instrument  for  measuring- 
small  lengths  with  precision  is  the  microineter  screw.  It  is  used  under  various 
forms,  but  the  principle  is  the  same  in  all,  and  may  be  conveniently  illustrated 
by  reference  to  the  spher'ometcr.  This  consists  of  an  accurately  turned  screw 
with  a  blunt  point  which  works  in  a  companion  supported  on  three  steel 
points  (fig.  2).  To  one  of  these  is  fixed  a  vertical  graduated  scale,  each 
division  of  which  is  equal  to  the  distance  between  two  threads  of  the  screw. 


On  Matter,  Force,  and  Motion. 


[11- 


Fig.  2. 


This  distance  may  be  accurately  determined  by  measuring  a  given  length  of 
the  screw  by  compasses,  and  counting  the  number  of  the  threads  in  this 
length.  A  milled  head  attached  to  the  screw  is  graduated  at  the  periphery 
into  any  given  number  of  parts,  say  500^ 
Suppose  now  the  distance  between  the 
threads  is  r  millimetre,  when  the  head  has 
made  a  complete  turn  it  will  have  risen  or 
sunk  through  one  millimetre,  and  so  on  in 
proportion  for  any  multiple  or  fraction  of  a 
turn. 

In  order  to  determine  the  thickness  of  a 
piece  of  glass  for  instance,  the  apparatus  is 
placed  on  a  perfectly  plane  polished  surface^ 
and  the  point  of  the  screw  is  brought  in. 
contact  with  the  glass.  The  division  on  the 
vertical  scale  immediately  abo\e  the  limb,, 
and  that  on  the  limb  are  read  off.  After 
removing  the  glass  plate  the  point  is  brought  in  contact  with  the  plane 
surface,  and  corresponding  readings  are  again  made,  from  which  the  thick- 
ness can  be  at  once  deduced. 

The  same  process  is  obviously  applicable  to  determining  the  diameter  of 
a  wire. 

To  ascertain  whether  a  surface  is  spherical,  three  points  are  applied  to 
the  surface,  and  the  screw  is  also  made  to  touch  as  described  above.  It  is 
then  moved  along  the  surface,  and  if  all  four  points  are  everywhere  in  con- 
tact the  surface  is  truly  spherical.  This  application  is  of  great  value  in 
ascertaining  the  exact  curvature  of  lenses. 

The  diameter  of  a  sphere  may  also  be  measured  by  its  means  ;  for  it 
can  be  shown  by  a  simple  geometrical  construction  that  the  distance  of  the 
movable  point  from  the  plane  of  the  fixed  points,  multiplied  by  the  diameter 
of  the  sphere,  is  equal  to  the  square  of  the  distance  of  the  movable  point 
from  one  of  the  fixed  points.  If//  is  the  distance  of  the  movable  point  from 
the  plane  of  the  fixed  points,  c  the  distance  of  the  movable  point  from  the 
fixed  point  when  in  the  same  plane,  and  which  is  known  once  for  all,  and  d 
the  diameter  of  the  circle,  then  it  can  be  shown  by  a  simple  geometrical  con- 
struction that  (^  =  ,  +  /^ 
h 

12.  Divisibility. — Divisibility  is  the  property  in  virtue  of  which  a  body 
may  be  separated  into  distinct  parts. 

Numerous  examples  may  be  cited  of  the  extreme  divisibility  of  matter  (3). 
The  tenth  part  of  a  grain  of  musk  will  continue  for  years  to  fill  a  room 
with  its  odoriferous  particles,  and  at  the  end  of  that  time  will  scarcely  be 
diminished  in  weight.  Blood  is  composed  of  red,  flattened  globules,  floating 
in  a  colourless  liquid  called  seriun.  In  man  the  diameter  of  one  of  these 
globules  is  less  than  the  3,500th  part  of  an  inch,  and  the  drop  of  blood  which 
might  be  suspended  from  the  point  o  a  needle  would  contain  about  a  million 
of  globules. 

Again,  the  microscope  has  disclosed  to  us  the  existence  of  insects  smaller 
even  than  these  particles  of  blood  ;  the  struggle  for  existence  reaches  even 


-13] 


Porosity. 


to  these  little  creatures,  for  they  devour  still  smaller  ones.  If  blood  runs  in 
the  veins  of  these  devoured  ones,  how  infinitesimal  must  be  the  magnitude 
of  its  component  globules  ! 

Although  experiment  fails  to  determine  whether  there  be  a  limit  to  the 
divisibility  of  matter,  many  facts  in  chemistry,  such  as  the  invariability  in 
the  relative  weights  of  the  elements  which  combine  with  each  other,  would 
lead  us  to  believe  that  such  a  limit  does  exist.  It  is  on  this  account  that 
bodies  are  conceived  to  be  composed  of  extremely  minute  and  indivisible 
parts  called  atoms  (3). 

13.  Porosity. — Porosity  is  the  quality  in  virtue  of  which  interstices  or 
pores  exist  between  the  molecules  of  a  body. 

Two  kinds  of  pores  may  be  distinguished  :  physical  pores.,  where  the 
interstices  are  so  small  that  the  surrounding  molecules  remain  within  the 
sphere  of  each  other's  attracting  or  repelling 
forces  ;  and  sensible  pores,  or  actual  cavities 
across  which  these  molecular  forces  cannot  act. 
The  contractions  and  expansions  resulting  from 
variations  of  temperature  are  due  to  the  exist- 
ence of  physical  pores,  whilst  in  the  organic 
world  the  sensible  pores  are  the  seat  of  the 
phenomena  of  exhalation  and  absorption. 

In  wood,  sponge,  and  a  great  number  of 
stones^ — for  instance,  pumice  stone — the  sensible 
pores  are  apparent ;  physical  pores  never  are. 
Yet,  since  the  volume  of  every  body  may  be 
diminished,  we  conclude  that  all  possess  physical 
pores. 

The  existence  of  sensible  pores  in  leather  or 
wood  may  be  shown  by  the  following  experi- 
ment : — A  long  glass  tube,  A  (fig.  3),  is  provided 
with  a  brass  cup  at  the  top,  and  a  brass  foot 
made  to  screw  on  to  the  plate  of  an  air-pump. 
The  bottom  of  the  cup  consists  of  a  thick  piece 
of  leather.  After  pouring  mercury  into  the  cup 
so  as  entirely  to  cover  the  leather,  the  air-pump 
is  put  in  action,  and  a  partial  vacuum  produced 
within  the  tube.  By  so  doing  a  shower  of  mer- 
cury is  at  once  produced  within  the  tube,  for  the 
atmospheric  pressure  on  the  mercury  forces  that 
liquid  through  the  pores  of  the  leather.  In  the 
same  manner  water  or  mercury  may  be  forced 
through    the    pores   of  wood  by  replacing  the 

leather  in  the  above  experiment  by  a  disc  of  wood  cut  perpendicularly  to  the 
fibres. 

When  a  piece  of  chalk  is  thrown  into  water,  air-bubbles  at  once  rise  to 
the  surface,  in  consequence  of  the  air  in  the  pores  of  the  chalk  being  expelled 
by  the  water.  The  chalk  will  be  found  to  be  heavier  after  immersion  than  it 
was  before,  and,  knowing  its  volume,  the  volume  of  its  pores  may  be  easily 
determined  from  the  increase  of  its  weight. 


8  On  Matter,  Force,  and  Motion.  [13- 

The  porosity  of  agate,  flint,  marble  is  evident  from  the  fact  that  they  are 
penetrated  by  liquids  such  as  oil,  on  which,  indeed,  the  artificial  coloration 
of  these  minerals  depends. 

The  porosity  of  gold  was  demonstrated  by  the  celebrated  Florentine 
experiment  made  in  1661.  Some  academicians  at  Florence,  wishing  to  try 
whether  water  was  compressible,  filled  a  thin  globe  of  gold  with  that  liquid, 
and,  after  closing  the  orifice  hermetically,  they  exposed  the  globe  to  pressure 
with  a  view  of  altering  its  form,  knowing  that  any  alteration  in  form  must  be 
accompanied  by  a  diminution  in  volume.  The  consequence  was,  that  the 
water  forced  its  way  through  the  pores  of  the  gold,  and  stood  on  the  outside 
of  the  globe  like  dew.  More  than  twenty  years  previously  the  same  fact  was 
demonstrated  by  Francis  Bacon  by  means  of  a  leaden  sphere  ;  the  experi- 
ment has  since  been  repeated  with  globes  of  other  metals,  and  similar  results 
obtained.  At  a  red  heat  both  platinum  and  iron  allow  gases  to  diffuse 
through  them. 

.\  glass  tube  about  a  metre  long,  closed  at  one  end,  is  half  filled  with 
water,  and  then  pure  alcohol  poured  upon  it  to  a  mark  near  the  top  ;  on 
then  closing  the  open  end  with  the  thumb  and  inverting  the  tube  several 
times  the  mixture  shrinks  so  that  its  level  is  now  nearly  an  inch  below  the 
mark  ;  at  the  same  time  very  minute  bubbles  are  seen  to  rise,  owing  to  the 
water  having  penetrated  into  the  pores  of  the  alcohol  and  expelled  the  air 
present. 

14.  Apparent  and  real  volumes. — In  consequence  of  the  porosity  of 
bodies,  it  becomes  necessary  to  distinguish  between  their  real  and  apparent 
\olumes.  The  real  volume  of  a  body  is  the  portion  of  space  actually  occu- 
pied by  the  matter  of  which  the  body  is  composed  ;  its  apparent  volume  is 
the  sum  of  its  real  volume  and  the  total  volume  of  its  pores.  The  real 
volume  of  a  body  is  invariable,  but  its  apparent  volume  can  be  altered  in 
\arious  wa)-s. 

1 5.  Applications. — The  property  of  porosity  is  utilised  in  filters  of  paper, 
felt,  stone,  charcoal,  &c.  The  pores  of  these  substances  are  sufficiently  large 
to  allow  liquids  to  pass,  but  small  enough  to  arrest  the  passage  of  any  sub- 
stances which  these  liquids  may  hold  in  suspension.  Again,  large  blocks  of 
stone  are  often  detached  in  quarries  by  introducing  wedges  of  dry  wood  into 
grooves  cut  in  the  rock.  These  wedges  being  moistened,  water  penetrates 
their  pores,  and  causes  them  to  swell  with  considerable  force.  Dry  cords, 
when  moistened,  increase  in  diameter  and  diminish  in  length — a  property  of 
which  advantage  has  been  taken  in  order  to  raise  great  weights. 

16.  Compressibility.— Cc';;//;-^.y^zW///j  is  the  property  in  virtue  of  which 
the  volume  of  a  body  may  be  diminished  by  pressure.  This  property  is  at 
once  a  consequence  and  a  proof  of  porosity. 

Bodies  differ  greatly  with  respect  to  compressibility.  The  most  com- 
pressible bodies  are  gases  ;  by  sufficient  pressure  they  may  be  made  to 
occupy  ten,  twenty,  or  even  some  hundred  times  less  space  than  they  do 
under  ordinary  circumstances.  In  most  cases,  howe\'er,  there  is  a  limit 
beyond  which,  when  the  pressure  is  increased,  they  become  liquids. 

The  compressibility  of  sohds  is  much  less  than  that  of  gases,  and  is  found 
in  all  degrees.  Cloths,  paper,  cork,  woods,  are  amongst  the  most  compres- 
sible.    Metals  are  so  also  to  a  great  extent,  as  is  proved  by  the  process  of 


-18]  Mobility,  Motion,  Rest.  9 

coining,  in  which  the  metal  receives  the  impression  from  the  die.  There  is, 
in  most  cases,  a  hmit  beyond  which,  when  the  pressure  is  increased,  bodies 
are  fractured  or  reduced  to  powder. 

The  compressibiUty  of  hquids  is  so  small  as  to  have  remained  for  a  long 
time  undetected  :  it  may,  however,  be  proved  by  experiment,  as  will  be  seen 
in  the  chapter  on  Hydrostatics. 

17.  Elasticity. — Elasticity  is  the  property  owing  to  which  bodies  resume 
their  original  form  or  volume,  when  the  force  which  altered  that  form  or 
volume  ceases  to  act.  Elasticity  may  be  developed  in  bodies  by  pressure, 
by  traction  or  pulliiig,  flexion  or  bending,  and  by  torsion  or  twisting.  In 
treating  of  the  general  properties  of  bodies,  the  elasticity  developed  by 
pressure  alone  requires  consideration ;  the  other  kinds  of  elasticity,  being 
peculiar  to  solid  bodies,  will  be  considered  amongst  their  specific  properties 
(arts.  89,  90,  91). 

Gases  and  liquids  are  perfectly  elastic  ;  in  other  words,  after  undergoing 
a  change  in  volume  they  regain  exactly  their  original  volume  when  the 
pressure  becomes  what  it  originally  was.  Solid  bodies  present  different  de- 
grees of  elasticity,  though  none  present  the  property  in  the  same  perfec- 
tion as  liquids  and  gases,  and  in  all  it  varies  according  to  the  time  during 
which  the  body  has  been  exposed  to  pressure.  Caoutchouc,  ivory,  glass, 
and  marble  possess  considerable  elasticity  ;  lead,  clay,  and  fats  scarcely 
any. 

There  is  a  limit  to  the  elasticity  of  solids,  beyond  which  they  either  break 
or  are  incapable  of  regaining  their  original  form  and  volume.  This  is  called 
the  limit  of  elasticity  ;  within  this  limit  all  substances  are  perfectly  elastic. 
In  sprains,  for  instance,  the  elasticity  of  the  tendons  has  been  exceeded. 
In  gases  and  liquids,  on  the  contrary,  no  such  limit  can  be  reached  ;  they 
always  regain  their  original  volume  when  the  original  pressure  is  restored  (152). 

If  a  ball  of  ivory,  glass,  or  marble  be  allowed  to  fall  upon  a  slab  of  polished 
marble,  which  has  been  previously  slightly  smeared  with  oil,  it  will  rebound 
and  rise  to  a  height  nearly  equal  to  that  from  which  it  fell.  On  afterwards 
examining  the  ball  a  circular  blot  of  oil  will  be  found  upon  it,  more  or  less 
extensive  according  to  the  height  of  the  fall.  From  this  we  conclude  that  at 
the  moment  of  the  shock  the  ball  was  flattened,  and  that  its  rebound  was 
caused  by  the  effort  to  regain  its  original  form. 

18.  Mobility,  motion,  rest.^ — Mobility  is  the  property  in  virtue  of  which 
the  position  of  a  body  in  space  may  be  changed. 

Motion  and  rest  may  be  either  relative  or  absolute.  By  the  relatii'e 
motion  or  rest  of  a  body  we  mean  its  change  or  permanence  of  position  with 
respect  to  surrounding  bodies  ;  by  its  absolute  motion  or  r-est  we  mean  the 
change  of  permanence  of  its  position  with  respect  to  ideal  fixed  points  in 
space. 

Thus  a  passenger  in  a  railway  carriage  may  be  in  a  state  of  relative  rest 
with  respect  to  the  train  in  which  he  travels,  but  he  is  in  a  state  of  relative 
motion  with  respect  to  the  objects,  such  as  trees,  houses,  &c.,  past  which  the 
train  rushes.  These  houses,  again,  enjoy  merely  a  state  of  relative  rest,  for 
the  earth  itself  which  bears  them  is  in  a  state  of  incessant  relative  motion 
with  respect  to  the  celestial  bodies  of  our  solar  system,  inasmuch  as  it  moves 
at  the  rate  of  more  than  eighteen  miles  in  a  second.     In  short,  absolute 


lo  On  Matter,  Force,  and  Motion.  [18— 

motion  and  rest  are  unknown  to  us  ;  in  nature,  relative  motion  and  rest  are 
alone  presented  to  our  observation. 

19.  Inertia. — Inertia  is  a  purely  negative  though  universal  property  of 
matter  (26)  ;  it  is  the  property  that  matter  cannot  of  itself  change  its  own 
state  of  motion  or  of  rest.  If  a  body  is  at  rest  it  remains  so  until  some 
force  acts  upon  it  ;  if  it  is  in  motion  this  motion  can  only  be  changed  by  the 
application  of  some  force. 

This  property  of  inertia  is  what  is  expressed  by  Newton's  first  law  of 
motion. 

A  body,  when  unsupported  in  mid-aii',  does  not  fall  to  the  earth  in  virtue 
of  any  inherent  property,  but  because  it  is  acted  upon  by  the  force  of  gravity. 
A  billiard  ball  gently  pushed  does  not  move  more  and  more  slowly,  and 
finally  stop,  because  it  has  any  preference  for  a  state  of  rest,  but  because  its 
motion  is  impeded  by  the  friction  on  the  cloth  on  which  it  rolls,  and  by  the 
resistance  of  the  air.  If  all  impeding  causes  were  withdrawn,  a  body  once 
in  motion  would  continue  to  move  for  ever  in  a  straight  line  with  unchanging 
velocity. 

20.  Illustrations. — Numerous  phenomena  may  be  explained  by  the 
inertia  of  matter.  For  instance,  before  leaping  a  ditch  we  run  towards  it,  in 
order  that  the  motion  of  our  bodies  at  the  moment  of  leaping  may  add  itself 
to  the  muscular  efi'ort  then  made. 

On  descending  carelessly  from  a  carriage  in  motion,  the  upper  part  of  the 
body  retains  its  motion,  whilst  the  feet  are  prevented  from  doing  so  by  fric- 
tion against  the  ground  ;  the  consequence  is  we  fall  towards  the  moving" 
carriage.  A  rider  falls  over  the  head  of  a  horse  if  it  suddenly  stops.  In 
striking  the  handle  of  a  hammer  against  the  ground  the  handle  suddenly 
stops,  but  the  head,  striving  to  continue  its  motion,  fixes  itself  more  firmly  on 
the  handle. 

By  the  property  of  inertia  may  also  be  explained  the  following  experi- 
ments : — Let  a  card  be  placed  upon  a  tumbler,  and  a  shilling  on  the  card  ; 
if  the  edge  of  the  card  be  smartly  flicked  with  the  finger  the  card  is  driven 
away  and  the  coin  falls  into  the  tumbler.  A  gentle  push  with  the  finger  will 
move  a  door  on  its  hinges  ;  but  if  a  pistol  bullet  be  fired  against  the  door  it 
perforates  the  door  without  moving  it.  So,  too,  a  pistol  shot  fired  through  a 
window-pane  produces  a  sharp  round  hole,  while  a  less  violent  shock  will 
smash  the  pane.  A  clay  tobacco  pipe,  which  is  suspended  by  two  vertical 
hairs,  may  be  cut  in  two  by  a  powerful  stroke  with  a  shajp  sword  without 
breaking  the  hairs. 

A  string  which  gently  applied  will  raise  a  weight  snaps  at  once  when  a 
sudden  pull  is  exerted.  Substances  which  explode  with  great  rapidity,  such 
as  fulminating  mercury,  chloride  of  nitrogen,  cannot  be  used  with  fire-arms, 
because  there  is  not  sufficient  time  to  transfer  the  motion  to  the  projectiles^ 
and  hence  the  weapons  are  burst. 

The  terrible  accidents  on  our  railways  are  chiefly  due  to  inertia.  When 
the  motion  of  the  engine  is  suddenly  arrested  the  carriages  strive  to  continue 
the  motion  they  have  acquired,  and  in  doing  so  are  shattered  against  each 
other.  Hammers,  pestles,  stampers  are  applications  of  inertia.  So  are  also 
the  enormous  iron  fly-wheels,  by  which  the  motion  of  steam-engines  is 
regulated. 


-22] 


Measure  of  Spaee. 


CHAPTER    III. 

ON   FORCE,   EQUILIBRIUM,   AND   MOTION. 

21.  Measure  of  time. — To  obtain  a  proper  measure  of  force  it  is 
necessary,  as  a  preliminary,  to  define  certain  conceptions  which  are  pre- 
supposed in  that  measure  ;  and,  in  the  first  place,  it  is  necessary  to  define 
the  unit  of  time.  Whenever  a  second  is  spoken  of  without  qualification 
it  is  understood  to  be  a  second  of  vieatt  solar  time.  The  exact  length  of 
this  unit  is  fixed  by  the  following  considerations.  The  instant  when  the  sun's 
centre  is  on  an  observer's  meridian — in  other  words,  the  instant  of  the  transit 
of  the  sun's  centre — can  be  determined  with  exactitude,  and  thus  the  interval 
which  elapses  between  two  successive  transits  also  admits  of  exact  determina- 
tion, and  is  called  an  apparent  day.  The  length  of  this  interval  differs 
slightly  from  day  to  day,  and  therefore  does  not  serve  as  a  convenient 
measure  of  time.  Its  average  length  is  not  open  to  this  objection,  and 
therefore  serves  as  the  required  measure,  and  is  called  a  ineaii  solar  day. 
The  short  hand  of  a  common  clock  would  go  exactly  twice  round  the  face 
in  a  mean  solar  day  if  it  went  perfectly.  The  mean  solar  day  consists  of  24 
equal  parts  called  hours,  these  of  60  ec^ual  parts  called  minutes,  and  these 
again  of  60  equal  parts  called  seconds.  Consec^uently,  the  second  is  the 
86,400th  part  of  a  mean  solar  day,  and  is  the  generally  received  unit  of  time. 

22.  Measure  of  space. — Space  may  be  either  length  or  distance,  which 
is  space  of  one  dimension  ;  area,  which  is  space  of  two  dimensions  ;  or 
volume,  which  is  space  of  three  dimensions.  In  England  the  standard  of 
length  is  the  British  Imperial  Yard,  which  is  the  distance  between  two  fixed 
points  on  a  certain  metal  rod,  kept  in  the  Tower  of  London,  when  the  tempera- 
ture of  the  whole  rod  is  60°  F.  =  i5°-5   C.     It  is,  however, 

usual  to  employ  as  a  unit,  a/cc/,  which  is  the  third  part  of  a 
yard.  In  France  the  standard  of  length  is  the  metre  ;  this 
is  approximately  equal  to  the  ten-millionth  part  of  a  qua- 
drant of  the  earth's  meridian,  that  is  of  the  arc  from  the 
Equator  to  the  North  Pole  ;  it  is  practically  fixed  by  the 
distance  between  two  marks  on  a  certain  standard  rod.  The 
standard  metre,  adopted  by  an    International  Committee  pig.  4. 

for  weights  and  measures,  is  constructed  of  an  alloy  of  90 
per  cent,  platinum  and  10  per  cent,  iridium,  which  is  characterised  by  great 
hardness,  and  unalterability.  Its  length  is  somewhat  over  a  metre,  and  its 
cross  section  is  represented  in  its  natural  size  in  figure  4.  This  shape  has 
the  advantage  of  giving  the  greatest  rigidity  and  of  soon  acquiring  the 
temperature  of  the  surrounding  medium.     The  exact  length  of  the  metre  is 


12  On  Matter,  Force,  and  Motion.  [22- 

marked  by  two  fine  lines  on  the  surface.  The  relation  between  these 
standards  is  as  follows  : 

I  yard    =0-914401  metre. 

I  metre  =  1-093612  yard. 

The  unit  of  length  having  been  fixed,  the  units  of  area  and  volume  are 
connected  with  it  thus  :  the  uftit  of  area  is  the  area  of  a  square,  one  side  of 
which  is  the  unit  of  length.  The  tinit  of  volume  is  the  volume  of  a  cube,  one 
edge  of  which  is  the  unit  of  length.  These  units  in  the  case  of  English  mea- 
sures are  the  square  yard  (or  foot)  and  the  cubic  yard  (or  foot)  respectively  ; 
in  the  case  of  French  measures,  the  square  metre  and  cubic  metre  respec- 
tively. The  length  of  the  seconds  pendulum,  in  lat.  45°,  which  is  about  that 
of  Milan,  is  o-9935m.,  and  thus  only  differs  from  a  metre  by  6-5  millimetres. 

23.  IVXeasure  of  mass. — Two  bodies  are  said  to  have  equal  masses  when, 
if  placed  in  a  perfect  balance  itt  vacuo,  they  counterpoise  each  other.  Suppose 
we  take  lumps  of  any  substance,  lead,  butter,  wood,  stone,  &c.,  and  suppose 
that  any  one  of  them  when  placed  on  the  one  pan  of  a  balance  will  exactly 
counterpoise  any  other  of  them  when  placed  on  the  opposite  pan — the  balance 
being  perfect  and  the  weighing  performed  in  vacuo  ;  this  being  the  case, 
these  lumps  are  said  to  have  equal  masses. 

The  British  unit  of  mass  is  the  standard  pound  (avoirdupois),  which  is  a 
certain  piece  of  platinum  kept  in  the  Exchequer  Office  in  London.  This  unit 
having  loeen  fixed,  the  mass  of  a  given  substance  is  expressed  as  a  multiple 
or  submultiple  of  the  unit. 

It  need  scarcely  be  mentioned  that  many  distances  are  ascertained  and 
expressed  in  yards  which  it  would  be  physically  impossible  to  measure 
directly  by  a  yard  measure.  In  like  manner  the  masses  of  bodies  are  fre- 
quently ascertained  and  expressed  numerically  which  could  not  be  placed  in 
a  balance  and  subjected  to  direct  weighing. 

24.  Density  and  relative  density. — If  we  consider  any  body  or  portion 
of  matter,  and  if  we  conceive  it  to  be  divided  into  any  number  of  parts  having 
equal  volumes,  then,  if  the  masses  of  these  parts  are  equal,  in  whatever 
way  the  division  be  conceived  as  taking  place,  that  body  is  one  of  uniform 
density.  The  density  of  such  a  body  is  the  mass  of  the  tmit  of  volume.  Con- 
sequently, if  M  denote  the  mass,  V  the  volume,  and  D  the  density  of  the 
body,  we  have 

M  =  VD. 

If  now  we  have  an  equal  volume  V  of  any  second  substance  whose  mass  is 
M'  and  density  D',  we  shall  have 

M'  =  VD'. 

Consequently,  D:D'::M:]\r;  that  is,  the  densities  of  substances  are 
in  the  same  ratio  as  the  masses  of  equal  volumes  of  those  substances. 
If  now  we  take  the  density  of  distilled  water  at  4°  C.  to  be  unity,  the  relative 
density  of  any  other  substance  is  the  ratio  which  the  mass  of  any  given 
volume  of  that  substance  at  that  temperature  bears  to  the  mass  of  an  equal 
volume  of  water.  Thus  it  is  found  that  the  mass  of  any  volume  of  platinum 
is  22-069  times  that  of  an  equal  volume  of  \\ater,  consequently  the  relative 
density  of  platinum  is  22-069. 


D. 

G. 

62-42 

l-ooo 

112-36 

I -Boo 

449-86 

7-207 

548-55 

8-788 

708-59 

11-352 

269-43 

20-332 

58-05 

0-930 

-25]  Velocity  and  its  Measure.  1 3 

The  relative  density  of  a  substance  is  generally  called  its  spccijic  gravity. 
Methods  of  determining  it  are  given  in  Book  111. 

In  the  table  below  the  densities  D  of  various  substances,  expressed  in 
pounds  to  the  cubic  foot,  are  given,  and  column  G  gives  the  relative  densities 
of  the  same  substances. 

It  is  evident  that  column  G  is  obtained  by  dividing  the  values  in  colunui 
D  by  62-42. 

Water 

Anthracite 

Cast  iron 

Cast  copper 

„      lead         ..... 

„  platinum  .... 
Melting  ice 

In  the  metric  system,  since  the  mass  of  the  cubic  centimetre  of  water 
is  one  gramme,  it  is  evident  that  the  density  D,  in  grammes  to  the  cubic 
centimetre,  has  the  same  numerical  value  as  the  relative  density  referred  to 
water. 

25.  Velocity  and  its  measure. — When  a  material  point  moves,  it  de- 
scribes a  continuous  line  which  may  be  either  straight  or  curved,  and  is 
called  its  path  and  sometimes  its  trajectory.  Motion  which  takes  place 
along  a  straight  line  is  called  rectilinear  motion  ;  that  which  takes  place 
along  a  curved  line  is  called  curniilijiear  motion.  The  rate  of  the  motion  of 
a  point  is  called  its  velocity.  Velocity  may  be  either  uniform  or  variable  ;  it 
is  uniform  when  the  point  describes  equal  spaces  or  portions  of  its  path  in 
all  equal  times  ;  it  is  variable  when  the  point  describes  unequal  portions  of 
its  path  in  any  equal  times. 

Uniform  velocity  is  measured  by  the  number  of  units  of  space  described 
in  a  given  unit  of  time.  The  units  commonly  employed  in  this  country 
are  feet  and  seconds.  If,  for  example,  a  velocity  5  is  spoken  of  without 
qualification,  this  means  a  velocity  of  5  feet  per  second.  Consequently, 
if  a  body  moves  for  /  seconds  with  a  uniform  velocity  7/,  it  will  describe 
vt  feet. 

The  following  are  a  few  examples  of  different  degrees  of  velocity  expressed 
in  this  manner.  A  snail  0-005  f^^t  in  a  second ;  the  Rhine  between  Worms 
and  Mainz  3-3  ;  military  quick  step  4-6  ;  moderate  wind  10  ;  fast  sailing- 
vessel  18-0  ;  Channel  steamer  22-0  ;  i-ailway  train  36  to  75  feet  ;  racehorse  and 
storm  50  feet ;  wave  in  a  tempest  72  feet;  eagle  no  feet;  carrier  pigeon 
120  feet  ;  a  hurricane  160  feet  ;  sound  at  0°  1,090  ;  a  shot  from  an  Armstrong 
gun  1,180  ;  a  Martini-Henry  rifle  bullet  1,330  ;  a  point  on  the  Equator  in  its 
rotation  about  the  earth's  axis  1,520  ;  velocity  of  the  vibratory  motion  of  par- 
ticles of  air  1,590;  maximum  tide  rate  3,005  ;  velocity  of  the  centre  of  the 
earth  101,000  feet  ;  light,  and  also  electricity  in  a  medium  destitute  of  resist- 
ance 192,000  miles. 

Variable  velocity  is  measured  at  any  instant  by  the  number  of  units  of 
space  a  body  would  describe  if  it  continued  to  move  uniformly  from  that 
instant  for  a  unit  of  time.  Thus,  suppose  a  body  to  run  down  an  inclined 
plane,  it  is  a  matter  of  ordinary  observation  that  it  mo\'es  more  and  more 


14  On  Matter,  Force,  and  Motion.  [25- 

quickly  during  its  descent  ;  suppose  that  at  any  point  it  has  a  velocity  15, 
this  means  that  at  that  point  it  is  moving  at  the  rate  of  15  ft.  per  second,  or, 
in  other  words,  if  from  that  point  all  increase  of  velocity  ceased,  it  would  de- 
scribe 1 5  ft.  in  the  next  second. 

26.  rorce. — Forces  manifest  themselves  to  us  by  the  changes  which  they 
produce,  or  tend  to  produce,  in  the  motion  of  matter.  The  action  of  forces 
in  causing  motion  is  best  expressed  in  Newton's  laws  :  The  first  law  is, 
Every  body  continues  in  its  state  of  rest  or  of  uniform  motion  in  a  straight 
line,  except  as  it  is  compelled  by  forces  to  change  that  state. 

A  body  may  be  at  rest,  or  may  be  moving  uniformly  in  a  straight  line, 
while  acted  upon  by  a  system  of  forces.  In  this  case  the  forces  are  said  to 
balance  each  other.  If  a  constant  unbalanced  force  act  upon  a  body,  it  will  no 
longer  move  uniformly.  The  velocity  will  increase  continually,  at  a  uniform 
rate.  A  familiar  case  of  this  kind  is  found  in  the  attraction  of  the  earth  for 
other  bodies.  According  to  Newton's  law  of  gravitation,  the  attraction 
between  two  masses,  one  of  which  contains  m  and  the  other  m'  units  of 

mass,  is ,  where  r  is  the  distance  between  the  centres  of  the  masses 

r- 
(62).     If  one  of  the    masses   be   the    unit  mass,  or   one  pound,  the  other 
being  the  earth,  the  above  expression  represents  the  pull  which  the  earth 
exerts  upon  a  pound  of  matter :  this  pull  is  the  weight  of  a  pound. 

It  is  important  to  distinguish  very  carefully  between  a  pound — the  unit 
of  mass — and  the  weight  of  a  pound,  which  is  a  force.  Weight  is  not  a 
necessary  property  of  matter.  If  physical  conditions  were  such  that  we 
could  visit  the  centre  of  the  earth,  we  should  find  matter  without  weight, 
although  its  other  properties  would  remain  unchanged.  A  bullet  fired  from 
a  gun,  although  weightless,  would  ha\'e  the  same  effect  as  at  the  surface  of 
the  earth,  this  effect  being  dependent,  as  will  be  shown,  upon  the  amount  of 
matter  (mass)  in  the  bullet  and  the  velocity  imparted,  and  having  no  relation 
whatever  to  the  weight  of  the  bullet.  A  pound  of  sugar  at  the  centre  of  the 
earth  would  have  precisely  the  same  sweetening  properties  as  at  the  surface. 
The  commercial  value  of  provisions,  drugs,  &c.,  is  therefore  strictly  propor- 
tional to  the  number  of  units  of  mass  purchased,  and  has  no  necessary  rela- 
tion to  the  weights  of  those  masses. 

It  is  also  to  be  observed  that,  if  masses  are  counterpoised  on  a  lever 
balance  at  any  one  locality,  they  would  remain  balanced  at  any  other  point, 
since  the  weights  of  the  masses  would  change  in  the  same  ratio.  Hence 
the  lever  balance  with  standard  '  weights '  really  measures  the  mass  of  a 
body,  and  not  its  weight,  and  the  standard  '  weights '  should  really  be  called 
masses.  A  spring  balance  determines  weight  and  not  mass,  since  its  indi- 
cations change  as  the  weight  of  the  mass  changes. 

At  the  centre  of  the  earth,  masses  could  not  be  determined  by  means  of 
a  balance,  since  they  weigh  nothing,  and  any  mass  would  counterpoise  any 
other  mass. 

27.  XVIeasure  of  Torce. — In  devising  a  unit  in  which  to  measure  force,  it  is 
most  convenient  to  make  use  of  the  attractive  force  of  the  earth.  Suppose  that 
two  equal  masses,  P,  are  balanced  on  a  pulley  with  fixed  axle,  that  the  string 
and  pulley  are  without  mass,  and  that  there  is  no  friction  or  air-resistance. 
The  masses  P  are  then  perfectly  inert.     The  tension  on  the  string  is  the 


-27]  Measure  of  Force.  1 5 

pull  of  the  earth  on  oue  of  the  masses  P,  or,  in  other  w  ords,  the  weight  of  P. 
If  the  pulley  is  started  by  a  force  which  then  ceases  to  act,  the  masses  will 
thereafter  move  uniformly  according  to  the  first  law  of  motion,  the  tension 
on  the  string  being,  as  before,  the  weight  of  P.    This  will  all  be 
true,  whatever  may  be  the  amount  of  matter  in  the  masses  P.        /"""^ 
If,  now,  the  masses  P  being   at  rest,  an  additional  mass   in       I 
be  placed  on  one  side,  the  system  will  begin  to  move.     The        \.,_^ 
4:ension  on  the  string  is  now  greater  than  the  weight  of  P,  and 
less  than  the  weight  of  P  +  m.     The  force  which  causes  the 
motion  is  the  pull  of  the  earth  on  m,  or  the  weight  of  the  added  f^p 

mass.     The  motion  is  now  uniformly  accelerated.     At  the  in- 
stant of  starting,  the  velocity  is  zero.     At  the  end  of  the  first     Pip 
second,  the  velocity  will  be — say  a  ;  at  the  end  of  the  second  p-jg  . 

second,  la ;  and  at  the  end  of  /  seconds,  the  velocity  will  be  at. 
The  increase  in  the  velocity  per  second  is  «,  which  is  called  the  accelera- 
tion. 

If  the  mass  m  be  entirely  disconnected  from  the  masses  P  and  allowed 
to  fall  freely,  it  also  falls  with  a  uniformly  accelerated  motion  ;  but  experi- 
ment shows  that  the  acceleration  is  greater  than  in  the  former  case.  This 
acceleration  of  a  freely  falling  body  is  usually  denoted  by  g.  The  force 
-which  causes  the  motion  is,  however,  the  same  as  before,  being  the  weight 
of  VI.  The  difference  in  the  two  cases  is  that,  in  the  latter  case,  the  pull  of 
the  earth  on  in  is  employed  in  setting  in  motion  the  mass  in  only  ;  while,  in 
the  former  case,  the  two  inert  masses  P  are  attached  to  ;«,  and  are  con- 
strained to  move  with  it,  the  mass  to  be  moved  being  thus  increased  without 
a  corresponding  increase  of  the  force  employed  in  moving. 

It  is  evident  that  if  the  masses  P  should  diminish  to  zero,  or  the  mass  m 
should  increase  until  it  became  very  large,  or  infinite,  the  weight  of  m  would 
impart  a  greater  and  greater  acceleration,  until  finally  the  acceleration 
would  become  g.  On  the  other  hand,  if  the  masses  P  should  become  very 
large,  or  infinite,  or  the  mass  m  very  small,  or  zero,  the  acceleration  would 
become  zero.  It  is  shown  by  experiment  that  if  the  mass  in  is  made  n 
times  as  great  (so  that  the  moving  force  is  //  times  as  great),  and  the  masses 
P  are  equally  diminished — so  that  zV  -r  m  is  unchanged — the  acceleration 
becomes  n  times  as  great,  so  that,  the  mass  to  be  moved  being  unchanged, 
the  acceleration  is  directly  proportional  to  the  force  applied.  If,  however, 
the  mass  ;;/  be  made  11  times  as  great,  and  it  is  desired  to  have  the  accelera- 
tion remain  unchanged,  it  is  found  that  the  masses  P  must  be  equally 
increased  in  such  a  way  that  2P  + ;«  has  also  become  n  times  as  great. 
This  shows  that,  the  acceleration  remaining  constant,  the  force  applied  must 
change  in  the  same  ratio  as  the  mass. 

From  these  experiments  it  follows  that  if  any  force  F  is  applied  in  giving 
uniformly  accelerated  motion  to  a  mass  M,  the  acceleration  being  ^,  then 

F  =  YM.a. 

Here  M  is  measured  in  pounds,  and  the  acceleration  a  measures  the 
change  in  velocity  of  M  in  feet  per  second.  K  is  a  constant,  the  numerical 
value  of  which  will  depend  upon  the  unit  which  we  now  adopt  in  which  to 
measure  F.     If,  as  is  customary,  we  adopt  as  the  unit  force  that  force  which 


1 6  Ou  Matter,  Force,  and  Motion.  [27- 

will  make  a  =  i  when  M  =  i,  then  we  at  the  same  time  necessarily  niake  the 
remaining  quantity  K  in  the  last  equation  equal  to  i  ;  and,  measured  in  these 
units, 

F  =  Via. 

The  unit  force  is  then  that  force  which  can  impart  unit  acceleration  to 
unit  mass. 

If  V  represent  the  initial  velocity  of  a  body,  and  %'  its  final  velocity,  the 
change  in  velocity  having  taken  place  in  /  seconds,  then  the  change  per 
second  is 

7/-V 

a  = . 

t 

This  value  of  a  in  the  previous  equation  gives 
P_M7'-MV 

28.  Momentum. — It  thus  appears  that  the  number  of  units  of  force  in 
any  force  which,  acting  for  t  seconds  on  a  mass  M,  is  capable  of  changing  its 
velocity  from  V  to  v,  is  measured  by  the  change  per  second  in  the  product 
M7/.  This  quantity  M?/,  being  thus  an  important  one,  has  received  a  special 
name — inoinenhiin.  We  may  now  say  that  the  number  of  units  in  a  force  is 
measured  by  the  change  in  momentum  which  it  can  produce  per  second, 
which  is  the  substance  of  Newton's  second  law  of  motion. 

29.  Acceleration  of  Gravity. — At  London,  the  force  with  which  the 
earth  attracts  a  pound  of  matter  is  capable  of  imparting  to  the  pound  an 
acceleration  of  32-1912.  At  other  places,  the  acceleration  is  different,  and 
may  be  denoted  by^.  Hence,  at  London,  the  weight  of  a  pound,  expressed 
in  the  units  which  we  have  chosen  for  measuring  forces,  will  be  32-1912.  At 
any  other  point  on  the  earth,  or  in  the  interior  of  the  earth,  or  at  any  point 
outside,  where  the  acceleration  of  a  falling  body  is  g^  the  number  of  units  of 
force  in  the  weight  of  a  pound  is  g.  The  number  w  of  units  of  force  in  the 
w  eight  of  /;/  pounds  is  given  by  the  equation 

ia  =  mg. 

If  at  some  point  where  the  acceleration  is  32  it  is  found  that  the  weight 
of  10  lb.,  or  320  units  of  force,  is  sufficient  to  serve  as  the  driving-weight  to 
a  certain  clock,  then  at  some  other  point,  where  the  acceleration  is  16,  it 
would  be  necessary  to  use  the  weight  of  20  lb.  in  order  to  secure  the  same 
effect. 

The  weight  of lb.,  or  0-49  oz.,  at  London,  is  a  unit  of  force.     At 

32-1912 

any  other  point,  where  the  acceleration  is  g,  the  weight  of  -  lb.  is  the  unit  of 

force.  Where  great  accuracy  is  not  required,  it  is  customary  to  take  the 
weight  of  the  pound  as  the  unit  of  force,  and  then  the  intensity  of  the  force 
is  given  in  pounds  weight,  a  unit  which  varies  slightly  for  different  places  on 
the  earth,  as  g  varies.  In  like  manner,  for  ordinary  purposes,  a  land 
surveyor  does  not  find  it  necessary  to  make  corrections  for  the  varying 
length  of  his  chain  due  to  changes  in  temperature,  although  such  correc- 


-30]  Representation  of  Forces.  17 

tions  are  highly  important  in  the  more  refined  operations  of  a  geodetic 
survey. 

Pendulum  observations  (79)  show  that  at  any  given  place  the  acceleration 
of  a  falling  body  is  constant,  but  it  is  found  to  have  different  values  at  dif- 
ferent places  ;  adopting  the  units  of  feet  and  seconds,  it  is  found  that  very 
approximately 

^=^'(1-0-00256  cos  2<^), 

at  a  station  whose  latitude  is  <^,  where  g'  denotes  the  number  32-1724,  or 
the  value  of^at  lat.  45°. 

Experience  teaches  that  in  all  cases  where  a  force  is  exerted  there  must 
be  two  bodies,  between  which  the  force  acts.  Newton's  third  law  asserts 
that  the  mutual  action  of  the  two  bodies  is  always  equal  and  oppositely 
directed. 

The  attraction"  of  the  earth  for  in  pounds  of  matter  is  w^,  where  ^  is  the 
acceleration  of  the  body.  The  attraction  of  the  m  pounds  for  the  earth  is 
M  a,  where  M  is  the  mass  of  the  earth  in  pounds,  and  a  is  the  acceleration 
with  which  it  moves  towards  w.     According  to  the  third  law  of  motion 

M.a  =  ing. 

Um  is  a  small  body,  like  a  few  thousand  pounds,  then,  since  the  mass  of  the 
earth  is  very  large,  the  acceleration  of  the  earth  will  be  inappreciable.  If ;;/ 
and  M  were  equal,  a  and  g  would  be  equal.  Remembering  that  the  accele- 
ration is  the  change  per  second  in  the  velocity,  if  the  two  bodies  move 
towards  each  other  for  /  seconds,  the  initial  velocities  being  Vj  and  V.,,  and 
the  final  velocities  v^  and  v.,,  the  above  expression  becomes 

M^z/i  -  M Vj  _  mvo  —  mV^ 
}  "  /        ^' 

As  /  divides  out  of  this  equation,  it  will  follow  that  the  two  bodies  which 
mutually  attract  each  other  will  suffer  equal  changes  of  momenta  in  the 
same  time.  If  the  two  bodies  start  from  rest  at  the  same  instant,  so  that  Vj 
and  v.,  are  zero,  then 

Mt'i  =  ;/i7'.,, 

or  they  will  have  equal  momenta  at  the  same  instant.  The  momenta  of  a 
freely-suspended  rifle  and  of  a  bullet  fired  from  it  will  be  equal  so  long  as  the 
ball  is  in  the  barrel.  If  the  rifle  is  supported,  the  supporting  body  must  be 
included  with  the  rifle  in  the  value  M. 

30.  Representation  of  forces. — Draw  any  straight  line  AB  (fig.  6),  and 
fix  on  any  point  O  in  it.  We  may  suppose  a  force  to  act  on  the  point  O, 
along  the  line  AB,  either  towards  A  or  B  :  then  O  is 

called  the  point  of  application  of  the  force,  AB  its  line    g — -; jlj — ^ 

of  action  ;  if  it  acts  towards  A,  its  direction  is  OA,  if  Fig.  6. 

towards  B,  its  direction  is  OB.    It  is  rarely  necessary 

to  make  the  distinction  between  the  line  of  action  and  direction  of  a  force  ; 
it  being  very  convenient  to  make  the  convention  that  the  statement — a  force 
acts  on  a  point  O  along  the  line  OA — means  that  it  acts  from  O  to  A.  Let 
us  suppose  the  force  which  acts  on  O  along  OA  to  contain  P  units  of  force  ; 

c 


1 8  071  Matter,  Force,  and  Motion.  [30- 

from  O  towards  A  measure  ON,  containing  P  units  of  length,  the  Hne  ON  is 
said  to  represejit  the  force.  The  analogy  between  the  line  and  the  force  is 
very  complete  ;  the  line  ON  is  drawn  from  O  in  a  given  direction  OA,  and 
contains  a  given  number  of  units  P,  just  as  the  force  acts  on  O  in  the  direc- 
tion OA,  and  contains  a  given  number  of  units  P.  It  is  scarcely  necessary 
to  add,  that  if  an  equal  force  were  to  act  on  O  in  the  opposite  direction,  it 
would  be  said  to  act  in  the  direction  OB,  and  would  be  represented  by  OM, 
equal  in  magnitude  to  ON. 

When  we  are  considering  several  forces  acting  along  the  same  line  we 
may  indicate  their  directions  by  the  positive  and  negative  signs.  Thus  the 
forces  mentioned  above  would  be  denoted  by  the  symbols  +  P  and  —  P 
respectively. 

31.  Forces  acting-  along-  the  same  line. — If  forces  act  on  the  point  O 
in  the  direction  OA  equal  to  P  and  Q  units  respectively,  they  are  equivalent 
to  a  single  force  R  containing  as  many  units  as  P  and  Q  together — that  is, 

R  =  P  +  Q. 
If  the  sign  +  in  the  above  equation  denote  algebraical  addition,  the  equation 
will  continue  true  whether  one  or  both  the  forces  act  along  OA  or  OB.  It 
is  plain  that  the  same  rule  can  be  extended  to  any  number  of  forces,  and  if 
several  forces  have  the  same  line  of  action,  they  are  equivalent  to  one  force 
containing  the  same  number  of  units  as  their  algebraical  sum.  Thus  if 
forces  of  3  and  4  units  act  on  O  in  the  direction  OA,  and  a  force  of  8  in  the 
direction  OB,  they  are  equivalent  to  a  single  force  containing  R  units  given 
by  the  equation 

R=3+4-8=    -i; 

that  is,  R  is  a  force  containing  one  unit  acting  along  OB.  This  force  R  is 
called  their  resultant.  If  the  forces  are  in  equilibrium  R  is  equal  to  zero. 
In  this  case  the  forces  have  equal  tendencies  to  move  the  point  O  in  opposite 
directions. 

32.  Resultant  and  components. — In  the  last  article  we  saw  that  a  single 
force  R  could  be  found  equivalent  to  several  others  ;  this  is  by  no  means 
peculiar  to  the  case  in  which  all  the  forces  have  the  same  line  of  action  ;  in 

fact,  when  a  material  point,  A  (fig.  7),  remains  in  equili- 
brium under  the  action  of  several  forces,  S,  P,  Q,  it  does 
so  because  any  one  of  the  forces,  as  S,  is  capable  of 
neutralising  the  combined  effects  of  all  the  others.  If  the 
force  S,  therefore,  had  its  direction  reversed,  so  as  to  act 
along  AR,  the  prolongation  of  AS,  it  would  produce  the 
same  effect  as  the  system  of  forces  P,  Q. 

Now,  a  force  whose  effect  is  equivalent  to  the  combined 
effects  of  several  other  forces  is  called  their  resultant,  and 
with  respect  to  this  resultant,  the  other  forces  are  termed 
components. 

When  the  forces  P,  Q  act  on  a  point  they  can  only 
have  o?ie  resultant  ;  but  any  single  force  can  be  resolved 
into  components  in  an  indefinite  number  of  ways. 
If  a  point  move  from  rest,  under  the  action  of  any  number  of  forces,  it 
will  begin  to  move  in  the  direction  of  their  resultant. 


-33]  Paralklograui  of  Forces.  19 

2,^.  Parallelogram  of  forces. — When  two  forces  act  on  a  point  their 
resultant  is  found  by  the  following  theorem,  known  as  the  principle  of  the 
parallelogram  of  forces  : — If  two  forces  act  on  a  point.,  and  if  lines  be  drazun 
from  that  poitit  representing  the  forces  in  magnitude  and  direction,  and  a 
parallelogram  be  constructed  on  these  lines  as  sides,  their  resultatit  will  be 
represented  in  magnitude  and  direction  by  that  diagonal  which  passes  throiigJi 
the  point.  Thus  let  P  and  Q  (fig.  8)  be  two  forces  acting  on  the  point  A 
along  AP  and  AQ  respectively,  and  let  AB  and  AC  be  taken  containing  the 
same  number  of  units  of  length  that  P  and  Q  contain  units  of  force  ;  let  the 
parallelogram  ABDC  be  completed,  and  the  diagonal  AD  drawn  ;  then  the 
theorem  states  that  the  resultant,  R,  of  P  and  Q  is  represented  by  AD  ;  that 
is  to  say,  P  and  Q  together  are  equal  to  a  single  force  R  acting  along  the 
line  AD,  and  containing  as  many  units  of  force  as  AD  contains  units  of 
length. 

Proofs  of  this  theorem  are  given  in  treatisfes  on  Mechanics  ;  we  will  here 
give  an  account  of  a  direct  experimental  verification  of  its  truth  ;  but  before 
doing  so  we  must  premise  an  account  of  a  very  simple  experiment. 

Let  A  (fig.  9)  be  a  small  pulley,  and  let  it  turn  on  a  smooth,  hard,  and 
thin  axle,  with  little  or  no  friction  :  let  W  be  a  weight  tied  to  the  end  of  a 
fine  thread  which  passes  over  the  pulley  ;  let  a  spring  CD  be  attached  by 
one  end  to  the  end  C  of  the  thread  and  by  the  end  D  to  another  piece  of 
thread,  the  other  end  of  which  is  fastened  to  a  fixed  point  B  ;  a  scale  CE 
can  be  fastened  by  one  end  to  the  point  C  and  pass  inside  the  spring  so  that 


the  -elongation  of  the  spring  can  be  measured.  Now  it  will  be  found  on  trial 
that  with  a  given  weight  W  the  elongation  of  the  spring  will  be  the  same 
whatever  the  angle  contained  between  the  parts  of  the  string  WA  and  BA. 
Also  it  would  be  found  that  if  the  whole  were  suspended  from  a  fixed  point, 
instead  of  passing  over  the  pulley,  the  weight  would  in  this  case  stretch  the 
string  to  the  same  extent  as  before.  This  experiment  shows  that  when  care 
is  taken  to  diminish  to  the  utmost  the  friction  of  the  axle  of  the  pulley,  and 
the  imperfect  flexibility  of  the  thread,  the  weight  of  W  is  transmitted  with- 
out sensible  diminution  to  B,  and  exerts  on  that  point  a  pull  or  force  along 
the  line  BA  virtually  equal  to  W. 

This  being  premised,  an  experimental  proof,  or  illustration  of  the  paral- 
lelogram of  forces,  may  be  made  as  follows  : — 

Suppose  H  and  K  (fig.  10)  to  be  two  pulleys  with  axles  made  as  smooth 
and  fine  as  possible  ;  let  P  and  Q  be  two  w^eights  suspended  from  fine  and 

.c  2 


20  On  Matter,  Fojre,  and  Motion.  [33- 

flexible  threads  which,  after  passing  over  H  and  K,  are  fastened  at  A  to  a 
third  thread  AL,  from  which  hangs  a  weight  R  ;  let  the  three  weights  come 
to  rest  in  the  positions  shown  in  the  figure.  Now  the  point  A  is  acted  on  by- 
three  forces  in  equiHbrium— viz.  P  from  A  to  H,  Q  from  A  to  K,  and  R 
from  A  to  L,  consequently  any  one  of  them  must  be  equal  and  opposite  to 
the  resultant  of  the  other  two.  Now  if  we  sup- 
pose the  apparatus  to  be  arranged  immediately 
in  front  of  a  large  slate,  we  can  draw  lines  upon 
it  coinciding  with  AH,  AK,  and  AL.  If  now  we 
measure  off  along  AH  the  part  AB  containing 
as  many  inches  as  P  contains  pounds,  and  along 
AK  the  part  AC  containing  as  many  inches  as 
Q  contains  pounds,  and  complete  the  parallelo- 
gram ABCD,  it  will  be  found  that  the  diagonal 
AD  is  in  the  same  line  as  AL,  and  contains  as 
many  inches  as  R  weighs  pounds.  Consequently,  the  resultant  of  P  and  Q 
is  represented  by  AD.  Of  course,  any  other  units  of  length  and  force  might 
have  been  employed.  Now  it  will  be  found  that  when  P,  Q,  and  R  are 
changed  in  any  way  whatever,  consistent  with  equilibrium,  the  same  con- 
struction can  be  made — the  point  A  will  have  different  positions  in  the 
different  cases  ;  but  when  equilibrium  is  established,  and  the  parallelogram 
ABCD  is  constructed,  it  will  be  found  that  AD  is  vertical,  and  contains  as 
many  units  of  length  as  R  contains  units  of  force,  and  consequently  it  repre- 
sents a  force  equal  and  opposite  to  R — that  is,  it  represents  the  resultant  of 
P  and  Q. 

34.  Resultant  of  any  number  of  forces  acting;  in  one  plane  on  a 
point —  Let  the  forces  P,  Q,  R,  S  (fig.  ri)  act  on  the  point  A,  and  let  them 

be  i-epresented  by  the  lines  AB,  AC,  AD,  AE,  as 
shown  in  the  figure.  First,  complete  the  parallelo- 
gram ABFC  and  join  AF  ;  this  line  represents  the 
resultant  of  P  and  Q.  Secondty,  complete  the 
parallelogram  AFGD  and  join  AG  ;  this  line  re- 
presents the  resultant  of  P,  Q,  R.  Thirdly,  com- 
plete the  parallelogram  AG  HE  and  join  AH  ;  this 
line  represents  the  resultant  of  P,  Q,  R,  S.  It  is 
manifest  that  the  construction  can  be  extended  to 
any  number  of  forces.  A  little  consideration  will 
show  that  the  line  AH  might  be  determined  by  the 
following  construction  :—  Through  B  draw  BF 
parallel  to,  equal  to,  and  towards  the  same  part  as  AC  ;  through  F  draw 
FG  parallel  to,  equal  to,  and  towards  the  same  part  as  AD  ;  through  G  draw 
GH  parallel  to,  equal  to,  and  towards  the  same  part  as  AE  ;  join  AH,  then 
AH  represents  the  required  resultant. 

35.  Triang^Ie  of  Forces. — If  the  resultant  of  the  forces  is  zero,  they  have 
no  joint  tendency  to  move  the  point,  and  consequently  are  in  equilibrium. 

The  case  of  three  forces  acting  on  a  point  is  of  such  importance  that  we 
may  give  a  brief  statement  of  it.  Let  P,  Q,  R  (fig.  12)  be  three  forces  in 
equilibrium  on  the  point  O.  From  any  point  B  draw  BC  parallel  to  and 
towards  the  same  part  as  OP,  from  C  draw  CA  parallel  to  and  towards  the 


-37]         Composition  and  Resolution  of  Parallel  Forces.  2 1 

same  part  as  OQ,  and  take  CA  such  that  P  :  Q  : :  BC  :  CA  ;  then,  on  joining 
AB,  the  third  force  R  must  act  along  OR  parallel  to  and  towards  the  same 
part  as  AB,  and  must  be  proportional  in  magnitude  to 
AB.  This  construction  is  frequently  called  the  Triangle 
of  Forces.  It  is  evident  that  while  the  sides  of  the 
triangle  are  severally  proportional  to  P,  Q,  R,  the  angles 
A,  B,  C  are  supplementary  to  QOR,  ROP,  POQ  re- 
spectively ;  consequently,  every  trigonometrical  relation 
existing  between  the  sides  and  angles  of  ABC  will 
equally  exist  between  the  forces  P,  Q,  R,  and  the  sup- 
plements of  the  angles  between  their  directions.  Thus 
in  the  triangle    ABC    it    is   known   that    the    sides  are  Fig.  12. 

proportional  to  the  sines  of  the  opposite  angles  ;  now, 
since  the  sines  of  the  angles  are  equal  to  the  sines  of  their  supplements,  we 
at  once  conclude  that  when  three  forces  arc  in  equilibrium.,  each  is  propor- 
tional  to  the  sine  of  the  angle  between  the  directions  of  the  other  two. 

36.  Moments  of  Forces. — Let  P  (fig.  13)  denote  any  force  acting  from  B 
to  P,  take  A  any  point,  let  fall  AN  a  perpendicular  from  A  on  BP.  The 
product  of  the  number  of  units  of  force  in  P,  and  the  number  of  units  of 
length  in  AN,  is  called  the  moment  of  P  with  respect  to  A.  Since  the  force 
P  can  be  represented  by  a  straight  line,  the  moment  of  P  can  be  represented 
by  an  area.  In  fact,  if  BC  is  the  line  representing  P,  the  moment  is  properly 
represented  by  twice  the  area  of  the  triangle  ABC.  The  perpendicular  AN 
is  sometimes  called  the  arm  of  the  pressure.  Now  if  a  watch  were  placed 
with  its  face  upwards  on  the  paper,  the  force  P  would  cause  the  arm  AN  to 
turn  round  A  in  the  contrary  direction  to  the  hands  of  the 

watch.  Under  these  circumstances,  it  is  usual  to  con- 
sider the  moment  of  P  with  respect  to  the  point  A  to  be 
>positive.  If  P  acted  from  C  to  B,  it  would  turn  NA  in 
the  same  direction  as  the  hands  of  the  watch,  and  now  its 
moment  is  reckoned  negative. 

It  is  a  simple  geometrical  consequence  of  the  paral- 
lelogram of  forces  {j)-^  that  the  moment  of  the  resultant 
equals  the  sum  of  the  moments  of  the  component  forces,  regard  being  had  to 
the  signs  of  the  moments. 

If  the  point  about  which  the  moments  are  measured  be  taken  in  the  direc- 
tion of  the  resultant,  its  moment  with  respect  to  that  point  will  be  zero  ;  and 
consequently  the  sum  of  the  moments  with  respect  to  such  point  will  be  zero. 

37.  Composition  and  resolution  of  parallel  forces. — The  case  of  the 
equilibrium  of  three  parallel  forces  is  merely  a  particular  case  of  the  equili- 
brium of  three  forces  acting  on  a  point.  In  fact,  let  P  and  Q  be  two  forces 
whose  directions  pass  through  the  points  A  and  B,  and  intersect  in  O, 
fig.  14  ;  let  them  be  balanced  by  a  third  force  R  whose  direction  produced 
intersects  the  line  AB  in  C.  Now  suppose  the  point  O  to  move  along  AO, 
gradually  receding  from  A,  the  magnitude  and  direction  of  R  will  continually 
change,  and  also  the  point  C  will  continually  change  its  position,  but  will 
always  lie  between  A  and  B.  In  the  limit  P  and  Q  become  parallel  forces, 
acting  towards  the  same  part  balanced  by  a  parallel  force  R  acting  towards 
Ihe  contrary  part  through  a  point  X  between  A  and  B.     The  question  is  : — 


N 
Fig. 


On  Matter,  Force,  and  Motioii. 


[37- 


Fig.  14. 


FU'st,  in  this  limiting  case,  what  is  the  value  of  R  ;  secondly,  what  is  the 
position  of  X  ?  Now  with  regard  to  the  first  point  it  is  plain  that  if  a  triangle 
abc  be  drawn  as  in  art.  35,  the  angles  a  and  b  in  the 
limit  will  vanish,  and  c  will  become  180°,  consequently 
ab  ultimately  equals  ac  +  cb  ; 

or  R  =  P  +  Q. 

With  regard  to  the  second  point  it  follows  from  last 
article  (36)  that  the  moments  of  P  and  Q  about  C 
are  always  equal,  whence 

AX  :  XB  : :  Q  :  P, 

a  proportion  which  determines  the  position  of  X. 
Hence  the  following  rules  for  the  composition  of  any 
two  parallel  forces,  viz. — 

I.  When  two  parallel  forces  P  and  Q  act  towards  the  same  part,  at  rigidly 
connected  points  A  and  B,  their  resultant  is  a  parallel  force  acting  towards 
the  same  part,  equal  to  their  sum,  and  its  direction  divides  the  line  AB 
into  two  parts  AC  and  CB  inversely  proportional  to  the  forces  P  and  Q. 

II.  When  two  parallel  forces  P  and  Q  act  towards  contraiy  parts 
at  rigidly  connected  points  A  and  B,  of  which  P  is  the  greater,  their 
resultant  is  a  parallel  force  acting  towards  the  same  part  as  P,  equal  to  the 
excess  of  P  over  Q,  and  its  direction  divides  BA  produced  in  a  point  C  such 
that  CA  and  CB  are  inversely  proportional  to  P  and  Q. 

In  each  of  the  above  cases  if  we  were  to  apply  R  at  the  point  C,  in 
opposite  directions  to  those  shown  in  the  figure,  it  would  plainly  (by  the  above 
theorem)  balance  P  and  Q,  and  therefore  when  it  acts  as  shown  in  figs.  15 
and  16  it  is  the  resultant  of  P  and  Q  in  those  cases  respectively.  It  will,  of 
course,  follow  that  the  force  R  acting  at  C  can  be  resolved  into  P  and  Q 
acting  at  A  and  B  respecti\ely. 


Fig. 


Fig.  16. 


If  the  second  of  the  above  theorems  be  examined,  it  will  be  found  that 
no  force  R  exists  equivalent  to  P  and  Q  when  these  forces  are  equal.  Two 
such  forces  constitute  a  couple,  which  may  be  defined  to  be  two  equal  parallel 
forces  acting  towards  contrary  parts  ;  they  possess  the  remarkable  property 
that  they  are  incapable  of  being  balanced  by  any  single  force  whatsoever. 

In  the  case  of  more  than  two  parallel  forces  the  resultant  of  any  two  caa 


-40]  TJu  Lever.  23 

be  found,  then  of  that  and  a  third,  and  so  on  to  any  number  ;  it  can  be 
shown  that  however  great  the  number  of  forces  they  will  either  be  in  ecjuili- 
brium  or  will  reduce  to  a  single  resultant  or  to  a  couple. 

38.  Centre  of  parallel  forces. — On  referring  to  figs.  15  and  16,  it  will 
be  remarked  that  if  we  conceive  the  points  A  and  B  to  be  fixed  in  the 
directions  AP  and  BQ  of  the  forces  P  and  Q,  and  if  we  suppose  those 
directions  to  be  turned  round  A  and  B,  so  as  to  continue  parallel  and  to 
make  any  given  angle  with  their  original  directions,  then  the  direction  of 
their  resultant  will  continue  to  pass  through  C  ;  that  point  is  therefore  called 
the  centre  of  the  parallel  forces  P  and  Q. 

It  appears  from  investigation,  that  whenever  a  system  of  parallel  forces 
reduces  to  a  single  resultant,  those  forces  will  have  a  centre  ;  that  is  to  say^ 
if  we  conceive  each  of  the  forces  to  act  at  a  fixed  point,  there  will  be  a  point 
through  which  the  direction  of  their  resultant  will  pass  when  the  directions 
of  the  forces  are  turned  through  any  equal  angles  round  their  points  of 
application  in  such  a  manner  as  to  retain  the  parallelism  of  their  dii'ections. 

The  most  familiar  example  of  a  centre  of  parallel  forces  is  the  case  in 
which  the  forces  are  the  weights  of  the  parts  of  a  body  ;  in  this  case  the 
forces  all  acting  towards  the  same  part  will  have  a  resultant,  viz.  their  sum  ; 
and  their  centre  is  called  the  centre  of  gravity  of  the  body. 

39.  Equality  of  action  and  reaction. — We  will  proceed  to  exemplify 
some  of  the  principles  now  laid  down  by  investigating  the  conditions  of 
equilibrium  of  bodies  in  a  few  simple  cases  ;  but  before  doing  so  we  refer 
again  to  the  law  stated  in  art.  (29)  and  which  holds  good  whenever  a  mutual 
action  is  called  into  play  between  two  bodies.  Reaction  is  always  equal  and 
contrary  to  action  :  that  is  to  say,  the  mutual  actio?ts  of  two  bodies  on  each 
other  are  always  forces  equal  in  amount  and  opposite  in  direction.,  and  this  is 
equally  true  when  the  bodies  are  in  motion  as  well  as  when  they  are  at  rest. 
A  very  instructive  example  of  this  law  has  already  been  given  (j,'^.,  in  which 
the  action  on  the  spring  CD  (fig.  8)  is  the  weight  W  transmitted  by  the 
spring  to  C,  and  balanced  by  the  reaction  of  the  ground  transmitted  from  B 
to  D.  Under  these  circumstances  the  spring  is  said  to  be  stretched  by  a 
force  W.  If  the  spring  were  removed,  and  the  thread  were  continuous  from 
A  to  B,  it  is  clear  that  any  part  of  it  s  stretched  by  two  equal  forces,  viz.  an 
action  and  reaction,  each  equal  to  W,  and  the  thread  is  said  to  sustain  a 
tension  W.  When  a  body  is  urged  along  a  smooth  surface,  the  mutual 
action  can  only  take  place  along  the  common  perpendicular  at  the  point  of 
contact.  If,  however,  the  bodies  are  rough,  this  restriction  is  partially  re- 
moved, and  now  the  mutual  action  can  take  place  in  any  direction  not 
making  an  angle  greater  than  some  determinate  angle  with  the  common 
perpendicular.  This  determinate  angle  has  different  values  for  different 
substances,  and  is  sometimes  called  the  limititig  angle  of  resistance,  sovi\&- 
times  the  angle  of  repose. 

40.  The  lever  is  a  name  given  to  any  bar  straight  or  curved,  AB  (fig.  17) 
resting  on  a  fixed  point  or  edge  c  called  i\\e  fulcrufn.  The  forces  acting  on 
the  lever  are  the  zueight  or  resistance  Q,  the  power  P,  and  the  reaction 
of  the  fulcrum.  Since  these  are  in  equilibrium,  the  resultant  of  P  and  Q 
must  act  through  c,  for  otherwise  thay  could  not  be  balanced  by  the  reaction. 
Draw  cb  at  right  angles  to  QB  and  ca  to   PA  produced  ;  then  observing- 


24  On  Matter,  Force,  and  Motion.  [40- 

that  P  X  ca,  and  Q  x  cb  are  the  moments  of  P  and  Q  with  respect  to  c,  and 
that  they  have  contrary  signs,  we  have  by  (36), 

P  : ;  ca=(:^xcb; 

an  equation  commonly  expressed  by  the  rule,  that  in  the  lever  the  power 
is  to  the  weight  ift  the  ijtverse  ratio  of  their  arms. 

Levers  are  divided  into  three  kinds, 
according  to  the  position  of  the  fulcrum 
with  respect  to  the  points  of  apphcation  of 
the  power  and  the  weight.  In  a  lever  of 
the  first  kind  the  fulcrum  is  between  the 
power  and  resistance,  as  in  fig.  17,  and  as 
in  a  poker  and  in  the  common  steelyard  ; 
a  pair  of  scissors  and  a  carpenter's  pincers 
are  double  levers  of  this  kind.  In  a  lever 
of  the  second  kind\h&  resistance  is  between 
the  power  and  the  fulcrum,  as  in  a  wheel- 
barrow, or  a  pair  of  nutcrackers,  or  a 
door  ;  in  a  lever  of  the  third  kind  the 
power  is  between  the  fulcrum  and  the 
Fig.  17.  resistance,  as    in  a  pair  of  tongs  or   the 

treadle  of  a  lathe. 
41.  Pulleys. — The  pulley  is  a  hard  circular  disc  of  wood  or  of  metal,  in 
the  edge  of  which  is  a  groove,  and  which  can  turn  freely  on  an  axis  in  the 
centre.     Pulleys  are  either  yf.ir^,  as  in  fig.  18,  where  the  stirrup  or  fork  is 
rigidly  connected  with  some  immovable  body,  and  where  the  axis  rotates  in 

19,  where  the  axis  is  fixed  to 
the  fork,and  it  passes  through 
a  hole  in  the  centre  of  the 
disc.  The  rope  which  passes 
round  the  pulley  in  fig.  18, 
supports  a  weight  at  one  end; 
while  at  the  other  a  pull  is 
applied  to  hold  this  weight 
in  equilibrium. 

We  may  look  upon  the 
power  and  the  resistance  as 
acting  at  the  circumference 
of  the  circle  ;  hence  as  the 
radii  are  equal,  if  we  consider 
the  pulley  as  a  lever,  the 
two  arms  are  equal,  and 
equilibrium  will  pre\ail  when 
the  power  and  the  resistance 
are  equal.  The  fixed  pulley 
affords  thus  no  mechanical 
appli- 


the  stirrup  ;  or  it  may  be  movable,  as  in  fi^ 


Fig.  19. 


advantage,  but  is  simply  convenient  in  changing  the  direction  of  th 
cation  of  a  force. 

In  the  case  of  the  movable  pulley  one  end  of  the  rope  is  suspended  to 


-42]  JV/iec/  and  Axle.  25 

fixed  point  in  a  beam,  and  the  weight  is  attached  to  the  hook  on  which  the 
pulley  acts.  The  tension  of  the  rope  is  everywhere  the  same;  one  portion 
of  the  weight  is  supported  by  the  fixed  part  and  the  other  by  the  power, 
and  these  are  equal  to  each  other,  and  are  together  equal  to  the  weight, 
including  the  pulley  itself ;  hence  in  this  case  P  =  i  Q. 

If  several  pulleys  are  joined  together  on  a  common  axis  in  a  special 
sheath,  which  is  fixed,  and  a  rope  passes  round  all  those  and  also  round  a 
similar  but  movable  combination  of  pulleys,  such  an  arrangement,  which  is 
represented  in  fig.  20,  is  called  a  block  a?id  tackle. 

If  we  consider  the  condition  of  the  rope  it  will  be  found  to  have  every- 
where the  same  tension  ;  the  weight  Q  which  is  attached  to  the  hook 
common  to  the  whole  system  is  supported  by  the  six  portions  of  the  rope  : 
hence  each  of  these  portions 
will  sustain  one  sixth  of  the 
weight ;  the  force  which  is 
applied  at  the  free  end  of  the 
rope  which  passes  over  the 
upper  pulley,  and  which  de- 
termines the  tension,  will  have 
the  same  value  ;  that  is  to 
say,  it  will  support  one  sixth 
of  the  weight. 

The  relation  between 
power  and  resistance  in  a 
block  and  tackle  is  expressed 

by    the  equation    P  =  — ,    in 

// 
which  P  is  the  power,  Q  the 
weight,  and  ;/  the  number  of 
cords  by  which  the  weight  is 
supported. 

42.  The  wheel  and  axle. 
— The  older  form  of  this  ma- 
chine, fig.  21,  is  that  of  an 
axle,  to  which  is  rigidly  fixed, 
concentric  with  it,  a  wheel  of 
larger  diameter.  The  power 
is  applied  tangentially  on  the 
wheel,  and  the  resistance  tan- 
gentially to  the  axle,  as  for 
instance  in  the  treadmill  and 
water-wheel.  Sometimes,  as 
in  the  case  of  the  capstan, 
the  power  is  applied  to  spokes  fixed  in  the  axle,  which  represent  semi- 
diameters  of  the  wheel  ;  in  other  cases,  as  in  the  windlass,  the  handle  is 
rigidly  fixed  to  the  axis. 

In  all  its  modifications  we  may  regard  the  wheel  and  axle  as  an  applica- 
tion of  the  lever,  the  arms  of  which  are  the  radii  of  the  wheel  and  axle  re- 
spectively ;  and  in  all  cases  equilibrium  exists  where  the  power  is   to  the 


Fig.  20, 


On  Matter,  Force,  and  Mot  ion. 


[42- 

Thus 


resistance  as  the  radius  of  the  axle  is  to  the   radius  of  the  wheel, 
in  fig.  21,  P  :  Q  =  ab :  rt^,  or  P  x  a^  =  Q  x  ab. 

Frequent  applications  of  wheels  of  different  diameters  are  met  with  in 
which  the  motion  of  one  wheel  is  transmitted  to  another,  either  by  means 
of  teeth  fitting  in  each  other  on  the  circumference  of  the  wheels,  as  in  fig.  22^ 
or  by  means  of  bands  passing  over  the  two  wheels,  as  in  the  illustration  of 
Ladd's  Magneto-Electrical  Machine  (see  Book  viii.). 

In  fig.  22,  which  represents  the  essential  parts  of  a  crab  winch,  in  order 
to  raise  the  weight  Q  a  power  p  must  be  applied  at  the  circumference  of 

the  wheel  such  that  ^  =  Q  =- ,  in  which  r  and  R  arc  the  radii  of  the  axle 
R 

b  and  of  the  toothed  wheel  a  respectively. 

The  rotation  of  the  wheel  a  is  effected  by  means  of  the  smaller  wheel  cor 

crab,  the  teeth  of  which  fit  in  those  of  a.     But  if  this  wheel  c  is  to  exert  at 

its  circumference  a  power  p,  the  power  P  which  is  applied  at  the  end  of 

r' 
the  handle  must  be  P  =  —^p,  in  which  r'  is  the  radius  of  r,  R'  the  length  of 

R' 
a  lever  at  the  end  of  which  P  acts,  and  consequently 

RR'^ 

The  radius  of  the  wheel  c  is  to  that  of  the  wheel  a  as  their  respective  circum- 
ferences ;  and,  as  the  teeth  of  each  are  of  the  same  size,  the  circumferences 
will  be  as  the  number  of  teeth. 

Trains  of  wheelwork  are  used,  not  only  in  raising  great  weights  by  the 
exertion  of  a  small  power  ;  as  in  screw  jacks,  cranes,  crab  winches,  &c.,  but 
also  in  clock  and  watch  works,  and  in  cases  in  which  changes  in  velocity  or 
in  power  or  even  in  direction  are  required.  Numerous  examples  will  be  met 
with  in  the  various  apparatus  described  in  this  work. 

43.  Inclined  Plane The  properties  and  laws  of  the  inclined  plane  may 

be  conveniently  demonstrated  by  means  of  the  apparatus  represented  in 
fig.  23.  RS  represents  the  section  of  a  smooth  piece  of  hard  wood  hinged  at 
R  ;  by  means  of  screw  it  can  be  clamped  at  any  angle  x  against  the  arc- 
shaped  support,  by  which  at  the 
same  time  the  angle  can  be  mea- 
sured ;  (^?  is  a  cylindrical  roller, 
to  the  axis  of  which  is  attached 
a  string  passing  over  a  pulley 
to  a  scale-pan  P. 

It  is  thus  easy  to  ascertain 
by  direct  experiments  what 
weights  R  must  be  placed  in  the 
pan  P  in  order  to  balance  a  roller 
of  any  given  weight,  or  to  cause 
it  to  move  with  a  gi\en  angle  of 
inclination. 

The  line  RS  represents  the 
length,  ST  the  height,  and  RT  the  base  of  the  inclined  plane. 

In  ascertaining  the  theoretical  conditions  of  equilibrium  we  ha\e  a  useful 


-43]  Inclined  Plane.  27 

application  of  the  parallelogram  of  forces.  Let  the  hne  ab,  fig.  23,  represent 
the  force  which  the  weight  W  of  the  cylinder  exerts  acting  vertically  down- 
wards ;  this  may  be  decomposed  into  two  others  ;  one,  ad,  acting  at  right 
angles  against  the  plane,  and  representing  the  pressure  which  the  weight 
exerts  against  the  plane  ;  and  which  is  counterbalanced  by  the  reaction  of 
the  plane  ;  the  other,  ac,  represents  the  component  which  tends  to  move  the 
weight  down  the  plane,  and  this  component  has  to  be  held  in  equilibrium  by 
the  weight  P,  equal  to  it  and  acting  in  the  opposite  direction. 

It  can  be  readily  shown  that  the  triangle  abc  is  similar  to  the  triangle 
SRT,  and  that  the  sides  ac  and  ab  are  in  the  same  proportion  as  the  sides 
ST  and  SR.  But  the  line  ac  represents  the  power,  and  the  line  ab  the 
weight  ;  hence 

ST:SR  =  P:W; 

that  is,  on  an  inclined  plane,  equilibrium  obtains  when  the  power  is  to  the 
weight  as  the  height  of  the  inclined  plane  to  its  length. 

ST 
Since  the  ratio     ^  is  the  sine  of  the  angle  x,  we  may  also  state  the  prm- 
SR 
ciple  thus  : 

P  =  \V  sin  X. 

The  component  da  or  be,  which  represents  the  actual  pressure  against 
the  plane,  is  equal  to  W  cos  x ;  that  is,  the  pressure  against  the  plane  is  to 
the  weight  as  the  base  is  to  the  length  of  the  inclined  plane. 

In  the  above  case  it  has  been  considered  that  the  power  acts  parallel  to 
the  inclined  plane.  It  may  be  applied  so  as  to  act  horizontally.  It  will  then 
be  seen  from  fig.  24  that  the  weight  W  may  be  decomposed  into  two  forces, 
one  of  which,  ab,  acts  at  right  angles  to  the  plane,  and  the  other,  ac,  parallel 
to  the  base.  It  is  this  latter  which  is  to  be  kept  in  equilibrium  by  the  power. 
From  the  similarity  of  the  two  triangles  acb  and  STR,  ac  :  bc='S>T  :  TR 
=  h:  b  ;  but  be  is  equal  to  W,  and  ac  is  equal  to  P,  hence  the  power  which 
must  be  applied  at  b  to  hold  the  weight  W  in  equilibrium  is  as  the  height 
of  the  inclined  plane  is  to  the  base,  or  as  the  tangent  of  the  angle  of  inclina- 
tion X  ;  that  is,  P  =  W  tan  x.    The  pressure  upon  the  plane  in  this  case  may 

be  easily  shown  to  be  ab  =  

cos  X 

that  is  = .     This  is  sometimes 

cos  X 

called    the  relative  weight  on  the 

plane. 

If  the  force  P  which  is  to 
counterbalance  W  is  not  parallel  to 
the  plane,  but  forms  an  angle,  E,  with 
it,  this  force  can  be  decomposed  into  ^'^'  ^'^' 

one  which  is  parallel  to  it,  and  one  which  is  at  right  angles.  Of  these  onlj- 
the  first  is  operative,  and  is  equal  to  P  cos  E. 

In  most  cases  of  the  use  of  the  inclined  plane,  such  as  in  moving  carriages 
and  waggons  along  roads,  in  raising  casks  into  waggons  or  warehouses,  the 
power  is  applied  parallel  to  the  inclined  plane.  An  instance  of  a  case  in 
which  a  force  acts  parallel  to  the  base  is  met  with  in  the  screw. 


On  Matter,  Force,  and  Motion. 


[43- 

Owing  to  the  unevenness  of  the  surfaces  in  actual  use,  the  laws  of  equili- 
brium and  of  motion  on  an  inclined  plane  undergo  modification.  T\\&fric- 
tion,  for  instance,  which  comes  into  play  amounts  on  ordinary  roads  to  from 
Is  to  ^,  and  on  railways  to  from  x|o  to  5 jo  *^f  the  relative  weight.  This  must 
be  looked  upon  as  a  hindrance  to  be  continually  overcome,  and  must  be 
deducted  from  the  force  required  to  keep  a  body  from  falling  down  an 
inclined  plane,  or  must  be  added  to  it  in  the  case  in  which  a  body  is  to  be 
moved  up  the  plane.  Hence  the  use  of  the  inclined  plane  in  unloading  heavy 
casks  into  cellars,  &c. 

A  body  which  cannot  roll  does  not  move  on  the  inclined  plane,  provided 
the  inclination  is  below  a  certain  amount  (39).  The  determination  of  this 
limiting  afigle  of  resistance,  at  which  a  body  on  an  inclined  plane  just  begins 
to  move,  may  serve  as  a  rough  illustration  of  a  mode  of  ascertaining  the 
'  coefficient  of  friction.' 

For  in  the  case  in  which  the  power  is  applied  parallel  to  the  plane,  the 
component  of  the  weight  which  presses  against  the  plane  or  the  actual  load, 
L,  is  W  cos  X  ;  and  the  component  which  tends  to  move  the  body  down  the 
plane  is  equal  to  W  sin  x.     If  the  friction,  R,  is  just  sufficient  to  hold  this  in 

equihbrium,  the  coefficient  of  friction  will  be  ,  =^,-, =  tan  x. 

^  L     W  cos  X 

Thus  if  we  place  on  the  plane  a  block  of  the  same  material,  by  gradually 
increasing  the  inclination  it  will  begin  to  move  at  a  certain  angle,  which 
will  depend  on  the  nature  of  the  material  ;  this  angle  is  the  limiting  angle 
of  resistance,  and  its  tangent  is  the  coefficient  of  friction  for  that  material. 

44.  The  'Wedge. — The  ordinary  form  of  the  wedge  is  that  of  a  three- 
sided  prism  of  iron  or  steel,  one  of  whose  angles  is  very  acute.  Its  most 
frequent  use  is  in  splitting  stone,  timber,  &c.  Fig.  25  represents  in  section 
the  application  of  the  wedge  to  this  purpose.  The  side  ab  is  the  back,  the 
vertex  of  the  angle  acb  which  the  two  faces  ac  and 
be  make  with  each  other  represents  the  edge,  and 
the  faces  ac  and  be  the  sides  of  the  wedge.  The 
power  P  is  usually  applied  at  right  angles  to  the 
back  ;  and  we  may  look  upon  the  cohesion  be- 
tween the  fibres  of  the  wood  as  representing  the 
resistance  to  be  overcome  ;  as  corresponding  to 
what  in  other  machines  is  the  weight.  Suppose 
this  to  act  at  right  angles  to  the  two  faces  of 
the  wedge,  and  to  be  represented  by  the  lines 
fe  and  ge  ;  complete  the  parallelogram  gef,  then 
the  diagonal  he  will  represent  the  resultant  of 
the  reaction  of  the  fibres  tending  to  force  the 
wedge  out  ;  the  force  which  must  be  applied  to 
hold  this  wedge  in  equilibrium  must  therefore  be 
equal  to  eh.  Now  efh  is  similar  to  the  triangle 
acb,  therefore  ab:  ac^eh:  ef;  but  these  lines  re- 
present the  pressure  applied  at  the  back  of  the 
wedge,  and  the  pressure  on  the  face  ac,  hence  if  P 
represent  the  former  and  Q  the  latter,  there  is  equilibrium  when  ^  :C  =  ab:bc, 
that  is,  when  the  power  is  to  the  resistance  in  the  same  ratio  as  the  back  of 


Fig.  25- 


-45] 


TJie  Screw. 


29 


the  wedge  bears  to  one  of  the  sides.  The  relation  between  power  and  re- 
sistance is  more  favourable  the  sharper  the  edge,  that  is,  the  smaller  the 
angle  which  the  sides  make  with  each  other. 

The  action  of  all  sharp  cutting  instruments,  such  as  chisels,  knives, 
scissors,  &c.,  depends  on  the  principle  of  the  wedge.  It  is  also  appUed  when 
very  heavy  weights  are  to  be  raised  through  a  short  distance,  as  in  launching 
ships,  and  in  bracing  columns  and  walls  to  the  perpendicular. 

45.  The  Screw. — Let  us  suppose  a  piece  of  paper  in  the  shape  of  a 
rio'ht-angled  triangle  aee'  to  be  applied  with  its  vertical  side  ac'e'  against  a 
cylinder,  and  parallel  to  the  axis,  and  to  be  wrapped  round  the  cyhnder  ;  the 
hypotenuse  will  describe  a  screw  line  or  helix  on  the  surface  of  the  cylinder 
(fig.  26)  ;  the  points  ab  c  de  will  occupy  the  positions  respectively  a  b'  c'  d'  e'. 
If  the  dimensions  be  so  chosen  that  the  base  of  the  triangle,  cc\  is  equal 
to  the  circumference  of  the  cylinder,  then  the  hypotenuse  abc  becomes  an 
inclined  plane  traced  on  the  surface  of  the  cylinder  ;  the  distance  ac'  being 
the  height  of  the  plane. 


Fig.  27. 


Fig.  26. 

An  ordinary  screw  consists  of  an  elevation  on  a  solid  cylinder ;  this 
elevation  may  be  either  square,  as  in  fig.  27,  or  acute,  and  such  screws  are 
called  square  or  sharp  screws  accordingly. 

When  a  corresponding  groove  is  cut  in  the 
hollow  cylinder  or  nut  of  the  same  diameter 
as  the  bolt,  this  gives  rise  to  an  internal  or 
companion  screw  or  nut^  fig.  28. 

The  vertical  distance  between  any  two 
threads  of  a  screw  measured  parallel  to  the 
axis  is  called  the  pitch,  and  the  angle  ace'  or  aee'  is  called  the  inclination  of 
the  screw. 

In  practice,  a  raised  screw  is  used  with  its  companion  in  such  a  manner 
that  the  elevations  of  the  one  fit  into,  and  coincide  with,  the  depressions  of 
the  other.  The  screw  is  a  modification  of  the  inclined  plane,  and  the  condi- 
tions of  equilibrium  are  those  which  obtain  in  the  case  of  the  plane.  The 
resistance,  which  is  either  a  weight  to  be  raised  or  a  pressure  to  be  exerted, 
acts  in  the  direction  of  the  vertical,  and  the  power  acts  parallel  to  the  base  ; 
hence  we  have  P  :  R  =  //  :  (5,  and  the  length  of  the  base  is  the  circumference 
of  the  cylinder  ;  whence  P  :  R  =  /^  :  Ztrr  ;  r  being  the  radius  of  the  cylinder, 
and  h  the  pitch  of  the  screw. 

The  power  is  usually  applied  to  the  screw  by  means  of  a  lever,  as  in  the 
bookbinders'  press,  the  copying  press,  &c.,  and  the  principle  of  the  screw 
may  be  stated  to  be  generally  that  the  power  of  the  screw  is  to  the  resistance 
in  the  same  ratio  as  that  of  the  pitch  of  the  screw  to  the  circumference  of  the 
circle  through  which  the  power  acts. 


30 


On  Matter,  Force,  a)id  Motion. 


[46- 


Fig.  29. 


46.  Virtual  Velocity.^ — If  the  point  of  application  of  a  force  be  slightly 

displaced,  the  resolved  part  of  the  displacement  in  the  direction  of  the  force 

is  termed  the  virtual  velocity  of  the  force,  and  is'  considered  as  positive  or 

negative,  according  as  it  is  in  the  same  direction  as  the  force,  or  in  the 

opposite  direction.     Thus  in  fig.  29  let  the  point  of 

application  A  of  the  force  P  be  displaced  to  A',  and 

draw  A'rt  perpendicular  to  AP.    Then  A<-?  is  the  virtual 

velocity  of  the  force  P,  and  being,  in  this  case,  in  the 

direction  of  P,  is  to  be  considered  positive. 

The  principle  of  virtual  velocities  asserts  that  if  any 
machine  or  system  be  kept  in  equilibrium  by  any 
number  of  forces,  and  the  machine  or  system  then  re- 
ceive any  vc7y  small  displacement,  the  algebraic  sum  of  the  products  formed 
by  multiplying  each  force  by  its  virtual  velocity  will  be  zero.  Of  course,  the 
displacement  of  the  machine  is  supposed  to  be  such  as  not  to  break  the 
connection  of  its  parts  ;  thus  in  the  wheel  and  axle  the  only  possible  dis- 
placement is  to  turn  it  round  the  fixed  axle ;  in  the  inclined  plane  the  weight 
must  still  continue  to  rest  on  the  plane  :  in  the  various  systems  of  pulleys 
the  strings  must  still  continue  stretched,  and  must  not  alter  in  length,  &c. 

The  complete  proof  of  this  principle  is  beyond  the  scope  of  the  present 
work,  but  we  may  easily  establish  its  truth  in  any  of  the  machines  we  have 
already  considered.  It  will  be  found  in  eveiy  case  that,  if  the  machine 
receive  a  small  displacement,  the  virtual  velocities  of  P  and  W  will  be  of 
opposite  signs,  and  that,  neglecting  the  signs,  P  x  P's  virtual  velocity  =  W  x 
W's  virtual  velocity.  Thus,  to  take  the  case  of  a  bent  lever,  let  P  and  Q  be 
the  forces  acting  at  the  extremities  of  the  arms  of  the  bent  lever  AFB  (fig.  30), 
and  let  the  lever  be  turned  slightly  round  its  fulcrum  F,  bringing  A  to  A',  and 
B  to  B'.  Draw  A'^and  B'^  perpendicular  to  P  and  Q  respectively  ;  then  Ka 
is  the  virtual  velocity  of  P,  and  V>b  that  of  Q,  the  former  being  positive  and 
the  latter  negative.  Let  Yp,  Yq  be  the  perpendiculars  from  the  fulcrum 
upon  P  and  Q,  or  what  we  have  called  (art.  40)  the  arms  of  P  and  Q.  Now, 
as  the  displacement  is  very  small,  the  angles  FAA',  FBB'  will  be  very  nearly 
right  angles  ;  and,  therefore,  the  right-angled  triangles  A«A',  B^B'  will 
ultimately   be   similar    to    the   triangles    F^A,    F^B    respectively,    whence 

.\a      Yp        ,   Bb 

=    ^and    — 

AA'     FA'         BB' 

AA'         ,    Bl?      BB' 

FA-'  "'"^   Y,  ^  FB- 

triangles  FAA',  FBB'  are  similar, 


^?    or  ^^  - 
FB'        Yp  - 

But     the 


if  the  lever  be  in  equilibrium  (art.  40). 


and   ^, 
Iq 

jles  FAA' 

as    they   are    both    isosceles,    and 

their  vertical  angles  are  equal,  so 

„    ,  AA'     BB'        ,  Art     Bb 

that  :^--  =  ^^--  ;  whence       -  =  =^ 

FA      FB   '  Yp     Yg 

P  X  Aa 

or,  as  we  may  put  it,  - —  = 
'  B  xYp 

Qj<  Bb 

q.Yq- 

these  two  equal  fractions  are  equal, 
Hence  the  numerators  are  equal,  or 


Now  the  denominators  of    ,^ 


-46a]  Machines.  3 1 

P  X  P"s  virtual  velocity  =  Q  x  Q's  virtual  velocity. 

As  a  further  and  simpler  example,  take  the  case  of  the  block  and  tackle 
described  in  article  41.  Suppose  the  weight  to  be  raised  through  a  space//  ; 
then  the  virtual  velocity  of  the  weight  is  k,  and  is  negative.  Now,  as  the 
distance  between  the  block  and  tackle  is  less  than  before  by  the  space  //,  and 
as  the  rope  passes  over  this  space  71  times,  in  order  to  keep  the  rope  still 
tight  the  power  will  have  to  move  through  a  space  equal  to  7ih.  This  is  the 
virtual  velocity  of  P,  and  is  positive,  and  as  W  =  «P,  we  see  that 
W  X  W's  virtual  velocity  =  P  x  P's  virtual  velocity. 

46a.  niacblnes. — In  many  machines  in  common  use,  two  forces  can  readily 
be  distinguished.  One  is  a  force  applied  in  order  to  drive  the  machine,  and  the 
■other  is  a  force  overcome,  and  is  called  the  resistance.  The  force  applied  is 
usually,  though  improperly,  called  the  power.  In  general  these  forces  are  un- 
equal. If  the  machine  moved  without  friction  these  forces  might  be  exactly 
balanced,  in  such  a  way  that  if  either  of  them  were  increased  in  the  slightest 
degree,  the  machine  would  begin  to  move  with  a  uniformly  accelerated  motion. 
If  such  a  machine  thus  balanced  were  to  be  started  by  an  impulse  which 
should  the7t  cease  to  act,  the  machine  would  move  continuously  at  a  uniform 
rate  until  acted  upon  by  some  other  external  force.  If  we  imagine  a  balanced 
frictionless  machine  to  become  a  machine  with  friction,  then  either  of  the  two 
forces  might  be  varied  between  certain  limits,  without  setting  the  machine 
into  motion.  Hence,  if  the  machine  is  to  move  uniformly,  the  force  applied 
in  driving  it  must  be  greater  than  would  be  necessary  to  give  uniform  motion 
to  a  frictionless  machine.  The  force  applied,  P,  and  the  resistance  overcome, 
R,  may  be  expressed  in  pounds  weight,  which  may  be  converted  into  absolute 
units  by  multiplying  by  the  value  of_^at  the  place.  While  P  moves  over  a 
certain  distance  p,  R  moves  over  a  distance  r.  These  distances  can  be  deter- 
mined by  measurement.  The  ratio  of  r  to  p  can  often  be  seen  by  simple  in- 
spection, since  its  value  depends  upon  the  gearing  or  construction  of  the 
machine. 

If  the  force  P  is  exerted  over  a  distance/,  the  work  applied  is  Vp  foot- 
pounds. While  this  work  is  being  applied  to  the  machine,  a  certain  amount 
of  work,  Rr,  is  transmitted  through  the  machine,  and  is  done  upon  the  resist- 
ance. Experiment  shows  that  the  work  applied  Vp  is  always  greater  than 
the  work  Rr  transmitted  through  the  machine.  This  difference  represents 
the  work  which  is  required  to  move  the  parts  of  the  machine  upon  each 
other,  and  is  called  internal  work.  If  the  internal  work  is  represented  by  I, 
the  condition  for  uniform  action  of  a  machine  is  given  by  the  equation 
P/=Rr+I. 

It  will  be  assumed  that  a  small  force  V"  is  applied,  sufficient  to  move 
the  machine  uniformly  when  unloaded.  This  value  of  V"  is  not  included 
in  P.  In  this  case,  the  work  of  friction  is  due  wholly  to  the  load  which  the 
machine  carries,  and  I  becomes  zero  when  R  =  o.  The  quantity  I  is  of  the 
same  nature  as  the  other  two  quantities  n  the  equation,  being  the  product  of 
a  certain  force  of  friction  into  a  certain  distance,  but  in  general  these  factors 
cannot  be  determined  separately.  It  is  found  that  I  diminishes  in  value  as 
the  parts  of  the  machine   in  contact  are   made  smoother,  and  is  further 


32  On  Matter,  Force,  and  Motion.  [46a- 

diminished  by  oiling  the  bearings — that  is  to  say,  the  quantities  Vp  and  Rr^ 
which  can  be  easily  determined,  become  more  nearly  equal. 
The  equation  may  also  be  put  into  the  following  form  :  — 

P      r  I 

—  =  -  +  z    where  /  =  — . 
R     i^  R^ 

It  is  evident  that  the  ratio  -  is  a  constant  quantity,  for  a  given  machine., 
P 

P 
geared  in  a  definite  manner.     Experiment  shows  that  the    ratio  -—  is  also- 

R 

practically  constant,  so  that  the  quantity  i  may  also  be  considered  constant 
for  a  given  machine  in  a  definite  condition.  It  would,  however,  be  changed 
by  oiling  the  bearings,  as  this  would  make  it  necessary  to  diminish  P  in 
order  to  preserve  uniform  motion,  and  it  also  depends  upon  the  arrangement 
of  the  machine,  as  will  be  pointed  out  further  on. 

47.  Friction. — In  the  cases  of  the  actions  of  machines  which  have  hitherto- 
been  described,  the  resistances  which  are  offered  to  motion  have  not  been 
at  all  considered.  The  surfaces  of  bodies  in  contact  are  never  perfectly 
smooth  ;  even  the  smoothest  present  inequalities  which  can  neither  be 
detected  by  the  touch  nor  by  ordinary  sight  ;  hence  when  one  body  moves 
over  the  surface  of  another,  the  elevations  of  one  sink  into  the  depressions 
of  the  other,  like  the  teeth  of  wheels,  and  thus  offer  a  certain  resistance  to- 
motion  ;  this  is  what  is  called y^zV/Zw;.  It  must  be  regarded  as  a  force  which, 
continually  acts  in  opposition  to  actual  or  possible  motion. 

Friction  is  of  two  kinds  :  sliding,  as  when  one  body  glides  over  another  ; 
this  is  least  when  the  two  surfaces  in  contact  remain  the  same,  as  in  the 
motion  of  an  axle  in  its  bearing  ;  and  rolli)7g  friction,  which  occurs  when  one 
body  rolls  over  another,  as  in  the  case  of  an  ordinary  wheel.  The  latter  is 
less  than  the  former,  for  by  the  rolling  the  inequalities  of  one  body  are  raised 
over  those  of  the  other.  As  rolling  friction  is  considerably  less  than  sliding 
friction,  it  is  a  great  saving  of  power  to  convert  the  latter  into  the  former  ;  as 
is  done  in  the  case  of  the  casters  of  chairs  and  other  furniture,  and  also  in 
that  of  friction  wheels.  This,  however,  is  not  always  the  case  ;  thus  a  sledge 
experiences  less  friction  on  snow  than  a  carriage,  for  in  this  case  the  wheels 
sink  and  friction  on  the  sides  results.  On  the  other  hand,  it  is  sometimes 
useful  to  change  rolling  into  sliding  friction,  as  when  drags  are  placed  on 
carriage  wheels. 

Friction  is  directly  proportional  to  the  pressure  of  the  two  surfaces 
against  each  other.  That  fraction  of  the  pressure  which  must  act  as  moving 
force  merely  to  overcome  friction  is  called  the  coefficient  of  friction. 

Friction  is  independent  of  the  extent  of  the  surfaces  in  contact  if  the  pres- 
sui'e  is  the  same.  Thus,  suppose  a  board  with  a  surface  of  a  square  deci- 
metre resting  on  another  board  to  be  loaded  with  a  weight  of  a  kilogramme. 
If  this  load  be  distributed  over  a  similar  board  of  two  square  decimetres 
surface,  the  total  friction  will  be  the  same,  while  the  friction  per  square 
centimetre  is  one-half,  for  the  pressure  on  each  square  centimetre  is  one-half 
of  what  it  was  before.  So,  too,  a  rectangular  stone  experiences  the  same 
friction  whether  it  is  laid  on  the  narrow  or  on  the  broad  side.  Friction  is 
diminished  by  polishing  and  by  smearing,  but  is  increased  by  heat.     It  is 


48] 


Resistance  to  Motion  in  a  Fluid  Medium. 


33 


greater  as  a  body  passes  from  the  state  of  rest  to  that  of  motion  than  during 
motion,  but  seems  independent  of  the  velocity.  The  coefficient  of  friction 
depends  on  the  nature  of  the  substance  in  contact ;  similar  bodies  experience 
in  general  greater  friction  than  dissimilar  ones,  for  with  the  former  the  in- 
equalities fit  more  into  one  another  ;  thus  for  oak  upon  oak  it  is  0*4 1 8  when 
the  fibres  are  parallel,  and  o'293  when  they  cross  ;  for  beech  upon  beech  it 
is  0-36.  Greasy  substances,  which  are  not  absorbed  by  the  body,  diminish 
friction,  but  increase  it  if  they  are  absorbed.  Thus  moisture  and  oil  increase, 
while  tallow,  soap,  and  graphite  diminish,  the  friction  of  wooden  surfaces. 
In  the  sliding  friction  of  cast  iron  upon  bronze  the  coefficient  was  found  to 
be  0-25  without  grease  ;  with  oil  it  was  0-17,  fat  o-ii,  soap  0-03,  and  with  a 
mixture  of  fat  and  graphite  0-02.  The  coefficient  of  rolling  friction  for  cast- 
iron  wheels  on  iron  rails  as  in  railways  is  about  0-004  j  for  ordinary  wheels 
on  an  ordinary  road  it  is  0-04,  hence  a  horse  can  draw  ten  times  as  great  a 
load  on  rails  as  on  an  ordinary  road,  and  this  is  indeed  a  main  use  of  rail  and 
tram  ways.  The  coefficient  of  steel  upon  smooth  ice  has  been  determined 
by  a  skater  holding  in  his  hand  a  spring  balance  (88)  attached  to  a  cord  by 
which  he  was  drawn  along  by  a  second  skater.  At  starting  the  spiral  showed 
a  pull  of  5  to  6  kilos,  but  during  the  motion  this  varied  between  i  and  2  kilos. 
As  the  weight  of  the  skater  was  62  kilos,  the  coefficient  of  friction  during 
the  motion  was  -^  to  ---,  or  i'6  to  3*2  per  cent. 

Without  friction  on  the  ground,  neither  man  nor  animals,  neither  ordinary 
carriages  nor  railway  carriages,  could  move.  Friction  is  necessary  for  the 
transmission  of  power  from  one  wheel  to  another  by  means  of  loands  or 
ropes  ;  and  without  friction  we  could  hold  nothing  in  the  hands. 

48.  Resistance  to  IVSotion  in  a  Fluid  Medium. — A  body  in  moving 
through  any  medium  such  as  air  or  water  experiences  a  certain  resistance  ; 
for  the  moving  body  sets  in  motion  those  parts  of  the  medium  with  which  it 
is  in  contact,  whereby  it  loses  an  equivalent  amount 
of  its  own  motion. 

This  resistance  increases  with  the  surface  of  the 
moving  body  ;  thus  a  soap-bubble  or  a  snow-flake 
falls  more  slowly  than  does  a  drop  of  water  of  the 
same  weight.  It  also  increases  with  the  density  of 
the  medium  ;  thus  in  rarefied  air  it  is  less  than  in  air 
under  the  ordinary  pressure  ;  and  in  this  again  it  is 
less  than  in  water. 

The  influence  of  this  resistance  may  be  illustrated 
by  means  of  the  apparatus  represented  in  fig.  31, 
which  consists  of  two  vanes,  ww,  fixed  to  a  horizontal 
axis,  xx\  to  which  is  also  attached  a  bobbin  s.  The 
rotation  of  the  vanes  is  effected  by  means  of  the  falling 
of  a  weight  attached  to  the  string  coiled  round  the 
bobbin.  The  vanes  can  be  adjusted  either  at  right 
angles  or  parallel  to  the  axis.  In  the  rormer  position 
the  vanes  rotate  rapidly  when  the  weight  is  allowed  to 
act  ;  in  the  latter,  however,  where  they  press  with  their 
entire  surface  against  the  air,  the  resistance  greatly  lessens  the  rapidity  of 
rotation. 


34  On  Matter,  Force,  and  Motion.  [48- 

The  resistance  increases  with  the  velocity  of  the  moving  body,  and  for 
moderate  velocities  is  proportional  to  the  square  ;  for,  supposing  the  velo- 
cities of  a  body  made  twice  as  great,  it  must  displace  twice  as  much  matter, 
and  must  also  impart  to  the  displaced  particles  twice  the  velocity.  For 
high  velocities  the  resistance  in  a  medium  increases  in  a  more  rapid  ratio 
than  that  of  the  square,  for  some  of  the  medium  i^  carried  along  with  the 
moving  body,  and  this,  by  its  friction  against  the  other  portions  of  the 
medium,  causes  a  loss  of  velocity. 

It  is  this  resistance  which  so  greatly  increases  the  difficulty  and  cost  of 
attaining  very  high  speeds  in  steam- vessels.  Use  is  made,  on  the  other  hand, 
of  this  resistance  in  parachutes  (fig.  175)  and  in  the  windvanes  for  dimi- 
nishing the  velocity  of  falling  bodies  (fig.  55),  the  principle  of  which  is 
illustrated  by  the  apparatus,  fig.  31.  Light  bodies  fall  more  slowly  in  air 
than  heavy  ones  of  the  same  surface,  for  the  moving  force  is  smaller  com- 
pared with  the  resistance.  The  resistance  to  a  falling  body  may  ultimately 
equal  its  weight  ;  it  then  moves  uniformly  forward  with  the  velocity  which 
it  has  acquired.  Thus,  a  rain-drop  falling  from  a  height  of  3,000  feet 
should,  when  near  the  ground,  have  a  velocity  of  nearly  440  feet,  or  that 
of  a  musket-shot ;  owing,  however,  to  the  resistance  of  the  air,  its  actual 
velocity  is  probably  not  more  than  30  feet  in  a  second.  On  railways  the 
resistance  of  the  air  is  appreciable  ;  with  a  carriage  exposing  a  surface  of 
22  square  feet,  it  amounts  to  16  or  17  pounds  when  the  speed  of  the  train 
is  16  feet  a  second,  or  11  miles  an  hour. 

By  observing  the  rate  of  diminution  in  the  number  of  oscillations  of  a 
horizontal  disc  suspended  by  a  thread  when  immersed  in  water,  Meyer  de- 
termined the  coefficient  of  the  frictional  or  internal  resistance  of  water,  and 
found  that  at  10°  it  was  equal  to  o'oi567  gramme  on  a  square  centimetre  ; 
and  for  air  it  was  about  I-  as  much. 

49.  Uniformly  Accelerated  Rectilinear  IVSotion. — Let  us  suppose  a 
body  containing  ;//  units  of  mass  to  move  from  rest  under  the  action  of  a 
force  of  F  units,  the  body  will  move  in  the  line  of  action  of  the  force,  and 
will  acquire  in  each  second  an  additional  velocity  y given  by  the  equation 

F  =  mf; 
consequently,  if  7/  is  its  velocity  at  the  end  of  /  seconds,  we  have 

v=ff.  (I) 

To   determine  the  space  it  will    describe  in  t  seconds,  we  may  reason  as 
follows  : — The  velocity  at  the  time  /  being//,  that  at  a  time  t  +  t  will  be  / 
(/  +  t).     If  the  body  moved  uniformly  during  the  time  r  with  the  former 
velocity,  it  would  describe  a  space  s  equal  to  ftr  ;  if  with  the  latter  velocity 
a  space  s^  equal  to  /(/  +  T)r.     Consequently, 

s\:s::t  +  T:f; 

therefore,  when  r  is  indefinitely  small,  the  limiting  values  of  s  and  j-j  are 
equal.  Now,  since  the  body's  velocity  is  continually  increasing  during  the 
time  r,  the  space  actually  described  is  greater  thim  or  and  less  than  Sy  But 
since  the  limiting  values  of  s  and  s^  are  equal,  the  limiting  value  of  the  space 
described  is  the  same  as  that  oi  s  or  s^     In  other  words,  if  we  suppose  the 


-49]  Uniformly  Accelerated  Rectilinear  Motion.  35 

whole  time  of  the  body's  motion  to  be  divided  into  any  number  of  equal 

parts,  if  we  determine  the  velocity  of  the  body  at  the  beginning  of  each  of 

these  parts,  and  if  we  ascertain  the  spaces  described  on  the  supposition  that 

the  body  moves  uniformly  during  each  portion 

of  time,  the  limiting  value  of  the  sum  of  these 

spaces  will  be  the  space  actually  described  by 

the  body.     Draw  a  line  AC  (fig.  32),  and  at  A 

construct  an  angle  CAB,  whose  tangent  equals 

/";  divide  AC  into  any  number  of  equal  parts  in  . 

D,  E,  F,...and   draw   PD,    QE,    RF,...BC  at  /-^P"' 


right  angles  to  AC ;  then  since  PD  =  AD   x  yj       ■^^ — K      ^     G     H 
QE  =  AE  X  /  RF  =  AF  x  /  EC  =  AC  x/  &c..  Fig.  3,. 

PD  will  represent  the  velocity  of  the  body  at  the 

end  of  the  time  represented  by  AD,  and  similarly  QE,  RF,...BC,  will  represent 
the  velocity  at  the  end  of  the  times  AE,  AF,...AC.  Complete  the  rectangles 
D^,  Ey^  F^. . .  These  rectangles  represent  the  space  described  by  the  body  on 
the  alDove  supposition  during  the  second,  third,  fourth, ...portions  of  the  time. 
Consequently,  the  space  actually  described  during  the  time  AC  is  the  limit 
of  the  sum  of  the  rectangles  ;  the  limit  being  continually  approached  as  the 
number  of  parts  into  which  AC  is  divided  is  continually  increased.  But  this 
limit  is  the  area  of  the  triangle  ABC  :  that  is  ^AC  x  CB  or  iAC  x  AC  x  / 
Therefore,  if  AC  represents  the  time  /  during  which  the  body  describes  a 
space  .?,  we  have 

s  =  \ft\  (2) 

Since  this  equation  can  be  written 

2/.  =  PP 
we  find,  on  comparison  with  equation  (i),  that 

v-  =  2fs.  (3) 

To  illustrate  these  equations,  let  us  suppose  the  accelerative  effect  of  the 
force  to  be  6  ;  that  is  to  say  that,  in  virtue  of  the  action  of  the  force,  the  body 
acquires  in  each  successive  second  an  additional  velocity  of  6  feet  per  second, 
and  let  it  be  asked  what,  on  the  supposition  of  the  body  moving  from  rest, 
will  be  the  velocity  acquired,  and  the  space  described,  at  the  end  of  12 
seconds  ;  equations  i  and  2  enable  us  to  answer  that  at  that  instant  it  will  be 
mo\'ing  at  the  rate  of  72  feet  per  second,  and  will  have  described  432  feet. 

The  following  important  result  follows  from  equation  2.  At  the  end  of 
the  first,  second,  third,  fourth,  &c.,  second  of  the  motion,  the  body  will  have 
described  \f,  \f^  4,  f /"x  9,  f_/"x  16,  &c.,  feet  ;  and  consequently  during  the 
first,  second,  third,  fourth,  &c.,  second  of  the  motion  will  have  described  hf^ 
\'f  '^  3)  i/x  5)  2/^  7j  &c.,  feet,  namely  spaces  in  arithmetical  progression. 

The  results  of  the  above  article  can  be  stated  in  the  form  of  laws  which 
apply  to  the  state  of  a  body  moving  from  a  state  of  rest  under  the  action  of 
a  constant  force  :— 

I.  TJie  velocities  arc  proportional  to  the  times  during  lukich  the  motion 
has  lasted. 

II.  The  spaces  described  are  proportional  to  the  squares  of  the  times  em.' 
ployed  in  their  description. 

D  2 


36  On  Matter,  Force,  and  Motion.  [49- 

III.  The  spaces  described  are  proportioial  to  t/ie  squares  of  tJie  velocities 
acquired  during  their  description. 

IV.  The  spaces  described  in  equal  successive  periods  of  time  increase  by  a 
constafit  quantity. 

Instead  of  supposing  the  body  to  begin  to  move  from  a  state  of  rest,  we 
may  suppose  it  to  have  an  initial  velocity  V,  in  the  direction  of  the  force.  In 
this  case  equations  i,  2,  and  3  can  be  easily  shown  to  take  the  following 
forms,  respectively  : — 

v  =  Y  -^ft, 
^  =  V/  +  hft\ 
ir  =  V-  4  2fs. 

If  the  body  move  in  a  direction  opposite  to  that  of  the  force,/  must  be 
reckoned  negative. 

The  most  important  exemplification  of  the  laws  stated  in  the  present 
article  is  in  the  case  of  a  body  falling  freely  in  vacuo.  Here  the  force  causing 
the  acceleration  is  that  of  gravity,  and  the  acceleration  produced  is  denoted 
by  the  letter  g :  it  has  already  been  stated  (29)  that  the  numerical  value  of 
_^is  32-1912  at  London,  when  the  unit  of  time  is  a  second  and  the  unit  of 
length  a  foot.  Adopting  the  metre  as  unit  of  length,  the  value  of  _c^at  London 
is  9-8117. 

50.  Motion  on  an  Inclined  Plane. — Referring  to  (43),  suppose  the  force 
P  not  to  act ;  then  the  mass  M  is  acted  on  by  an  unbalanced  force  M  g  sin  x, 
in  the  direction  SR,  consequently  the  acceleration  down  the  plane  is  g 
sin  X,  and  the  motion  becomes  a  particular  case  of  that  discussed  in  the 
last  article.  If  it  begins  to  move  from  rest,  it  will  at  the  end  of  /  seconds 
acquire  a  velocity  v  given  by  the  equation 

V  =gt  sin  X, 
and  will  describe  a  length  ^  of  the  plane  given  by  the  equation 

.y  =  hgt'  sin  X. 

Also,  if  V  is  the  velocity  acquired  while  describing  s  feet  of  the  plane, 

v"-  =  2gs  sin  X. 

Hence  (fig.  23)  if  a  body  slides  down  the  plane  from  S  to  R  the  velocity 
which  it  acquires  at  R  is  equal  to  ^/-g-  RS  sin  R  or  •f2g.  ST  ;  that  is  to  say, 
the  velocity  which  the  body  has  at  R  does  not  depend  on  the  angle  x,  but 
only  on  the  perpendicular  height  ST.  The  same  would  be  true  if  for  RS 
we  substituted  any  smooth  curve  ;  and  hence  we  may  state  generally,  that 
when  a  body  moves  along  any  smooth  line  under  the  action  of  gravity,  the 
change  of  velocity  it  experiences  in  moving  from  one  point  to  another  is  that 
due  to  the  vertical  height  of  the  former  point  above  the  latter. 

51.  Motion  of  Projectiles. — The  equations  given  in  the  above  article 
apply  to  the  case  of  a  body  thrown  vertically  upwards  or  downwards  with  a 
certain  initial  velocit)'.  We  will  now  consider  the  case  of  a  heavy  body 
thrown  in  a  horizontal  direction.  Let  a,  fig.  ^2ii  be  such  a  body  thrown  with 
an  initial  velocity  of  v  feet  in  a  second,  and  let  the  line  ab  represent  the  space 
described  in  any  interval  ;  then  at  the  end  of  the  2,  3,  4...   equal  interval, 


-51] 


Motion  of  Projectiles. 


6/ 

the  body,  in  virtue  of  its  inertia,  will  have  reached  the  points  c  d  e,  &c. 
But  during-  all  this  time  the  body  is  under  the  influence  of  gravity,  which, 
if  it  alone  acted,  would  cause  the  body  to  fall  through  the  distances  repre- 
sented on  the  vertical  line  ;  these  are  determined 
by  the  successive  values  of  hgt',  which  is  the 
formula  for  the  space  described  by  a  freely 
falling  body  (50).  The  effect  of  the  combined 
action  of  the  two  forces  is  that  at  the  end  of  the 
first  interval,  &c.,  the  body  will  be  at  b',  at  the 
end  of  the  second  interval  at  c',  of  the  third  at 
d',  Sec,  the  spaces  t>d',  cc\  dd'...  being  propor- 
tional to  the  squares  of  ab,  ac,  ad,  respectively, 
and  the  line  joining  these  points  represents  the 
path  of  the  body.  By  taking  the  intervals  of 
time  sufficiently  small  we  get  a  regularly  curved 
line  of  the  form  known  as  \h&  parabola. 

If  the  direction  in  which  the  body  is  thrown 
makes  an  angle  of  a  with  the  horizon  (fig.  34), 
then  after  /  seconds  it  would  have  travelled  a 
distance  ab  =  vt,^\\&x&  7' is  the  original  velo- 
city ;  during  this  time,  however,  it  will  have 
fallen  through  a  distance  bc  =  \gt''-  ;  the  height  which  it  will  have  actually 
reached  is  =bd  -bc  =  vt  sin  a-hgt"' \   and  the  horizontal  distance  will  be 


Fig-  33 


Fig.  34. 

ad=ab  cos  a  =  vt  cos  a.     The  range  of  the  body,  or  the  greatest  distance 
through  which  it  is  thrown,  will  be  reached  when  the  height  is  again  =  o  ;  that 

is,  when  7'/  sin  a  -  ^  £r^  =  o,  from  which  /  =  ?'^:iA^5Jf.      Introducing   this    value 

^     .          ,                •       r        1       T  .            J          \.         J    27'-  sin  a  cos  a      ,  •  , 
of  /  mto  the  equation  for  the  distance  d,  we  have  d= ,  which 

by  a  trigonometrical  transformation  =  '_Lli!L^.      The    greatest   height    is 


attained  in  half  the  time  of  flight,  or  when  t  = ",  from  which    we  get 

2^ 
It   follows  from  the  formula  that  the  height  is  greatest  when  sin  a  is 
greatest,  which  is  the  case  when  it  =  90°,  or  when  the  body  is  thrown  vertically 
upwards  ;  the  range  is  greatest  where  sin  2a  is  a  maximum,  that  is,  when 
2a  =  90°  or  a  =  45°. 


38  On  Matter,  Force,  and  Motion.  [51- 

In  these  formulae- it  has  been  assumed  that  the  air  offers  no  resistance. 
This  is,  however,  far  from  the  case,  and  in  practice,  particularly  if  the  velo- 
city of  projection  is  very  great,  the  path  differs  from  that  of  a  parabola. 
Fig.  34  approximately  represents  the  path,  allowing  for  the  resistance  of  the 
air.  The  divergence  from  the  true  theoretical  path  is  affected  by  the  fact 
that  in  the  modern  rifled  arms  the  projectiles  are  not  spherical  in  shape  ; 
and  also  because,  along  with  their  motion  of  translation,  they  have,  in  con- 
sequence of  the  rifling,  a  rotatory  motion  about  their  axis. 

52.  Composition  of  Velocities. — The  principle  for  the  composition  of 
velocities  is  the  same  as  that  for  the  composition  of  forces  :  this  follows  evi- 
dently from  the  fact  that  forces  are  measured  by  the  momentum  they  com- 
municate, and  are  therefore  to  one  another  in  the  same  ratio  as  the  velocities 
they  communicate  to  the  same  body.  Thus  (fig.  7,  art.  32),  if  the  point  has 
at  any  instant  a  velocity  AB  in  the  direction  AP,  and  there  is  communicated 
to  it  a  velocity  AC  in  the  direction  AQ,  it  will  move  in  the  direction  AR  with 
a  velocity  represented  by  AD.  And  conversely,  the  velocity  of  a  body  re- 
presented by  AD  can  be  resolved  into  two  component  velocities  AB  and  AC. 
This  suggests  the  method  of  determining  the  motion  of  a  body  when  acted 
on  by  a  force  in  a  direction  transverse  to  the  direction  of  its  velocity  ;  namely, 
suppose  the  time  to  be  divided  into  a  great  number  of  intervals,  and  suppose 
the  velocity  actually  communicated  by  the  force  to  be  communicated  at  once; 
then  by  the  composition  of  velocities  we  can  determine  the  motion  during 
each  interval,  and  therefore  during  the  whole  time  ;  the  actual  motion  is  the 
limit  to  which  the  motion,  thus  determined,  approaches  when  the  number  of 
intervals  is  increased. 

53.  IVIotion  in  a  Circle — Centrifugal  Force. — When  a  body  is  once  in 
motion,  unless  it  be  acted  upon  by  some  force,  it  will  move  uniformly 
forward  in  a  straight  line  with  unchanged  velocity  (26).  If,  therefore,  a  body 
moves  uniformly  in  any  other  path  than  a  straight  line — in  a  circle,  for 
instance — this  must  be  because  some  force  is  constantly  at  work  which 
continuously  deviates  it  from  this  straight  line. 

We  have  already  seen  an  example  of  this  in  the  case  of  the  motion  of 
projectiles  (51),  and  will  now  consider  it  in  the  case  of  central  motion  or 
motion  in  a  circle,  of  which  we  have  an  example  in  the  motion  of  the 
celestial  bodies,  or  in  the  motion  of  a  sling. 

In  the  latter  case,  if  the  string  is  cut,  the  stone,  ceasing  to  be  acted  upon 
by  the  tension  of  the  string,  will  move  in  a  straight  line  with  the  velocity 
which  it  already  possesses — that  is,  in  the  direction  of  the  tangent  to  the 
curve  at  the  point  where  the  stone  was  when  the  string  was  cut.  The  tension 
of  the  string,  the  effect  of  which  is  to  pull  the  stone  towards  the  centre  of 
the  circle  and  to  cause  the  stone  to  move  in  its  circular  path,  is  called  the 
ceiitripetal  or  coitral  force  ;  the  reaction  of  the  stone  upon  the  string,  which 
is  equal  and  opposite  to  this  force,  is  called  the  centj'ifiigal  force.  The 
amount  of  the  forces  may  be  arrived  at  as  follows  : — 

Let  us  suppose  a  body  moving  in  a  circle  with  given  uniform  velocity 
to  be  at  the  point  a  (fig.  35) ;  then,  had  it  not  been  acted  on  by  a  force 
in  the  direction  ac,  it  would,  in  a  small  succeeding  interval  of  time  /,  have 
continued  to  move  in  the  direction  of  the  tangent  at  a,  and  have  passed 
through  a  distance  which  we  will  represent  by  ab.     In  consequence,  however. 


53] 


Motion  in  a  Circle-  Centrifugal  Force. 


39 

of  this  force,  it  has  not  followed  this  direction,  but  has  arrived  at  the  point  d 
on  the  curve  ;  hence  the  force  has  made  it  traverse  the  distance  bd=ac  in 
this  interval.  If  /  be  the  acceleration  with  which  the  body  is  drawn  to- 
wards the  centre  ae  =  k/t'-,  and  if  ad  be  very  small,  it 
may  be  taken  as  equal  to  ad  or  vt,  where  v  is  the 
velocity  of  the  moving  body.  Now  if  an  is  the  dia- 
meter of  the  circle,  the  triangle  adn  is  inscribed  in  a 
semicircle  and  is  right-angled,  whence  ad^  -aex  an  = 
ae  X  2r.  Substituting  their  values  for  ad  and  ae  in 
this  equation,  we  find  that  v't'-  =  h  ft'  x  2r,  from  which 


/  = 


that    is,  in  order  that  a  body  with  a  certain 


velocity  may  move  in  a  circle,  it  must  be  drawn  to 
the  centre  by  a  force  which  is  directly  as  the  square 
of  the  velocity  with  which  the  body  moves,  and  which 
is  inversely  as  the  radius  of  the  circle.  In  order  to 
express  this  in  the  ordinary  units  of  weight,  we  must 
multiply  the   above   expression    by  the   mass,  which 

gives  F  =  ^~ —  or .     To  keep  the  body  in  a  circle, 

an  attraction  towards  the  centre  is  needed,  which  is 


constantly  equal  to 


and  this  attraction   is  con- 


stantly neutralised  by  the  centrifugal  force. 

The  above  expression  may  be  put  in  a  form  which 
is  sometimes  more  convenient.  If  T  be  the  time  in 
seconds    required  to  traverse  the  circumference  2nr 

with    the   velocity    v,    then    v'-  =  '^^- ,    from    which 

P  ^4W7rV^4W7rV  Fig.  35. 

If  a  rigid  body  rotates  about  a  fixed  axis,  all  parts  of  the  body  describe 
circumferences  of  various  diameters,  but  all  in  the  same  time.  The  velocity 
of  the  motion  of  individual  particles  increases  with  the  distance  from  the  axis 
of  rotation.  By  angular  velocity  is  understood  the  velocity  of  a  point  at  unit 
distance  from  the  axis  of  rotation.    If  this  is  denoted  by  «,  the  velocity  v  of  a 

point  at  a  distance  from  the  axis  is  wr,  from  which  »  =—  =  -^  and  F=  rar. 

The  existence  of  centrifugal  force  may  be  demonstrated  by  means  of 
numerous  instructive  experiments,  such  as  the  centrifugal  railway.  If  a  small 
can  of  water  hung  by  the  handle  to  a  string  be  rapidly  rotated  in  a  vertical 
circle,  no  water  will  fall  out,  for,  at  a  suitable  velocity,  the  liquid  will  press 
against  the  bottom  of  the  vessel  with  a  force  at  right  angles  to  the  circle  and 
greater  than  its  own  weight. 

Centrifugal  force  has  been  used  in  chemical  laboratories  to  separate 
•crystals  from  the  mother  liquors,  and  also  to  promote  the  deposition  of  fine 
precipitates  which  under  ordinary  circumstances  settle  very  slowly  ;  it  is  also 
applied  industrially  in  sugar  factories  to  purify  sugar  from  syrup,  in  dye  works 
to  dry  yarn  and  cloth  rapidly,  and  in  laundries. 


40 


On  Matter,  Force,  and  Motion. 


[54 


54.  Motion  in  a  Vertical  Circle. — Let  ACBD  (fig.  36)  be  a  circle  whose 
plane  is  vertical  and  radius  denoted  by  r.  Suppose  a  point  placed  at  A,  and 
allowed  to  slide  down  the  curve,  what  velocity  will  it 
have  acquired  on  reaching  any  given  point  P  ?  Draw 
the  vertical  diameter  CD,  join  CA,  CP,  and  draw  the 
horizontal  lines  AMB  and  PNP'.  Now,  assuming  the 
curve  to  be  smooth,  the  velocity  acquired  in  falling 
from  A  to  P  is  that  due  to  MN,  the  vertical  height  of 
A  above  P  (51)  ;  if,  therefore,  v  denote  the  velocity  of 
the  point  at  P,  we  shall  have 

we  have 


Fig.  36. 


Now  by  similar  triangles  DCP,  PCN, 
DC  :  CP:  :CP  :  CN 
consequently,  if  we  denote  by  j-  the  chord  CP, 

2rNC  =  y-. 
In  like  manner  if  cz  denote  the  chord  CA, 

2rMC  =  rt', 
therefore  2rM  N  =  ^r  —  j'-, 


and 


^{cv-f). 


Now  V  will  have  equal  values  when  j  has  the  same  value,  whether  positive 
or  negative,  and  for  any  one  value  of  j'  there  are  two  equal  values  of  7/,  one 
positive  and  one  negative.  That  is  to  say,  since  CP'  is  equal  to  CP,  the 
body  will  have  the  same  velocity  at  P'  that  it  has  at  P,  and  at  any  point  the 
body  will  have  the  same  velocity  whether  it  is  going  up  the  curve  or  down 
the  curve.  Of  course  it  is  included  in  this  statement  that  if  the  body  begins 
to  move  from  A  it  will  just  ascend  to  a  point  B  on  the  other  side  of  C,  such 
that  A  and  B  are  in  the  same  horizontal  line.  It  will  also  be  seen  that  at  C 
the  value  of  s  is  zero  ;  consequently,  if  V  is  the  velocity  acquired  by  the 
body  in  falling  from  A  to  C,  we  have 

and,  on  the  other  hand,  if  the  body  begins  to  move  from  C  with  a  velocity  V, 
it  will  reach  a  point  A  such  that  the  chord  AC  or  a  is  given  by  the  same 
equation.  In  other  words,  the  velocity  at  the  lowest  point  is  proportional  to 
the  chord  of  the  arc  described. 

55.  Itlotion  of  a  Simple  Pendulum. — By  a  simple  pendulum  is  meant  a 
heavy  particle  suspended  b)'  a  fine  thread  from  a  fixed  point,  about  which  it 
oscillates  without  friction.  So  far  as  its  changes  of  velocity  are  concerned 
they  will  be  the  same  as  those  of  the  point  in  the  previous  article,  for  the 
tension  of  the  thread,  acting  at  each  position  in  a  direction  at  right  angles  to 
that  of  the  motion  of  the  point,  will  no  more  affect  its  motion  than  the  re- 
action of  the  smooth  curve  affects  that  of  the  point  in  the  last  article.  The 
time  of  an  oscillation — that  is,  the  time  in  which  the  point  moves  from  A  to 
B — can  be  easily  ascertained  when  the  arc  of  vibration  is  small ;  that  is,  when 
the  chord  and  the  arc  do  not  sensibly  differ. 


Fig.  37- 


-56]  Motion  of  a  Simple  Penduluiii.  41 

Thus,  let  AB  (fig.  yj)  equal  the  arc  or  chord  ACB  (fig.  36)  ;  with  centre 
C  and  radius  AC  or  a  describe  a  circle,  and  suppose  a  point  to  describe  the 
circumference  of  that  circle  with  a  uniform  velocity 

V  or  c?  A  /^.     At  any  instant  let  the  point  be  at  Q, 

join  CQ,  draw  the  tangent  QT,  also  draw  QP  at 
right  angles  and  QN  parallel  to  AB,  then  the  angles 
NQT  and  CQP  are  equal.     Now  the  velocity  of  Q 

resolved  parallel  to  AB  is  V  cos  TQN  or  «a/-. 

cos  CQP ;  that  is,  if  CP  equals  s,  the  velocity  of  Q 
parallel  to  AB  is 

^/^PQor,^/'^(.r-.^). 

But  if  we  suppose  a  point  to  move  along  AB  in  such  a  manner  that  its 
velocity  in  each  position  is  the  same  as  that    of  the    oscillating  body,  its 

velocity  at    P  would  also   equal  j^  f  S  (a- -  s") ;  and,    therefore,    this    point 

would  describe  AB  in  the  same  time  that  Q  describes  the  semicircumference 
AQB.      If  then  /  be  the  required  time  of  an  oscillation,  we  have 

This  result  is  independent  of  the  length  of  the  arc  of  vibration,  provided  its 
aiiiplitiaic,  that  is  AB,  be  small— not  exceeding  4  or  5  degrees,  for  instance. 
It  is  evident  from  the  formula  that  the  time  of  a  vibration  is  directly  pro- 
portional to  the  square  root  of  the  length  of  the  pendulum,  and  inversely 
proportional  to  the  square  root  of  the  accelerating  force  of  gravity. 

As  an  example  of  the  use  of  the  formula  we  may  take  the  following  : — It 
has  been  found  that  39-13983  inches  is  the  length  of  a  simple  pendulum 
whose  time  of  oscillation  at  Greenwich  is  one  second  ;  the  formula  at  once 
leads  to  an  accurate  determination  of  the  accelerating  force  of  gravity  g  ;  for 
using  feet  and  seconds  as  our  units  we  have  /=  i,  r=  3-26165,  and  rr  stands 
for  the  known  number  3-14159,  therefore  the  formula  gives  us 
.^=(3-14159)' X  3-26165  =  32-1912. 

This  is  the  value  employed  in  (29). 

Other  examples  will  be  met  with  in  the  Appendix. 

56.  Crapnic  Representation  of  the  Changes  of  Velocity  of  an  Oscil- 
lating- Body.— The  changes  which  the  velocity  of  a  vibrating  body  under- 
goes may  be  graphically  represented  as  follows  : — Draw  a  line  of  indefinite 
length  and  mark  off  AH  (fig.  38)  to  represent  the  time  of  one  vibration,  HH' 

P  H 

-<"  ^  A 

'^  >~ 

Fig.  38. 

to  represent  the  time  of  the  second  vibration,  and  so  on.  During  the  first 
vibration  the  velocity  increases  from  zero  to  a  maximum  at  the  half-vibration, 
and  then  decreases  during  the  second  half-vibration  from  the  maximum  to 


42  On  Matter,  Force,  and  Motion.  [56- 

zero.  Consequently,  a  curved  line  or  arc  AQH  may  be  drawn,  whose 
ordinate  QM  at  any  point  Q  will  represent  the  velocity  of  the  body  at  the 
time  represented  by  AM.  If  a  similar  curved  line  or  arc  HPH'  be  drawn, 
the  ordinate  PN  of  any  point  P  will  represent  the  velocity  at  a  time  denoted 
by  AN.  But  since  the  direction  of  the  velocity  in  the  second  oscillation  is 
contrary  to  that  of  the  velocity  in  the  first  oscillation,  the  ordinate  NP  must 
be  drawn  in  the  contrary  direction  to  that  of  MQ.  If,  then,  the  curve  be 
continued  by  a  succession  of  equal  arcs  alternately  on  opposite  sides  of  AD, 
the  variations  of  the  velocity  of  the  vibrating  body  will  be  completely  repre- 
sented by  the  varying  magnitudes  of  the  ordinates  of  successive  points  of  the 
curve.     The  last  article  shows  this  to  be  the  curve  of  sines  for  a  pendulum. 

57.  Impulsive  Forces. — When  a  force  acts  on  a  body  for  an  inappre- 
ciably short  time,  and  yet  sensibly  changes  its  velocity,  it  is  termed  an  instan- 
taneous ox  impulsive  {oxcq.  Such  a  force  is  called  into  play  when  one  body 
strikes  against  another.  A  force  of  this  character  is  nothing  but  a  finite 
though  very  large  force,  acting  for  a  time  so  short  that  its  duration  is  nearly, 
or  quite,  insensible.  In  fact,  if  M  is  the  mass  of  the  body,  and  the  force 
contains  M/ units,  it  will,  in  a  time  t,  communicate  a  velocity  ft ;  now,  how- 
ever small  /  may  be,  M/and  therefore  f  may  be  so  large  that  //  may  be  of 
sensible  or  even  considerable  magnitude.  Thus  if  M  contains  a  pound  of 
matter,  and  if  the  force  contains  ten  thousand  units,  though  t  were  so  short 
as  to  be  only  the  —^  of  a  second,  the  velocity  communicated  by  the  force 
would  be  one  of  10  feet  per  second.  It  is  also  to  be  remarked  that  the  body 
will  not  sensibly  move  while  this  velocity  is  being  communicated  ;  thus,  in 
the  case  supposed,  the  body  would  only  move  through  \ft'  or  the  5^5  of  a 
foot  while  the  force  acts  upon  it. 

When  one  body  impinges  on  another,  it  follows  from  the  law  of  the 
equality  of  action  and  reaction  (39)  that  whatever  force  the  first  body  exerts 
upon  the  second,  the  second  will  exert  an  equal  force  upon  the  first  in  the 
opposite  direction.  Now  forces  are  proportional  to  the  momenta  generated 
in  the  same  time  ;  consequently,  these  forces  generate,  during  the  whole  or 
any  part  of  the  time  of  impact,  in  the  bodies  respectively,  equal  momenta 
with  contrary  signs  ;  and  therefore  the  sum  of  the  momenta  of  the  two  bodies 
will  remain  constant  during  and  at  the  end  of  the  impact.  It  is  of  course 
understood  that  if  the  two  bodies  move  in  contrary  directions  their  momenta 
have  opposite  signs,  and  the  sum  is  an  algebraical  sum.     In  order  to  test 

the  physical  validity  of  this  conclusion, 
Newton  made  a  series  of  experiments, 
which  may  be  thus  briefly  described — 
Two  balls  A  and  B  (fig.  39)  are  hung 
from  points  C,  D  in  the  same  horizontal 
line  by  threads  in  such  a  manner  that 
their  centres  A  and  B  are  in  the  same 
horizontal  line.  With  centre  C  and  ra- 
Pig  3g_  dius    CA    describe   a   semicircle    EAF, 

and  with  centre  D  and  radius  DB 
describe  a  semicircle  GBH,  on  the  wall  in  front  of  which  the  balls  hang. 
Let  A  be  moved  back  to  R,  and  be  allowed  to  descend  to  A  ;  it  there  im- 
pinges on  B  ;  both  A  and  B  will  now  move  along  the  arcs  AF  and  BH 


-58]  Direct  Collision  of  Tivo  Bodies.  43 

respectively  ;  let  A  and  B  come  to  their  highest  points  at  r  and  k  respectively. 
Now  if  V  denote  the  velocity  with  which  A  reaches  the  lowest  point,  v  and  ii 
the  velocities  with  which  A  and  B  leave  the  lowest  points  after  impact,  and 
r  the  radius  AC,  it  follows  from  (54)  that 


V  =  chd  AR  ^  A,  7'  =  chd  Ar .,  A  and  //  =  chd  ^k  ,^f 


y-J,,..  =  cnaAry 


therefore  if  A  and  B  are  the  masses  of  the  two  balls,  the  momentum  at  the 
instant  before  impact  was  proportional  to  A  x  chd  AR,  and  the  momentum 
after  impact  was  proportional  to  A  x  chd  Ar+  B  x  chd  B/&.  Now  when  the 
positions  of  the  points  R,  r,  and  k  had  been  properly  corrected  for  the 
resistance  of  the  air,  it  was  found  that  these  two  expressions  were  equal  to 
within  quantities  so  small  that  they  could  be  pi'operly  referred  to  errors  of 
observation.  The  experiment  succeeded  ec[ually  under  every  modification, 
whether  x\  impinged  on  B  at  rest  or  in  motion,  and  whatever  the  materials  of 
A  and  B  might  be. 

58.  Direct  Collision  of  Two  Bodies. — Let  A  and  B  be  two  bodies 
moving  with  velocities  V  and  U  respectively,  along  the  same  line,  and  let  their 
mutual  action  take  place  in  that  line  ;  if  the  one  overtake  the  other,  what 
will  be  their  respective  velocities  at  the  instant  after  impact  ?  We  will  answer 
this  question  in  two  extreme  cases. 

i.  Let  us  suppose  the  bodies  to  be  quite  inelastic.  In  this  case,  when  A 
touches  B,  it  will  continue  to  press  against  B  until  their  velocities  are 
equalised,  when  the  mutual  action  ceases.  For  whatever  deformation  the 
bodies  may  have  undei'gone,  they  have  no  tendency  to  recover  their  shapes. 
If,  therefore,  x  is  their  common  velocity  after  impact,  we  shall  have  Kx -v  'Qx 
their  joint  momentum  at  the  end  of  impact,  but  their  momentum  before 
impact  was  AV  +  BU.     Whence 

(A+B).r=AV  +  BU, 
an  equation  which  determines  x. 

ii.  Let  us  suppose  the  hodA&s  perfectly  elastic.  In  this  case  they  recover 
their  shapes,  with  a  force  exactly  equal  to  that  with  which  they  were  com- 
pressed. Consequently  the  whole  momentum  lost  by  the  one,  and  gained  by 
the  other,  must  be  exactly  double  of  that  lost  while  compression  took  place  ; 
that  is,  up  to  the  instant  at  which  their  velocities  were  equalised.  But  these 
are  respectively  A\^  -  A.t-  and  Bar-  BU  ;  therefore,  if  v  and  u  are  the  required 
final  velocities, 

At/  =  AV  -  2(AV  -  Ax)  or  2/  =  -  V  +  2x 

Bzi  =  BU  +  2(B.r-  BU)  or  u  =  2x-  U, 

hence  (A  +  B)7'  =  2BU  +  (A- B)V 

and  (AhB)«-2AV-(A-B)U. 

The  following  conclusion  from  these  equations  may  be  noticed  :  suppose  a 
ball  A,  moving  with  a  velocity  V,  to  strike  directly  an  equal  ball  B  at  rest. 
In  this  case  A  =  B  and  U  =  o,  consequently  v  =  o  and  te  =  V  ;  that  is,  the 
former  ball  A  is  brought  to  rest,  and  the  latter  B  moves  on  with  a  velocity  V. 
If  now  B  strike  on  a  third  equal  ball  C  at  rest,  B  will  in  turn  be  brought 
to  rest,  and  C  will  acquire  the  velocity  V.     And  the  same  is  true  if  there  is 


44  On  Matter,  Force,  and  Motion.  [58- 

a  fourth,  or  fifth,  or  indeed  any  number  of  balls.     This  result  may  be  shown 
with  ivory  balls,  and  is  a  very  remai-kable  experiment. 

59.  Work:  Meaning-  of  the  Term.— It  has  been  pointed  out  (ig,  26) 
that  a  moving-  body  has  no  power  of  itself  to  change  either  the  direction  or 
the  speed  of  its  motion,  and  that,  if  any  such  change  takes  place,  it  is  a  proof 
that  the  body  is  acted  upon  by  some  external  force.  But  although  change  of 
motion  thus  always  implies  the  action  of  force,  forces  are  often  exerted  with- 
out causing  any  change  in  the  motion  of  the  bodies  on  which  they  act.  For 
instance,  when  a  ship  is  sailing  at  a  uniform  speed,  the  force  exerted  on  it  by 
the  wind  causes  no  change  in  its  motion,  but  simply  prevents  such  a  change 
being  produced  by  the  resistance  of  the  water  ;  or,  when  a  railway-train  is 
running  with  uniform  velocity,  the  force  of  the  engine  does  not  change,  but 
only  maintains  its  motion  in  opposition  to  the  forces,  such  as  friction  and  the 
resistance  of  the  air,  which  tend  to  destroy  it. 

These  two  classes  of  cases— namely,  first,  those  in  which  forces  cause  a 
change  of  motion  ;  and  secondly,  those  in  which  they  prevent,  wholly  or  in 
part,  such  a  change  being  produced  by  other  forces — include  all  the  effects 
to  which  the  action  of  forces  can  give  rise.  When  acting  in  either  of  these 
ways,  a  force  is  said  to  do  work  :  an  expression  which  is  used  scientifically 
in  a  sense  somewhat  more  precise,  but  closely  accordant  with  that  in  which 
it  is  used  in  common  language.  A  little  reflection  will  make  it  evident  that, 
in  all  cases  in  which  we  are  accustomed  to  speak  of  work  being  done — 
whether  by  men,  horse-power,  or  steam-power,  and  however  various  the  pro- 
ducts may  be  in  different  cases — the  physical  part  of  the  process  consists 
solely  in  producing  or  changing  motion,  or  in  keeping  up  motion  in  opposition 
to  resistance,  or  in  a  combination  of  these  actions.  The  reader  will  easily 
convince  himself  of  this  by  calling  to  mind  what  the  definite  actions  are  which 
constitute  the  work  done  by  (say)  a  navvy,  a  joiner,  a  mechanic,  a  weaver  ;  that 
done  by  a  horse,  whether  employed  in  drawing  a  vehicle,  or  in  turning  a  gin  ; 
or  that  of  a  steam-engine,  whether  it  be  used  to  drag  a  railway-train  or  to 
drive  machinery.  In  all  cases  the  work  done  is  reducible,  from  a  mechanical 
point  of  view,  to  the  elements  that  have  been  mentioned,  although  it  may  be 
performed  on  different  materials,  with  different  tools,  and  with  different 
degrees  of  skill. 

It  is,  moreover,  easy  to  see  (comp.  53)  that  any  possible  change  or 
motion  may  be  represented  as  a  gain  by  the  moving  body  of  an  additional 
(positive  or  negative)  velocity  either  in  the  direction  of  its  previous  motion, 
or  at  right  angles  to  it  ;  but  a  body  which  gains  velocity  is  (27)  said  to  be 
accelerated.  Hence,  what  has  been  said  above  may  be  summed  up  as 
follows  : — When  a  force  produces  acceleration,  or  when  it  maintains  inoiion 
unchanged  in  opposition  to  resistattce,  it  is  said  to  do  WORK. 

60.  ivxcasure  of  Work. — In  considering  how  work  is  to  be  measured,  or 
how  the  relation  between  different  cjuantities  of  work  is  to  be  expressed 
numerically,  we  have,  in  accordance  with  the  above,  to  consider  first,  wt>r>^<?/" 
acceleration  ;  and  secondly,  work  against  resistance.  But  in  order  to  make 
the  evaluation  of  the  two  kinds  of  work  consistent,  we  must  bear  in  mind 
that  one  and  the  same  exertion  of  force  will  result  in  work-  of  either  kind 
according  to  the  conditions  under  which  it  takes  place  ;  thus,  the  force  of 
gravity  acting  on  a  weight  let  fall  from  the  hand  causes  it  to  move  with  a 


-60]  Measure  of  Work.  45 

continually  accelerated  velocity  until  it  strikes  the  ground  ;  but  if  the  same 
weight,  instead  of  being  allowed  to  fall  freely  through  the  air,  be  hung  to  a 
cord  passing  round  a  cylinder  by  means  of  which  various  degrees  of  friction 
can  be  applied  to  hinder  its  descent,  it  can  be  made  to  fall  with  a  very  small 
and  practically  uniform  velocity.  Hence,  speaking  broadly,  it  may  be  said 
that,  in  the  former  case,  the  work  done  by  gravity  upon  the  weight  is  work  of 
acceleration  only,  while  in  the  latter  case  it  is  work  against  resistance  (friction) 
only.  But  it  is  very  important  to  note  that  an  essential  condition,  without 
which  a  force,  however  great,  cannot  do  work  either  of  one  kind  or  the  other, 
is  that  the  thing  acted  on  by  it  shall  move  while  the  force  continues  to  act. 
This  is  obvious,  for  if  no  motion  takes  place  it  clearly  cannot  be  either 
accelerated  or  maintained  against  resistance.  The  motion  of  the  body  on 
which  a  force  acts  being  thus  necessarily  involved  in  our  notion  of  work 
being  done  by  the  force,  it  naturally  follows  that,  in  estimating  how  much 
work  is  done,  we  should  consider  how  much — that  is  to  say,  how  far — the 
body  moves  while  the  force  acts  upon  it.  This  agrees  with  the  mode  of 
estimating  quantities  of  work  in  common  life,  as  will  be  evident  if  we  consider 
a  veiy  simple  case— for  instance,  that  of  a  labourer  employed  to  carry  bricks 
up  to  a  scaffold  :  in  such  a  case  a  double  number  of  bricks  carried  would 
represent  a  double  quantity  of  work  done,  but  so  also  would  a  double  height 
of  the  scaffold,  for  whatever  amount  of  work  is  done  in  raising  a  certain 
number  to  a  height  of  twenty  feet,  the  same  amount  must  be  done  again  to 
raise  them  another  twenty  feet,  or  the  amount  of  work  done  in  raising  the 
bricks  forty  feet  is  twice  as  great  as  that  done  when  they  are  raised  only 
twenty  feet.  It  is  also  to  be  noted  that  no  direct  reference  to  ///;/£■  enters  into 
the  conception  of  a  quantity  of  work  :  if  we  want  to  know  how  much  work  a 
labourer  has  done,  we  do  not  ask  how  long  he  has  been  at  work,  but  what  he 
has  done — for  instance,  how  many  bricks  he  has  carried,  and  to  what  height  ; 
and  our  estimate  of  the  total  amount  of  work  is  the  same  whether  the  man 
has  spent  hours  or  days  in  doing  it. 

The  foregoing  relations  between  force  and  work  may  be  put  into  definite 
mathematical  languag'e  as  follows  : — If  the  point  of  application  of  a  force 
moves  in  a  straight  line,  and  if  the  part  of  the  force  resolved  along  this  line 
acts  in  the  direction  of  the  motion,  the  product  of  that  component  and  the 
length  of  the  line  is  the  work  done  by  the  force.  If  the  component  acts  in 
the  opposite  direction  to  the  motion,  the  component  may  be  considered  as 
a  resistance,  and  the  product  is  work  done  against  the  resistance.  Thus,  in 
(43),  if  we  suppose  a  to  move  up  the  plane  from  R  to  S,  the  work  done  by  P 
is  P  X  RS  :  the  work  done  against  the  resistance  W  is  W  sin  x  x  RS.  It 
will  be  observed  that  if  the  forces  are  in  equilibrium  during  the  motion,  so 
that  the  velocity  of  a  is  uniform,  P  equals  W  sin  x,  and  consequently  the 
work  done  by  the  power  equals  that  done  against  the  resistance.  Also,  since 
RS  sin  X  equals  ST,  the  work  done  against  the  resistance  equals  W  x  ST. 
In  other  words,  to  raise  W  from  R  to  S  requires  the  same  amount  of  work 
as  to  raise  it  from  T  to  S. 

If,  however,  the  forces  are  not  in  equilibrium,  the  motion  of  a  will  not  be 
uniform,  but  accelerated  ;  the  work  done  upon  it  will  nevertheless  still  be 
represented  by  the  product  of  the  resultant  force  resohed  along  the  direction 
of  motion  into  the  distance  through  which  it  moves. 


46  On  Matter,  Force,  and  Motion.  [60- 

In  order  to  ascertain  the  relation  between  the  amount  of  work  done 
and  the  change  produced  by  it  in  the  velocity  of  the  moving  mass,  we  must 
recall  one  or  two  elementary  mechanical  principles.  Let  F  be  the  resultant 
force  resolved  along  the  direction  of  motion,  and  S  the  distance  through 
which  its  point  of  application  moves  :  then,  according  to  what  has  been  said, 
the  work  done  by  the  force  =  FS.  Further,  it  has  been  pointed  out  (29)  that 
a  constant  force  is  measured  by  the  momentum  produced  by  it  in  a  unit  of 
time  :  hence,  if  T  be  the  time  during  which  the  force  acts,  V  the  velocity  of 
the  mass  M  at  the  beginning  of  this  period,  and  Vj  the  velocity  at  the  end, 
the  momentum  produced  during  the  time  T  is  MVj  -  MV,  and  consequently 
the  momentum  produced  m  a  unit  of  time,  or,  in  other  words,  the  measure 
of  the  force,  is 

M(V,-V) 
T 

The  distance  S  through  which  the  mass  M  moves  while  its  velocity 
changes  from  the  value  V  to  the  value  V,  is  the  same  as  if  it  had  moved 
during  the  whole  period  T  with  a  velocity  equal  to  the  average  value  of  the 
varying  velocity  which  it  actually  possesses.  But  a  constant  force  acting 
upon  a  constant  mass  causes  its  velocity  to  change  at  a  uniform  rate  ;  hence, 
in  the  present  case,  the  average  velocity  is  simply  the  arithmetical  mean  of 
the  actual  and  final  velocities  : 

S  =  KV.  +  V)T. 

Combining  this  with  the  last  equation,  we  get  as  the  expression  for  the 
work  done  by  the  force  F  : 

FS  =  ^M(V,--V-); 

or,  in  words,  when  a  co7ista7it  force  acts  on  a  mass  so  as  to  change  its  velocity^ 
the  work  done  by  the  force  is  equal  to  half  the  product  of  the  mass  into  the 
change  of  the  square  of  the  velocity. 

The  foregoing  conclusion  has  been  arrived  at  by  supposing  the  force  F 
to  be  constant,  but  it  is  easy  to  show  that  it  holds  good  equally  if  F  is  the 
average  magnitude  of  a  force  which  varies  from  one  part  to  another  of  the 
total  distance  through  which  it  acts.  To  prove  this,  let  the  distance  S  be 
subdivided  into  a  very  great  number  n  of  very  small  parts,  each  equal  to  s, 
so  that  ns  =  S.  Then,  by  supposing  ^  to  be  sufficiently  small,  we  may  with- 
out any  appreciable  error  consider  the  force  as  constant  within  each  of  these 
intervals,  and  as  changing  suddenly  as  its  point  of  application  passes  from 
one  interval  to  the  next.  Let  F,,  F.,,  F.,  .  .  .  .  F,i,  be  the  forces  acting 
throughout  the  ist,  2nd,  3rd  ....  ;7th  interval  respectively,  and  let  the 
velocity  at  the  end  of  the  same  intervals  be  7/,,  7/.,  ta,  ....  v^^  (  =  V,). 
respectively  ;  then,  for  the  work  done  in  the  successive  intervals,  we  have  : 

F,.y  =  iM(7/;'-V'') 

F.j  =  iM(7/.,2-7/,^) 

F,>=iM(7A;--7'„^) 


Yj  =  iM(7/,;-  -  7',,  -  ;-)  =  ^M(v,-  -  7'^- ;-), 


-61j  Unit  of  Work.     Power.  47 

or,  for  the  total  work, 

(F,  +  F,  +  F3+ +F„>  =  iM(\V-V^); 

where   the   quantity  of  the    left-hand    side    of  the    equation    may  also    be 

written l1 -  "^    '  ' n.  «j'  =  FS,  if  we  put  F  to  stand  for  the  average  (or 

n 
arithmetical  mean)  of  the  forces  F,,  F.,,  &c. 

An  important  special  case  of  the  application  of  the  above  formula  arises 
when  either  the  initial  or  the  final  velocity  of  the  mass  M  is  nothing  ;  that 
is  to  say,  when  the  effect  of  the  force  is  to  make  a  body  pass  from  a  state 
of  rest  into  one  of  motion,  or  from  a  state  of  motion  into  one  of  rest.  The 
general  expression  then  assumes  one  of  the  following  forms,  namely  : — 

FS  =  iMVi-or, 
-FS  =  |MV-; 

the  first  of  which  denotes  the  quantity  of  work  which  must  be  done  on  a  body 
of  mass  M  in  order  to  give  to  it  the  velocity  Vj,  while  the  second  expresses 
the  work  that  must  be  done  in  order  to  bring  the  same  mass  to  rest  when  it 
is  moving  with  the  velocity  V,  the  negative  sign  in  the  latter  case  showing 
that  the  force  here  acts  in  opposition  to  the  actual  motion,  and  is  therefore 
to  be  regarded  as  a  resistance. 

In  practice,  the  case  which  most  frecjuently  occurs  is  where  work  of  ac- 
celeration and  work  against  resistance  are  performed  simultaneously.  Thus, 
recurring  to  the  inclined  plane  already  referred  to  in  art.  43  ;  if  the  force  P 
(where  P  is  the  constant  force  with  which  the  string  pulls  W  up  the  plane) 
be  greater  than  W  sin  x,  the  body  W  will  move  up  the  incline  with  a  con- 
tinually increasing  velocity,  and  if  the  point  of  application  of  P  be  displaced 
from  R  to  S,  the  total  amount  of  work  done,  namely,  P  x  RS,  consists  of  a 
portion  =  W  sin  x  RS,  done  against  the  resistance  of  the  weight  W,  and  of  a 
portion  =  (P  -  W  sin  x)  RS  expended  in  accelerating  the  weight.  Hence,  to 
determine  the  velocity  v  with  which  W  arrives  at  the  top  of  the  incline,  we 
have  the  ecjuation 

(P-Wsin,r)  RS  =  iW-./"-; 

for  the  portion  of  P  which  is  in  excess  of  what  is  required  to  produce  equili- 
brium with  the  weight  W,  namely,  P-W  sin  x,  corresponds  to  the  resultant 
force  F  supposed  in  the  foregoing  discussion,  and  RS  to  the  distance  through 
which  this  resultant  force  acts. 

61.  Unit  of  "Work.  Power. — For  strictly  scientific  purposes  a  unit  of 
work  is  taken  to  be  the  work  done  by  a  unit  offeree  when  its  point  of  appli- 
cation moves  through  one  foot  in  the  direction  of  its  action  ;  but,  as  a  con- 
venient and  sufficiently  accurate  standard  for  practical  purposes,  the  quantity 
of  work  which  is  done  in  lifting  i  pound  through  the  height  of  i  foot  is 
commonly  adopted  as  the  unit,  and  this  quantity  of  work  is  spoken  of  as  one 
'  foot-pound.'  It  is,  however,  important  to  observe  that  the  foot-pound  is  not 
perfectly  invariable,  since  the  weight  of  a  pound,  and  therefore  the  work  done 
in  lifting  it  through  a  given  height,  differs  at  different  places,  being  a  little 
greater  near  the  Poles  than  near  the  Equator. 

On  the  metrical  system  the  kilograniuietre  is  the  unit ;  it  is  the  work 


48  On  Matter,  Force,  and  Motion.  [61- 

done  when  a  weight  of  a  kilogramme  is  raised  through  a  heig"ht  of  a 
metre.  This  is  equal  to  7-24  foot-pounds,  and  one  foot-pound  = -1381  of  a 
kilogrammetre. 

In  estimating  the  usefulness  of  an)^  motor  it  becomes  necessary  to  know 
the  time  required  by  it  for  doing  a  given  amount  of  work.  The  amount  of 
work  per  second  is  the  power  of  the  motor.  The  unit  of  power  is  the 
power  required  to  do  a  unit  of  work  in  a  unit  of  time.  For  measuring  the 
power  of  engines  the  unit  used  is  the  horse-power.,  which  represents  a  rate 
of  work  of  33,000  foot-pounds  per  minute. 

It  is  to  be  observed  that  in  every  case  the  unit  is  of  the  same  denomina- 
tion as  the  thing  or  quantity  measured.  The  unit  of  length  must  be  a  length  ; 
the  unit  of  value  must  be  a  definite  quantity  of  some  valuable  commodity. 
The  numbers,  to  determine  which  is  one  of  the  objects  of  physical  research, 
are  to  be  considered  as  abstract  numbers,  representing  how  many  times  the 
unit  is  taken. 

bia.  Systems  of  Units. — The  units  of  mass,  length,  and  time  are  said 
to  be  fiindamcntal  units,  as  all  other  units,  such  as  those  of  area,  velocity, 
acceleration,  power,  &c.,  are  referred  to  them.  These  latter  units  are  there- 
fore called  derived  units.  The  magnitudes  of  the  fundamental  units  are, 
however,  arbitrary.  A  large  class  of  writers  use  the  centimetre,  gramme, 
and  second,  and  this  system  is  usually  called  the  C.G.S.  system  ;  others 
use  the  foot,  pound,  and  second.  It  thus  becomes  important  to  have  a 
systematic  method  of  reducing  measurements  from  one  system  of  units  to 
another. 

Let  L,  M,  T  represent  respectively  the  magnitude  or  dimensio7is  of  the 
centimetre,  the  gramme,  and  the  second,  and  L',  M',  T'  represent  the 
dimensions  of  the  foot,  the  pound,  and  the  minute.  Then,  if  a  wire  is  found 
to  be  /  cm.  or  /'  ft.  in  length,  its  length  may  be  represented  either  by  /L  or 
/'L',  and  hence 

/L  =  /'L',  or/=f^V. 

The  ratio       is  the  length  of  a  foot  in  centimetres,  and  has  been  found 

by  direct  comparison  to  be  30'4797.  Hence  any  measurement,  /'  in  feet,  is 
converted  into  centimetres  by  multiplying  i'  by  this  number. 

In  a  similar  manner,  if  ///  and  ///'  represent  the  number  of  units  of  mass 
in  a  piece  of  matter  in  the  two  systems, 

M'    , 

ni  =  ^,  III  , 

M       ' 

where  the  unit  ratio  is  the  number  of  grammes  in  a  pound,  or  453'59. 
For  converting  a  volume  v'  into  the  equivalent  7', 

(/'L')^  =  (/L)",  or  F'  =  {^^  /'3 


/LV     , 


For  Density,    ^ 


-61a]  Systems  of  Units  49 

m     M.  ^m'     M' 
p'  i}- in  •  L'3' 

M     Vl7 

Here  the  ratio    -  is  said  to  be  a  measure  of  the  magnitude  or  dimensions 

of  the  unit  of  density,  in  terms  of  the  dimensions  of  the  fundamental  units 

of  mass  and  length.     If  a  substance  is  said  to  have  a  unit  density,  then  if  M 

is  the  gramme  and  L^  the  cubic  centimetre,  the  density  of  the  substance 

would  be  that  ^of  water.      If,  however,  M  were  the  kilogramme  and  L^  the 

cubic  centimetre,   the   density  would  be  a  thousand  times  that  of  water. 

If,  again,  L^    represents  a  cubic  decimetre,  and   M   the  kilogramme,   the 

density  would  again  be  that  of  water.     It  appears,  then,  that  the  magnitude 

of  the  unit  of  density  is  directly  proportional  to  the  magnitude  of  the  unit 

of  mass,  and  mversely  as  the  magnitude  of  the  unit  of  volume  or  the  cube  of 

the  unit  of  length.     As  the  unit  density  is  the  density  of  a  unit  mass  to  the 

M 
unit  volume,  it  is  clear  that     „  measures  the  dimensions  of  the  unit  of  density. 

Similar  explanations  apply  in  the  succeeding  cases. 
/ 


For   Velocity^  v-- 


~,         ^-    T      second      i 
i  he  ratio  — -  ■■ 


/  '  T  /  ■  T' 

L'  T 

')=■■-  —  .11 

L  T' 


T'     minute     60 

T 

If  the  units  of  time  were  the  same,  the  unit  factor  — =  i,  and  the  velo- 
city in  centimetres  would  be 

L'    , 
v=  --  V, 

where  v'  is  the  velocity  in  feet  per  second. 
vil 


For  Momentum^  inv  = 

iiii 
t 

nd 
t 

ML     in' I'     M'L' 
T         t'    '     T' 

or 

VIV-- 

M' 

M 

^^•-- 

For  Acceleration,  <z  =  - 

_  I 

/ 

L 

/'      L' 

i~ 

•  yx 

t"  '  T^^' 

a 

1/ 
L 

ar-' 

where  a'  is  the  acceleration  in 

feet 

per  minute. 

so 

On  Matter,  Force,  and  Motion. 

For  Force ^  F  = 

ml 

--  ma  =  — J 

ml     ML     m'V     WL' 
M     L    W) 

In  the  C.G.S. 

system  the  unit  is  called  the  Dyne. 

For  Work,W^Yl==^'^^ 

mP     MU     m'l'"-     M'L'2 

In  the  C.G.S. 

system  the  unit  of  work  is  called  the  Erg. 

Rale  0)  Work 

^,orPower,Y  =  ^l='^ 
t        /3 

mP     M.U     m'l'^     M'L'2 

[61a- 


-l'(D'©' 


If  work  is  expressed  in  foot-pounds  or  kilogramme-metres,  the  unit  of 
force  being  the  weight  of  a  pound  or  kilogramme,  then  to  convert  a  certain 
number  of  foot-pounds  into  kilogramme-metres  we  have 

wl .  WL  =  w'l'  WU. 
Work  (kgT.-m.)  =  (~—  .  —  j  work,  foot-pounds, 

L'       foot  o 

T-    =   =  0-3048, 

L     metre 
the  unit  factor  being  thus  0-1383. 

Similarly,  to  convert  foot-pounds  per  minute  mto  kilogr. -metres  per  second, 

p     /W'L'TW 
VW   L  TV     ' 
where  the  conversion  factor  becomes  0-00230. ' 

The  units  commonly  used  for  measuring  the  power  ot  engmes  are  the 
horse-power,  which  is  33,000  times  as  great  as  the  unit  in  which  P'  of  the 
last  equation  was  measured,  and  the  force  de  cheval,  which  is  75  times  as 
great  as  the  unit  in  which  P  was  measured.  Hence,  if  P'  is  to  be  in  horse- 
power, and  P  \\\fo7-ce  de  cheval,  the  equation  will  become 

P  =  0-00230  X  33^52?p/ 
75 
=  1-0139  P', 
and  hence  one  British  horse-power  =  I'oi'^c)  force  de  cheval. 


-63]  Varieties  of  Energy.  5 1 

These  examples  will  be  sufficient  to  indicate  the  method  of  converting 
measurements  from  one  system  of  units  to  any  other,  and  the  treatment  of 
other  derived  units  may  be  deferred  until  they  are  needed. 

62.  Energ^y. — The  fact  that  any  agent  is  capable  of  doing  work  is  usually 
expressed  by  saying  that  it  possesses  Ene^'gy,  and  the  quantity  of  energy  it 
possesses  is  measured  by  the  amount  of  work  it  can  do.  For  example,  in 
the  case  of  the  inclined  plane  above  referred  to,  the  working  power  or  energy 
of  the  force  P  is  P  x  RS  ;  and  if  this  force  acts  under  the  conditions  last 
supposed,  by  the  time  its  own  energy  is  exhausted  (in  consec[uence  of  its 
point  of  application  having  arrived  at  S,  the  limit  of  the  range  through  which 
it  is  supposed  able  to  act),  it  has  conferred  upon  the  weight  W  a  quantity  of 
energy  equal  to  that  which  has  been  expended  ;  for,  in  the  first  place,  W 
has  been  raised  through  a  vertical  height  equal  to  ST,  and  could  by  falling 
again  through  the  same  height  do  an  amount  of  work  represented  by  W  x  ST  ; 
and  in  the  second  place  W  can  do  work  by  virtue  of  the  velocity  that  has 
been  imparted  to  it,  and  can  continue  moving  in  opposition  to  any  given 
resistance  R  through  a  distance  s,  such  that 

The  energy  possessed  by  the  mass  M  in  consequence  of  having  been  raised 
from  the  ground  is  commonly  distinguished  as  energy  oj positio?t  or  potential 
energy,  and  is  measured  by  the  product  of  the  force  tending  to  cause  motion, 
into  the  distance  through  which  the  point  of  application  of  the  force  is 
capable  of  being  displaced  in  the  direction  in  which  the  force  acts.  The 
energy  possessed  by  a  body  in  consequence  of  its  velocity  is  commonly  dis- 
tinguished as  e?tergy  of  motion,  or  kinetic  energy:  it  is  measured  by  half  the 
product  of  the  moving  mass  into  the  square  of  its  velocity. 

63.  Varieties  of  energry. — It  will  be  seen,  on  considering  the  definition 
oiivork  gi\'en  above,  that  a  force  is  said  to  do  work  when  it  produces  any 
change  in  the  condition  of  bodies  ;  for  the  only  changes  which,  according  to 
the  definition  oi  force  given  previously  (26),  a  force  is  capable  of  producing, 
are  changes  in  the  state  of  rest  or  motion  of  bodies  and  changes  of  their 
place,  in  opposition  to  resistances  tending  to  prevent  motion  or  to  produce 
motion  in  an  opposite  direction.  There  are,  however,  many  other  kinds  of 
physical  changes  which  can  be  produced  under  appropriate  conditions,  and 
the  recent  progress  of  investigation  has  shown  that  the  conditions  under 
which  changes  of  all  kinds  occur  are  so  far  analogous  to  those  required  for 
the  production  of  work  by  mechanical  forces  that  the  term  work  has  come 
to  be  used  in  a  more  extended  sense  than  formerly,  and  is  now  often  used  to 
signify  the  production  of  any  sort  of  physical  change. 

Thus  work  is  said  to  be  done  when  a  body  at  a  low  temperature  is  raised 
to  a  higher  temperature,  just  as  much  as  when  a  weight  is  raised  from  a 
lower  to  a  higher  level  ;  or,  again,  work  is  done  when  an  electrical,  magnetic, 
or  chemical  change  is  produced.  This  extension  of  the  meaning  of  the 
term  work  involves  a  similar  extension  of  the  meaning  of  energy,  which  in 
this  wider  sense  may  be  defined  as  the  capacity  for  producing  physical 
change. 

As  examples  of  energy  in  this  more  general  sense,  the  following  may  be 
mentioned  : — {a)  the  energy  possessed  by  gunpowder  in  virtue  of  the  mutual 


52  On  Matter,  Force,  and  Motion.  [63- 

chemical  affinities  of  its  constituents,  whereby  it  is  capable  of  doing  work  by 
generating  heat  or  by  acting  on  a  cannon-ball  so  as  to  change  its  state  of 
rest  into  one  of  rapid  motion  ;  {b)  the  energy  of  a  charged  Leyden  jar,  which, 
according  to  the  way  in  which  the  jar  is  discharged,  can  give  rise  to  changes 
of  temperature,  to  changes  of  chemical  composition,  to  mechanical  changes, 
or  to  changes  of  magnetic  or  electrical  condition  ;  (c)  the  energy  of  a  red-hot 
ball,  which,  amongst  other  effects  it  is  capable  of  producing,  can  raise  the 
temperature  and  increase  the  volume  of  bodies  colder  than  itself,  or  can 
change  ice  into  water  or  water  into  steam  ;  the  energy  of  the  stretched 
string  of  a  bow  :  here  work  has  been  consumed  in  stretching  the  string  ; 
when  it  is  released  the  work  reappears  in  the  velocity  imparted  to  the 
arrow. 

64.  Transformation  of  energ-y. — It  has  been  found  by  experiment 
that  when  one  kind  of  energy  disappears  or  is  expended,  energy  of  some 
other  kind  is  produced,  and  that,  under  proper  conditions,  the  disappearance 
of  any  one  of  the  known  kinds  of  energy  can  be  made  to  give  rise  to  a  greater 
or  less  amount  of  any  other  kind.  One  of  the  simplest  illustrations  that  can 
be  given  of  this  transformation  of  energy  is  afforded  by  the  oscillations  of  a 
pendulum.  When  the  pendulum  is  at  rest  in  its  lowest  position  it  does  not 
possess  any  energy,  for  it  has  no  power  of  setting  either  itself  or  other  bodies 
in  motion,  or  of  producing  in  them  any  kind  of  change.  In  order  to  set  the 
pendulum  oscillating,  work  must  be  done  upon  it,  and  it  thereafter  possesses 
an  amount  of  energy  corresponding  to  the  work  that  has  been  expended. 
When  it  has  reached  either  end  of  its  path,  the  pendulum  is  for  an  instant  at 
rest  ;  but  it  possesses  energy  by  virtue  of  its  position,  and  can  do  an  amount  of 
work  while  falling  to  its  lowest  position,  which  is  represented  by  the  product 
of  its  weight  into  the  vertical  height  through  which  its  centre  of  gravity  de- 
scends. When  at  the  middle  of  its  path  the  pendulum  is  passing  through  its 
position  of  equilibrium,  and  has  no  power  of  doing  work  by  falling  lower  ;  but 
it  now  possesses  energy  by  virtue  of  the  velocity  which  it  has  gained,  and 
this  energy  is  able  to  carry  it  up  on  the  second  side  of  its  lowest  position  to 
a  height  equal  to  that  from  which  it  has  descended  on  the  first  side.  By 
the  time  it  reaches  this  position  the  pendulum  has  lost  all  its  velocity,  but  it 
has  regained  the  power  of  falling  :  this,  in  its  turn,  is  lost  as  the  pendulum 
returns  again  to  its  lowest  position,  but  at  the  same  time  it  regains  its  pre- 
vious velocity.  Thus,  during  every  quarter  of  an  oscillation  the  energy  of 
the  pendulum  changes  from  potential  energy  of  position  into  actual  energy 
or  energy  of  motion,  or  vice  versa. 

A  more  complex  case  of  the  transformation  of  energy  is  afforded  by  a 
thermo-electric  pile,  the  terminals  of  which  are  connected  by  a  conducting 
wire  :  the  application  of  energy  in  the  form  of  heat  to  one  face  of  the  pile 
gives  rise  to  an  electric  current  in  the  wire,  which,  in  its  turn,  reproduces 
heat,  or  by  proper  arrangements  can  be  made  to  produce  chemical,  magnetic, 
or  mechanical  effects,  such  as  those  described  below  in  the  chapters  on 
Electricity. 

It  has  also  been  found  that  the  transformations  of  energy  always  take 
place  according  to  fixed  proportions.  For  instance,  when  coal  or  any  other 
combustible  is  burned,  its  chemical  energy,  or  power  of  combining  with 
oxygen,  vanishes,  and  heat  or  thermal  energy  is  produced,  and  the  quantity 


-65]  Conservation  of  Energy.  53 

of  heat  produced  by  the  combustion  of  a  given  amount  of  coal  is  fixed  and 
invariable.  If  the  combustion  take  place  under  the  boiler  of  a  steam-engine, 
mechanical  work  can  be  obtained  by  the  expenditure  of  part  of  the  heat  pro- 
duced, and  here  again  the  cjuantitative  relation  between  the  heat  expended 
and  the  work  gained  in  place  of  it  is  perfectly  constant. 

65.  Conservation  of  energ-y. — Another  result  of  great  importance,  which 
has  been  arrived  at  by  experiment,  is  that  the  total  amount  of  enei'gy  possessed 
by  any  system  of  bodies  is  unaltered  by  any  transformations  arising  from  the 
action  of  one  part  of  the  system  upon  another,  and  can  only  be  increased  or 
dmiinished  by  effects  produced  on  the  system  by  external  agents.  In  this 
statement  it  is  of  course  understood  that  in  reckoning  the  sum  of  the  energy 
of  various  kinds  which  the  system  may  possess,  those  amounts  of  the 
different  forms  of  energy  which  are  mutually  convertible  into  each  other  are 
taken  as  being  numerically  equal ;  or,  what  comes  virtually  to  the  same 
thing,  the  total  energy  of  the  system  is  supposed  to  be  reduced — either  ac- 
tually, or  by  calculation  from  the  known  ratio  of  transformation  of  the  various 
forms  of  energy — to  energy  of  some  one  kind  ;  then  the  statement  is  equivalent 
to  this  :  that  the  total  energy  of  any  one  form  to  which  the  energy  of  a  given 
system  of  bodies  is  reducible  is  unalterable  so  long  as  the  system  is  not  acted 
on  from  without.  Practically  it  is  always  possible,  in  one  way  or  another,  to 
convert  the  whole  of  the  energy  possessed  by  any  body  or  system  of  bodies 
into  heat,  but  it  cannot  be  all  converted  without  loss  into  any  other  form  of 
energy  ;  hence  the  principle  stated  at  the  beginning  of  this  article  can  be 
enunciated  in  the  closest  conformity  with  the  direct  results  of  experiment  by 
saying  that,  so  long  as  any  system  of  bodies  is  not  acted  on  from  without, 
the  total  quantity  of  heat  that  can  be  obtained  from  it  is  unalterable  by  any 
changes. which  may  go  on  within  the  system  itself.  For  instance,  a  quantity 
of  air  compressed  into  the  i-eservoir  of  an  air-gun  possesses  energy  which  is 
represented  partly  by  the  heat  which  gives  to  it  its  actual  temperature  above 
the  absolute  zero  (460),  and  partly  by  the  work  which  the  air  can  do  in  expand- 
ing. This  latter  portion  can  be  converted  into  heat  in  various  ways,  as,  for 
example,  by  allowing  the  air  to  escape  through  a  system  of  capillary  tubes 
so  fine  that  the  air  issues  from  them  without  any  sensible  velocity  ;  if,  how- 
ever, the  expanding  air  be  employed  to  propel  a  bullet  from  the  gun,  it 
produces  considerably  less  heat  than  in  the  case  previously  supposed,  the 
deficiency  being  represented  for  a  time  by  the  energy  of  the  moving  bullet, 
but  reappearing  in  the  form  of  heat  in  the  friction  of  the  bullet  against  the 
air,  and,  when  the  motion  of  the  bullet  is  destroyed,  by  striking  against  an 
inelastic  obstacle  at  the  same  level  as  the  gun.  But  whatever  the  mode  and 
however  numerous  the  intermediate  steps  by  which  the  energy  of  the  com- 
pressed air  is  converted  into  heat,  the  total  quantity  of  heat  finally  obtainable 
from  it  is  the  same. 


54  Gravitation  and  Molecular  Attraction.  [66- 


BOOK    II. 

GRAVITATION    AND   MOLECULAR   ATTRACTION. 


CHAPTER   L 
GRAVITY.      CENTRE  OF   GRAVITY.      THE   BALANCE, 

66.  Universal  attraction:  its  laws. —  Uiiiversal  attractiofi  is  a  force 
in  virtue  of  which  the  material  particles  of  all  bodies  tend  incessantly  to 
approach  each  other  ;  it  is  a  mutual  action,  however,  which  all  bodies,  at 
rest  or  in  motion,  exert  upon  one  another,  no  matter  how  great  or  how  small 
the  space  between  them  may  be,  or  whether  this  space  be  occupied  or  un- 
occupied by  other  matter. 

A  vague  hypothesis  of  the  tendency  of  the  matter  of  the  earth  and  stars 
to  a  common  centre  was  adopted  even  byDemocritus  and  Epicurus.  Kepler 
assumed  the  existence  of  a  mutual  attraction  between  the  sun,  the  earth,  and 
the  other  planets.  Bacon,  Galileo,  and  Hooke  also  recognised  the  existence 
of  universal  attraction.  But  Newton  was  the  first  who  established  the  law, 
and  the  universality  of  gravitation. 

Since  Newton's  time  the  attraction  of  matter  by  matter  was  experimentally 
established  by  Cavendish.  This  eminent  English  physicist  succeeded,  by 
means  of  a  delicate  torsion  balance  (89),  in  rendering  visible  the  attraction 
between  a  large  leaden  and  a  small  copper  ball. 

The  attraction  between  any  two  bodies  is  the  resultant  of  the  attractions 
of  each  molecule  of  the  one  upon  every  molecule  of  the  other  according  to 
the  law  of  Newton,  which  may  be  thus  expressed  :  the  attraction  between 
two  material  particles  is  directly  proportional  to  the  p?'odzict  of  their  masses 
and  inversely  proportional  to  the  square  of  their  distances  asunder.  To 
illustrate  this,  we  may  take  the  case  of  two  spheres,  which,  owing  to  their 
symmetry,  attract  each  other  just  as  if  their  masses  were  concentrated  in 
their  centres.  If  without  other  alteration  the  mass  of  one  sphere  were 
doubled,  tripled,  &c.,  the  attraction  between  them  would  be  doubled,  tripled, 
&c.  If,  however,  the  mass  of  one  sphere  being  doubled,  that  of  the  other 
were  increased  three  times,  the  distance  between  their  centres  remaining  the 
same,  the  attraction  would  be  increased  six  times.  Lastly,  if,  without  alter- 
ing their  masses,  the  distance  between  their  centres  were  increased  from  i 
to  2,  3,  4  ...  .  units,  the  attraction  would  be  diminished  to  the  4th,  9th, 


-67j  Terrestrial  Gravitation.  55 

1 6th  ....  part  of  its  former  intensity.  In  short,  if  we  define  the  unit  of 
attraction  as  that  which  would  exist  between  two  units  of  mass  whose 
distance  asunder  was  the  unit  of  length,  the  attraction  of  two  molecules, 
having  the  masses  vi   and  ni' ,  at   the  distance  r,  would  be  expressed  by 


67.  Terrestrial  gravitation. — The  tendency  of  any  body  to  fall  towards 
the  earth  is  due  to  the  mutual  attraction  of  that  body  and  the  earth,  or  to 
terrestrial  gravitation,  and  is,  in  fact,  merely  a  particular  case  of  universal 
attraction. 

At  any  point  of  the  earth's  surface,  the  direction  of  gravity — that  is,  the 
line  which  a  falling  body  describes — is  called  the  vertical  line.  The  vertical 
lines  drawn  at  different  points  of  the  earth's  surface  converge  very  nearly  to 
the  earth's  centre.  For  points  situated  on  the  same  meridian  the  angle  con- 
tained between  the  vertical  lines  equals  the  difference  between  the  latitudes 
of  those  points. 

The  directions  of  the  earth's  attraction  upon  neighbouring  bodies,  or  upon 
different  molecules  of  one  and  the  same  body,  must,  therefore,  be  considered 
as  parallel,  for  the  two  vertical  lines  form  the  sides  of  a  triangle  whose  vertex 
is  near  the  earth's  centre,  about  4,000  miles  distant,  and  whose  base  is  the 
small  distance  between  the  molecules  under  consideration. 

A  plane  or  line  is  said  to  be  horisontat  when  it  is  perpendicular  to  the 
vertical  line. 

The  vertical  line  at  any  point  of  the  globe  is  generally  determined  by  the 
plui)ib-li)ie  (fig.  40),  which  consists  of  a  weight  attached  to  the  end  of  a  string. 
It  is  evident  that  the  weight  cannot  be  in  equiUbrium  un- 
less the  direction  of  the  earth's  attraction  upon  it  passes 
through  the  point  of  support,  and  therefore  coincides  with 
that  of  the  string. 

The  horizontal  plane  is  also  determined  with  great 
ease,  since  it  coincides,  as  will  be  afterwards  shown,  with 
the  level  surface  of  every  liquid  when  in  a  state  of  equili- 
brium. 

When  the  mean  figure  of  the  earth  has  been  approxi- 
mately determined,  it  becomes  possible  to  compare  the 
direction  of  the  plumb-line  at  any  place  with  that  of  the 
normal  to  the  mean  figure  at  that  place.  When  any  differ- 
ence in  these  directions  can  be  detected,  it  constitutes  a 
deviation  of  the  plumb-line,  and  is  due  to  the  attraction  of  ^p- 

some  great  mass  of  matter  in  the  neighbourhood,  such  as 
a  mountain.  Thus,  in  the  case  of  the  mountain  of  Schehallien,  in  Perthshire, 
it  was  found  by  Dr.  Maskelyne  that  the  angle  between  the  directions  of  two 
plumb-lines,  one  at  a  station  to  the  north,  and  the  other  to  the  south,  of  the 
mountain  was  greater  by  11'^ -6  than  the  angle  between  the  normals  of  the 
mean  surface  of  the  earth  at  those  points  ;  in  other  words,  each  plumb-line 
was  deflected  by  about  6"  towards  the  mountain.  By  calculating  the  volume 
and  mass  of  the  mountain,  it  was  inferred  from  this  observation  that  the 
mean  density  of  the  mountain  was  to  that  of  the  earth  in  the  ratio  of  5  :  9, 
and  that  the  mean  density  of  the  earth  is  about  five  times  that  of  water— a 


56 


Gravitation  and  Molecular  Attraction. 


[67- 


result  agreeing  pretty  closely  with  that  deduced  from  Cavendish's  experiment 
referred  to  in  the  last  article. 

68.  Centre  of  gravity,  its  experimental  determination. — Into  what- 
ever position  a  body  may  be  turned  with  respect  to  the  earth,  there  is  a 
certain  point,  invariably  situated  with  respect  to  the  body,  through  which 
the  resultant  of  the  attracting  forces  between  the  earth  and  its  several  mole- 
cules always  passes.  This  point  is  called  the  centre  of  gravity ;  it  may  be 
within  or  without  the  body,  according  to  the  form  of  the  latter  ;  its  existence, 
however,  is  easily  established  by  the  following  considerations  :  let  vi  m'  m" 
m'".  .  .  .  (fig.  41)  be  molecules  of  any  body.  The  earth's  attraction  upon 
these  molecules  will  constitute  a  system  of  parallel  forces,  having  a  common 
vertical  direction,  whose  resultant  will  be  found  by  seeking  first  the  resultant 
of  the  forces  which  act  on  any  two  molecules,  m  and  in\  then  that  of  this 
resultant  and  a  third  force  acting  on  in'\  and  so  on  until  we  arrive  at  the 
final  resultant  W,  representing  the  weight  of  the  body  and  applied  at  a 
certain  point  G.  If  the  body  be  now  turned  into  the  position  shown  in 
fig.  42,  the  molecules  ;;/,  ;//',  in".  .  .  .  will  continue  to  be  acted  on  by  the 


Fig.  41. 

same  forces  as  before,  the  resultant  of  the  forces  on  ;//  and  w'  will  pass 
through  the  same  point  0  in  the  line  mm\  the  following  resultant  will  again 
pass  through  the  same  point  o'  in  om",  and  so  on  up  to  the  final  resultant 
P,  which  will  still  pass  through  the  same  point  C,  which  is  the  centre  of 
gravity. 

To  find  the  centre  of  gravity  of  a  body  is  a  purely  geometrical  problem  ; 
in  many  cases,  however,  it  can  be  at  once  determined.  For  instance,  the 
centre  of  gravity  of  a  right  line  of  uniform  density  is  the  point  which  bisects 
its  length  ;  in  the  circle  and  sphere  it  coincides  with  the  geometrical  centre  ; 
in  cylindrical  bars  it  is  the  middle  point  of  the  axis.  The  centre  of  gravity 
of  a  plane  triangle  is  in  the  line  which  joins  any  vertex  with  the  middle  of 
the  opposite  side,  and  at  a  distance  from  the  vertex  equal  to  two-thirds  of 
this  line  :  in  a  cone  or  pyramid  it  is  in  the  line  which  joins  the  vertex  with 
the  centre  of  gravity  of  the  base,  and  at  a  distance  from  the  vertex  equal  to 
three-fourths  of  this  line.  These  rules,  it  must  be  remembered,  presuppose 
that  the  several  bodies  are  of  uniform  density. 

In  order  to  determine  experimentally  the  centre  of  gravity  of  a  body,  it 
is  suspended  by  a  string  in  two  different  positions,  as  shown  in  figs.  43  and 
44  ;  the  point  where  the  directions  AB  and  CD  of  the  string  in  the  two  ex- 


70] 


Different  States  of  EquilibriuDi. 


Fig.  43 


Fig.  44. 


57 

periments  intersect  each  other  is  the  centre  of  gravity  required.  For,  the 
resultant  of  the  earth's  attraction  being  a  vertical  force  applied  at  the  centre 
of  gravity,  the  body  can  only  be  in  equilibrium  when  the  point  lies  vertically 
under  the  point  of  suspension  ;  that  is,  in  the  prolongation  of  the  suspended 
string.  But  the  centre  of  gravity, 
being  in  AB  as  well  as  in  CD,  must 
coincide  with  the  point  of  intersec- 
tion of  these  two  lines. 

The  centre  of  gravity  of  a  thin 
piece  of  cardboard  of  irregular 
shape,  for  instance,  may  be  found 
by  balancing  it  in  two  positions  on 
a  knife-edge  ;  the  centre  of  gravity 
will  then  lie  in  the  intersection  of 
the  two  lines. 

69.  Equilibrium  of  heavy 
bodies. — Since  the  action  of  gravity 
upon  a  body  reduces  itself  to  a 
single  vertical  force  applied  at  the 
centre  of  gravity  and  directed  to- 
wards the  earth's  centre,  equili- 
brium will  be  established  only  when  this  resuhant  is  balanced  by  the 
resultant  of  other  forces  and  resistances  acting  on  the  body  at  the  fixed  point 
through  which  it  passes. 

When  only  one  point  of  the  body  is  fixed,  it  will  be  in  equilibrium  if  the 
vertical  line  through  its  centre  of  gravity  passes  through  the  fixed  point.  If 
more  than  one  point  is  supported,  the  body  will  be  in  equilibrium  if  a  vertical 
line  through  the  centre  of  gra\'ity  passes  through  a  point  within  the  polygon 
formed  by  joining  the  points  of  support. 

The  Leaning  Tower  of  Pisa  continues  to  stand  because  the  vertical  line 
drawn  through  its  centre  of  gravity  passes  within  its  base. 

It  is  easier  to  stand  on  our  feet  than  on  stilts,  because  in  the  latter  case 
the  smallest  motion  is  sufficient  to  cause  the  vertical  line  through  the  centre 
of  gravity  of  our  bodies  to  pass  outside  the  supporting  base,  which  is  here 
reduced  to  a  mere  line  joining  the  feet  of  the  stilts.  A  man  carrying  a  load 
on  his  back  must  lean  forward  :  if  he  carries  it  in  the  left  hand  he  must  incline 
the  upper  part  of  his  body  to  the  right,  for  otherwise  the  centre  of  gravity  of 
the  body  and  of  the  load  would  fall  outside  the  line  joining  the  feet  and  he 
would  fall.  Again,  it  is  impossible  to  stand  on  one  leg  if  we  keep  one  side 
of  the  foot  and  head  close  to  a  vertical  wall,  because  the  latter  prevents 
us  from  throwing  the  body's  centre  of  gravity  vertically  above  the  supporting 
base. 

70.  Sifferent  states  of  equilibrium. — Although  a  body  supported  by  a 
fixed  point  is  in  equilibrium  whenever  its  centre  of  gravity  is  in  the  vertical 
line  through  that  point,  the  fact  that  the  centre  of  gravity  tends  incessantly 
to  occupy  the  lowest  possible  position  leads  us  to  distinguish  between  three 
states  of  equilibrium — stable,  unstable,  neutral. 

A  body  is  said  to  be  in  stable  equilibrium  if  it  tends  to  return  to  its  first 
position  after  the  equilibrium  has  been  slightly  disturbed.     Every  body  is  in 


58 


Gravitation  and  Molecular  Attraction. 


[70- 


this  state  when  its  position  is  such  that  the  sHghtest  alteration  of  the  same 
elevates  its  centre  of  gravity  ;  for  the  centre  of  gravity  will  descend  again 
when  permitted,  and  after  a  few  oscillations  the  body  will  return  to  its 
original  position. 

The  pendulum  of  a  clock  continually  oscillates  about  its  position  of  stable 
equilibrium,  and  an  t.gg  on  a  level  table  is  in  this  state  when  its  long  axis 
is  horizontal.  We  have  another  illustration  in  the  toy  represented  in  the 
adjoining  fig.  45.  A  small  figure  cut  in  ivory  is  made  to  stand  on  one  foot 
at  the  top  of  a  pedestal  by  being  loaded  with  two  leaden  balls,  «,  b,  placed 
sufficiently  low  to  throw  the  centre  of  gravity,  g,  of 
the  whole  compound  body  below  the  foot  of  the 
figure.  After  being  disturbed,  the  httle  figure  oscil- 
lates like  a  pendulum,  having  its  point  of  suspen- 
sion at  the  toe,  and  its  centre  of  gravity  at  a  lower 
point,  g. 

A  body  is  said  to  be  in  imstable  equilibrium  when, 
after  the  slightest  disturbance,  it  tends  to  depart  still 
more  from  its  original  position.  A  body  is  in  this  state 
when  its  centre  of  gravity  is  vertically  above  the  point 
of  support,  or  higher  than  it  would  be  in  any  adjacent 
position  of  the  body.  An  egg  standing  on  its  end,  or  a 
stick  balanced  upright  on  the  finger,  is  in  this  state. 

Lastly,   if  in    any   adjacent   position    a   body  still 
remains    in    equilibrium,    its    state    of    equilibrium  is 
said  to  be  jieutral.     In  this  case  an  alteration  in  the 
Fis-  45-  position    of   the   body   neither   raises   nor   lowers    its 

centre  of  gravity.     A  perfect  sphere  resting  on  a  horizontal  plane  is  in  this 


Fig.  46  represents  three  cones.  A,  B,  C,  placed  respectively  in  stable, 
unstable   and  neutral  equilibrium  upon  a  horizontal  plane.     The  letter  g  in 

each  shows  the  position 
of  the  centre  of  gravity. 
71.  The  balance. — 
The  balance  is  an  in- 
strument for  determi- 
ning the  relative  weights 
or  masses  of  bodies. 
There  are  many  varie- 
ties. 

The  ordinary  balance  (fig.  47)  consists  of  a  lever  of  the  first  kind,  called 
the  beam,  AB,  with  its  fulcrum  in  the  middle  ;  at  the  extremities  of  the  beam 
are  suspended  two  scale-pans,  C  and  D,  one  intended  to  receive  the  object 
to  be  weighed,  and  the  other  the  counterpoise.  The  fulcrum  consists  of  a 
steel  prism,  n,  commonly  called  a  knife-edge,  which  passes  through  the  beam, 
and  rests  with  its  sharp  edge,  or  axis  of  suspension,  upon  two  supports  ;  these 
are  formed  of  agate,  in  order  to  diminish  the  friction.  A  needle  or  pointer 
is  fixed  to  the  beam,  and  oscillates  with  it  in  front  of  a  graduated  arc,  a  : 
when  the  beam  is  perfectly  horizontal  the  needle  points  to  the  zero  of  the 
graduated  arc. 


-72] 


Conditions  to  be  satisfied  by  a  Balance. 


59 

Since  by  (40)  two  equal  forces  in  a  lever  of  the  first  kind  cannot  be  in 
equilibrium  unless  their  leverages  are  equal,  the  length  of  the  arms  «A  and 
«B  ought  to  remain  equal  during  the  process  of  weighing.  To  secure  this 
the  scales  are  suspended  from  hooks,  whose  curved  parts  have  sharp  edges, 
and  rest  on  similar  edges  at  the  ends  of  the  beam.  In  this  manner  the 
scales  are  in  effect  supported  on  mere  points,  which  remain  unmoved  during 
the  oscillations  of  the  beam.     This  mode  of  suspension  is  represented  in 

fig-  47- 

72.  Conditions  to  be  satisfied  by  a  balance. — A  good  balance  ought 
to  satisfy  the  following  conditiQns  : — 

i.  The  two  arms  of  the  beam  ought  to  be  precisely  equal,  otherwise, 
according  to  the  principle  of  the  lever,  unequal  weights  will  be  required  to 
produce  equilibrium.     To  test  whether  the  arms  of  the  beam  are  equal, 


ihi'iiiiiiiaiiiiiiiiiii'iiiiriHiiiiniiiiiriiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii 


iiiiiiiiiimiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii 


iiiiiiiiiiiiiiiiii 


Fig.  47. 

weights  are  placed  in  the  two  scales,  until  the  beam  becomes  horizontal  ; 
the  contents  of  the  scales  being  then  interchanged,  the  beam  will  remain 
horizontal  if  its  arms  are  equal,  but  if  not,  it  will  descend  on  the  side  of  the 
longer  arm. 

ii.  The  balance  ought  to  be  z?t  equilibrium  whefi  the  scales  are  empty.,  for 
otherwise  unequal  weights  must  be  placed  in  the  scales  in  order  to  produce 
equilibrium.  It  must  be  borne  in  mind,  however,  that  the  arms  are  not 
necessarily  equal,  even  if  the  beam  remains  horizontal  when  the  scales  are 
empty  ;  for  this  result  might  also  be  produced  by  giving  to  the  longer  arm 
the  lighter  scale. 

iii.  The  beam  being  horizo7ttal.,  its  centre  of  gravity  ought  to  be  i?t  the  ■ 
same  vertical  line  with  the  edge  of  the  fulcrum,  and  a  little  below  the  latter, 
for  otherwise  the  beam  would  not  be  in  stable  equilibrium  (70). 


6o 


Gravitation  and  Molecular'  Attraction. 


[72- 

The  effect  of  changing  the  position  of  the  centre  of  gravity  may  be  shown 
by  means  of  a  beam  (fig.  48),  whose  fulcrum,  being  the  nut  of  a  screw,  a,  can 
be  raised  or  lowered  by  turning  the  screw-head,  b. 

When  the  fulcrum  is  at  the  top  of  the  groove  c,  in  which  it  slides,  the 
centre  of  gravity  of  the  beam  is  below  its  edge,  and  the  latter  oscillates 


■ -^ 

Fig.  48. 

freely  about  a  position  of  stable  equilibrium.  By  gradually  lowering  the 
fulcrum  its  edge  may  be  made  to  pass  through  the  centre  of  gravity  of  the 
beam  when  the  latter  is  in  neutral  equilibrium  ;  that  is  to  say,  it  no  longer 
oscillates,  but  remains  in  equilibrium  in  all  positions.  When  the  fulcrum 
is  lowered  still  more,  the  centre  of  gravity  passes  above  its  edge,  the 
beam  is  in  a  state  of  unstable  equilibrium,  and  is  overturned  by  the  least 
displacement. 

"JT).  Belicacy  of  the  balance. — A  balance  is  said  to  be  delicate  when  a 
very  small  difference  between  the  weights  in  the  scales  causes  a  perceptible 
deflection  of  the  pointer. 

Let  A  and  B  (figs.  49  and  50)  be  the  points  from  which  the  scale-pans 
are  suspended,  and  C  the  axis  of  suspension  of  the  beam.     A,  B,  and  C  are 


Fig.  49.  Fig.  50. 

assumed  to  be  in  the  same  sti'aight  line,  according  to  the  usual  arrangement. 
Suppose  weights  P  and  Q  to  be  in  the  pans,  suspended  from  A  and  B  re- 
spectively, and  let  G  be  the  centre  of  gravity  of  the  beam  ;  then  the  beam 
will  come  to  rest  in  the  position  shown  in  the  figure,  where  the  line  DCN  is 
vertical,  and  ECG  is  the  direction  of  the  pointer.  According  to  the  above 
statement,  the  greater  the  angle  ECD  for  a  given  difference  between  P  and 
Q,  the  greater  is  the  delicacy  of  the  balance.  Draw  ON  at  right  angles 
to  CO. 

Let  W  be  the  weight  of  the  beam,  then  from  the  properties  of  the  lever  (40) 
it  follows  that  measuring  moments  with  respect  to  C,  the  moment  of  P  equals 
the  sum  of  the  moments  of  Q  and  W,  a  condition  which  at  once  leads  to  the 
relation 

(P-Q)AC  =  WxGN 


74] 


Physical  and  Chejnical  Balances. 


6i 


Now  it  is  clear  that  for  a  given  value  of  CG  the  angle  GCN  (that  is  ECD, 
which  measures  the  delicacy)  is  greater  as  ON  is  greater ;  and  from  the 
formula  it  is  clear  that  for  a  given  value  of  P  — Q  we  shall  have  GN  greater 
as  AC  is  greater,  and  as  W  is  less.  Again,  for  a  given  value  of  GN  the 
angle  GCN  is  greater  as  GC  is  less.  Hence  the  means  of  rendering  a 
balance  delicate  are — 

i.   To  make  the  arms  of  the  balance  long. 

ii.  To  7nake  the  weight  of  the  beam  as  small  as  is  consistent  with  its 
rigidity. 

iii.  To  brifi^  the  coitre  of  gravity  of  the  beam  a  very  little  below  the  point 
of  support. 

Moreover,  since  friction  will  always  oppose  the  action  of  the  force  that 
tends  to  preponderate,  the  balance  will  be  rendered  more  delicate  by  diminish- 
ing friction.  To  secure  this  advantage  the  edges  from  which  the  beam  and 
scales  are  suspended  are  made  as  sharp  and  as  hard  as  possible,  and  the 
supports  on  which  they  rest  are  very  smooth  and  hard.  This  is  effected  by 
the  use  of  agate  knife-edges.  And,  further,  the  pointer  is  made  long,  since 
its  elongation  renders  a  given  deflection  more  perceptible  by  increasing  the 
arc  which  its  end  describes. 

The  sensitiveness  of  a  balance  is  expressed  by  the  ratio  of  the  smallest 
weight,  which  will  produce  a  measurable  deflection  of  the  pointer,  to  the  load. 

74.  Physical  and  chemical  balances. — Fig.  51  represents  one  of  the 
accurate  balances  ordinarily  used  for  chemical  analysis.     Its  sensitiveness  is 


Fig.  5 


such  that  when  charged  with  a  kilogramme  (1,000  grms.)  in  each  scale  an 
excess  of  a  tenth  of  a  milligramme  (jo^o  of  ^  bi™-)  i"  either  scale  produces 
a  very  perceptible  deflection  of  the  index. 


62  Gravitatio7t  and  Molecular  Attraction.  [74- 

In  order  to  protect  the  balance  from  air-currents,  dust,  and  moisture, 
it  is  always,  even  when  weighing,  surrounded  by  a  glass  case,  Avhose  front 
slides  up  and  down,  to  enable  the  operator  to  introduce  the  objects  to  be 
weighed.  Where  extreme  accuracy  is  desired  the  case  is  constructed  so 
that  the  space  may  be  exhausted,  and  the  weighing  made  in  vacuo. 

In  order  to  preserve  the  edge  of  the  fulcrum  as  much  as  possible,  the 
whole  beam,  BB,  with  its  fulcrum  K,  can  be  raised  from  the  support  on 
which  the  latter  rests  by  simply  turning  the  button  O  outside  the  case. 

The  horizontality  of  the  beam  is  determined  by  means  of  a  long  index, 
which  points  downwards  to  a  graduated  arc  near  the  foot  of  the  supporting 
pillar.  Lastly,  the  button  C  serves  to  alter  the  sensitiveness  of  the  balance  ; 
by  turning  it,  the  centre  of  gravity  of  the  beam  can  be  made  to  approach  or 
recede  from  the  fulcrum  (6g). 

75.  iviethod  of  double  weighing-. — Even  if  a  balance  be  not  perfectly 
accurate,  the  true  weight  of  a  body  may  still  be  determined  by  its  means.  To 
do  so,  the  body  to  be  weighed  is  placed  in  one  scale,  and  shot  or  sand  poured 
into  the  other  until  equilibrium  is  produced  ;  the  body  is  then  replaced 
by  known  weights  until  equilibrium  is  re-established.  The  sum  of  these 
weights  will  necessarily  be  equal  to  the  weight  of  the  body,  for,  acting  under 
precisely  the  same  circumstances,  both  have  produced  precisely  the  same 
effect. 

The  exact  weight  of  a  body  may  also  be  determined  by  placing  it  suc- 
cessively in  the  two  pans  of  a  balance,  and  then  deducing  its  true  weight. 

For  having  placed  in  one  pan  the  body  to  be  weighed,  whose  true  weight 
is  X,  and  in  the  other  the  weight  /,  required  to  laalance  it,  let  a  and  b  be 
the  arms  of  levers  corresponding  to  jir  and /.  Then  from  the  principle  of 
the  lever  (40)  we  have  ax=pb.  Similarly,  if/j  is  the  weight  when  the  body 
is  placed  in  the  other  pan,  then  bx  =  ap^.  Hence  abx'^  =  abpp^^  from  which 
x=^^ppy  This  method  was  invented  by  Pere  Amiot,  but  is  ordinarily 
known  as  Bordds  MetJwd. 

Jolly  made  use  of  a  very  delicate  balance  to  determine  the  constant  of 
gravity.  The  balance  was  placed  in  a  room  in  the  tower  of  the  University 
of  Munich,  and  to  each  of  the  scale-pans  was  attached,  by  a  wire  21  metres 
in  length,  a  second  scale-pan.  A  mass  of  mercury  of  5  kilogrammes  contained 
in  a  glass  vessel  was  first  counterpoised  in  the  upper  scale-pans  ;  it  was  then 
moved  to  the  lower  one,  and  it  was  found  necessary  to  add  31  "683  mgr.  to 
the  upper  pan  in  order  to  counterbalance  the  increase  in  attractiveness  due 
to  the  greater  force  in  the  lower  pan. 

Taking  the  radius  of  the  earth  at  Munich  at  6,365,722  metres,  the  number 
calculated  from  the  formula  in  (82)  is  33  mgr.  ;  a  sufficiently  close  result 
when  the  difficulties  of  the  experiments  are  taken  into  account. 

A  large  lead  sphere  was  then  placed  immediately  below  the  mass  in  the 
lower  pan,  and  produced  a  measurable  attraction.  From  the  attraction  thus 
produced  by  the  known  mass  of  the  lead  it  was  possible  to  deduce  the  mass 
and  the  mean  density  of  the  earth  (67)  ;  the  number  obtained  was  5-69. 
Similar  experiments'  have  been  made  by  Prof  Poynting  and  have  led  to  the 
same  number. 


-76] 


Laivs  of  Falling  Bodies. 


63 


CHAPTER    II. 


LAWS  OF   FALLING   BODIES.      INTENSITY   OF   TERRESTRIAL   GRAVITY. 
THE   PENDULUM. 


76.  Xiaws  of  falling-  bodies. — Since  a  body 
falls  to  the  ground  in  consequence  of  the  earth's 
attraction  on  eacJi  of  its  molecules,  it  follows  that, 
everything  else  being  the  same,  all  bodies,  great 
and  small,  light  and  heavy,  ought  to  fall  with  equal 
rapidity,  and  a  lump  of  sand  without  cohesion  should, 
during  its  fall,  retain  its  original  form  as  perfectly 
as  if  it  were  compact  stone.  The  fact  that  a  stone 
falls  more  rapidly  than  a  feather  is  due  solely  to  the 
unequal  resistances  opposed  by  the  air  to  the  descent 
of  these  bodies ;  in  a  •vacuum  all  bodies  fall  with 
eqtial  rapidity.  To  demonstrate  this  by  experiment 
a  glass  tube  about  two  yards  long  (fig.  52)  may  be 
taken,  having  one  of  its  ends  completely  closed, 
and  a  brass  cock  fixed  to  the  other.  After  having 
introduced  bodies  of  different  weights  and  densities 
(pieces  of  lead,  paper,  feather,  &c.)  into  the  tube, 
the  air  is  withdrawn  from  it  by  an  air-pump,, and 
the  cock  closed.  If  the  tube  be  now  suddenly  re- 
versed, all  the  bodies  will  fall  equally  quickly.  On 
introducing  a  little  air  and  again  inverting ^he  tube, 
the  lighter  bodies  become  slightly  retarded,  and 
this  retardation  increases  with  the  quantity  of  air 
introduced. 

The  resistance  opposed  by  the  air  to  falling 
bodies  is  especially  remarkable  in  the  case  of 
liquids.  The  Staubbach  in  Switzerland  is  a  good 
illustration ;  an  immense  mass  of  water  is  seen  fall- 
ing over  a  high  precipice,  but  before  reaching  the 
bottom  it  is  shattered  by  the  air  into  the  finest 
mist.  In  a  vacuum,  however,  liquids  fall  like 
solids  without  separation  of  their  molecules.  The 
ivater-hamme}'  illustrates  this  :  the  instrument  con- 
sists of  a  thick  glass  tube  about  a  foot  long,  half 
filled  with  water,  the  air  having  been  expelled  by 
ebullition  previous  to  closing  one  extremity  with  the 
blow-pipe.  When  such  a  tube  is  suddenly  inverted, 
the  water  falls  in  one  undivided  mass  against  the 


64 


Gravitation  and  Molecular  Attraction. 


[76- 


other  extremity  of  the  tube,  and  produces  a  sharp  dry  sound,  resembhng  that 

which  accompanies  the  shock  of  two  solid  bodies. 

From  Newton's  law  (66)  it 
follows  that  when  a  body  falls 
to  the  earth  the  force  of  attrac- 
tion which  causes  it  to  do 
so  increases  as  the  body  ap- 
proaches the  earth.  Unless  the 
height  from  which  the  body 
falls,  however,  be  very  great, 
this  increase  will  be  altogether 
inappreciable,  and  the  force  in 
question  may  be  considered  as 
constant  and  continuous.  If 
the  resistance  of  the  air  were 
removed,  therefore,  the  motion 
of  all  bodies  falling  to  the  earth 
would  be  uniformly  accelerated, 
and  would  ol^ey  the  laws  already 
explained  (49). 

TT.  Atwood's  macbine. — 
Several  instruments  have  been 
invented  for  illustrating  and 
experimentally  verifying  the 
laws  of  falling  bodies.  Galileo, 
who  discovered  these  laws  in 
the  early  part  of  the  seven- 
teenth century,  illustrated  them 
by  means  of  bodies  falling  down 
inclined  planes.  The  great 
object  of  all  such  instruments 
is  to  diminish  the  rapidity  of 
the  fall  of  bodies  without 
altering  the  character  of  their 
motion,  for  by  this  means 
their  motion  may  not  only  be 
better  observed,  but  it  will  be 
less  modified  by  the  resistance 
of  the  air  (48). 

The  most  convenient  instru- 
ment of  this  kind  is  that  invented 
by  Atwood  at  the  end  of  the 
last  century,  and  represented  in 
fig.  53.  It  consists  of  a  stout 
pillar  of  wood,  about  2|  yards 
high,  at  the  top  of  which  is  a 
brass  pulley,  whose  axle  rests  and 
turns  upon  four  other  wheels,  called  jtiction  wheels,  inasmuch  as  they  serve 
to  diminish  friction.     Two  equal  weights,  M  and  M',  are  attached  to  the  ex- 


Fig.  S3- 


-77]  Atlvood's  Machine.  '     65 

tremities  of  a  fine  silk  thread,  which  passes  round  the  pulley  ;  a  timepiece, 
H,  fixed  to  the  pillar,  is  regulated  by  a  seconds  pendulum,  P,  in  the  usual 
way  ;  that  is  to  say,  the  oscillations  of  the  pendulum  are  communicated  to  a 
ratchet,  whose  two  teeth,  as  seen  in  the  figure,  fit  into  those  of  the  ratchet 
wheel.  The  axle  of  this  wheel  gives  motion  to  the  seconds  hand  of  the  dial, 
and  also  to  an  eccentric  behind  the  dial,  as  shown  at  E  by  a  separate  figure. 
This  eccentric  plays  against  the  extremity  of  a  lever  D,  which  it  pushes 
until  the  latter  no  longer  supports  the  small  plate  i  ;  and  thus  the  weight  M, 
which  at  first  rested  on  this  plate,  is  suddenly  exposed  to  the  free  action  of 
gravity.  The  eccentric  is  so  constructed  that  the  little  plate  /  falls  precisely 
when  the  hand  of  the  dial  points  to  zero. 

The  weights  M  and  M',  being  equal,  hold  each  other  in  equilibrium  ; 
the  weight  M,  however,  is  made  to  descend  slowly  by  putting  a  small  bar  or 
overweight  jh  upon  it  ;  and,  to  measure  the  spaces  which  it  describes,  the  rod 
or  scale  Q  is  divided  into  feet  and  inches,  commencing  from  the  plate  i. 
To  complete  the  instrument  there  are  a  number  of  plates,  A,  A',  C,  <Z\  and 
a  number  of  rings,  B,  B',  which  may  be  fixed  by  screws  at  any  part  of  the 
scale.  The  plates  arrest  the  descending  weight  M,  the  rings  only  arrest  the 
bar  or  overweight  ;;/,  which  was  the  cause  of  motion,  so  that  after  passing 
through  them,  the  weight  M,  in  consequence  of  its  inertia,  will  move  on 
uniformly  with  the  velocity  it  had  acquired  on  reaching  the  ring.  The 
several  parts  of  the  apparatus  being  described,  a  few  words  will  suffice  to 
explain  the  method  of  experimenting. 

Let  the  hand  of  the  dial  be  placed  behind  the  zero  point,  the  lever  D 
adjusted  to  support  the  plate  /,  on  which  the  weight  M  with  its  o\erweight 
HI  rests,  and  the  pendulum  put  in  motion.  As  soon  as  the  hand  of  the  dial 
points  to  zero  the  plate  z  will  fall,  the  weights  M  and  w  will  descend,  and  by 
a  little  attention  and  a  few  trials  it  will  be  easy  to  place  a  plate  A  so  that  M 
may  reach  it  exactly  as  the  dial  indicates  the  expiration  of  one  second.  To 
make  a  second  experiment  let  the  weights  M  and  ;;/,  the  plate  /,  and  the 
lever  D  be  placed  as  at  first ;  remove  the  plate  A,  and  in  its  place  put  a  ring, 
B,  so  as  to  arrest  the  overweight  m  just  when  the  weight  M  would  have 
reached  A  ;  on  putting  the  pendulum  in  motion  again  it  will  be  easy,  after  a 
few  trials,  to  put  a  plate,  C,  so  that  the  weight  M  may  fall  upon  it  precisely 
when  the  hands  of  the  dial  point  to  two  seconds.  Since  the  overweight  Jii 
in  this  experiment  was  arrested  by  the  ring  B  at  the  expiration  of  one  second, 
the  space  BC  was  described  by  M  in  one  second  purely  in  virtue  of  its  own 
inertia,  and  consequently  by  (24)  BC  will  indicate  the  velocity  of  the  falling- 
mass  at  the  expiration  of  one  second. 

Proceeding  in  the  same  manner  as  before,  let  a  third  experiment  be  made 
in  order  to  ascertain  the  point  B'  at  which  the  weights  M  and  in  arrive  after 
the  lapse  of  two  seconds,  and  putting  a  ring  at  B',  ascertain  by  a  fourth 
experiment  the  point  C  at  which  M  arrives  alone,  three  seconds  after  the 
descent  commenced  ;  WC  will  then  express  the  velocity  acquired  after  a 
descent  of  two  seconds.  In  a  similar  manner,  by  a  fifth  and  sixth  experiment, 
we  may  determine  the  space  OB"  described  in  three  seconds,  and  the  velo- 
city B"C"  acquired  during  those  three  seconds,  and  so  on  ;  we  shall  find 
that  B'C  is  twice,  and  B''C"  three  times  as  great  as  BC — in  other  words, 
that  the  velocities  BC,  B'C,  B"C"  increase  in  the  same  proportion  as  the 

F 


66  Gravitation  and  Molecular  Attraction.  [77- 

times  (i,  2,  3,  .  .  .  seconds)  employed  in  their  acquirement.  By  the  defi- 
nition (49),  therefore,  the  motion  is  uniformly  accelerated.  The  same  ex- 
periments will  also  serve  to  verify  and  illustrate  the  four  laws  of  uniformly 
accelerated  motion  as  enunciated  in  (49).  For  example,  the  spaces  OB, 
OB',  OB",  ....  described  from  a  state  of  rest  in  i,  2,  3,  ...  .  seconds, 
will  be  found  to  be  proportional  to  the  numbers  i,  4,  9  .  .  .  ;  that  is  to  say, 
to  the  squares  of  those  numbers  of  seconds,  as  stated  in  the  third  law. 

Lastly,  if  the  overweight  in  be  changed,  the  acceleration  or  velocity  BC 
acquired  per  second  will  also  be  changed,  and  we  may  easily  verify  the 
assertion  in  (27),  that  force  is  proportional  to  the  product  of  the  mass  moved, 
into  the  acceleration  produced  in  a  given  time.  For  instance,  assuming  the 
pulley  to  be  so  light  that  its  inertia  can  be  neglected,  then  if  m  weighed  half 
an  ounce,  and  M  and  M'  each  15I  ounces,  the  acceleration  BC  would  be  found 
to  be  six  inches  ;  whilst  if  m  weighed  one  ounce,  and  M  and  M'  each  63.3 
ounces,  the  acceleration  BC  would  be  found  to  be  three  inches. 

Now  in  these  cases  the  forces  producing  motion,  that  is  the  overweights, 
are  in  the  ratio  of  i  :  2  ;  while  the  products  of  the  masses  and  the  accelera- 
tions are  in  the  ratio  of  (|+  15I -1-  15I)  x  6  to  (i  +  63^  +  63^)  x  3  ;  that  is,  they 
are  also  in  the  ratio  i  :  2.  Now  the  same  result  is  obtained  in  whatever 
way  the  magnitudes  of  ;/;,  M,  and  M' are  varied,  and  consequently  in  all 
cases  the  ratio  of  the  forces  producing  motion  equals  the  ratio  of  the  mo- 
menta generated. 

78.  nXorin's  apparatus. — The  principle  of  this  apparatus,  the  original 
idea  of  which  is  due  to  General  Poncelet,  is  to  make  the  falling  body  trace 
its  own  path.  Fig.  54  gives  a  view  of  the  whole  apparatus,  and  fig.  55 
gives  the  details.  The  apparatus  consists  of  a  wooden  framework,  about 
7  feet  high,  which  holds  in  a  vertical  position  a  very  light  wooden  cylinder, 
M,  which  can  turn  freely  about  its  axis.  This  cylinder  is  coated  with 
paper  divided  into  squares  by  equidistant  horizontal  and  vertical  lines.  The 
latter  measure  the  path  traversed  by  the  body  falling  along  the  cylinder, 
while  the  horizontal  lines  are  intended  to  divide  the  duration  of  the  fall  into 
equal  parts. 

The  falling  body  is  a  mass  of  iron,  P,  provided  with  a  pencil  which  is 
pressed  against  the  paper  by  a  small  spring.  The  iron  is  guided  in  its  fall 
by  two  light  iron  wires  which  pass  through  guide-holes  on  the  two  sides 
The  top  of  this  mass  is  provided  with  a  tipper  which  catches  against  the  end 
of  a  bent  lever,  AC.  This  being  pulled  by  the  string  K  attached  at  A,  the 
weight  falls.  If  the  cylinder  M  were  fixed,  the  pencil  would  trace  a  straight 
line  on  it  ;  but  if  the  cylinder  moves  uniformly,  the  pencil  traces  the  line 
w;/,  which  serves  to  deduce  the  law  of  the  fall. 

The  cylinder  is  rotated  by  means  of  a  weight,  Q,  suspended  to  a  cord 
which  passes  round  the  axle  G.  At  the  end  of  this  is  a  toothed  wheel,  r, 
which  turns  two  endless  screws,  a  and  b,  one  of  which  turns  the  cylinder, 
and  the  other  two  vanes,  .rand  x'  (fig.  55).  At  the  other  end  is  a  ratchet 
wheel,  in  which  fits  the  end  of  a  lever,  B  ;  by  pulling  at  a  cord  fixed  to  the 
other  end  of  B,  the  wheel  is  liberated,  the  weight  Q  descends,  and  the  whole 
system  begins  to  turn.  The  motion  is  at  first  accelerated,  but  as  the  air 
offers  a  resistance  to  the  vanes  (48),  which  increases  as  the  rotation  becomes 
more  rapid,  the  resistance  finally  equals  the  acceleration  which  gravity  tends 


-78] 


Marines  Apparatus. 


67 


to  impart.  From  this  time  the  motion  becomes  uniform.  This  is  the  case 
■when  the  weight  Q  has  traversed  about  three-quarters  of  its  course  ;  at  this 
moment  the  weight  P  is  detached  by  pulling  the  cord  K,  and  the  pencil  then 
traces  the  curve  »ui. 

If,  by  means  of  this  curve,  we  examine  the  double  motion  of  the  pencil 
on  the  small  squares  which  divide  the  paper,  we  see  that,  for  displacements 


I-^'g-  55- 


f  ig-  54- 


I,  2,  3  ....  in  a  horizontal  direction,  the  displacements  are  i,  4,  9  .  .  .  . 
in  a  vertical  direction.  This  shows  that  the  paths  traversed  in  the  direction 
of  the  fall  are  directly  as  the  squares  of  the  lines  in  the  direction  of  the 
rotation,  which  verifies  the  second  law  of  falling  bodies. 

From  the  relation  which  exists  between  the  two  dimensions  of  the  curve 
w«,  it  is  concluded  that  this  curve  is  2, parabola. 

Y  2 


68 


Gravitation  and  Molecular  Attraction. 


[79- 


79.  The  lengrtb  of  tlie  compound  pendulum. — The  formula  deduced  in 
article  (55),  and  the  conclusions  which  follow  therefrom,  refer  to  the  case  of  the 
simple  or  mathematical  pendulum  ;  that  is,  to  a  single  heavy  point  suspended 
by  a  thread  without  weight.  Such  a  pendulum  has  only  an  imaginary 
existence,  and  any  pendulum  which  does  not  realise  these  conditions  is 
called  a  compound  or  physical  pendulum.  The  laws  for  the  time  of  vibra- 
tion of  a  compound  pendulum  are  the  same  as  those  which  regulate  the 
motion  of  the  simple  pendulum,  though  it  will  be  necessary  to  define  ac- 
curately what  is  meant  by  the  letigth  of  such  a  pendulum.  A  compound 
pendulum  being  formed  of  a  heavy  rod  terminated  by  a  greater  or  less  mass, 
it  follows  that  the  several  material  points  of  the  whole  system  will 
strive  to  perform  their  oscillations  in  different  times,  their  distances 
from  the  axis  of  suspension  being  different,  and  the  more  distant 
points  requiring  a  longer  time  to  complete  an  oscillation.  From 
this,  and  from  the  fact  that  being  points  of  the  same  body  they 
must  all  oscillate  together,  it  follows  that  the  motion  of  the  points 
near  the  axis  of  suspension  will  be  retarded,  whilst  that  of  the  more 
distant  points  will  be  accelerated,  and  between  the  two  extremities 
there  will  necessarily  be  a  series  of  points  whose  motion  will  be 
neither  accelerated  nor  retarded,  but  which  will  oscillate  precisely 
as  if  they  were  perfectly  free  and  unconnected  with  the  other  points 
of  the  system.  These  points,  being  equidistant  from  the  axis  of 
suspension,  constitute  a  parallel  axis  known  as  the  axis  of  oscil- 
lation ;  and  it  is  to  the  distance  between  these  two  axes  that  the 
term  length  of  the  coinpoitnd  pendulum  is  applied  :  we  may  say, 
therefore,  that  the  leitgth  of  a  compound  pendulum  is  that  of  the 
simple  penduhnn  which  would  describe  its  oscillations  in  the  same 
time. 

Huyghens,  the  celebrated  Dutch  physicist,  discovered  that  the 
axes  of  suspension  and  oscillation  are  mutually  convertible  ;  that 
is  to  say,  the  time  of  oscillation  will  remain  unaltered  when  the 
pendulum  is  suspended  from  its  axis  of  oscillation.  This  enables  us 
to  determine  experimentally  the  length  of  the  compound  pendulum. 
P"or  this  purpose  the  reversible  pendulum  devised  by  Bohnenberger 
and  Kater  may  be  used.  One  form  of  this  (fig.  56)  is  a  rod  with 
the  knife-edges  a  and  b  turned  towards  each  other.  W  and  V  are 
lens-shaped  masses  the  relative  positions  of  which  may  be  varied. 
By  a  series  of  trials  a  position  can  be  found  such  that  the  number 
of  oscillations  of  the  pendulum  in  a  given  time  is  the  same  whether 
it  oscillates  about  the  axis  a  or  the  axis  b.  This  being  so,  the  dis- 
tance ab  represents  the  length  /  of  a  simple  pendulum  which  has 
the  same  time  of  oscillation.  From  the  value  of  /,  thus  obtained, 
it  is  easy  to  determine  the  length  of  the  seconds  pendulum. 
The  length  of  the  seconds  pendulum — that  is  to  say,  of  the  pendulum 
which  makes  one  oscillation  in  a  second — varies,  of  course,  with  the 
force  of  gravity.  The  following  table  gives  its  value  at  the  sea-level  at 
\-arious  places  as  determined  by  observation.  The  accelerative  effect  of 
gravity  at  these  places,  according  to  formula  (55),  is  obtained  in  feet  and 


Fig.  56. 


-80]  Verification  of  the  Laws  of  the  Pendulum.  69 

metres,  by  multiplying  the  length  of  the  seconds  pendulum,  reduced  to  feet 
and  metres  respectively,  by  the  square  of  3-14159  or  9-87. 


" 

Acceleration  of  Gravity  in         | 

Latitude 

Length  of  Pen- 
dulum in  inches 

Feet 

Metres 

Hammerfest    . 

70°.4o'N. 

39-1948 

32-2364 

9-8258 

Aberdeen 

57 

9 

39-1550 

32-2066 

9-8164 

Konigsberg 

54 

42 

39-1507 

32-2002 

9-8142 

Manchester 

53 

29 

39-1466 

32-1968 

9-8134 

Dublin     . 

53 

21 

39-1461 

32-1968 

9-8132 

Berlin       . 

52 

30 

39-1439 

32-1945 

9-8124 

Greenwich 

51 

29 

39-1398 

32-1912 

9-8115 

Paris 

48 

50 

39-1285 

32-1819 

9-8039 

Rome 

41 

54 

39-1145 

32-1712 

9-8053 

New  York 

40 

43 

39-1012 

32-1594 

9-8019 

Washington 

38 

54 

39-0968 

32-1558 

9-8006 

Madras    . 

13 

4 

39-0268 

32-0992 

9-7836 

Ascension 

7 

56 

39-0242 

32-0939 

9-7817 

St.  Thomas 

0 

25 

39-0207 

32-0957 

9-7826 

Cape  of  Good  Hope 

2,1> 

55  s. 

39-0780 

32-1404 

9-7962 

Consequently,  \g  or  the  space  described  in  the  first  second  of  its  motion 
by  a  body  falling  in  vacuo  from  a  state  of  rest  (49)  is 

16-0478  feet  or  4-891  metres  at  St.  Thomas, 
16-0956  „  „  4-905  „  at  London,  and 
16-1182     „     „  4-913       „       at  Hammerfest. 

In  all  calculations  which  are  merely  used  for  the  sake  of  illustration  we 
may  take  32  feet,  or  9-8  metres,  as  the  accelerative  effect  due  to  gravity. 

From  observations  of  this  kind,  after  applying  the  necessary  corrections, 
and  taking  into  account  the  effect  of  rotation  (82),  the  form  of  the  earth  can 
be  deduced. 

80.  Verification  of  the  laws  of  the  pendulum. — In  order  to  verify  the 
laws  of  the  simple  pendulum  (55)  we  are  compelled  to  employ  a  compound 
one,  whose  construction  differs  as  little  as  possible  from  that  of  the  former. 
For  this  purpose  a  small  sphere  of  a  very  dense  substance,  such  as  lead  or 
platinum,  is  suspended  from  a  fixed  point  by  means  of  a  very  fine  metal  wire. 
A  pendulum  thus  formed  oscillates  almost  like  a  simple  pendulum,  whose 
length  is  equal  to  the  distance  of  the  centre  of  the  sphere  from  the  point  of 
suspension. 

In  order  to  verify  the  isochronism  of  small  oscillations,  it  is  merely  necessary 
to  count  the  number  of  oscillations  made  in  equal  times,  as  the  amplitudes  of 
these  oscillations  diminish  from  3  degrees  to  a  fraction  of  a  degree  ;  this 
number  is  found  to  be  constant. 

That  the  time  of  vibration  is  proportional  to  the  square  root  of  the  length 
is  verified  by  causing  pendulums,  whose  lengths  are  as  the  numbers  i,  4, 
9,  ....  to  oscillate  simultaneously.  The  corresponding  numbers  of  oscil- 
lations in  a  given  time  are  then  found  to  be  proportional  to  the  fractions 


/O 


Gravitation  and  UTo/eadar  Attraction. 


[80- 


I,  i,  f,  &c.,  ....  which  shows  that  the  tunes  of  oscillation  increase  as  the 
numbers  i,  2,  3,  .  .  .  .  &c. 

By  taking  several  pendulums  of  exactly  ecjual  length,  B,  C,  D  (fig.  57), 
but  with  spheres  of  different  substances — lead, 
copper,  ivory — it  is  found  that,  neglecting  the 
resistance  of  the  air,  these  pendulums  oscillate 
in  equal  times,  thereby  showing  that  the  acce- 
lerative  effect  of  gravity  on  all  bodies  is  the 
same  at  the  same  place. 

By  means  of  an  arrangement  resembling  the 
above,  Newton  verified  the  fact  that  the  masses 
of  bodies  are  determined  by  the  balance  ;  which, 
it  will  be  remarked,  lies  at  the  foundation  of 
the  measure  of  force  (28).  For  it  will  be  seen 
on  comparing  (54)  and  (55)  with  (49)  that  the 
law  of  the  time  of  a  small  oscillation  is  obtained 
on  the  supposition  that  the  force  of  gravity  on 
all  bodies  is  represented  by  M.g,  in  which  M  is 
determined  by  the  balance.  In  order  to  verify 
this,  he  had  made  two  round  equal  wooden 
boxes  ;  he  filled  one  with  wood,  and  as  nearly 
as  possible  in  the  centre  of  oscillation  of  the 
other  he  placed  an  ecjual  weight  of  gold.  He 
then  suspended  the  boxes  by  threads  eleven 
feet  long,  so  that  they  formed  pendulums  exactly 
equal  so  far  as  weight,  figure,  and  resistance  of 
the  air  were  concerned.  Their  oscillations  were 
performed  in  exactly  the  same  time.  The  same 
results  were  obtained  when  other  substances 
were  used,  such  as  silver,  lead,  glass,  sand,  salt,  wood,  water,  corn.  Now  all 
these  bodies  had  equal  weights,  and  being  contained  in  the  same  boxes  they 
experienced  the  same  resistance  by  the  air,  and  if  the  inference,  that  therefore 
they  had  equal  masses,  had  been  erroneous,  by  as  little  as  the  one-thou- 
sandth part  of  the  whole,  the  experiment  would  have  detected  it. 

81.  Application  of  the  pendulum  to  Clocks. — The  regulation  of  the 
motion  of  clocks  is  effected  by  means  of  pendulums,  that  of  watches  by 
balaiice-springs.  Pendulums  were  first  applied  to  this  purpose  by  Huyghens 
in  1658,  and  in  the  same  year  Hooke  applied  a  spiral  spring  to  the  balance 
of  a  watch.  The  manner  of  employing  the  pendulum  is  shown  in  fig.  58. 
The  pendulum  rod  passing  between  the  prongs  of  a  fork  a  communicates  its 
motion  to  a  rod  i^,  which  oscillates  on  a  horizontal  axis  0.  To  this  axis  is 
fixed  a  piece  ;;/;;,  called  an  escapei/ietit  or  crutch.,  terminated  by  two  projec- 
tions or  pallets.,  which  work  alternately  with  the  teeth  of  the  escapemeiif 
ivheel  R.  This  wheel  being  acted  on  by  the  weight  tends  to  move  con- 
tinuously, let  us  say,  in  the  direction  indicated  by  the  arrow-head.  Now,  if 
the  pendulum  is  at  rest,  the  wheel  is  held  at  rest  by  the  pallet  w,  and  with  it 
the  whole  of  the  clockwork  and  the  weight.  If,  however,  the  pendulum 
moves  and  takes  the  position  shown  by  the  dotted  line,  vi  is  raised,  the 
wheel  escapes  from  the  confinement  in  which  it  \\as  held  by  the  pallet,  the 


Fig.  57- 


82] 


Causes  which  modify   Terrestrial  Graviiatioii. 


weight  descends,  and  causes  the  wheel  to  turn  until  its  motion  is  arrested  by 
the  other  pallet  ;/  ;  which,  in  consequence  of  the  motion  of  the  pendulum, 
will  be  brought  into  contact  with  another  tooth  of  the  escapement  wheel.  In 
this  manner  the  descent  of  the  weight  is  alternately  permitted  and  arrested 
— or,  in  a  word,  regulated— hy  the  pendulum.  By 
means  of  a  proper  train  of  wheelwork  the  motion  of 
the  escapement  is  communicated  to  the  hands  of  the 
clock  :  and  consecjuently  their  motion,  also,  is  regu- 
lated by  the  pendulum.  In  watches  the  watch  spring- 
plays  the  part  of  the  weight  in  clocks. 

The  pendulum  has  also  been  used  for  measuring 
great  velocities.  A  large  wooden  box  filled  with  sand 
and  weighing  from  3  to  5  tons  is  coated  with  iron  ; 
against  this  arrangement,  which  is  known  as  a  ballistic 
pendulum^  a  shot  is  fired,  and  the  deflection  thereby 
produced  is  observed.  From  the  laws  of  the  impact 
of  inelastic  bodies,  and  from  those  of  the  pendulum, 
the  velocity  of  the  ball  may  be  calculated  from  the 
amount  of  this  deflection. 

The  gun  may  also  be  fastened  to  a  pendulum  ar- 
rangement ;  and,  when  fired,  the  reaction  causes  an 
angular  velocity,from  which  the  pressure  of  the  enclosed 
gases  can  be  deduced,  and  therefrom  the  initial  velocity 
of  the  shot, 

82.  Causes  'whicb  modify  tbe  intensity  of 
terrestrial  gravitation. — The  intensity  of  the  force 
of  gravity — that  is,  the  value  of  ^ — is  not  the  same  in 
all  parts  of  the  earth.  It  is  modified  by  several  causes, 
of  which  the  form  of  the  earth  and  its  rotation  are  the 
most  important. 

i.  The  attraction  which  the  earth  exerts  upon  a 
body  at  its  surface  is  the  sum  of  the  partial  attractions 
w  hich  each  part  of  the  earth  exerts  upon  that  body, 
and  the  resultant  of  all  these  attractions  may  be  considered  to  act  from  a 
single  point — the  centre.  Hence,  if  the  earth  were  a  perfect  sphere,  a  given 
body  would  be  equally  attracted  at  any  part  of  the  earth's  surface.  The 
attraction  would,  however,  vaiy  with  the  height  above  the  surface.  For  small 
alterations  of  level  the  differences  would  be  inappreciable  ;  but  for  greater 
heights  and  in  accurate  measurements  observations  of  the  value  of  g  must 
be  reduced  to  the  sea-level.  The  attraction  of  gravitation  being  inversel)' 
as   the   square    of    the    distance    from    the    centre    (66),    we    shall    have 

g  :  g^  =        :  ^— — -~  where  g  is  the  value  of  the  acceleration  of  gravity  at 
K'     (R  + /i) 

the  sea  level,  g^  its  value  at  any  height  //,  and  R  is  the  radius  of  the  earth. 

From  this,  seeing  that  h  is  very  small  compared  with  R,  and  that  therefore 

its  square  may  be  neglected,  we  get  by  simple  algebraical  transformation 

?  p-R 


Fig.  5S. 


g. 


72  Gravitation  and  Molecular  Attraction.  [82- 

But  even  at  the  sea-level  the  force  of  gravity  varies  in  different  parts  in 
consequence  of  the  form  of  the  earth.  The  earth  is  not  a  true  sphere,  but 
an  ellipsoid,  the  major  axis  of  which  is  12,754,796  metres,  and  the  minor 
12,712,160  metres.  The  distance,  therefore,  from  the  centre  being  greater  at 
the  Equator  than  at  the  Poles,  and  as  the  attraction  on  a  body  is  inversely 
as  the  square  of  these  distances,  calculation  shows  that  the  attraction  due  to 
this  cause  is  gi,,  greater  at  the  Poles  than  at  the  Equator.  This  is  what 
would  be  true  if,  other  things  being  the  same,  the  earth  were  at  rest. 

ii.  In  consequence  of  the  earth's  rotation,  the  force  of  gravity  is  further 
modified.  If  we  imagine  a  body  relatively  at  rest  on  the  Equator,  it  really 
shares  the  earth's  rotation,  and  describes,  in  the  course  of  one  day,  a  circle 
whose  centre  and  radius  are  the  centre  and  radius  of  the  earth.  Now,  since 
a  body  in  motion  tends  by  reason  of  its  inertia  to  move  in  a  straight  line,  it 
follo\\s  that  to  make  it  move  in  a  circle,  a  force  must  be  employed  at  each 
instant  to  deflect  it  from  the  tangent  (53).  Consequently,  a  certain  portion 
of  the  earth's  attraction  must  be  employed  in  keeping  the  above  body  on  the 
surface  of  the  earth,  and  only  the  remainder  is  sensible  as  weight  or  accele- 
rating force.  It  appears  from  calculation  that  at  the  Equator  the  ^'Ca.  part 
of  the  earth's  attraction  on  any  body  is  thus  employed,  so  that  the  magnitude 
of^at  the  Equator  is  less  by  the  jigth  part  of  what  it  would  be  were  the 
earth  at  rest. 

iii.  As  the  body  goes  nearer  the  Poles  the  force  of  gravity  is  less  and  less 
diminished  by  the  effect  of  centrifugal  force.  For  in  any  given  latitude  it 
will  describe  a  circle  coinciding  with  the  parallel  of  latitude  in  which  it  is 
placed  ;  but  as  the  radii  of  these  circles  diminish, 
so  does  the  centrifugal  force  until  the  Pole,  where 
the  radius  is  null.  Further,  on  the  Equator  the 
centrifugal  force  is  directly  opposed  to  gravitation  ; 
in  any  other  latitude  only  a  component  of  the  whole 
force  is  thus  employed.  This  is  seen  in  fig.  59,  in 
which  PP'  represents  the  axis  of  rotation  of  the 
earth,  and  EE'  the  Equator.  At  any  given  point 
E  on  the  Equator  the  centrifugal  force  is  directed 
along  CE,  and  acts  wholly  in  diminishing  the 
intensity  of  gravitation  ;  but  on  any  other  point,  a, 
nearer  the  Pole,  the  centrifugal  force  acting  on  a 
right  line  ab  at  right  angles  to  the  axis  PP',  while  gravity  acts  along  c?C, 
gravity  is  no  longer  directly  diminished  by  centrifugal  force,  but  only  by  its 
component  ad.,  which  is  less  the  nearer  a  is  to  the  Pole. 

The  combined  effect  of  these  two  causes — the  flattening  of  the  earth  at 
the  Poles,  and  the  centrifugal  force — is  to  make  the  attraction  of  gravitation 
at  the  Equator  less  by  about  the  jjo^d  part  of  its  value  at  the  Poles. 


-84]  Cohesion.  7S 


CHAPTER    III. 

MOLECULAR    FORCES. 

83.  ITature  of  molecular  forces. — The  various  phenomena  which  bodies 
present  show  that  their  molecules  are  under  the  influence  of  two  contrary 
forces,  one  of  which  tends  to  bring  them  together,  and  the  other  to  separate 
them  from  each  other.  The  fii'st  force,  which  is  called  molecular  attraction., 
varies  in  one  and  the  same  body  with  the  distance  only.  The  second  force 
is  due  to  the  vis  viva.,  or  moving  force,  which  the  molecules  possess.  It  is 
the  mutual  relation  between  these  forces,  the  preponderance  of  the  one  or  the 
other,  which  determines  the  molecular  state  of  a  body  (4) — whether  it  be 
solid,  liquid,  or  gaseous. 

Molecular  attraction  is  only  exerted  at  infinitely  small  distances.  Its 
effect  is  inappreciable  when  the  distance  between  the  molecules  becomes 
appreciable. 

According  to  the  manner  in  which  it  is  regarded,  molecular  attraction  is 
designated  by  the  terms  cohesion,  affinity,  or  adhesion. 

84.  Cohesion. — Cohesion  is  the  force  which  unites  adjacent  molecules  of 
the  same  nature  ;  for  example,  two  molecules  of  water,  or  two  molecules  of 
iron.  Cohesion  is  strongly  exerted  in  solids,  less  strongly  in  liquids,  and 
scarcely  at  all  in  gases.  Its  strength  decreases  as  the  temperature  mcreases, 
because  then  the  vis  viva  of  the  molecules  increases.  Hence  it  is  that  when 
solid  bodies  are  heated  they  first  liquefy,  and  are  ultimately  converted  into 
the  gaseous  state,  provided  that  heat  produces  in  them  no  chemical  change. 

Cohesion  varies  not  only  with  the  nature  of  bodies,  but  also  with  the 
arrangement  of  their  molecules  ;  thus,  the  difference  between  tempered  and 
untempered  steel  (94)  is  due  to  a  difference  in  the  molecular  arrangement 
produced  by  tempering.  Many  of  the  properties  of  bodies,  such  as 
tenacity,  hardness,  and  ductility,  are  due  to  the  modifications  which  this 
force  undergoes. 

In  large  masses  of  liquids  the  force  of  gravity  overcomes  that  of  cohesion. 
Hence  liquids  acted  upon  by  the  former  force  have  no  special  shape  ;  they 
take  that  of  the  vessel  in  which  they  are  contained.  But  in  smaller  masses 
cohesion  gets  the  upper  hand,  and  liquids  assume  then  the  spheroidal  form. 
This  is  seen  in  the  drops  of  dew  on  the  leaves  of  plants.  It  is  also  seen  when 
a  liquid  is  placed  on  a  solid  which  it  does  not  moisten  ;  as,  for  example, 
mercury  upon  wood.  The  experiment  may  also  be  made  with  water,  by 
sprinkling  upon  the  surface  of  the  wood  some  light  powder,  such  as  lyco- 
podium  or  lampblack,  and  then  dropping  a  little  water  on  it.  The  following 
experiment  is  an  illustration  of  the  force  of  cohesion  causing  a  liquid  to  assume 
the  spheroidal  form.     A  saturated  solution  of  zinc  sulphate  is  placed  in  a 


74  Gravitation  and  Molecular  Attraction.  [84- 

narrow-necked  bottle  (fig.  60),  and  a  few  drops  of  bisulphide  of  carbon,  coloured 
with  iodine,  made  to  float  on  the  surface.  If  pure  water  be  now  carefiilly  added, 
so  as  to  rest  on  the  surface  of  the  sulphate  of  zinc  solution> 
the  bisulphide  collects  in  the  form  of  a  flattened  spheroid, 
which  presents  the  appearance  of  blown  coloured  glass,  and 
is  larger  than  the  neck  of  the  bottle,  provided  a  sufficient 
quantity  has  been  taken. 
'||  1^     j  The  force  of  cohesion  of  liquids  may  be  illustrated  and 

Ij    '<^p'     I  qx^vl  measured  as  follows.    A  plane,  perfectly  smooth  disc,  D 

l|  (fig.  61),  is  suspended  horizontally  to  one  scale-pan  ^  of  a 

delicate   balance,  and    is  accurately  equipoised.     A  some- 
what wide  vessel  of  liquid  is  placed  below,  and  the  position 
!•  ig.  DO.  ^^  ^^  ^jg^  regulated  by  means  of  the  sliding  screw  S  until 

it  just  touches  the  liquid.  Weights  are  then  carefully  added  to  the  other 
scale-pan  until  the  disc  is  detached  from  the  liquid.  In  this  way  it  has  been 
found  that  the  weights  required  to  detach  the  disc  vary  with  the  nature  of 
the  liquid  ;  with  a  disc  of  118  mm.  diameter  the  numbers  for  waters,  alcohol, 
and  turpentine  were  59-4,  31,  and  34  grammes  respectively. 

The  results  were  the  same  whether  the  disc  was  of  glass,  of  copper,  or  of 
other  metals,  and  they  thus  only  depend  on  the  nature  of  the  Uquid.  It  is 
a  measure  of  the  cohesion  of  the  liquid,  for  a  layer  remains  adhering  to  the 
disc  ;  hence  the  weight  on  the  other  side  does  not  separate  the  disc  from 
the  liquid,  but  separates  the  particles  of  liquid  from  each  other. 

85.  Affinity. — Chemical  affinity,  or  ciionical  attraction,  is  the  force  which 
is  exerted  between  molecules  not  of  the  same  kind.  Thus,  in  water,  which 
is  composed  of  oxygen  and  hydrogen,  it  is  affinity  which  unites  these  ele- 
ments, but  it  is  cohesion  which  binds  together  two  molecules  of  water.  In 
compound  bodies  cohesion  and  affinity  operate  simultaneously,  while  in 
simple  bodies  or  elements  cohesion  has  alone  to  be  considered. 

To  affinity  are  due  all  the  phenomena  of  combustion,  and  of  chemical 
combination  and  decomposition. 

Those  causes  which  tend  to  weaken  cohesion  are  most  favourable  to  affinity; 
for  instance,  the  action  of  affinity  between  substances  is  facilitated  by  their 
division,  and  still  more  by  reducing  them  to  a  liquid  or  gaseous  state.  It  is 
most  powerfully  exerted  by  a  body  in  its  nascent  state — that  is,  the  state  in 
which  the  body  exists  at  the  moment  it  is  disengaged  from  a  compound  ;  the 
l)ody  is  then  free  and  ready  to  obey  the  feeblest  affinity.  An  increase  of 
temperature  modifies  affinity  differently  under  different  circumstances.  In 
some  cases  by  diminishing  cohesion,  and  increasing  the  distance  between 
the  molecules,  heat  promotes  combination.  Sulphur  and  oxygen,  which  at 
the  ordinary  temperature  are  without  action  on  each  other,  combine  to  form 
sulphur  dioxide  when  the  temperature  is  raised  :  in  other  cases  heat  tends 
to  decompose  compounds  by  imparting  to  their  elements  an  unequal  expan- 
sibility. Thus  it  is  that  many  metallic  oxides — as,  for  example,  those  of  silver 
and  mercury — are  decomposed,  by  the  action  of  heat,  into  gas  and  metal. 

86.  Adhesion. — The  molecular  attraction  exerted  between  \\\fisin-facesoi 
bodies  in  contact  is  called  adhesion. 

i.  Adhesion  takes  place  between  solids.  If  two  leaden  bullets  are  cut 
with  a  penknife  so  as  to  form  two  equal  and  brightly  polished  surfaces,  and 


-86]  Adhesion.  75 

the  two  faces  are  pressed  and  turned  against  each  other,  until  the^-  are  in  the 
closest  contact,  they  adhere  so  strongly  as  to  require  a  force  of  more  than 
100  grammes  to  separate  them.  The  same  experiment  may  be  made  with 
two  equal  pieces  of  glass  which  are  polished  and  made  perfectly  plane. 
When  they  are  pressed  one  against  the  other,  the  adhesion  is  so  powerful 
that  they  cannot  be  separated  without  breaking.  As  the  experiment  succeeds 
in  vacuo,  it  cannot  be  due  to  atmospheric  pressure,  but  must  be  attributed  to 
a  reciprocal  action  between  the  two  surfaces.  The  attraction  also  increases 
as  the  contact  is  prolonged,  and  is  greater  in  proportion  as  the  contact  is 
closer. 

In  the  operation  of  glueing  the  adhesion  is  complete,  for  the  pores  and 
crevices  of  the  fresh  surfaces  being  filled  with  liquid  glue,  so  that  there  is  no 
empty  space  on  drying,  wood  and  glue  form  one 
compact  whole.  In  some  cases  the  adhesion  of 
cemented  objects  is  so  powerful  that  the  mass 
breaks  more  readily  at  other  places  than  at  the 
cemented  parts.  Both  in  glueing  and  cementing 
the  layer  should  be  thin. 

Soldering  is  due  to  cohesion  ;  the  surface  of 
the  metals  must  be  quite  clean,  which  is  effected 
by  removing  the  layer  of  oxide,  with  which  they 
are  usually  coated,  by  acid  or  by  borax.  The 
solder  when  it  solidifies  only  adheres  to  clean 
metal  surfaces. 

There  is  no  real  difference  between  adhesion 
and  cohesion  ;  thus  when  two  freshly  cut  surfaces 
of  caoutchouc  are  pressed  together,  they  adhere 
with  considerable  force,  and  ultimately  form  one 
compact  solid  mass. 

ii.  Adhesion  also  takes  place  between  solids 
and  liquids.  If  we  dip  a  glass  rod  into  water,  on 
withdrawing  it  a  drop  will  be  found  to  collect  at 
its  lower  extremity,  and  remain  suspended  there. 
As  the  weight  of  the  drop  tends  to  detach  it,  there 
must  necessarily  be  some  force  superior  to  this 
weight  which  maintains  it  there  ;  this  force  is  the 
force  of  adhesion. 

This  is  the  cause  why  liquids  when  poured  out 
of  a  vessel  so  easily  run  down  the  outside  ;  it  is  prevented  by  greasing  the 
outer  edge,  and  thus  doing  away  with  the  adhesion. 

The  adhesion  between  liquids  and  solids  is  more  powerful  than  that 
between  solids.  Thus,  if  in  the  above  experiment  a  thin  layer  of  oil  is  inter- 
posed between  the  plates  they  adhere  firmly,  but  when  pulled  asunder  each 
plate  is  moistened  by  the  oil,  thus  showing  that  in  separating  the  plates  the 
cohesion  of  the  plates  is  overcome,  but  not  the  adhesion  of  the  oil  to  the 
metal. 

In  the  above  case  the  solid  is  wetted  by  the  liquid  ;  that  is,  some  remains 
adhering  even  when  the  drop  falls.  But  liquids  adhere  to  solids  even  when 
they  are  not  wetted.     Thus  if  a  smooth  glass  plate  be  suspended  horizontally 


Fig.  61 


yG  Gravitation  and  Moleadar  Attraction.  [86- 

from  one  arm  of  a  balance,  and  be  counterpoised  as  in  fig.  6i  ;  on  sliding  a 
mercuiy  level  under  the  plate,  so  that  they  touch,  a  considerable  weight  must 
be  placed  in  the  other  pan  so  as  to  detach  the  plate  from  the  mercury.  Small 
drops  of  mercury,  too,  adhere  to  the  under  side  of  a  glass  or  porcelain  plate. 

iii.  The  force  of  adhesion  operates,  lastly,  between  solids  and  gases. 
If  a  glass  or  metal  plate  be  immersed  in  water,  bubbles  will  be  found  to 
appear  on  the  surface.  As  air  cannot  penetrate  into  the  pores  of  the  plate, 
the  bubbles  could  not  arise  from  the  air  which  has  been  expelled.  It  is 
solely  due  to  the  layer  of  air  which  covered  the  plate,  and  moistened  it  like 
a  liquid.  In  many  cases  when  gases  are  separated  in  the  nascent  state 
on  the  surface  of  metals — as  in  electrolysis — the  layer  of  gas  which  covers 
the  plate  has  such  a  density  that  it  can  produce  chemical  actions  more  power- 
ful than  those  which  it  can  bring  about  in  the  free  state. 

The  collection  of  dust  on  walls,  writing  and  drawing  with  chalks  and 
pencils,  depend  on  the  adhesion  of  solids.  Yet  these  are  easily  rubbed  out, 
for  the  adhesion  is  only  to  the  surface  layer.  In  writing  with  ink,  and  in 
water-colour  painting,  the  liquid  penetrates  into  the  pores,  taking  the  solid 
with  it,  which  is  left  behind  as  the  liquid  evaporates,  and  hence  the  adhesion 
of  such  writing  and  painting  is  far  more  complete. 


88] 


Elasticitv  of  Traction. 


77 


CHAPTER    IV. 

PROPERTIES    PECULIAR    TO    SOLIDS, 


87.  Various  special  properties. — After  having  described  the  principal 
properties  common  to  soHds,  hquids,  and  gases,  we  shall  discuss  the  properties 
peculiar  to  solids.  They  are  elasticity  of  tfactio/7,  elasticity  of  tordoiu  elas- 
ticity offlexit7-c,  tenacity.,  ductility.,  and  hardness. 

88.  Elasticity  of  traction. — Elasticity,  as  a  general  property  of  matter, 
has  been  already  mentioned  (17),  but  simply  in  reference  to  the  elasticity 
developed  by  pressure  ;  in  solids  it  may  also  be  called  into  play  by  traction, 
by  torsion,  and  by  flexure.  The  definitions  there  given  require  some  exten- 
sion. In  ordinary  life  we  consider 
those  bodies  as  highly  elastic 
which,  like  caoutchouc,  imdergo 
considerable  change  on  the  appli- 
cation of  only  a  small  force.  Yet 
the  force  of  elasticity  is  greatest  in 
many  bodies,  such  as  iron,  which 
do  not  seem  to  be  very  elastic.  For 
hy  force  of  elasticity  \?,  understood 
the  force  with  which  the  displaced 
particles  tend  to  revert  to  their 
original  position,  and  which  force  is 
equivalent  to  that  which  has  brought 
about  the  change.  Considered  from 
this  point  of  view,  gases  have  the 
least  force  of  elasticity  ;  that  of 
liquids  is  considerably  greater,  and 
is,  indeed,  greater  than  that  of  many 
solids.  Thus  the  force  of  elasticity 
of  mercury  is  greater  than  that  of 
caoutchouc,  glass,  wood,  and  stone. 
It  is,  however,  less  than  that  of  the 
other  metals,  with  the  exception  of 
lead. 

This  seems  discordant  with  or- 
dinary ideas  about  elasticity  ;   but 
it  must  be  remembered  that  those 
bodies  which,  by  the  exertion  of  a    small   force,  undergo  a  considerable 
change,  generally  have  also  the  property-  of  undergoing  this  change  without 


Fig.  62. 


78  Gravitation  and  Molecular  Attraction.  [88- 

losing  the  property  of  reverting  completely  to  their  original  state.  They 
have  a  wide  limit  of  elasticity  (17).  Those  bodies  which  require  great  force 
to  effect  a  change  are  also,  for  the  most  part,  those  on  which  the  exertion 
of  a  force  produces  a  permanent  alteration  ;  when  the  force  is  no  longer 
exerted,  they  do  not  completely  revert  to  their  original  state. 

In  order  to  study  the  laws  of  the  elasticity  of  traction,  Savart  used  the 
apparatus  repi-esented  in  fig.  62.  It  consists  of  a  wooden  support  from  which 
are  suspended  the  rods  or  wires  taken  for  experiment.  At  the  lower  ex- 
tremity there  is  a  scale-pan,  and  on  the  wire  two  points,  A  and  B,  are  marked, 
the  distance  between  which  is  measured  by  means  of  the  catJietonieter  before 
the  weights  are  added. 

The  cathetometer  consists  of  a  strong  upright  brass  support,  K,  divided 
into  millimetres,  and  which  can  be  adjusted  in  an  exactly  vertical  position 
by  means  of  levelling  screws  and  the  plumb-line.  A  small  telescope,  exactly 
at  right  angles  to  the  scale,  can  be  moved  up  and  down,  and  is  provided  with 
a  vernier  which  measures  fiftieths  of  a  millimetre.  By  adjusting  the  telescope 
successively  on  the  two  points  A  and  B,  as  represented  in  the  figure,  the 
distance  between  these  points  is  obtained  on  the  graduated  scale.  Placing, 
then,  weights  in  the  pan,  and  measuring  again  the  distance  from  A  to  B,  the 
elongation  is  obtained. 

By  experiments  of  this  kind  it  has  been  ascertained  that  for  elasticity  of 
traction  or  pressure — 

The  alteration  in  length  within  the  limits  of  elasticity  is  in  proportion  to 
the  length  and  to  the  load  acting  on  the  body.,  and  is  inversely  as  the  cross 
section. 

It  depends,  moreover,  on  the  specific  elasticity;  that  is,  on  a  special 
property  of  the  material  of  the  body.  If  this  coefficient  be  denoted  by  E, 
and  if  the  length,  cross  section,  and  load  be  respectively  designated  by  /,  s, 
and  P,  then  for  the  alteration  in  length,  ^,  we  have 

T^/P 

^  =  E — • 


If  in  the  above  expression  the  sectional  area  be  a  square  millimetre,  and 
P  iDe  one  kilogramme,  then 

^  =  E/,  from  which  E  =  -' 

which  expresses  by  what  fraction  the  length  of  a  bar  a  square  millimetre  in 
section  is  altered  by  a  load  of  a  kilogramme.  This  is  called  the  coefficient  of 
elasticity  ;  it  is  a  very  small  fraction,  and  it  is  therefore  desirable  to  use  its 

reciprocal,  that  is  -  or  ^,  as  the   modulus  of  elasticity  ;    or  the  weight  in 

kilogrammes  which  applied  to  a  bar  would  elongate  it  by  its  own  length, 
assuming  it  to  be  perfectly  elastic.  This  coefficient  is  known  as  Yoiing^s 
modulus.  This  cannot  be  observed,  for  no  body  is  perfectly  elastic,  but  it 
may  be  calculated  from  any  accurate  observations  by  means  of  the  above 
formula. 


-88]  Elasticity  of  Traction.  79 

The  following  are  the  best  values  for  some  of  the  principal  substances  : — 


Wrought-iron 
Steel-iron 
Platinum 
Copper 
Slate     . 
Zinc 
Brass    . 
Crown  Glass 
Plate  Glass  . 
Rock  Salt     . 
Marble 
Lead     . 
Bone    . 
Acacia . 
Pine      . 
Oak      . 
Whalebone  . 
Sandstone    . 
Fir 

Gypsum 
Ice 


20,869 

0-000048 

18,809 

0-000053 

17,044 

0-000058 

12,500 

0-000080 

11,035 

0-000090 

8,734 

0-000114 

8,543 

0-000117 

7,917 

0-000126 

7,015 

0-000142 

4,230 

0-000236 

2,309 

0-000382 

1,803 

0-000555 

1,635 

0-000612 

1,262 

0-000792 

1,113 

0-000890 

921 

0-001085 

700 

0-001428 

631 

0-001521 

564 

0-001768 

400 

0-002500 

236 

0-004236 

Thus,  to  double  the  length  of  a  wrought-iron  wire  a  square  millimetre  in 
section,  would  (if  these  were  possible)  require  a  weight  of  19,000  kilogrammes  ; 
but  a  weight  of  15  kilogrammes  produces  a  permanent  alteration  in  length 
of  jg^^th,  and  this  is  the  limit  of  elasticity.  The  weight,  which  when  applied 
to  a  body  of  unit  section,  just  brings  about  an  appreciable  permanent  change, 
is  a  measure  of  the  //;;///  of  elasticity.  Whalebone  has  only  a  modulus  of  700, 
and  experiences  a  permanent  elongation  by  a  weight  of  5  kilogrammes  ;  its 
limit  is,  therefore,  relatively  greater  than  that  of  iron.  Steel  has  a  high 
modulus,  along  with  a  wide  limit. 

Longitudinal  stretching  is  accompanied  by  a  lateral  contraction,  and 
the  ratio  of  the  contraction  to  the  proportional  stretching  is  known  as 
Poissoiis  coefficiejit.  It  was  taken  by  him  to  be  |,  but  later  experiments 
have  found  the  ratio  to  be  about  \.  When  a  wire  is  stretched  by  a  load  to 
within  the  limit  of  elasticity,  some  time  often  elapses  before  the  full  effect  is 
produced,  and  conversely  when  the  load  is  removed,  it  does  not  at  once 
wholly  resume  its  original  condition,  but  a  small  portion  of  the  deformation 
remains,  and  it  only  reverts  to  its  initial  state  after  the  lapse  of  some  time. 
This  phenomenon  which  is  met  with  in  most  elastic  changes  of  form  is 
-called  the  clastic  after  action  or  effect.,  or  the  elastic  fatigue. 

Both  calculation  and  experiment  show  that  when  bodies  are  lengthened 
by  traction  their  volume  increases. 

When  weights  are  placed  on  a  bar,  the  amount  by  which  it  is  shortened, 
or  the  coefficient  of  contraction.,  is  equal  to  the  elongation  which  it  would 
experience  if  the  same  weights  were  suspended  to  it,  and  is  represented  by 
the  above  numbers. 


8o  Gravitation  and  Molecular  Attraction.  [88- 

The  influence  of  temperature  on  the  elasticity  of  iron,  copper,  and  brass 
was  investigated  by  Kohlrausch  and  Loomis.  They  found  that  the  altera- 
tion in  the  coefficient  of  elasticity  by  heat  is  the  same  as  that  which  heat 
produces  in  the  coefficient  of  expansion  and  in  the  refractive  power  ;  it  is 
also  much  the  same  as  the  change  in  the  permanent  magnetism,  and  in  the 
specific  heat,  while  it  is  less  than  the  alteration  in  the  conductivity  for  elec- 
tricity. 

As  an  application  may  be  mentioned  Jolly's  spriiig  balance.  This  con- 
sists of  a  long  steel  wire  ab.,  wound  in  the  form  of  a  spiral,  which  is  suspended 
in  front  of  an  accurately  graduated  scale.  To  the 
lower  end  of  the  spiral  two  scale-pans,  c  and  d.,  are 
hung  by  a  thread,  the  lower  one,  d.,  dipping  in  a  small 
vessel  of  water  on  an  adjustable  support.  The  insti-u- 
ment  is  graduated  empirically  by  observing  what  dis- 
placement of  the  mark  in  is  produced  by  putting  a 
known  weight  in  the  scale-pan  d.  Knowing  then  once 
for  all  the  constant  of  the  instrument,  it  is  easy  to 
determine  the  weight  of  a  body  by  reading  the  dis- 
placement which  it  produces  along  the  scale. 

89.  Elasticity  of  torsion. — The  laws  of  the  torsion 
of  wires  were  determined  by  Coulomb,  by  means  of  an 
apparatus  called  the  torsion  balance  (fig.  64).  It  consists 
essentially  of  a  metal  wire,  clamped  at  one  end  in  a 
support.  A,  and  holding  at  the  other  a  metal  sphere,  B, 
to  which  is  affixed  an  index,  C.  Immediately  below  this 
there  is  a  graduated  circle,  CD.  If  the  needle  is 
turned  from  its  position  of  equilibrium  through  a  cer- 
tain angle,  which  is  the  angle  of  torsio?!,  the  force 
necessary  to  produce  this  effect  is  the  force  of  torsion. 
When,  after  this  deflection,  the  sphere  is  left  to  itself, 
the  reaction  of  torsion  produces  its  effect,  the  wire  un- 
twists itself,  and  the  sphere  rotates  about  its  vertical 
axis  with  increasing  rapidity  until  it  reaches  its  position 
of  equilibrium.  It  does  not  however,  rest  there  ;  in 
virtue  of  its  inertia  it  passes  this  position,  and  the  wire 
undergoes  a  torsion  in  the  opposite  direction.  The 
equilibrium  being  again  destroyed,  the  wire  again  tends 
to  untwist  itself,  the  same  alterations  are  again  pro- 
duced, and  the  needle  does  not  rest  at  zero  of  the  scale 
until  after  a  certain  number  of  oscillations  about  this 
point  have  been  completed. 
By  means  of  this'apparatus  Coulomb  found  that  when  the  amplitude  of 
the  oscillations  is  within  certain  limits,  the  oscillations  arc  subject  to  the 
following  laws  : 

I.  The  oscillations  arc  very  nearly  isochronous. 

II.  For  the  same  wire.,  the  angle  of  torsion  is  proportional  to  the  moment 
of  the  force  of  torsion. 

III.  With  the  same  force  of  torsion,  and  with  wires  of  the  same  diameter, 
the  angles  of  torsion  are  proportional  to  the  length  of  the  wires. 


Fig.  63. 


-90] 


Elasticity  of  Flexure. 


8i 


IV.  Tlic  same  force  of  /orsion  being  applied  to  wires  of  the  savie  length, 
the  angles  of  torsion  are  ijiversely  proportio7tal  to  the  fourth  powers  of  the 
diameters. 

Wertheim  examined  the  elasticity  of  torsion  in  the  case  of  stout  rods 
by  means  of  a  different  apparatus,  and  found  that  it  is  also  subject  to  these 
laws.  He  further  found  that,  all  dimensions  being  the  same,  different  sub- 
stances undergo  different  degrees  of  torsion  for  the 
same  force,  and  each  substance  has  its  own  coefficient 

of  torsion,  which  is  usually  denoted  by  —  or  by  r. 

The  value  of  this  coefficient  is  about  |  that  of  the 
modulus  of  elasticity. 

The  laws  of  torsion  may  be    enunciated   in  the 

I    F/     • 
formula  '^'^  =  „     i  ;   in  which  w  is  the  angle  of  tor- 
sion, F  the   moment  of  the   force  of  torsion,  /  the 
length  of  the  wire,   r  its  radius,  and  —  the  specific 

torsion-coefficient. 

As  the  angle  of  torsion  is  inversely  proportional 
to  the  fourth  power  of  the  radius,  rods  of  some 
thickness  require  very  great  force  to  produce  even 
small  twists.  With  very  small  diameters,  such  as 
those  of  a  cocoon  or  glass  thread,  the  proportionality 
between  the  angle  of  torsion  and  the  twisting  force 
holds  even  for  several  complete  turns.  We  may 
here  mention  a  very  ingenious  method  of  obtaining  Fig.  64. 

very  fine  threads  of  glass  and  even  of  cjuartz  and 

other  minerals  which  has  been  devised  by  Mr.  Boys.  It  consists  in  attaching 
a  stout  thread  of  the  substance  in  question  to  a  small  arrow  of  straw,  melting 
the  end  so  as  to  form  a  small  drop.  When  the  arrow  is  shot  from  a  small 
cross-bow,  the  drop  remains  behind  in  virtue  of  its  inertia  (17),  and  a  thread 
practically  uniform  but  of  excessive  tenuity  is  spun  out  from  it  and  carried 
along  with  the  arrow.  In  this  way  glass  threads  90  feet  in  length  and  jouoo^h 
of  an  inch  in  diameter  have  been  produced.  By  the  same  method  melting 
quartz  with  the  oxyhydrogen  blowpipe,  threads  of  this  substance  have  been 
produced  which  are  not  more  than  o-ooooi  inch  in  diameter.  Such  threads 
are  of  great  value  in  torsion  experiments,  for,  while  they  possess  great 
tenacity,  they  are  almost  destitute  of  the  property  of  elastic  fatigue. 

90.  Elasticity  of  flexure. — A  solid,  when  cut  into  a  rod  or  thin  plate, 
and  fixed  at  one  end,  after  having  been  more  or  less  bent,  strives  to  return 
to  its  original  position  when  left  to  itself  This  property  is  known  as  the 
elasticity  of  flexure,  and  is  very  distinct  in  steel,  caoutchouc,  wood,  and 
paper. 

If  a  rectangular  bar  A  B  be  clamped  at  one  end  and  loaded  at  the  other 
end  by  a  weight  W  (fig.  65),  a  flexure  will  be  produced  which  may  be  observed 
by  the  cathetometer.  The  amount  of  this  flexure  e  is  represented  by  the 
formula 


6^^ 


82 


Gravitation  aftd  Molecular  Attraction. 


[90 


where  P  is  the  load,  /  the  length  of  the  bar,  b  its  breadth,  h  its   depth  or 
thickness,  all  in  mm.,  and  ^  the  modulus  of  elasticity. 
If  the  section  of  the  bar  is  a  circle  of  radius  r,  then 

3  TrrV  ■ 
It  is  clear  that  an  accurate  measurement  of  the  flexure  of  a  bar  furnishes 
a  means  of  determining  its  modulus  of  elasticity. 

The  elasticity  of  flexure  is  applied  in  a  vast  variety  of  instances— for 
example,  in  bows,  watch-springs,  carriage-springs  ;  in  spring  balances  it  is 

used  to  determine  weights, 
in  dynamometers  to  de- 
termine the  force  of  agents 
in  prune  movers  ;  and,  as  a 
property  of  wool,  hair,  and 
feathers,  it  is  applied  to 
domestic  uses  in  cushions 
and  mattresses. 

Whatever  be  the  kind 
of  elasticity,  there  is,  as 
has  been  already  said  (88), 
a  limit  to  it — that  is,  there 
is  a  molecular  displace- 
ment, beyond  which 
bodies  are  broken,  or  at 
any  rate  do  not  regain  their  primitive  form.  This  limit  is  affected  by 
various  causes.  The  elasticity  of  many  metals  is  increased  by  hardening, 
whether  by  cold,  by  means  of  the  draw-plate,  by  rolling,  or  by  hammering. 
Some  substances,  such  as  steel,  cast  iron,  and  glass,  become  both  harder 
and  more  elastic  by  tempering  (94). 

Elasticity,  on  the  other  hand,  is  diminished  by  annealing,  which  consists 
in  raising  the  body  to  a  temperature  lower  than  that  necessary  for  tempering, 
and  allowing  it  to  cool  slowly.  By  this  means  the  elasticity  of  springs 
may  be  regulated  at  pleasure.  Glass,  when  it  is  heated,  undergoes  a 
true  tempering  in  being  rapidly  cooled,  and  hence,  in  order  to  lessen  the 
fragility  of  glass  objects,  they  are  reheated  in  a  furnace,  and  are  carefully 
allowed  to  cool  slowly,  so  that  the  particles  have  time  to  assume  their  most 
stable  position  (94). 

9 1.  Tenacity. —  Tenacity  is  the  resistance  which  a  body  opposes  to  the 
total  separation  of  its  parts.  According  to  the  manner  in  which  the  external 
force  acts,  we  may  have  various  kinds  of  tenacity  :  tenacity  in  the  ordinary 
sense,  or  resistance  to  traction  ;  7'etative  tenacity,  or  resistance  to  fracture  ; 
reactive  tenacity,  or  resistance  to  crushing  ;  sheerifig  tenacity,  or  resistance 
to  displacement  of  particles  in  a  lateral  direction  ;  and  torsional  tenacity,  or 
resistance  to  twisting.  Ordinary  tenacity  is  determined  in  different  bodies 
by  forming  them  into  cylindrical  or  prismatic  wires,  and  ascertaining  the 
weight  necessary  to  break  them. 


-91]  Tenacity.  S3 

Mere  increase  in  length  does  not  influence  the  breaking  weight,  for  the 
weight  acts  in  the  direction  of  the  length,  and  stretches  all  parts  as  if  it  had 
been  directly  applied  to  them. 

Tenacity  is  directly  proportional  to  the  breaking  weight.,  and  inversely 
proportional  to  the  area  of  a  transz'erse  section  of  the  wire. 

Tenacity  diminishes  with  the  duration  of  the  traction.  A  small  force 
continuously  applied  for  a  long  time  will  often  break  a  wire,  which  would  not 
at  once  be  broken  by  a  larger  weight. 

Not  only  does  tenacity  vary  with  different  substances,  but  it  also  varies 
with  the  form  of  the  body.  Thus,  with  the  same  sectional  area,  a  cylinder 
has  greater  tenacity  than  a  prism.  The  cjuantity  of  matter  being  the  same, 
a  hollow  cylinder  has  greater  tenacity  than  a  solid  one  ;  and  the  tenacity  of 
this  hollow  cylinder  is  greatest  when  the  external  radius  is  to  the  internal 
one  in  the  ratio  of  1 1  to  5.  The  shape  has  also  the  same  influence  on  the 
resistance  to  crushing  as  it  has  on  the  resistance  to  traction.  A  hollow 
cylinder  with  the  same  mass,  and  the  same  weight,  offers  a  greater  resistance 
than  a  solid  cylinder.  Thus  it  is  that  the  bones  of  animals,  the  feathers  of 
birds,  the  stems  of  corn  and  other  plants,  offer  greater  resistance  than  if  they 
were  solid,  the  mass  remaining  the  same. 

Tenacity,  like  elasticity,  is  different  in  different  directions  in  bodies.  In 
wood,  for  example,  both  the  tenacity  and  the  elasticity  are  greater  in  the  direc- 
tion of  the  fibres  than  in  a  transverse  direction.  And  this  difference  obtains 
in  general  in  all  bodies,  the  texture  of  which  is  not  the  same  in  all  directions. 

Wires  by  being  worked  acquire  greater  tenacity  on  the  surface,  and  have 
therefore  a  higher  coefficient,  than  even  somewhat  thicker  rods  of  the  same 
material  ;  and,  according  to  some  physicists,  solids  have  a  surface  tension 
analogous  to  that  of  liquids  (134).  A  strand  of  wires  is  stronger  than  a  rod 
whose  section  is  equal  to  the  sum  of  the  sections  of  the  wires. 

Wertheim  found  the  following  numbers  representing  the  weight  in  kilo- 
grammes for  the  limit  of  elasticity,  and  for  the  tenacity  of  wires,  imm.  in 
diameter. 


Lead. 
Tin  . 
Silver 
Copper 
Platinum 
Iron  . 
Steel  . 
Cast  steel 


(  drawn 
1  annealed 
I  drawn 
I  annealed 
f  drawn 
(  annealed 
f  drawn 
[  annealed 
(  drawn 
[  annealed 
(  drawn 
\  annealed 
(  drawn 
I  annealed 
f  drawn 
I  annealed 


Limit  of  Elasticity. 
Kilogrammes 
.          0-25 
0-20 

Tenacity. 

Kilogrammes 

2 -07 

I -So 

•         0-45 
0-20 

2-45 
170 

.       11-25 

29-00 

275 

1 6 -02 

.        I2-00 

3-00 

.        2600 

40-30 

30-54 
34-10 

•  14-50 

•  32-3 

23-50 
61-10 
46-88 
70-00 

.      5r-6 
•       5-0 

40-00 
8o-oo 

65-75 

84  Gravitation  and  Molecular  Attraction.  [91- 

The  table  shows  that  of  all  metals  cast  steel  has  the  greatest  tenacity. 
Yet  it  is  exceeded  by  fibres  of  unspun  silk,  a  thread  of  which  i  square  milli- 
metre in  section  can  carry  a  load  of  500  kilogrammes.  Single  fibres  of  cotton 
can  support  a  weight  of  100  to  300  grammes  ;  that  is,  millions  of  times  their 
own  weight. 

In  this  table  the  bodies  are  supposed  to  be  at  the  ordinary  temperature. 
At  higher  temperatures  the  tenacity  rapidly  decreases.  Seguin  made  some 
experiments  on  this  point  with  iron  and  copper,  and  obtained  the  following 
values  for  the  tenacity,  in  kilogrammes,  of  millimetre  wire  at  different  tem- 
peratures : — 

Iron         .         .  at  10°,  60  ;  at  370°,  54  ;  at  500°,  yj  ; 
Copper    .         .       „        21  ;         „         77  ;       „        o. 

92.  Ductility. — Ductility  is  the  property  in  virtue  of  which  a  great  num- 
ber of  bodies  change  their  forms  by  the  action  of  traction  or  pressure. 

With  certain  bodies,  such  as  clay,  wax,  &c.,  the  application  of  a  very 
little  force  is  sufficient  to  produce  a  change  ;  with  others,  such  as  the  resins 
and  glass,  the  aid  of  heat  is  needed,  while  with  the  metals  more  powerful 
agents  must  be  used,  such  as  percussion,  the  draw-plate,  or  the  rolling-mill. 

Malleability  is  that  modification  of  ductility  which  is  exhibited  by  ham- 
mering. The  most  malleable  metal  is  gold,  which  has  been  beaten  into 
leaves  about  the  ^,^^055^^  of  an  inch  thick. 

The  most  ductile  metal  is  platinum.  Wollaston  obtained  a  wire  of  it 
o'oooo3  of  an  inch  in  diameter.  This  he  effected  by  covering  with  silver  a 
platinum  wire  O'oi  of  an  inch  in  diameter,  so  as  to  obtain  a  cylinder  0-2  inch 
in  diameter  only,  the  axis  of  which  was  of  platinum.  This  was  then  drawn 
out  in  the  form  of  wire  as  fine  as  possible  ;  the  two  metals  were  ecjually  ex- 
tended. When  this  wire  was  afterwards  boiled  with  dilute  nitric  acid  the 
silver  was  dissolved,  and  the  platinum  wire  left  intact.  The  wire  was  so  fine 
that  a  mile  of  it  would  have  weighed  only  1-25  of  a  grain. 

The  glass  threads  drawn  by  Mr.  Boys'  method  (89)  are  so  fine,  being 
under  the  nioootl'^  °f  ^"  "'"^^'  ^^^*  ^  ""'^^  would  not  weigh  more  than  one-third 
of  a  grain.    Threads  of  quartz  have  a  tenacity  approaching  that  of  steel  wire. 

93.  Hardness. — Hardness  is  the  resistance  which  bodies  offer  to  being 
scratched  or  worn  by  others.  It  is  only  a  relative  property,  for  a  body  which 
is  hard  in  reference  to  one  body  may  be  soft  in  reference  to  others.  The  re- 
lative hardness  of  two  bodies  is  ascertained  by  trying  which  of  them  will 
scatch  the  other.  Diamond  is  the  hardest  of  all  bodies,  for  it  scratches  all, 
and  is  not  scratched  by  any.  The  hardness  of  a  body  is  expressed  by  re- 
ferring it  to  a  scale  of  hardness  :  that  usually  adopted  is — 

1.  Talc  5.  Apatite  8.  To])a/. 

2.  Rock  salt  6.  Felspar  9.   Coruntlum 

3.  Calcspar  7.  Quartz  10.    Diamond 

4.  Fluorspar 

Thus,  the  hardness  of  a  body  which  would  scratch  felspar,  but  would  be 
scratched  by  quartz,  would  be  expressed  by  the  number  6'5. 

Huegenay  determined  the  weight  necessary  to  force  a  steel  point  to  a 
depth  of  10  mm.,  and  found  the  order  of  the  metals  as  follows  :  lead,  tin, 
aluminium,  gold,  silver,  platinum,  zinc,  copper,  iron,  steel. 


-94]  rcmpcr.  85 

The  pure  metals  are  softer  than  their  alloys.  Hence  it  is  that,  for  jevrel- 
leiy  and  coinage,  gold  and  silver  are  alloyed  with  copper  to  increase  their 
hardness. 

The  hardness  of  a  body  has  no  relation  to  its  resistance  to  compression. 
Glass  and  diamond  are  much  harder  than  wood,  but  the  latter  offers  far 
greater  resistance  to  the  blow  of  a  hammer.  Hard  bodies  are  often  used 
for  polishing  powders;  for  example,  emery,  pumice,  and  tripoli.  Diamond, 
being  the  hardest  of  all  bodies,  can  only  be  ground  by  means  of  its  own 
powder. 

A  body  which  moves  with  great  velocity  can  cut  into  bodies  which  are 
harder  than  itself  Thus  a  disc  of  wrought  iron  rotating  with  a  velocity 
of  1 1  metres  in  a  second  was  cut  by  a  steel  graver  ;  while  when  it  rotated 
with  a  velocity  of  20  metres,  the  edge  of  the  disc  could  cut  the  graver,  and 
with  a  velocity  of  50  to  100  metres  it  could  even  cut  into  agate  and  quartz. 

A  brittle  body  is  one  in  which  the  connection  between  the  parts  is 
destroyed  by  the  application  of  a  small  force.  Arsenic,  bismuth,  and  heated 
zinc  are  examples  of  brittle  metals  ;  they  are  easily  reduced  to  powder. 

94.  Temper. — By  sudden  cooling  after  they  have  been  raised  to  a  high 
temperature,  many  bodies,  more  especially  steel,  become  hard  and  brittle. 
By  reheating  and  cooling  slowly,  which  is  called  anitealing^  hard  and  brittle 
steel  may  be  converted  into  a  soft,  flexible  material,  and  in  general,  by  varying 
the  limits  of  temperature  within  which  the  change  takes  place,  almost  any 
degree  of  elasticity  and  flexibility  may  be  given  to  it.  This  operation  is 
called  tetnperifig.  All  cutting  instruments  are  made  of  tempered  steel. 
There  are,  however,  some  few  bodies  upon  which  tempering  produces  quite 
a  contrary-  effect.  An  alloy  of  one  part  of  tin  and  four  parts  of  copper,  called 
tantaiii  metal,  is  ductile  and  malleable  when  rapidly  cooled,  but  hard  and 
brittle  as  glass  when  cooled  slowly. 


86  On  Liquids.  [95- 


BOOK    III. 

ON      LIQUIDS. 

CHAPTER  I. 
HYDROSTATICS. 

95.  Province  of  Hydrostatics. — The  science  of  Jiydrosfatics  treats  of  the 
conditions  of  the  equilibrium  of  hquids,  and  of  the  pressures  they  exert, 
whether  within  their  own  mass  or  on  the  sides  of  the  vessels  in  which  they 
are  contained. 

96.  General  characters  of  liquids.— It  has  been  already  seen  (4)  that 
liquids  are  bodies  whose  molecules  are  displaced  by  the  slightest  force. 
Their  fluidity,  however,  is  not  perfect ;  their  particles  always  adhere  slightly 
to  each  other,  and  when  a  thread  of  liquid  moves,  it  attempts  to  drag  the 
adjacent  stationaiy  particles  with  it,  and  conversely  is  held  back  by  them. 
This  property  is  called  viscosity  (147),  and  bodies  which  possess  this  property 
in  a  high  degree  are  said  to  be  viscous. 

Gases  also  possess  fluidity,  but  in  a  higher  degree  than  liquids.  The 
distinction  between  the  two  forms  of  matter  is  that  liquids  are  almost  incom- 
pressible and  are  comparatively  inexpansible,  while  gases  are  eminently 
compressible  and  expand  spontaneously. 

The  fluidity  of  liquids  is  seen  in  the  readiness  with  which  the}'  take  all 
sorts  of  shapes.  Their  compressibility  is  established  by  the  following  experi- 
ment. 

97.  Compressibility  of  liquids. — From  the  experiment  of  the  Florentine 
Academicians  (13),  liquids  were  for  a  long  time  regarded  as  being  completely 
incompressible.  Since  then  researches  have  been  made  on  this  subject  by 
various  physicists,  which  have  shown  that  liquids  are  really  compressible. 

The  apparatus  used  for  measuring  the  compressibility  of  liquids  has  been 
named  \he  pieso^neter  {ttu(o),  I  compress  ;  ^trpov,  measure).  That  shown  in 
fig.  66  consists  of  a  strong  glass  cylinder,  with  very  thick  sides,  and  an 
internal  diameter  of  about  3^  inches.  The  base  of  the  cylinder  is  firmly 
cemented  into  a  wooden  foot,  and  on  its  upper  part  is  fitted  a  metal  cylin- 
der closed  by  a  cap  which  can  be  unscrewed.  In  this  cap  there  is  a  funnel, 
R,  for  introducing  water  into  the  cylinder,  and  a  small  barrel  hermetically 
closed  by  a  piston,  which  is  moved  by  a  screw,  P. 


97] 


Compressibility  of  Liquids. 


87 


In  the  inside  of  the  apparatus  there  is  a  glass  vessel,  A,  containing  the 
liquid  to  be  compressed.  The  upper  part  of  this  vessel  terminates  in  a 
capillary  tube,  which  dips  under  mercury,  O.  This  tube  has  been  previously 
divided  into  parts  of  equal  capacity,  and  it  has  been  determined  how  many 
of  these  parts  the  vessel  A  contains.  The  latter  is  ascertained  by  finding  the 
weight,  P,  of  the  mercury  which  the  reservoir 
A,  contains,  and  the  weight,  ^,  of  the  mercury 
contained  in  a  certain  number  of  divisions,  /z, 
of  the  capillary  tube.  If  N  be  the  number  of 
divisions    of  the    small    tube    contained  in  the 

whole  reservoir,  we  ha\'e .  =  — ,  from  which  the 

;/      p 

value  of  N  is  obtained.  There  is  further  a 
manometer.  This  is  a  glass  tube,  B,  containing 
air,  closed  at  one  end,  and  the  other  end  ot 
which  dips  under  mercury.  When  there  is  no 
pressure  on  the  water  in  the  cylinder,  the  tube 
B  is  completely  full  of  air  ;  but  when  the  water 
within  the  cylinder  is  compressed  by  means  of 
the  screw  P,  the  pressure  is  transmitted  to  the 
mercury,  which  rises  in  the  tube,  compressing 
the  air  which  it  contains.  A  graduated  scale 
fixed  on  the  side  of  the  tube  shows  the  reduction 
of  volume,  and  this  reduction  of  volume  indicates 
the  pressure  exerted  on  the  liquid  in  the  cylin- 
der, as  will  be  seen  in  speaking  of  the  mano- 
meter (184). 

In  making  the  experiment,  the  vessel  A  is 
filled  with  the  liquid  to  be  compressed,  and  the 
end  dipped  under  the  mercury.  By  means  of 
the  funnel  R  the  cylinder  is  entirely  filled  with 
water.     The  screw  P   being   then   turned,  the 

piston  moves  downwards,  and  the  pressure  exerted  upon  the  water  is  trans- 
mitted to  the  mercury  and  the  air  ;  in  consequence  of  which  the  mercury 
rises  in  the  tube  B,  and  also  in  the  capillary  tube.  The  ascent  of  mercury 
in  the  capillary  tube  shows  that  the  liquid  in  the  vessel  A  has  diminished  in 
volume,  and  gives  the  amount  of  its  compression,  for  the  capacity  of  the 
whole  vessel  A  in  terms  of  the  graduated  divisions  on  the  capillary  tube  has 
been  previously  determined. 

In  his  first  experiments.  Oersted  assumed  that  the  capacity  of  the  vessel 
A  remained  the  same,  its  sides  being  compressed  both  internally  and  ex- 
ternally by  the  liquid.  But  this  capacity  diminishes  in  consequence  of  the 
external  and  internal  pressures.  Colladon  and  Sturm  made  some  experiments 
allowing  for  this  change  of  capacity,  and  found  that  for  a  pressure  equal  to 
that  of  the  atmosphere,  mercury  experiences  a  compression  of  0-000003  part 
of  its  original  volume,  water  a  compression  of  0-00005,  'irid  ether  a  compression 
of  0-000133  part  of  its  original  bulk.  The  compressibility  of  sea  water  is  only 
about  0-000044  :  it  is  not  materially  denser  even  at  great  depths  ;  thus  at 
the  depth  of  a  mile  its  density  would  be  only  about  i\^t\i  the  greater.     The 


On  Liquids. 


[97- 


compressibility  is  greater  the  higher  the  temperature  ;  thus  that  of  ether  at 
14°  is  one-fourth  greater  than  its  compressibihty  at  0°. 

It  appears  from  recent  researches  that  the  comi^ressibiHty  of  water 
diminishes  with  increase  of  temperature  up  to  a  certain  hmit,  beyond  which 
it  increases  again.     This  hmit  seems  to  be  at  about  63°  C. 

As  the  pressure  increases,  the  average  compressibihty  for  each  atmo- 
sphere diminishes. 

Whatever  be  the  pressure  to  which  a  hquid  has  been  subjected,  experi- 
ment shows  that  as  soon  as  the  pressure  is  removed  the  hquid  regains 
its  original  vokuiie.  from  which  it  is  conchided  that  hquids  are  perfectly 
elastic. 

98.  Equality  of  pressures.  Pascal's  law. — By  considering  liquids  as 
perfectly  fluid,  and  assuming  them  to  be  uninfluenced  by  the  action  of  gravity, 
the  following  law  has  been  established.  It  is  often  called  Pascal's  law,  for 
it  was  first  enunciated  by  him. 

Pressure  exerted  anywhere  upon  a  mass  of  liquid  is  transmitted  undi- 
minished iti  all  directions.,  and  acts  with  the  same  force  on  all  equal  surfaces., 
and  in  a  direction  at  right  angles  to  those  surfaces. 

To  get  a  clearer  idea  of  the  truth  of  this  principle,  let  us  conceive  a  vessel 
of  any  given  form  in  the  sides  of  which  are  placed  various  cylindrical  aper- 
tures, all  of  the  same  size,  and  closed  by  movable 
pistons.  Let  us,  further,  imagine  this  vessel  to  be 
filled  with  liquid  and  unaffected  by  the  action  of 
gravity  ;  the  pistons  will,  obviously,  have  no  ten- 
dency to  move.  If  now  a  weight  of  P  pounds  be 
ITT^  '^'^\       placed  upon  the  piston   A    (fig.  67),  which  has   a 

^'^    -  ^   ^  ^       surface    «,    it    will    be    pressed    inwards,  and    the 

pressure  will  be  transmitted  to  the  internal  faces 
of  each  of  the  pistons  B,  C,  D,  and  E,  which  will 
each  be  forced  outwards  by  a  pressure  P,  their 
surfaces  being  equal  to  that  of  the  first  piston. 
Since  each  of  the  pistons  undergoes  a  pressure  P, 
equal  to  that  on  A,  let  us  suppose  two  of  the  pis- 
tons united  so  as  to  constitute  a  surface  2a,  it  will  have  to  support  a  pres- 
sure 2 P.     Similarly,  if  the  piston  were  equal  to  3^,  it  would  experience  a 

pressure  of  3P  ;  and  if  its  area 
were  100  or  1,000  times  that  of 
a,  it  would  sustain  a  pressure  of 
100  or  1,000  times  P.  In  other 
words,  the  pressure  on  any  part 
of  the  internal  walls  of  the 
vessel  would  be  proportional  to 
the  surface. 

The  principle  of  the  equality 
of  pressure    is    assumed    as   a 
consequence  of  the  constitution 
of  fluids.      By  the  following  ex- 
it can  be   shown  that   pressure  is  transmitted  in  all    directions, 
it    cannot  be  shown  that  it  is  equally  transmitted.     P^  cylinder 


Fig.  67. 


permient 
although 


i-l4' 


-99]  Vertical  Dozumvard  Pressure  :    its  Laivs.  89 

provided  with  a  piston  is  fitted  into  a  hollow  sphere  (fig.  68),  in  which 
small  cylindrical  jets  are  placed  perpendicular  to  the  sides.  The  sphere 
and  the  cylinder  being  both  filled  with  water,  when  the  piston  is  moved  the 
liquid  spouts  forth  from  all  the  orifices,  and  not  merely  from  that  which  is 
opposite  to  the  piston. 

The  reason  why  a  satisfactory  cjuantitative  experimental  demonstration 
of  the  principle  of  tiie  equality  of  pressure  cannot  be  given  is,  that  the  in- 
fluence of  the  weight  of  the  liciuid  and  of  the  friction  of  the  pistons  cannot  be 
altogether  eliminated. 

Yet  an  approximate  verification  may  be  effected  by  the  experiment 
represented  in  fig.  69.  Two  cylinders  of  different  diameters  are  joined  by  a 
tube  and  filled  with  water.  On  the  surface  of  the  liquid  are  two  pistons  P 
and  /,  which  hermetically  close  the  cylinders,  but  move  without  friction. 
Let  the  area  of  the  large  piston  be, 
for  instance,  thirty  times  that  of  the 
smaller  one.  That  being  assumed,  let 
a  weight,  say  of  two  pounds,  be  placed 
upon  the  small  piston  ;  this  pressure 
will  be  transmitted  to  the  water  and 
to  the  large  piston,  and  as  this  pres- 
sure amounts  to  two  pounds  on  each 
portion  of  its  surface  equal  to  that  oj 
the  small  piston,  the  large  piston  must 
be  exposed  to  an  upward  pressure 
thnty  times  as  much,  or  of  sixty  pounds.  If  now  this  weight  be  placed 
upon  the  large  piston,  both  will  remain  in  equihbrium  ;  but,  if  the  weight  is 
greater  or  less,  this  is  no  longer  the  case.  If  S  and  .y  are  the  areas  of  the 
large  and  small  piston  respectively,  and  P  and  p  the  corresponding  loads, 

then^  =  ^  ;  whence  P  =  ^-. 
p      s  s 

It  is  important  to  observe  that  in  speaking  of  the  transmission  of  pres- 
sures to  the  sides  of  the  containing  vessel,  these  pressures  must  always  be 
supposed  to  be  perpendicular  to  the  sides  ;  for  any  oblique  pressure  may  be 
decomposed  into  two  others,  one  at  right  angles  to  the  side,  and  the  other 
acting  parallel  with  the  side  ;  but,  as  the  latter  has  no  action  on  the  side,  the 
perpendicular  pressure  is  the  only  one  to  be  considered. 


Fig.  69. 


PRESSURE  PRODUCED  IN  LIQUIDS  BY  GRAVITY. 

99.  Vertical  downward,  pressure  :  its  laws. — Any  given  liquid  being 
in  a  state  of  rest  in  a  vessel,  if  we  suppose  it  to  be  divided  into  horizontal 
layers  of  the  same  density,  it  is  evident  that  each  layer  supports  the  weight 
of  those  above  it.  Gravity,  therefore,  produces  internal  pressures  in  the 
mass  of  a  liquid  which  vary  at  different  points.  These  pressures  are  sub- 
mitted to  the  following  general  laws: — 

I.  The  pressure  in  each  layer  is  proportional  to  the  deptJi. 

I I .  With  differetzt  liquids  and  the  same  depth,  the  pressure  is  proportional 
to  the  density  of  the  liquid. 

III.  The  pressure  is  the  same  at  all  points  of  the  same  horizontal  layer. 


90  On  Liquids.  [99- 

The  first  two  laws  are  self-evident ;  the  third  necessarily  follows  from  the 
first  and  from  Pascal's  principle. 

Meyer  has  found,  by  direct  experiments,  that  pressure  is  transmitted 
through  liquids  contained  in  tubes,  with  the  same  velocity  as  that  with  which 
sound  travels  in  the  same  circumstances. 

loo.  Vertical  upward  pressure. — The  pressure  which  the  upper  layers 
of  a  liquid  exert  on  the  lower  layers  causes  them  to  exert  an  equal  reaction 
in  an  upward  direction,  a  necessary  consequence  of  the  principle  of  trans- 
mission of  pressure  in  all  directions.  This  upward  pressure  is  termed  the 
buoyancy  of  licjuids  ;  it  is  very  sensible  when  the  hand  is  plunged  into  a 
liquid,  more  especially  one  of  great  density,  like  mercury. 

The  following  experiment  (fig.  70)  serves  to  exhibit  the  upward  pressure 
of  licjuids.  A  large  open  glass  tube  A,  one  end  of  which  is  ground,  is  fitted 
with  a  ground-glass  disc  O,  or  still  better  with  a 
thin  card  or  piece  of  mica,  the  weight  of  which  may 
be  neglected.  To  the  disc  is  fitted  a  string  C,  by 
which  it  can  be  held  against  the  bottom  of  the  tube. 
The  whole  is  then  immersed  in  water,  and  now  the 
disc  does  not  fall,  although  no  longer  held  by  the 
string  ;  it  is  consequently  kept  in  its  position  by  the 
upward  pressure  of  the  water.  If  water  be  now 
slowly  poured  into  the  tube,  the  disc  will  only  sink 
when  the  height  of  the  water  inside  the  tube  is 
equal  to  the  height  outside.  It  follows  thence  that 
the  upward  pressure  on  the  disc  is  equal  to  the 
pressure  of  a  column  of  water,  the  base  of  which  is 
'"■  ''"  the  internal  section  of  the  tube  A,  and  the  height 

the  distance  from  the  disc  to  the  upper  surface  of  the  liquid.  Hence  the 
tipivard  pressure  of  liquids  at  any  point  is  governed  by  the  same  laws  as  the 
downward  pressure. 

loi.  Pressure  is  independent  of  the  shape  of  the  vessel. — The 
pressure  exerted  by  a  liquid,  in  virtue  of  its  weight,  on  any  portion  of  the 
liquid,  or  on  the  sides  of  the  vessel  in  which  it  is  contained,  depends  on  the 
depth  and  density  of  the  liquid,  but  is  independent  of  the  shape  of  the  vessel 
and  of  the  quaiitity  of  the  liquid. 

This  principle,  which  follows  from  the  law  of  the  equality  of  pressure, 
may  be  experimentally  demonstrated  by  many  forms  of  apparatus.  The 
following  is  the  one  most  frequently  used,  and  is  due  to  Haldat.  It  consists 
of  a  bent  tube,  ABC  (fig.  71),  at  one  end  of  which.  A,  is  fitted  a  stop-cock,  in 
which  can  be  screwed  two  vessels,  M  and  P,  of  the  same  height,  but  different 
in  shape  and  capacity,  the  first  being  conical,  and  the  other  nearly  cylindri- 
cal. Mercury  is  poured  into  the  tube  ABC, until  its  level  nearly  reaches  A. 
The  vessel  M  is  then  screwed  on  and  filled  with  water.  The  pressure  of 
the  water  acting  on  the  mercury  causes  it  to  rise  in  the  tube  C,  and  its 
height  may  be  marked  by  means  of  a  little  collar,  a.,  which  slides  up  and 
down  the  tube.  The  level  of  the  water  in  M  is  also  marked  by  means  of  the 
movable  rod  o.  When  this  is  done,  M  is  emptied  by  means  of  the  stop-cock, 
unscrewed,  and  replaced  by  P.  When  water  is  now  poured  in  this,  the 
mercury,  which  had  resumed  its  original  level  in  the  tube  ABC,  again  rises 


-101]     Pressure  is  Independent  of  the  Shape  of  the   Vessel.     91 

in  C  ;  and  when  the  water  in  P  has  the  same  height  as  it  had  in  M,  which 
is  indicated  by  the  rod  o,  the  mercury  will  have  risen  to  the  height  it  had 


Fig.  71. 

before,  which  is  marked  by  the  collar  a.  Hence  the  pressure  on  the  mercury 
in  both  cases  is  the  same.  This  pressure  is  therefore  independent  of  the 
shape  of  the  vessels,  and,  consequently,  also  of  the  quantity  of  liquid.  The 
base  of  the  vessel  is  obviously  the  same  in  both  cases;  it  is  the  surface  of 
the  mercury  in  the  interior  of  the  tube  A. 

Another  mode  of  demonstrating  this  principle  is  by  means  of  an  apparatus 
devised  by  Masson.  In  this  (fig.  72)  the  pressure  of  the  water  contained  in 
the  vessel  M  is  not  exerted  upon  the  column  of  mercury,  as  in  thatof  Haldat, 
but  on  a  small  disc  or  stop  a,  which  closes  a  tubulure  <:,  on  which  is  screwed 
the  vessel  M.  The  disc  is  now  fixed  to  the  tubulure,  but  is  sustained  by  a 
thread  attached  to  the  end  of  a  scale-beam.  At  the  other  end  is  a  pan,  in 
which  weights  can  be  placed  until  they  counterbalance  the  pressure  exerted 
by  the  water  on  the  stop.  The  vessel  M  being  emptied  is  unscrewed, 
and  replaced  by  the  narrow  tube  P.  This  being  filled  to  the  same  height 
as  the  large  vessel,  which  is  observed  by  means  of  the  mark  o^  it  will  be 
observed  that  to  keep  the  disc  in  its  place  just  the  same  weight  must  be 
placed  in  the  pan  as  before,  which  leads,  therefore,  to  the  same  conclusion 
as  does  Haldat's  experiment.  The  same  result  is  obtained  if,  instead  of  the 
vertical  tube  P,  the  oblique  tube  Q  be  screwed  to  the  tubulure. 

From  a  consideration  of  these  principles  it  will  be  readily  seen  that  a 
very  small  quantity  of  water  can  produce  considerable  pressures.  Let  us 
imagine  any  vessel— a  cask,  for  example — filled  with  water,  and  with  a  long 
narrow  tube  tightly  fitted  into  the  side.  If  water  is  poured  into  the  tube, 
there  will  be  a  pressure  on.  the  bottom  of  the  cask  equal  to  the  weight  of  a 
column  of  water  whose  base  is  the  bottom  itself,  and  whose  height  is  equal 


92 


On  Liquids. 


[101- 


to  that  of  the  water  in  the  tube.  The  pressure  may  be  made  as  great  as  we 
please  ;  by  means  of  a  narrow  thread  of  water  forty  feet  high,  Pascal  suc- 
ceeded in  bursting  a  very  solidly  constructed  cask. 

The  toy  known  as  the  hydrostatic  bellows  depends  on  the  same  principle, 
and  we  shall  see  a  most  important  application  of  it  in  the  hydraulic  press 
(io8). 

From  the  principle  just  laid  down,  the  pressures  produced  at  the  bottom 
of  the  sea  may  be  calculared.  It  will  be  presently  demonstrated  that  the 
pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  sea  water  about 


thirty- three  teet  high.  At  sea  the  lead  has  frecjuently  descended  to  a  depth 
of  thirteen  thousand  feet  ;  at  the  bottom  of  some  seas,  therefore,  there  must 
be  a  pressure  of  four  hundred  atmospheres. 

I02.  Pressure  on  the  sides  of  vessels. — Since  the  pressure  caused  by 
gravity  in  the  mass  of  a  liquid  is  transmitted  in  every  direction,  according  to 
the  general  law  of  the  transmission  of  fluid  pressure,  it  follows  that  at  every 
point  of  the  side  of  any  vessel  a  pressure  is  exerted,  at  right  angles  to  the 
side,  which  we  will  suppose  to  be  plane.  The  resultant  of  all  these  pressures 
is  the  total  pressure  on  the  sides.  But  since  these  pressures  increase  in 
proportion  to  the  depth,  and  also  in  proportion  to  the  horizontal  extent  of 
their  side,  their  resultant  can  only  be  obtained  by  calculation,  which  shows 
that  the  total  pressure  on  any  given  portion  of  the  side  is  equal  to  the 
weight  of  a  column  of  liquid  which  has  this  portion  of  the  side  for  its  base., 
and  whose  height  is  the  vertical  distance  from  the  centre  of  gravity  of  the 
portion  to  the  surface  of  the  liquid.  If  the  side  of  a  vessel  is  a  curved  surface, 
the  same  rule  gives  the  pressure  on  the  surface,  but  the  total  pressure  is 
no  longer  the  resultant  of  the  fluid  pressures. 

The  point  in  the  side  supposed  plane,  at  which  the  resultant  of  all  the 
pressure  is  applied,  is  called  the  centre  of  pressure.,  and  is  always  below  the 


-104]         Equilibrium  of  a  Liquid  in  a  Single    Vessel.  93 

centre  of  gravity  of  the  side.  For  if  the  pressures  exerted  at  different  parts 
of  the  plane  side  were  equal,  the  point  of  application  of  their  resultant,  the 
centre  of  pressure,  would  obviously  coincide  with  the  centre  of  gravity  of  the 
side.  But  since  the  jjressure  increases  with  the  depth,  the  centre  of  pressure 
is  necessarily  below  the  centre  of  gravity.  This  point  is  determined  by  cal- 
culation, which  leads  to  the  following  results  : — 

i.  With  a  rectangular  side  whose  upper  edge  is  level  with  the  water,  the 
centre  of  pressure  is  at  two-thirds  of  the  line  which  joins  the  middle  of  the 
horizontal  sides  measured  from  the  top. 

ii.  With  a  triangular  side  whose  base  is  horizontal,  and  coincident  with 
the  level  of  the  water,  the  centre  of  pressure  is  at  the  middle  of  the  line  which 
joins  the  vertex  of  the  triangle  with  the  middle  of  the  base. 

iii.  With  a  triangular  side  whose  vertex  is  level  with  the  water,  the  centre 
of  pressure  is  in  the  line  joining  the  vertex  and  the  middle  of  the  base,  and 
at  three-fourths  of  the  distance  of  the  latter  from  the  vertex. 

103.  Hydrostatic  paradox. — We  have  already  seen  that  the  pressure  on 
the  bottom  of  a  vessel  depends  neither  on  the  form  of  the  vessel  nor  on  the 
quantity  of  the  liquid,  but  simply  on  the  height  of  the  liquid  above  the 
bottom.  But  the  pressure  thus  exerted  must  not  be  confounded  with  the 
pressure  which  the  vessel  itself  exerts  on  the  body  which  supports  it.  The 
latter  is  always  equal  to  the  combined  weight  of  the  liquid  and  the  vessel  in 
which  it  is  contained,  while  the  former  may  be  either  smaller  or  greater  than 
this  weight,  according  to  the  form  of  the  vessel. 
This  fact  is  often  termed  the  hydrostatic  paradox, 
because  at  first  sight  it  appears  paradoxical. 

CD  (fig.  T^)  is  a  vessel  composed  of  two  cylin- 
drical parts  of  unequal  diameters,  and  filled  with 
water  to  a.  From  what  has  been  said  before,  the 
bottom  of  the  vessel  CD  supports  the  same  pressure 
as  if  its  diameter  were  everywhere  the  same  as  that 
of  its  lower  part  ;  and  it  would  at  first  sight  seem 
that  the  scale  MN  of  the  balance,  in  which  the 
vessel  CD  is  placed,  ought  to  show  the  same 
weight  as  if  there  had  been  placed  in  it  a  cyhn- 
drical  vessel  having  the  same  height  of  water,  and 
having  the  diameter  of  the  part  D.  But  the 
pressure  exerted  on  the  bottom  of  the  vessel  is  not 
all  transmitted  to  the  scale  MN  ;  for  the  upward -prtssuxe  upon  the  surface  7to 
of  the  vessel  is  precisely  equal  to  the  weight  of  the  extra  quantity  of  water 
which  a  cylindrical  vessel  would  contain,  and  balances  an  equal  portion  of 
the  downward  pressure  on  in.  Consequently  the  pressure  on  the  plate  MN  is 
simply  equal  to  the  weight  of  the  vessel  CD  and  of  the  water  which  it  contains. 


Fig.  73- 


[04. 


CONDITIONS    OF    THE    EQUILIBRIUM    OF    LIQUIDS. 
Equilibrium  of  a  liquid  in  a  slngrle  vessel. — In  order  that  a  liquid 


may  remain  at  rest  in  a  vessel  of  any  given  form,  it  must  satisfy  the  two 
following  conditions  : — 

I.  Its  surface  must  be  everywhere  perpendicular  to  the  resultant  of  the 
forces  which  act  on  the  molecules  of  the  liquid. 


94 


On  Liquids. 


[104- 


II.  Every  niolecttle  of  the  mass  of  tlie  liquid  Jiiust  be  subject  in  every  direc- 
tion to  equal  and  contrary  pressures. 

The  second  condition  is  self-evident ;  for  if,  in  two  opposite  directions, 
the  pressures  exerted  on  any  given  molecule  were  not  equal  and  contrary, 
the  molecule  would  be  moved  in  the  direction  of  the  greater  pressure,  and 
there  would  be  no  equilibrium.  Thus  the  second  condition  follows  from  the 
principle  of  the  equality  of  pressures,  and  from  the  reaction  which  all  pres- 
sure causes  on  the  mass  of  liquids. 

To  prove  the  first  condition,  let  us  suppose  that  inp  is  the  resultant  of  all 
the  forces  acting  upon  any  molecule  vi  on  the 
surface  (fig.  74),  and  that  this  surface  is  inclined 
in  reference  to  the  force  mp.  The  latter  can 
consequently  be  decomposed  into  two  forces, 
niq  and  nif;  the  one  perpendicular  to  the  sur- 
face of  the  liquid,  and  the  other  to  the  direction 
nip.  Now  the  first  force  mq  would  be  destroyed 
by  the  resistance  of  the  liquid,  while  the  second 
n  the  direction  nif  which  shows  that  the  equili- 


1^ 


s 


Fig.  74- 


would  move  the  molecule 
brium  is  impossible. 

If  gravity  be  the  force  acting  on  the  liquid,  the  direction  nip  is  vertical  ; 
hence,  if  the  liquid  is  contained  in  a  basin  or  vessel  of  small  extent,  the  sur- 
face ought  to  be  plane  and  horizontal  (67),  because  then  the  direction  of 
gravity  is  the  same  in  every  point.  But  the  case  is  different  with  liquid  sur- 
faces of  greater  extent,  like  the  ocean.     The  surface  will  be  perpendicular 

to  the  direction  of  gravity  ;  but  as 
this  changes  from  one  point  to  another, 
and  always  tends  towards  a  point  near 
the  centre  of  the  earth,  it  follows  that 
the  direction  of  the  surface  of  the  ocean 
will  change  also,  and  assume  a  nearly 
spherical  form. 

105.  Equilibrium  of  the  same 
liquid  in  several  communicating' 
vessels. — When  several  vessels  of 
any  given  form  communicate  with 
each  other,  there  will  be  equili- 
brium when  the  liquid  in  each  vessel 
satisfies  the  two  preceding  conditions 
(104),  and  further,  when  the  surfaces  of 
the  liquids  in  all  the  vessels  are  in  the 
same  horizontal  plane. 
In  the  vessels  ABCD  (fig  75),  which  communicate  with  each  other,  let 
us  consider  any  transverse  section  of  the  tube  mn  ;  the  liquid  can  only 
remain  in  equilibrium  as  long  as  the  pressures  which  this  section  supports 
from  m  in  the  direction  of  ;;,  and  from  n  in  the  direction  of ;//,  are  equal  and 
opposite.  Now  it  has  been  already  proved  that  these  pressures  are  respec- 
tively equal  to  the  weight  of  a  column  of  water,  whose  base  is  the  supposed 
section,  and  whose  height  is  the  distance  from  the  centre  of  gravity  of  this 
section  to  the  surface  of  the  liquid.     If  we  conceive,  then,  a  horizontal  plane, 


Fig.  75- 


-107] 


Eqiiilibriiwt  of  Tzvo  Different  Liquids. 


95 


m/i,  drawn  through  the  centre  of  gravity  of  this  section,  it  will  be  seen  that 
there  will  only  be  equilibrium  as  long  as  the  height  of  the  liquid  above  this 
plane  is  the  same  in  each  vessel,  which  demonstrates  the  principle  enunciated. 

lo6.  Equilibrium  of  superposed  liquids. — In  order  that  there  should 
be  equilibrium  when  several  heterogeneous  liquids  are  superposed  in  the 
same  vessel,  each  of  them  must  satisfy  the  conditions  necessary  for  a  single 
liquid  (104)  ;  and  further,  there  will  be  stable  equilibriuin  only  when  the 
liquids  are  arranged  in  the  order  of  their  decreasing  densities  from  the 
bottom  upwards. 

The  last  condition  is  expermientally  demonstrated  by  means  oi  ihQ  phial 
of  four  ele/nents.  This  consists  of  a  long  narrow  bottle  containing  mercury, 
water  saturated  with  carbonate  of  potass,  alcohol  coloured  red,  and  petroleum. 
When  the  phial  is  shaken  the  liquids  mix,  but  when  it  is  allowed  to  rest  they 
separate  ;  the  mercury  sinks  to  the  bottom,  then  comes  the  water,  then  the 
alcohol,  and  then  the  petroleum.  This  is  the  order  of  the  decreasing  densi- 
ties of  the  bodies.  The  water  is  saturated  with  carbonate  of  potass  to  prevent 
its  mixing  with  the  alcohol. 

This  separation  of  the  liquids  is  due  to  the  same  cause  as  that  which 
enables  solid  bodies  to  float  on  the  surface  of  a  liquid  of  greater  density  than 
their  own.  It  is  also  on  this  account  that  fresh  water,  at  the  mouths  of 
rivers,  floats  for  a  long  time  on  the  denser  salt  water  of  the  sea  ;  and  it  is 
for  the  same  reason  that  cream,  which  is  lighter  than  milk,  rises  to  the  surface. 

107.  Equilibrium  of  two  different 
liquids  in  communicating'  vessels. — 
When  two  liquids  of  different  densities, 
which  do  not  mix,  are  contained  in  two 
communicating  vessels,  they  will  be  in 
equilibrium  when,  in  addition  to  the  pre- 
ceding principles,  they  are  subject  to  the 
following  :  that  the  heights  above  the  hot  i- 
zontal  surface  of  contact  of  two  columns  of 
liquid  in  equilibtium  are  in  the  inverse  ratio 
of  their  densities. 

To  show  this  experimentally,  mercury  is 
poured  into  a  bent  glass  tube,  w;?,  fixed 
against  an  upright  wooden  support  (fig.  76), 
and  then  water  is  poured  into  one  of  the 
legs,  AB.  The  column  of  water,  AB,  press- 
ing on  the  mercury  at  B,  lowers  its  level  in 
the  leg  AB,  and  raises  it  in  the  other  by  a 

quantity  CD  ;  so  that  if,  when  equilibrium  is  established,  we  imagine 
a  horizontal  plane,  BC,  to  pass  through  B,  the  column  of  water  in  AB  will 
balance  the  column  of  mercury  CD.  If  the  heights  of  these  two  columns  are 
then  measured  by  means  of  the  scales,  it  will  be  found  that  the  height  of  the 
column  of  water  is  about  13^  times  that  of  the  height  of  the  column  of  mercury. 
We  shall  presently  see  that  the  density  of  mercury  is  about  13^  times  that  of 
water,  from  which  it  follows  that  the  heights  are  inversely  as  the  densities. 

It  may  be  added  that  the  equilibrium  cannot  exist  unless  there  is  a  sufficient 
quantity  of  the  heavier  liquid  for  part  of  it  to  remain  in  both  legs  of  the  tube. 


96 


On  Liquids. 


[107- 


The  preceding  principle  may  be  deduced  by  a  veiy  simple  calculation. 
Let  d  and  d'  be  the  densities  of  water  and  mercury,  and  h  and  h'  their  re- 
spective heights,  and  let  g  be  the  force  of  gravity.  The  pressure  on  B  will 
be  proportional  to  the  density  of  the  liciuid,  to  its  height,  and  to  the  force  of 
gravity  ;  on  the  whole,  therefore,  to  the  product  dhg.  Similarly  the  pres- 
sure at  C  will  be  proportional  to  d'h'g.  But  in  order  to  produce  equilibrium, 
dlig  must  be  equal  to  d'h'g,  or  dh  =  d'h'.  This  is  nothing  more  than  an 
algebraical  expression  of  the  above  principle  ;  for  since  the  two  products 
must  always  be  equal,  d'  must  be  as  many  times  greater  than  d  as  h'  is  less 
than  //. 

In  this  manner  the  density  of  a  liquid  may  be  determined.  Suppose  one 
of  the  branches  contained  water  and  the  other  oil,  and  their  heights  were, 
respectively,  15  inches  for  the  oil  and  14  inches  for  the  water.  The  density 
of  water  being  taken  as  unity,  and  that  of  oil  being  called  x,  we  shall  have 

14 


15  X  .t-=  14  X  I  ;  whence  x  = 


0-933- 


APPLICATIONS    OF   THE    PRECEDING    HYDROSTATIC    PRINCIPLES. 

108.  Hydraulic  press. — The  law  of  the  equality  of  pressure  has  received 
a  most  important  application  in  the  hydraulic  press,  a  machine  by  which 


Fig.  77. 


enormous  pressures  may  be  produced.     Its  principle  is  due  to  Pascal,  but  it 
was  first  constructed  by  Bramah  in  1796. 


-108] 


Hydraulic  Press. 


97 

It  consists  of  a  cylinder  B,  with  very  strong  thick  sides  (fig.  77),  in 
which  there  is  a  cast-iron  ram  P  working  water-tight  in  the  collar  of  the 
cylinder.  On  the  ram  P  there  is  a  cast-iron  plate  on  which  the  substance 
to  be  pressed  is  placed.  Four  strong  columns  serve  to  support  and  fix  a 
second  plate  Q. 

By  means  of  a  leaden  pipe  K,  the  cylinder  B,  which  is  filled  with  water, 
communicates  with  a  small  force-pump  A,  which  works  by  means  of  a  lever 
M.  When  the  piston  of  this  pump/  ascends,  a  vacuum  is  produced,  and  the 
water  rises  in  the  tube  a,  at  the  end  of  which  there  is  a  rose,  to  prevent  the 
entrance  of  foreign  matters.  When  the  piston  p  descends,  it  drives  the  water 
into  the  cylinder  by  the  tube  K. 

Fig.  78  represents  a  section,  on  a  larger  scale,  of  the  system  of  valves 
necessary  in  working  the  apparatus.  The  valve  <?,  below  the  piston/,  opens 
when  the  piston  rises, 
and  closes  when  it 
descends.  The  valve 
o,  during  this  descent, 
is  opened  by  the 
pressure  of  the  water 
which  passes  by  the 
pipe  K.  The  valve  z 
is  a  safety-valve,  held 
by  a  weight  which 
acts  on  it  by  means  of 
a  lever.  By  weight- 
ing the  latter  to  a 
greater  or  less  extent 
the  pressure  can  be 
regulated,  for  as  soon  as  there  is  an  upward  pressure  greater  than  that  ot  the 
weight  upon  it,  it  opens  and  water  escapes.  A  screw  r  serves  to  relieve  the 
pressure,  for  when  it  is  opened  it  affords  a  passage  for  the  efflux  of  the  water 
in  the  cylinder  B. 

A  most  important  part  is  the  leather  collar,  ft,  the  invention  of  which  by 
Bramah  removed  the  difficulties  which  had  been  experienced  in  making  the 
large  ram  work  water-tight  when  submitted  to 
great  pressures.  It  consists  of  a  circular  piece  of 
stout  leather  (fig.  79),  saturated  with  oil  so  as  to 
be  impervious  to  water,  in  the  centre  of  which  a 
circular  hole  is  cut.  This  piece  is  bent  so  that 
a  section  of  it  i-epresents  a  reversed  U,  and  is 
fitted  into  a  groove  tt  made  in  the  neck  of  the  Fig.  79. 

cylinder.    This  collar  being  concave  downwards, 

in  proportion  as  the  pressure  increases,  it  fits  the  more  tightly  against  the 
ram  P  on  one  side  and  the  neck  of  the  cylinder  on  the  other,  and  quite  pre- 
vents any  escape  of  water. 

The  pressure  which  can  be  obtained  by  this  press  depends  on  the  relation 
of  the  piston  P  to  that  of  the  piston/.  If  the  former  has  a  transverse  section 
fifty  or  a  hundred  times  as  large  as  the  latter,  the  upward  pressure  on  the 
large  piston  will  be  fifty  or  a  hundred  times  that  exerted  upon  the  small  one. 

H 


Fig.  78. 


98  Oti  Liquids.  [108- 

By  means  of  the  lever  M  an  additional  advantage  is  obtained.  If  the 
distance  from  the  fulcrum  to  the  point  where  the  power  is  applied  is  five  times 
the  distance  from  the  fulcrum  to  the  piston^,  the  pressure  on/  will  be  five 
times  the  power.  Thus,  if  a  man  acts  on  M  with  a  force  of  sixty  pounds,  the 
force  transmitted  by  the  piston  p  will  be  300  pounds,  and  the  force  which 
tends  to  raise  the  piston  P  will  be  30,000  pounds,  supposing  the  section  of  P 
is  a  hundred  times  that  oi p. 

The  hydraulic  press  is  used  in  all  cases  in  which  great  pressures  are  re- 
quired. It  is  used  in  pressing  cloth  and  paper,  in  extracting  the  juice  of  beet- 
root, in  compressing  hay  and  cotton,  in  expressing  oil  from  seeds,  and  in 
bending  iron  plates  ;  it  also  sei'ves  to  test  the  strength  of  cannon,  of  steam 
boilers,  and  of  chain  cables.  The  parts  composing  the  tubular  bridge  which 
spans  the  Menai  Straits  were  raised  by  means  of  an  hydraulic  press.  The 
cylinder  of  this  machine,  the  largest  which  has  ever  been  constructed,  was 
nine  feet  long  and  twenty-two  inches  in  internal  diameter  ;  it  was  capable  of 
raising  a  weight  of  two  thousand  tons. 

The  principle  of  the  hydraulic  press  is  advantageously  employed  in  cases 
in  which  great  power  is  only  required  at  intervals,  such  as  in  opening  dock 
gates,  working  cranes,  in  lifts  in  hotels,  warehouses,  and  the  like.  It  has 
even  been  used  in  working  stage  machinery.  In  these  cases  an  hydraulic  accii- 
jiiiilator  is  used.  The  piston  P  is  loaded  with  very  great  weights,  and  water 
is  continually  forced  into  the  cylinder  B  by  powerful  pumps.  From  the  bottom 
of  this  cylinder  a  tube  conducts  water  to  any  place  where  the  power  is  to  be 
applied,  and  the  flow  of  even  small  quantities  of  water  which  is  under  high 
pressure  can  perform  a  great  amount  of  work. 

Suppose,  for  instance,  that  the  area  of  the  piston  P  is  four  square  feet,  and 
that  it  has  a  load  of  100  tons  ;  this  represents  a  pressure  of  over  370  pounds 
on  the  square  inch  or  more  than  25  atmospheres.  When  the  large  piston 
sinks  through  the  y^th  of  an  inch  about  a  pint  of  watei  will  flow  out,  and  this 
represents  a  work  of  about  1,100  foot-pounds.  In  London  hydraulic  power  is 
supplied  by  water  delivered  under  a  pressure  of  750  pounds  per  square  inch. 

109.  The  water-level. — The  water-level  is  an  application  of  the  con- 
ditions of  ecjuilibrium  in  communicating  vessels.     It  consists  of  a  metal  tube 


Fig.  So. 

bent  at  both  ends,  in  which  are  fitted  glass  tubes  D  and  E  (fig.  80).     It  is 
placed  on  a  tripod,  and  water  poured  in  until  it  rises  in  both  legs.    When  the 


Artesian    Wells. 


99 


-111] 

liquid  is  at  rest,  the  level  of  the  water  in  both  tubes  is  the  same  ;  that  is, 
they  are  both  in  the  same  horizontal  plane. 

This  instrument  is  used  in  levelling,  or  ascertaining  how  much  one  point 
is  higher  than  another.  If,  for  example,  it  is  desired  to  find  the  difference 
between  the  heights  of  B  and  A,  a  levelling-staff'x's,  fixed  on  the  latter  place. 
This  staff  consists  of  a  rule  formed  of  two  sliding  pieces  of  wood,  and  sup- 
porting a  piece  of  tin  plate  M,  in  the  centre  of  which  there  is  a  mark.  This 
staff  being  held  vertically  at  A,  an  observer  looks  at  it  through  the  level 
along  the  surfaces  D  and  E,  and  directs  the  holder  to  raise  or  lower  the  slide 
until  the  mark  is  in  the  prolongation  of  the  line  DE.  The  height  AM  is 
then  measured,  and  subtracting  it  from  the  height  of  the  level  the  height  of 
the  point  A  above  B  is  obtained. 

I  lo.  The  Spirit-level. — The  spirit-level  is  both  more  delicate  and  more 
accurate  than  the  water-level.  It  consists  of  a  glass  tube  AB  (fig.  8i),  very 
slightly  curved  ;  that  is, 
the  tube,  instead  of  being 
a  true  cylinder  as  it  seems 
to  be,  is  in  fact  slightly 
curved  in  such  a  manner 
that  its  axis  is  an  arc  of 
a  circle  of  very  large 
radius.  It  is  filled  with 
spirit  with  the  exception 
of  a  bubble  of  air,  which 
tends  to  occupy  the  high- 
est part.  The  tube  is 
placed   in    a    brass    case 

CD  (fig.  82),  which  is  so  arranged  that  when  it  is  in  a  perfectly  horizontal 
position  the  bubble  of  air  is  exactly  between  the  two  points  marked  in  the 
case. 

To  take  levels  with  this  apparatus,  it  is  fixed  on  a  telescope,  which  can 
be  placed  in  a  horizontal  position. 

III.  Artesian  wells. — All  natural  collections  of  water  exemplify  the 
tendency  of  water  to  find  its  level.  Thus  a  group  of  lakes,  such  as  the 
great  lakes  of  North  America,  may  be  regarded  as  a  number  of  vessels  in 
communication,  and  consequently  the  waters  tend  to  maintain  the  same 
level  in  all.  This,  too,  is  the  case  with  the  source  of  a  river  and  the  sea, 
and,  as  the  latter  is  on  the  lower  level,  the  river  continually  flows  down  to  the 
sea  along  its  bed,  which  is,  in  fact,  the  means  of  communication  between 
the  two. 

Perhaps  the  most  striking  instance  of  this  class  of  natural  phenomena  is 
that  of  artesian  wells.  These  wells  derive  their  name  from  the  province 
of  Artois,  where  it  has  long  been  customary  to  dig  them,  and  whence  their 
use  in  other  parts  of  France  and  Europe  was  derived.  It  seems,  however, 
that  at  a  very  remote  period  wells  of  the  same  kind  were  dug  in  China  and 
Egypt. 

To  understand  the  theory  of  these  wells  it  must  be  premised  that  the 
strata  composing  the  earth's  crust  are  of  two  kinds  :  the  one  permeable  to 
water,  such  as  sand,  gravel,  &c. ;  the  other  iupermeable,  such  as  clay.     Let 

H  2 


On  Liquids. 


[Ill- 


us  suppose,  then,  a  geographical  basin  of  greater  or  less  extent,  in  which  the 
two  impermeable  layers  AB,  CD  (fig.  83),  enclose  between  them  a  permeable 
layer  KK.  The  rain-water  falling  on  that  part  of  this  layer  which  comes  to  the 
surface,  and  which  is  called  the  outcrop,  will  filter  through  it,  and  following 
the  natural  fall  of  the  ground  will  collect  in  the  hollow  of  the  basin,  whence 
it  cannot  escape  owing  to  the  impermeable  strata  above  and  below  it.  If, 
now,  a  vertical  hole,  I,  be  sunk  down  to  the  water-bearing  stratum,  the  water 
striving  to  regain  its  level  will  spout  out  to  a  height  which  depends  on  the 
difference  between  the  levels  of  the  outcrop  and  of  the  point  at  which  the 
perforation  is  made. 

The  waters  which    feed   artesian  wells    often  come  fiom  a  distance  of 
sixty  or  seventy  miles.     The  depth  varies  in  different  places.     The  well  at 


^^ 


Crenelle  is  1,800  feet  deep  ;  it  gives  656  gallons  of  water  in  a  minute,  and 
is  one  of  the  deepest  and  most  abundant  which  have  been  made.  The 
temperature  of  the  water  is  27°  C.  It  follows  from  the  law  of  the  in- 
crease of  temperature  with  the  increasing  depth  below  the  surface  of  the 
ground,  that,  if  this  well  were  210  feet  deeper,  the  water  would  have  all 
the  year  round  a  temperature  of  32°  C. ;  that  is,  the  ordinary  temperature  of 
baths. 


BODIES    IMMERSED    IN    LIQUIDS. 

112.  Pressure  supported  by  a  body  Immersed  in  a  liquid. — When  a 
solid  is  immersed  in  a  liquid,  every  portion  of  its  surface  is  submitted  to  a 
perpendicular  pressure  which  increases  with  the  depth.  If  we  imagine  all 
these  pressures  decomposed  into  horizontal  and  vertical  pressures,  the  first 
set  are  in  equilibrium.  The  vertical  pressures  are  obviously  unequal,  and 
will  tend  to  move  the  body  upwards. 

Let  us  imagine  a  cube  immersed  in  a  mass  of  water  (fig.  84),  and  that 
four  of  its  edges  are  vertical.  The  pressures  upon  the  four  vertical  faces  being 
clearly  in  equilibrium,  we  need  only  consider  the  pressures  exerted  on  the 
horizontal  faces  A  and  B.  The  first  is  pressed  downwards  by  a  column  of 
water  whose  base  is  the  face  A,  and  whose  height  is  AD  ;  the  lower  face  B 
is  pressed  upwards  by  the  weight  of  a  column  of  water  whose  base  is  the 


-113] 


Principle  of  Archimedes. 


Fig.  84. 


face  itself,  and  whose  height  is  BD  (100).  The  cube,  therefore,  is  urged 
upwards  by  a  force  equal  to  the  difference  between  these  two  pressures, 
which  latter  is  manifestly  equal  to  the  weight  of  a  column  of  water  having 
the  same  base  and  the  same  height  as  this  cube.  Consequently,  this  upward 
pressure  is  equal  to  the  weight  of  the  volitme  of  water  displaced  by  the  im- 
mersed body. 

We  shall  readily  see  from  the  following  reasoning  that  every  body 
immersed  in  a  liquid  is  pressed  upwards  by  a  force  equal  to  the  weight  of 
the  displaced  liquid.  In  a  liquid  at  rest  let  us  sup- 
pose a  portion  of  it  of  any  given  shape,  regular 
or  irregular,  to  become  solidified,  without  either 
increase  or  decrease  of  volume.  The  liquid  thus 
solidified  will  remain  at  rest,  and  therefore  must 
be  acted  upon  by  a  force  equal  to  its  weight,  and 
acting  vertically  upwards  through  its  centre  of 
gravity  ;  for  otherwise  motion  would  ensue.  If  in 
the  place  of  the  solidified  water  we  imagine  a  solid 
of  another  substance  of  exactly  the  same  volume 
and  shape,  it  will  necessarily  receive  the  same 
pressures  from  the  surrounding  liquid  as  the  solidi- 
fied portion  did ;  hence,  like  the  latter,  it  will  sustain 
the  pressure  of  a  force  acting  vertically  upwards 
through  the  centre  of  gravity  of  the  displaced  liquid, 
and  equal  to  the  weight  of  the  displaced  liquid.  If,  as  almost  invariably 
happens,  the  liquid  is  of  uniform  density,  the  centre  of  gravity  of  the  displaced 
liquid  means  the  centre  of  gravity  of  the  immersed  part  of  the  body  supposed  to 
be  of  uniform  density.  This  distinction  is  sometimes  of  importance  :  for  ex- 
ample, if  a  sphere  is  composed  of  a  hemisphere  of  iron  and  another  of  wood, 
its  centre  of  gravity  would  not  coincide  with  its  geometrical  centre,  but,  if  it 
were  placed  under  water,  the  centre  of  gravity  of  the  displaced  water  would 
be  at  the  geometrical  centre — that  is,  would  have  the  same  position  as  the 
centre  of  gravity  of  the  sphere  if  of  uniform  density. 

1 1 3.  Principle  of  Archimedes. — The  preceding  principles  prove  that 
every  body  immersed  in  a  liquid  is  submitted  to  the  action  of  two  forces  : 
gravity  which  tends  to  lower  it,  and  the  buoyancy  of  the  liquid  which  tends 
to  raise  it  with  a  force  equal  to  the  weight  of  the  liquid  displaced.  The 
weight  of  the  body  is  either  totally  or  partially  overcome  by  its  buoyancy, 
from  which  it  is  concluded  that  a  body  immersed  ift  a  liquid  loses  apart  of 
its  weight  equal  to  the  weight  of  the  displaced  liquid. 

This  principle,  which  is  the  basis  of  the  theory  of  immersed  and  floating 
bodies,  is  called  the  principle  of  Archimedes,  after  the  discoverer.  It  may 
be  shown  experimentally  by  means  of  the  hydrostatic  balance  (fig.  85).  This 
is  an  ordinary  balance,  each  pan  of  which  is  provided  with  a  hook  ;  the 
beam  can  be  raised  by  means  of  a  toothed  rack,  which  is  worked  by  a  little 
pinion  C.  A  catch,  D,  holds  the  rack  when  it  has  been  raised.  The  beam 
being  raised,  a  hollow  brass  cylinder.  A,  is  suspended  from  one  of  the  pans, 
and  below  this  a  solid  cylinder,  B,  whose  volume  is  exactly  equal  to  the 
capacity  of  the  first  cylinder  ;  lastly,  an  equipoise  is  placed  in  the  other  pan. 
If  now  the  hollow  cylinder  A  be  filled  with  water,  the  equilibrium  is  disturbed  ; 


On  Liquids. 


[113- 


I02 

but  if  at  the  same  time  the  beam  is  lowered  so  that  the  sohd  cylinder  B  be- 
comes immersed  in  a  vessel  of  water  placed  beneath  it,  the  equilibrium  will 
be  restored.  By  being  immersed  in  water  the  cylinder  B  loses  a  portion  of 
its  weight  equal  to  that  of  the  water  in  the  cylinder  A.  Now,  as  the  capacity 
of  the  cylinder  A  is  exactly  equal  to  the  volume  of  the  cylinder  B,  the  prin- 
ciple which  has  been  before  laid  down  is  proved. 


es^pa 


Fig.  85. 

114.  Determination  of  the  volume  of  a  body. — The  principle  of 
Archimedes  furnishes  a  method  for  obtaining  the  volume  of  a  body  of  any 
shape,  provided  it  is  not  soluble  in  water.  The  body  is  suspended  by  a  fine 
thread  to  the  hydrostatic  balance,  and  is  weighed  first  in  the  air,  and  then  in 
distilled  water  at  4°  C.  The  loss  of  weight  is,^'the  weight  of  the  displaced 
water,  from  which  the  volume  of  the  displaced  water  is  readily  calculated. 
But  this  volume  is  manifestly  that  of  the  body  itself.  Suppose,  for  example, 
155  grammes  is  the  loss  of  weight.  This  is  consequently  the  weight  of  the 
displaced  water.  Now  it  is  known  that  a  gramme  is  the  w-eight  of  a  cubic 
centimetre  of  water  at  4°;  consequently,  the  volume  of  the  Ijody  immersed 
is  155  cubic  centimetres. 

115.  Equilibrium  of  floating-  bodies. — A  body  when  floating  is  acted 
on  by  two  forces,  namely,  its  weight,  which  acts  vertically  downwards 
through  its  centre  of  gravity,  and  the  resultant  of  the  fluid  pressures,  which 


-115]  Equilibrium  of  Floating  Bodies.  103 

(112)  acts  vertically  upwards  through  the  centre  of  gravity  of  the  fluid 
displaced  ;  but  if  the  body  is  at  rest  these  two  forces  must  be  equal  and 
act  in  opposite  directions  ;  whence  follow  the  conditions  of  equilibrium', 
namely, — 

i.  The  jioating  body  must  displace  a  volume  of  liquid ivJiose  weight  equals 
that  of  the  body. 

ii.  The  centre  of  gravity  of  the  floating  body  must  be  i?t  the  same  vertical 
line  with  that  of  the  fluid  displaced. 

Thus  in  fig.  86,  if  C  is  the  centre  of  gravity  of  the  body,  and  G  that  of 
the  displaced  fluid,  the  line  GC  must  be  vertical,  since  when  it  is  so  the 
weight  of  the  body  and  the  fluid  pressure  will  act  in  opposite  directions 
along  the  same  line,  and  will  be  in  equilibrium  if  equal.  It  is  convenient, 
with  reference  to  the  subject  of  the  present  article,  to  speak  of  the  line  CG 
produced  as  the  axis  of  the  body. 

Next  let  it  be  inquired  whether  the  equilibrium  be  stable  or  unstable. 
Suppose  the  body  to  be  turned  through  a  small  angle  (fig.  87),  so  that  the 
axis  takes  a  position 
inclined  to  the  vertical. 
The  centre  of  gravity 
of  the  displaced  fluid 
will  no  longer  be  G, 
but  some  other  point, 
G'.  And  since  the  fluid 
pressure  acts  vertically 
upwards  through  G', 
its  direction  will  cut 
the  axis  in  some  point 
M',  which  will  gene- 
rally have  different  positions  according  as  the  inclination  of  the  axis  to  the 
vertical  is  greater  or  smaller.  If  the  angle  is  indefinitely  small,  M'will  have 
a  definite  position  M,  which  always  admits  of  determination,  and  is  called 
the  metacentre. 

If  we  suppose  M  to  be  above  C,  an  inspection  of  fig.  88  will  show  that 
when  the  body  has  received  an  indefinitely  small  displacement,  the  weight  of 
the  body  W,  and  the  resultant  of  the  fluid  pressures  R,  tend  to  bring  the 
body  back  to  its  original  position  ;  that  is,  in  this  case,  the  equilibrium  is 
stable  (70).  If,  on  the  contrary,  M  is  below  C,  the  forces  tend  to  cause  the 
axis  to  deviate  farther  from  the  vertical,  and  the  equilibrium  is  unstable. 
Hence  the  rule — ■ 

iii.  The  equilibrium  oj  a  floating  body  is  stable  or  unstable  according  as 
the  metacentre  is  above  or  below  the  centre  of  gravity. 

The  determination  of  the  metacentre  can  rarely  be  effected  except  by 
means  of  a  somewhat  difficult  mathematical  process.  When,  however,  the 
form  of  the  immersed  part  of  a  body  is  spherical,  it  can  be  readily  determined  ; 
for  since  the  fluid  pressure  at  each  point  converges  to  the  centre,  and  con- 
tinues to  do  so  when  the  body  is  slightly  displaced,  their  resultant  must  in 
all  cases  pass  through  the  centre,  which  is  therefore  the  metacentre.  •  To 
illustrate  this  :  let  a  spherical  body  float  on  the  surface  of  a  liquid  (fig.  89)  ; 
then,  its  centre  of  gravity  and   the   metacentre   both  coinciding  with   the 


Fig.  89. 


104  On  Liquids.  [115- 

geometrical  centre  C,  its  equilibrium  is  neutral  (70).  Now  suppose  a  small 
heavy  body  to  be  fastened  at  P,  the  summit  of  the  vertical  diameter.  The 
centre  of  gravity  will  now  be  at  some  point  G  above  C.  Consequently,  the 
equilibrium  is  unstable,  and  the  sphere,  left  to  itself,  will  instantly  turn  over 
and  will  rest  when  P  is  the  lower  end  of  a  vertical  diameter. 

On  investigating  the  position  of  the  metacentre 
of  a  cylinder,  it  is  found  that,  when  the  ratio  of 
the  radius  to  the  height  is  greater  than  a  certain 
quantity,  the  position  of  stable  equilibrium  is  that 
in  which  the  axis  is  vertical  ;  but  if  it  be  less  than 
that  quantity,  the  equilibrium  is  stable  when  the 
axis  is  horizontal.  For  this  reason  the  stump  of  a 
tree  floats  lengthwise,  but  a  thin  disc  of  wood  floats 
flat  on  the  water.  Hence,  also,  if  it  is  required  to 
make  a  cylinder  of  moderate  length  float  with 
its  axis  vertical,  it  is  necessary  to  load  it  at  the 
lower  end.  By  so  doing  its  centre  of  gravity  is  brought  below  the  meta- 
centre. 

The  determination  of  the  metacentre  and  of  the  centre  of  gravity  is  of 
great  importance  in  the  stowage  of  vessels,  for  on  their  relative  positions 
the  stability  depends. 

1 16.  Cartesian  diver — The  different  effects  of  suspension,  immersion, 

and  floating  are  reproduced  by  means  of  a  well- 
known  hydrostatic  toy,  the  Cartesian  diver  (fig.  90). 
It  consists  of  a  glass  cylinder  nearly  full  of  water, 
on  the  top  of  which  a  brass  cap,  provided  with  a 
piston,  is  hermetically  fitted.  In  the  liquid  there  is 
a  little  porcelain  figure  attached  to  a  hollow  glass 
ball  a,  which  contains  air  and  water,  and  floats  on 
the  surface.  In  the  lower  part  of  this  ball  there  is 
a  little  hole  by  which  water  can  enter  or  escape, 
according  as  the  air  in  the  interior  is  more  or  less 
compressed.  The  quantity  of  water  in  the  globe 
is  such  that  very  little  more  is  required  to  make  it 
sink.  If  the  piston  is  slightly  lowered  the  air  is 
compressed,  and  this  pressure  is  transmitted  to  the 
water  of  the  vessel  and  the  air  in  the  bulb.  The 
consequence  is  that  a  small  quantity  of  water  pene- 
trates into  the  bulb,  which  therefore  becomes 
heavier  and  sinks.  If  the  pressure  is  relieved,  the 
air  in  the  bulb  expands,  expels  the  excess  of  water 
which  had  entered  it,  and  the  apparatus,  being 
now  lighter,  rises  to  the  surface.  The  experiment 
may  also  be  simplified  by  replacing  the  brass  cap 
and  piston  by  a  cover  of  sheet  india-rubber,  which 
Fig,  go.  is  tightly  tied  over  the  mouth  ;  when  this  is  pressed 

by  the  hand  the  same  effects  are  produced. 

117.  Swimmingr-bladder  of  fishes — Most  fishes  have  an  air-bladder 
below  the  spine,  which  is  called  the  sivimming-bladder.     The  fish  can  com- 


-120]  Specific  Gravity  of  Solids.  105 

press  or  dilate  this  at  pleasure  by  means  of  a  muscular  effort,  and  produce 
the  same  effects  as  those  just  described — that  is,  it  can  either  rise  or  sink  in 
water. 

1 1 8.  Swimming:. — The  human  body  is  lighter,  on  the  whole,  than  an 
equal  volume  of  water  :  it  consequently  floats  on  the  surface,  and  still  better 
in  sea-water,  which  is  heavier  than  fresh  water.  The  difficulty  in  swimming 
consists  not  so  much  in  floating,  as  in  keeping  the  head  above  water,  so  as 
to  breathe  freely.  In  man  the  head  is  heavier  than  the  lower  parts,  and 
consecjuently  tends  to  sink,  and  hence  swimming  is  an  art  which  requires  to 
be  learned.  With  quadrupeds,  on  the  contrary,  the  head,  being  less  heavy 
than  the  posterior  parts  of  the  body,  remains  above  water  without  any  effort, 
and  these  animals  therefore  swim  naturally. 


SPECIFIC   GRAVITY — HYDROMETERS. 

119.  Determination  of  specific  gravities. — It  has  been  already  ex- 
plained (24)  that  the  specific  gravity  of  a  body,  whether  solid  or  liquid,  is  the 
number  which  expresses  the  relation  of  the  weight  of  a  given  volume  of  this 
body  to  the  weight  of  the  same  volume  of  distilled  water  at  a  temperature 
of  4°.  In  order,  therefore,  to  calculate  the  specific  gravity  of  a  body,  it  is 
sufficient  to  determine  its  weight  and  that  of  an  equal  volume  of  water,  and 
then  to  divide  the  first  weight  by  the  second  :  the  quotient  is  the  specific 
gravity  of  the  body. 

Three  methods  are  commonly  used  in  determining  the  specific  gravities 
of  solids  and  liquids.  These  are — ist,  the  method  of  the  hydrostatic  balance ; 
2nd,  that  of  the  hydrometer  ;  and  3rd,  the  specific  gravity  flask.  All  three, 
however,  depend  on  the  same  principle — that  of  first  ascertaining  the  weight 
of  a  body,  and  then  that  of  an  equal  volume  of  water.  We  shall  first  apply 
these  methods  to  determining  the  specific  gravity  of  solids,  and  then  to  the 
specific  gravity  of  liquids. 

120.  Specific  gravity  of  solids. — i.  Hydrostatic  balance. — To  obtain  the 
specific  gravity  of  a  solid  by  the  hydrostatic  balance  (fig.  85),  it  is  first 
weighed  in  the  air,  and  is  then  suspended  to  the  hook  of  the  balance  and 
weighed  in  water  (fig.  91).  The  loss  of  weight  which  it  experiences  is, 
according  to  Archimedes'  principle,  the  weight  of  a  volume  of  water  equal 
to  its  own  volume  ;  consequently,  dividing  the  weight  in  air  by  the  loss  of 
weight  in  water,  the  quotient  is  the  specific  gravity  required.  If  P  is  the 
weight  of  the  body  in  air,  P'  its  weight  in  water,  and  D  its  specific  gravity, 

p 
P  -  P'  being  the  weight  of  the  displaced  water,  we  have  D  = . 

It  may  be  observed  that  though  the  weighing  is  performed  in  air,  yet, 
strictly  speaking,  the  quantity  required  is  the  weight  of  the  body  in  vacuo  ; 
and,  when  great  accuracy  is  required,  it  is  necessary  to  apply  to  the  observed 
weights  a  con-ection  for  the  weights  of  the  unequal  volumes  of  air  displaced 
by  the  substance,  and  the  weights  in  the  other  scale-pan.  The  water  in 
which  bodies  are  weighed  is  supposed  to  be  distilled  water  at  the  standard 
temperature. 

ii.  Nicholsoii' s   hydrometer. — The  apparatus  consists  of  a  hollow  metal 


io6 


On  Liquids. 


[120- 


cylinder  B  (fig.  92),  to  which  is  fixed  a  cone  C,  loaded  with  lead.  The 
object  of  the  latter  is  to  bring  the  centre  of  gravity  below  the  metacentre, 
so  that  the  cylinder  may  float  with  its  axis  vertical.  At  the  top  is  a  stem 
terminated  by  a  pan,  in  which  is  placed  the  substance  whose  specific  gravity 
is  to  be  determined.     On  the  stem  a  standard  point,  0,  is  marked. 

The  apparatus  stands  partly  out  of  the  water,  and  the  first  step  is  to 

ascertain  the  weight  which 
must  be  placed  in  the  pan  in 
order  to  make  the  hydrometer 
sink  to  the  standard  point  0. 
Let  this  weight  be  125  grains, 
and  let  sulphur  be  the  sub- 
stance whose  specific  gravity 
is  to  be  determined.  The 
weights  are  then  removed 
from  the  pan,  and  replaced 
by  a  piece  of  sulphur  which 
weighs  less  than  125  grains, 
and  weights  added  till  the  hy- 
drometer is  again  depressed 
to  the  standard  o.  If,  for 
instance,  it  has  been  neces- 
sary to  add  55  grains,  the 
weight  of  the  sulphur  is  evi- 
dently the  difference  between 
125  and  55  grains  ;  that  is,  70 
grains.  Having  thus  deter- 
mined the  weight  of  the  sulphur  in  air,  it  is  now  only  necessary  to 
ascertain  the  weight  of  an  equal  volume  of  water.  To  do  this,  the  piece  of 
sulphur  is  placed  in  the  lower  pan  C  at  ;;z,  as  represented  in  the  figure.  The 
whole  weight  is  not  changed,  nevertheless  the  hydrometer  no  longer  sinks  to 
the  standard  ;  the  sulphur,  by  immersion,  has  lost  a  part  of  its  weight  equal 
to  that  of  the  water  displaced.  Weights  are  added  to  the  upper  pan  until 
the  hydrometer  sinks  again  to  the  standard.  This  weight,  34-4  grains,  for 
example,  represents  the  weight  of  the  volume  of  water  displaced ;  that  is,  of 
the  volume  of  water  equal  to  the  volume  of  the  sulphur.  It  is  only  necessary, 
therefore,  to  divide  70  grains,  the  weight  in  air,  by  34-4  grains,  and  the 
quotient,  2-03,  is  the  specific  gravity. 

If  the  body  in  question  is  lighter  than  water,  it  tends  to  rise  to  the  surface, 
and  will  not  remain  on  the  lower  pan  C.  To  obviate  this,  a  small  movable 
cage  of  fine  wire  is  adjusted  so  as  to  prevent  the  ascent  of  the  body.  The 
experiment  is  in  other  respects  the  same. 

121.   Specific  gravity  bottle.     Pyknometer When  the  specific  gravity 

of  a  substance  in  a  state  of  powder  is  required,  it  can  be  found  most  conve- 
niently by  means  of  \\\q.  pyknometer,  or  specific  gravity  bottle.  This  instru- 
ment is  a  bottle,  in  the  neck  of  which  is  fitted  a  thermometer  A,  an  enlarge- 
ment on  the  stem  being  carefully  ground  for  this  purpose  (fig.  93).  In  the 
side  is  a  narrow  capillary  stem  widened  at  the  top  and  provided  with  a 
stopper,  as  shown  in  the  figure.     On  this  tube  is  a  mark  w,  and  the  thermo- 


Fig.  91. 


Fig.  92. 


122] 


Bodies  Soluble 


Water. 


to; 


meter  stopper  having  been  inserted,  the  bottle  is  filled  with  water  exactly  to 
this  mark  at  each  weighing.  The  bottle  may  conveniently  have  dimensions 
such  that  when  the  thermometer  stopper  is  inserted  and  the  liquid  filled  to 
the  mark  m,  it  represents  a  definite  volume.  This  is  done  by  filling  the 
bottle  when  wholly  under  water,  and  putting  in  the  stopper  while  it  is  im- 
mersed. The  bottle  and  the  tube  are  then  completely  filled,  and  the  quantity 
of  water  in  excess  is  removed  by  blotting-paper.  To  find  the  specific  gravity 
proceed  as  follows  :  Having  weighed  the  powder,  place  it  in  one  of  the 
scale-pans,  and  with  it  the  bottle  filled  exactly 
to  in,  and  carefully  dried.  Then  balance  it  by 
placing  small  shot,  or  sand,  in  the  other  pan. 
Next,  remove  the  bottle  and  pour  the  powder 
into  it,  and,  as  before,  fill  it  up  with  water  to 
the  mark  a.  On  replacing  the  bottle  in  the 
scale-pan  it  will  no  longer  balance  the  shot, 
since  the  powder  has  displaced  a  volume  of 
water  equal  to  its  own  volume.  Place  weights 
in  the  scale-pan  along  with  the  bottle  until 
they  balance  the  shot.  These  weights  give 
the  weight  of  the  water  displaced.  Then  the 
weight  of  the  powder  and  the  weight  of  an 
equal  bulk  of  water  being  known,  its  specific 
gravity  is  determined  as  before.  The  thermo- 
meter gives  the  temperature  at  which  the 
determination  is  made,  and  thus  renders  it  easy 
to  make  a  correction  (124). 

It  is  important  in  this  determination  to  I'e- 
move  the  layer  of  air  which  adheres  to  the 
powder,  and  unduly  increases  the  quantity  of 
water  expelled.  This  is  effected  by  placing  the 
bottle  under  the  receiver  of  an  air-pump  and 
exhausting.  The  same  result  is  obtained  by 
boiling  the  water  in  which  the  powder  is 
placed. 

1 22.  Bodies  soluble  in  water. — If  the  body, 
whose  specific  gravity  is  to  be  determined  by 
any  of  these  methods,  is  soluble  in  water,  the 
determination  is  made  in  some  liquid  in  which 

it  is  not  soluble,  such  as  oil  of  turpentine  or  naphtha,  the  specific  gravity  of 
which  is  known.  The  specific  gravity  is  obtained  by  multiplying  the  number 
obtained  in  the  experiment  by  the  specific  gravity  of  the  liquid  used  for  the 
determination. 

Suppose,  for  example,  a  determination  of  the  specific  gravity  of  potassium 
has  been  made  in  naphtha.     For  equal  volumes,  P  represents  the  weight  of 
the  potassium,  P'  that  of  the  naphtha,  and  P"  that  of  water  ;  consequently, 
p 
—will  be  the  specific  gravity  of  the  substance  in  reference  to  naphtha,  and 


Fig-  93- 


P' 


-the  specific  gravity  of  the  naphtha  in  reference  to  water.     The  product 


io8 


On  Liquids. 


[122- 


of  these  two  fractions   —  is  the  specific  gravity  of  the  substance  compared 

with  water. 

In  determining  the  specific  gravity  of  porous  substances,  they  are  varnished 
before  being  immersed  in  water,  which  renders  them  impervious  to  moisture 
without  altering  their  volume. 


Specific  gravity  of  solids  at  zero  as  compared  with  di stilted  water  at  4°  C. 

Platinum,  rolled     .  .  22*069  Aluminium     .         .         .  2-680 

„          cast         .  .  20-337  Rock  crystal  .         .          .  2-653 

Gold,  stamped        .  .  19-362  St.  Gobin  glass       .         .  2-488 

„     cast       .         .  .  19-258  China  porcelain      .         .  2-380 

Lead,  cast      .         .  .  11-352  Sevres  porcelain     .         .  2.140 

Silver,  cast     .         .  .  10-474  Native  sulphur       .         .  2-043 

Bismuth,  cast         .  .  9-822  Ivory      ....  1-917 

Copper,  drawn  wire  .  8-878  Anthracite      .         .         .  1-800 

„         cast  .         .  .  8-788  Magnesia       ,         .         .  1-740 

Bronze  coinage       .  .  8-66  Boxwood        .         .         .  1-330 

German  silver        .  .  8-432  Compact  coal          .         .  1-329 

Brass      ....  8-383  Amber    ....  1-078 

Steel,  not  hammered  .  7-816  Sodium.         .         .         .  0-970 

Iron,  bar        .         .  .  7-788  Melting  ice     .         .         .  0-930 

„     cast       .         .  ■  .  7-207  Paraffin ....  0-874 

Tin,  cast         .         .  .7-291  Potassium       .         .         .  0-865 

Zinc,  cast        .         .  .  6-861  Beech     ....  0-852 

Antimony,  cast       .  .  6-712  Oak        ....  0-845 

Iodine    ....  4"95o  Elm        ....  0-800 

Heavy  spar    .         .  .  4.430  Yellow  pine    .         .         .  0-657 

Faraday's  glass      .  .  4-36  Lithium           .         .         .  0-585 

Diamond        .         3'53i  to  3-501  Common  poplar     .  .  0-389 

Flint  glass      .         .  .  3-329  Cork       ....  0-240 

Statuary  marble     .  .  2-837 

In  this  table  the  different  woods  are  supposed  to  be  in  the  ordinary  air- 
dried  condition. 

123.  Specific  gravity  of  liquids. — i.  Method  of  the  hydrostatic  balance. 
From  the  pan  of  the  hydrostatic  balance  a  body  is  suspended,  on  which 
the  liquid  whose  specific  gravity  is  to  be  determined  exerts  no  chemical 
action  ;  for  example,  a  ball  of  platinum.  This  is  then  successively  weighed 
in  air,  in  distilled  water,  and  in  the  liquid.  The  loss  of  weight  of  the  body 
in  these  two  liquids  is  noted.  They  represent  respectively  the  weights  of 
equal  volumes  of  water  and  of  the  given  liquid,  and  consequently  it  is  only 
necessary  to  divide  the  second  of  them  by  the  first  to  obtain  the  required 
specific  gravity. 

Let  P  be  the  weight  of  the  platinum  ball  in  air,  P'  its  weight  in  water,  P" 
its  weight  in  the  given  liquid,  and  let  D  be  the  specific  gravity  sought.  The 
weight  of  the  water  displaced  by  the  platinum  is  P  —  P',  and  that  of  the 

P  — P'' 

P",  from  which  we  get  D  =    — -. 


second  liquid  is  P 


-124]        Temperature  in  ascertaining  Specific  Gravities.         109 

ii.  Fahrenheit's  hydrometer. — This  instrument  (fig.  94)  resembles  Nichol- 
son's hydrometer,  but  it  is  made  of  glass,  so  as  to  be  used  in  all  liquids.  At 
its  lower  extremity,  instead  of  a  pan,  it  is  loaded  with  a  small  bulb  containing 
mercury.     There  is  a  standard  mark  on  the  stem. 

The  weight  of  the  instrument  is  first  accurately  determined  in  air  ;  it 
is  then  placed  in  water,  and  weights  added  to  the  scale-pan  until  the  mark 
on  the  stem  is  level  with  the  water.  It  follows,  from  the  first  principle  of 
the  equilibrium  of  floating  bodies,  that  the  weight  of  the  hydrometer,  together 
with  the  weight  in  the  scale-pan,  is  equal  to  the  weight  of  the  volume  of  the 
displaced  water.  In  the  same  manner  the  weight  of  an  equal  volume  of 
the  given  liquid  is  determined,  and  the  specific 
gravity  is  found  by  dividing  the  latter  weight  by 
the  former. 

Neither  Fahrenheit's  nor  Nicholson's  hydro- 
meter gives  such  accurate  results  as  the  hydro- 
static balance  or  the  specific  gravity  bottle. 

iii.  Specific  g7'avity  bottle. — This  has  been 
already  described  (121).  In  determining  the 
specific  gravity  of  a  liquid,  a  bottle  of  special 
construction  is  used  ;  it  consists  of  a  cylindrical 
reservoir  b  (fig.  95),  to  which  is  fused  a  capillary 
tube  c,  and  to  this  again  a  wider  tube  a,  closed 
with  a  stopper.  The  bottle  is  first  weighed 
empty,  and  then  successively  full  of  water  to 
the  mark  c  on  the  capillary  stem,  and  of  the 
given  liquid.  If  the  weight  of  the  bottle  be 
subtracted  from  the  two  weights  thus  obtained, 
the    result    represents    the    weights    of    equal 

volumes  of  the  liquid  and  of  water,  from  which  the  specific  gravity  is  obtained 
by  division. 

iv.  Specific  gravity  bulbs. — The  specific  gravity  of  a  liquid  is  often  de- 
termined for  technical  and  even  scientific  purposes  by  means  of  specific 
gravity  bulbs  ;  these  are  small  hollow  glass  bulbs,  which  are  prepared  in 
series,  loaded  and  adjusted  so  that  they  exactly  float  in  a  liquid  of  a  definite 
specific  gravity.  When  carefully  prepared  they  are  susceptible  of  considerable 
accuracy. 

Solutions  of  certain  metallic  salts  of  high  specific  gravity  have  been  used 
for  the  mechanical  separation  of  individual  minerals  of  certain  rocks.  Such 
minerals  will  float  or  sink  according  as  their  specific  gravities  are  lower  or 
higher  than  that  of  a  given  solution.  A  saturated  solution  of  the  double 
iodide  of  barium  and  mercury,  the  specific  gravity  of  which  is  3-58,  has  been 
used  for  this  purpose. 

124.  On  the  observation  of  temperature  in  ascertainine:  specific 
grravities. — As  the  volume  of  a  body  increases  with  the  temperature,  and 
as  this  increase  varies  with  different  substances,  the  specific  gravity  of  any 
given  body  is  not  exactly  the  same  at  different  temperatures  ;  and,  con- 
,sequently,  a  certain  fixed  temperature  is  chosen  for  these  determinations. 
That  of  water,  for  example,  has  been  made  at  4°  C,  for  at  this  point  it  has 
the  greatest  density.     The  specific  gravities  of  other  bodies  are  assumed  to 


Fig.  94. 


F!g.  95. 


no  On  Liquids.  [124- 

be  taken  at  zero  ;  but,  as  this  is  not  always  possible,  certain  corrections  must 
be  made,  which  we  shall  consider  in  the  Book  on  Heat. 

Specific  gravities  of  liquids  at  zero,  compared  %uith  that  of  luater  at  4°  C. 
as  tinlty. 


Mercury 

•   13-598 

Sea  water 

1-026 

Bromine 

.     2-960 

Urine 

I -020 

Ethylic  iodide 

■     1-946 

Distilled  water  at  4° 

C.  . 

I -000 

Sulphuric  acid 

.     1-841 

„         „         at  0° 

C.  . 

0-999 

Chloroform   . 

■     1-525 

Claret     . 

0-994 

Nitric  acid    . 

.     I  -420 

Olive  oil 

0-915 

Bisulphide  of  carbon     , 

.     1-293 

Oil  of  turpentine     . 

0-870 

Glycerine 

I  -260 

Oil  of  lemon   . 

0-852 

Hydrochloric  acid 

I  -240 

Petroleum 

0-836 

Blood    .         .         .         . 

I  -060 

Absolute  alcohol     . 

0-793 

Milk     .         .         .         . 

1-029 

Ether      . 

0-713 

125.  Use  of  tables  of  specific  gravity. — Tables  of  specific  gravity 
admit  of  numerous  applications.  In  mineralogy  the  specific  gravity  of  a 
mineral  is  often  a  highly  distinctive  character.  By  means  of  tables  of 
specific  gravities  the  weight  of  a  body  may  be  calculated  when  its  volume  is 
known,  and  conversely  the  volume  when  its  weight  is  known. 

With  a  view  to  explaining  the  last-mentioned  use  of  these  tables,  it  will  be 
well  to  premise  a  statement  of  the  connection  existing  between  the  British 
units  of  length,  capacity,  and  weight.  It  will  be  sufficient  for  this  purpose 
to  define  that  which  exists  between  the  yard,  gallon,  and  pound  avoirdupois, 
since  other  measures  stand  to  these  in  well-known  relations.  The  yard, 
consisting  of  36  inches,  may  be  regarded  as  the  primary  unit.  Though  it  is 
essentially  an  arbitrary  standard,  it  is  determined  by  this,  that  the  simple 
pendulum  which  makes  one  oscillation  in  a  mean  second,  at  London  on  the 
sea-level,  is  39'i3983  inches  long.  The  gallon  contains  2j'j-2jj^  cubic  inches. 
A  gallon  of  distilled  water  at  the  standard  temperature  weighs  ten  pounds 
avoirdupois  or  70,000  grains  troy ;  or,  which  comes  to  the  same  thing,  one 
cubic  inch  of  water  weighs  252-5  grains. 

On  the  French  system  the  metre  is  a  primary  unit,  and  is  so  chosen 
that  10,000,000  metres  are  the  length  of  a  quadrant  of  the  meridian  from 
either  pole  to  the  equator.  The  metre  contains  10  deci/iietres,  or  100  centi- 
metres, or  1,000  millimetres  ;  its  length  equals  1-0936  yards.  The  unit 
of  the  measure  of  capacity  is  the  litre  or  cubic  decimetre.  The  unit  of 
weight  is  the  gramme,  which  is  the  weight  of  a  cubic  centimetre  of  distilled 
water  at  4°  C.  The  kilogramme  contains  1,000  grammes,  or  is  the  weight 
of  a  decimetre  of  distilled  water  at  4°  C.     T^x^  gramme  equals  15-443  grains. 

If  V  is  the  number  of  cubic  centimetres  (or  decimetres)  in  a  certain 
quantity  of  distilled  water  at  4°  C,  and  P  its  weight  in  grammes  (or  kilo- 
grammes), it  is  plain  that  P  =  V.  Now  consider  a  substance  whose  specific 
gravity  is  D  ;  every  cubic  centimetre  of  this  substance  will  weigh  as  much 
as  D  cubic  centimetres  of  water,  and  therefore  V  centimetres  of  this  sub- 
stance will  weigh  as  much  as  DV  centimetres  of  water.  Hence,  if  P  is 
the  weight  of  the  substance  in  grammes,  we  have  P  =  DV,     If,  however,  V 


-427J 


Beaume's  Hydrometer. 


the  volume  in  cubic  inches,  and  P  the  weight  in  grains,  we  shall  have 
P  =  252-5  DV. 

As  an  example,  we  may  calculate  the  internal  diameter  of  a  glass  tube. 
Mercury  is  introduced,  and  the  length  ahd  weight  of  the  column  at  4°  C. 
are  accurately  determined.  As  the  column  is  cylindrical,  we  have  V  =  Trr'-/, 
where  r  is  the  radius,  and  /  the  length  of  the  column  in  centimetres.  Hence, 
if  D  is  the  specific  gravity  of  mercury,  and  P  the  weight  of  the  column  in 
grammes,  we  have  P  =  7rrVD,  and  therefore 


\ 


I, 


If  rand /are  in  inches  and  P  in  grains,  we  shall  have  P  =  252-57rr-/D 
and  therefore 

P 


\/^. 


52-57rD/ 

In  a  similar  manner,  by  weighing  a  given  length,  the  diameter  of  very  fine 
metal  wires  can  be  determined  with  great  accuracy. 

126.  Hydrometers  of  variable  immersion. — The  hydrometers  of 
Nicholson  and  Fahrenheit  are  called  hydrometers  of  constant  i/ninersion 
but  variable  weight,  because  they  are  always  immersed  to  the  same  extent, 
but  carry  different  weights.  There  are  also  hydrometers  of  variable  immer- 
sion but  of  constant  weight. 

12J.  Beaume's  hydrometer. — This,  which  was  the  first  of  these  instru- 
ments, may  serve  as  a  type  of  them.  It  consists  of  a  glass  tube  (fig.  96) 
loaded  at  the  bottom  with  mercury,  and  with  a  bulb  blown  in  the  middle. 
The  stem,  the  external  diameter  of  which  is  as  regular  as  possible,  is  hollow, 
and  the  scale  is  marked  upon  it. 

The  graduation  of  the  instrument  differs  according  as  the  lic|uid,  for 
which  it  is  to  be  used,  is  heavier  or  lighter  than  water.  In 
the  first  case,  it  is  so  constructed  that  it  sinks  in  water 
nearly  to  the  top  of  the  stem,  to  a  point  A,  which  is  marked 
zero.  A  solution  of  fifteen  parts  of  salt  in  eighty-five  parts  of 
water  is  made,  and  the  instrument  immersed  in  it.  It  sinks 
to  a  certain  point  on  the  stem,  B,  which  is  marked  15  ;  the 
distance  between  A  and  B  is  divided  into  1 5  equal  parts,  and 
the  graduation  continued  to  the  bottom  of  the  stem.  Some- 
times the  graduation  is  on  a  piece  of  paper  inside  the 
stem. 

The  hydrometer  thus  graduated  only  serves  for  liquids 
of  a  greater  specific  gravity  than  water,  such  as  acids  and 
saline  solutions.  For  liquids  lighter  than  water  a  different 
plan  must  be  adopted.  Beaume  took  for  zero  the  point  to 
which  the  apparatus  sank  in  a  solution  of  10  parts  of  salt  in 
90  of  water,  and  for  10°  he  took  the  level  in  distilled  water. 
This  distance  he  divided  into  10°,  and  continued  the  division 
to  the  top  of  the  scale. 

TweddeWs  hydrometer  is  in  common  use  in  England 
for  testing  liquids  denser  than  water.     It  is  graduated  in  such  a  manner 


Fig.  96. 


112  On  Liquids.  [127- 

that  the  reading  or  number  of  degrees  multiplied  by  five  and  added  to  i,ooo 
gives  the  specific  gravity  with  reference  to  water  at  i,ooo.  Thus  io° 
Tweddell  represents  the  specific  gravity  1050,  and  90°  represents  1450. 

The  graduation  of  these  hydrometers  is  entirely  conventional,  and  they 
give  neither  the  densities  of  the  liquids  nor  the  quantities  dissolved.  But 
they  are  very  useful  in  making  mixtures  or  solutions  in  given  proportions, 
and  in  evaporating  acids,  alkaline  liquids,  solutions  of  salts,  worts,  syrups, 
and  the  like  to  a  proper  degree  of  concentration,  the  results  they  give  being 
sufficiently  near  in  the  majority  of  cases. 

128.  Gay-lussac's  alcoholometer. — This  instrument  is  used  to  deter- 
mine the  strength  of  spirituous  liquors  ;  that  is  the  proportion  of  pure 
alcohol  which  they  contain.  It  differs  from  Beaume's  hydrometer  in  the 
graduation. 

The  alcoholometer  is  so  constructed  that,  when  placed  in  pure  distilled 
water,  the  bottom  of  its  stem  is  level  with  the  water,  and  this  point  is  zero. 
It  is  next  placed  in  absolute  alcohol,  which  marks  100°,  and  then  successively 
in  mixtures  of  alcohol  and  water  containing  10,  20,  30,  &c.,  per  cent.  The 
divisions  thus  obtained  are  not  exactly  equal,  but  their  difference  is  not  great, 
and  they  are  subdivided  into  10  divisions,  each  of  which  marks  one  per  cent, 
of  absolute  alcohol  in  a  liquid.  Thus  a  brandy  in  which  the  alcoholometer 
stood  at  48°  would  contain  48  per  cent,  of  absolute  alcohol,  and  the  rest 
would  be  water. 

All  these  determinations  are  made  at  15°  C,  and  for  that  temperature 
only  are  the  indications  correct.  For,  other  things  being  the  same,  if  the 
temperature  rises  the  liquid  expands,  and  the  alcoholometer  will  sink,  and 
the  contrary  if  the  temperature  fall.  To  obviate  this  error,  Gay-Lussac  con- 
structed a  table  which  for  each  percentage  of  alcohol  gives  the  reading  of 
the  instrument  for  each  degree  of  temperature  from  0°  up  to  30°.  When  the 
exact  analysis  of  an  alcoholic  mixture  is  to  be  made,  the  temperature  of  the 
liquid  is  first  determined,  and  then  the  point  to  which  the  alcoholometer  sinks 
in  It.  The  number  in  the  table  corresponding  to  these  data  indicates  the 
percentage  of  alcohol.  From  its  giving  the  percentage  of  alcohol,  this  is 
often  called  the  cenfesifnal  alcoholometer. 

129.  Salimeters. — Salivietcrs^  or  instruments  for  indicating  the  per- 
centage of  a  salt  contained  in  a  solution,  are  made  on  the  principle  of  the 
centesimal  alcoholometer.  They  are  graduated  by  immersing  them  in  pure 
water,  which  gives  the  zero,  and  then  in  solutions  containing  different  percent- 
ages of  the  salt,  and  marking  on  the  scale  the  corresponding  points.  These 
instruments  are  open  to  the  objection  that  eveiy  salt  requires  a  special 
instrument.  Thus  one  graduated  for  common  salt  would  give  false  indications 
in  a  solution  of  nitre. 

Lactometers  are  similar  instruments,  and  are  based  on  the  fact  that 
the  average  density  of  a  good  natural  quality  of  milk  is  ro29.  Hence  if 
water  is  added  to  milk,  it  will  indicate  a  lower  specific  gravity.  But  a 
common  plan  of  adulteration  is  to  remove  cream  from  the  milk,  by  which 
its  specific  gravity  is  increased,  and  then  add  water  so  as  to  reproduce  the 
original  density  ;  the  lactometer  will  not  reveal  a  fraud  of  this  kind.  Urino- 
victers  are  frequently  used  in  medicine  to  test  the  variations  in  the  density 
of  urine,  which  accompany  and  characterise  certain  forms  of  disease. 


-130]  Densimeter.  113 

130.  Densimeter. — Rousseaii's  densimeter  (fig.  97)  is  of  great  use  in  many 
scientific  investigations,  in  determining  the  specific  gravity  of  a  small 
quantity  of  a  liquid.  It  has  the  same  form  as  Beaume's 
hydrometer,  but  there  is  a  small  tube  AC  at'  the  top 
of  the  stem  in  which  is  placed  the  substance  to  be  de- 
termined. A  mark  A  on  the  side  of  the  tube  indicates 
a  measure  of  a  cubic  centimetre. 

The  instrument  is  so  constructed  that  when  AC  is 
empty  it  sinks  in  distilled  water  to  a  point  B,  just  at 
the  bottom  of  the  stem.  It  is  then  filled  with  distilled 
water  to  the  height  measured  on  the  tube  AC,  which 
indicates  a  cubic  centimetre,  and  the  point  to  which  it 
now  sinks  is  20°.  The  interval  between  o  and  20  is 
divided  into  20  equal  parts,  and  this  graduation  is 
continued  to  the  top  of  the  scale.  As  this  is  of  uniform 
bore,  each  division  corresponds  to  -\7  gramme  or  0-05. 

To  obtain  the  density  of  any  liquid,  bile  for  ex- 
ample, the  tube  is  filled  with  it  up  to  the  mark  A  ;  if 
the   densimeter   sinks   to  20    divisions,  its  weight  is 
0-05  X  20-5  =  1-025  ;  that  is  to  say,  with  equal  volumes,  the  weight  of  water 
being  i,  that  of  bile  is  1-025.     The  specific  gravity  of  bile  is  therefore  1-025. 


Fig.  97- 


114 


On  Liquids. 


[131- 


CHAPTER  II, 


CAPILLARITY,  ENDOSMOSE,  EFFUSION,  AND  ABSORPTION. 


131.  Capillary  phenomena. — When  solid  bodies  are  placed  in  contact 
with  liquids,  phenomena  are  produced  which  are  classed  under  the  general  head 
oi  capillary  phe7ioi)iefta,  because  they  are  best  seen  in  tubes  whose  diameters 
are  so  small  as  to  be  coxnparable  with  that  of  a  hair.  These  phenomena  are 
treated  of  in  physics  under  the  head  of  capilhwity  or  capillary  attraction  ;  the 
latter  expression  is  also  applied  to  the  force  which  produces  the  phenomena. 

The  phenomena  of  capillarity  are  very  various,  but  may  all  be  referred 
to  the  relation  of  the  attraction  of  the  liquid  molecules  for  each  other,  to  the 
attraction  between  these  molecules  and  solid  bodies.  The  following  are 
some  of  these  phenomena  : — 

When  a  body  is  placed  in  a  liquid  which  wets  it — for  example,  a  glass 
rod  in  water— the  liquid,  as  if  not  subject  to  the  laws  of  gravitation,  is  raised 
upwards  against  the  sides  of  the  solid,  and  its  surface,  instead  of  being  hori- 
zontal, becomes  sHghtly  concave   (fig.  98).     If  on  the  contrary,  the  solid  is 


L.^.__ 


Fig.  98. 


Fig.  99. 


Fig.  100. 


one  which  is  not  moistened  by  the  hquid,  as  glass  by  mercury,  the  liquid  is 
depressed  against  the  sides  of  the  solid,  and  assumes  a  convex  shape,  as 
represented  in  fig.  99.  The  surface  of  the  liquid  exhibits  the  same  concavity 
or  convexity  against  the  sides  of  a  vessel  in  which  it  is  contained,  accord- 
ing as  the  sides  are  or  are  not  moistened  by  the  liquid. 

These  phenomena  are  much  more  marked  when  a  tube  of  small 
diameter  is  placed  in  a  liquid.  And  according  as  the  tubes  are  or  are  not 
moistened  by  the  liquid,  an  ascent  or  a  depression  of  the  liquid  is  produced, 
which  is  greater  in  proportion  as  the  diameter  is  less  (figs.  100  and  loi). 

When  the  tubes  are  moistened  by  the  liquid,  its  surface  assumes  the 
form  of  a  concave  hemispherical  segment,  called  the  concave  moiiscus 
(fig.  100) ;  when  the  tubes  are  not  moistened,  there  is  a  convex  meniscus 
(fig.  lOl). 


-132]  Ascent  aitd  Depression  in   Capilhny   Tubes.  1 1  5 

132.  ILaws  of  the  ascent  and  depression  in  capillary  tubes. — The 

most  important  law  in  reference  to  capillarity  is  known  as  Jiiriiis  law.  It 
is  :  For  the  same  liquid,  atid  the  same  temperature,  the  mean  height  of  the 
ascent  in  a  capillary  tube  is  inversely  as  the  diameter  of  the  tube.  Thus,  if 
water  rises  to  a  height  of  30  mm.  in  a  tube  i  mm.  in  diameter,  it  will  only 
rise  to  a  height  of  15  mm.  in  a  tube  2  mm.  in  diameter,  but  to  a  height  of 
300  mm.  in  a  tube  OT  mm.  in  diameter.  This  law  has  been  verified  with 
tubes  whose  diameters  ranged  from  5  mm.  to  0-07  mm.  It  presupposes  that 
the  liquid  has  previously  moistened  the  tube. 

The  mean  height  is  the  height  of  a  cylinder  with  a  circular  base  which 
has  exactly  the  same  volume  as  the  liquid  column  raised.  If  h  is  this 
height  and  2r  the  diameter  of  the  tube,  Jurin's  law  may  be  expressed  by  the 
equation 

2rh  =  const. 


X= 


If  r,  the  radius,  is  taken  at  i  mm.,  then  the  height  in  millimetres  to 
which  any  liquid  rises  is  a  measure  of  the  capillary  constant. 

For  various  liquids,  and  the  same  temperature,  the  mean  heights  raised  in 
capillary  tubes  of  the  same  diameter  vary  with  the  nature  of  the  liquid.  Of 
all  liquids  water  rises  the  highest  ;  thus  in  a  glass  tube  i  -29  mm.  in  diameter, 
the  heights  of  water,  alcohol,  and  turpentine  are  respectively  23-16,  9-18,  and 
9-85  mm. 

For  the  same  liquid,  and  the  same  temperature,  the  7nean  heights  are 
independent  of  the  form  of  the  capillary  tube.  That  is  to  say,  the  shape  of 
the  tube  above  or  below  the 
meniscus  has  no  effect  on  the  j 

phenomenon.     The  columns  ^r*"  »ihI  r-Ju L 

raised  would  be  of  very  un- 
equal weights,  but  of  equal 
heights  h,  in  the  tubes  repre-  ^ 
sented  in  fig  102,  all  of  which  ^ 
have  the  same  diameter  when 
the  liquid  stops.  The  co- 
efficient r  is  the  diameter 
which  corresponds  to  the  region  of  the  meniscus. 

Provided  the  liquid  moistens  the  tube,  neither  its  thickness  nor  its  nature 
has  any  influence  on  the  height  to  which  the  Hquid  rises.  Thus  water  rises 
to  the  same  height  in  tubes  of  different  kinds  of  glass,  and  of  rock  crystal, 
provided  the  diameters  are  the  same. 

The  height  to  which  a  given  liquid  rises  in  a  capillary  tube  diminishes 
as  the  temperature  increases.  Thus  in  a  capillary  tube  in  which  water  stood 
at  a  height  of  307  mm  at  0°,  it  stood  at  28-6  mm.  at  35°,  and  at  26  mm.  at  80°. 
This  diminution  of  height  is  considerably  greater  than  is  accounted  for  by  the 
diminished  density  of  the  water  ;  for,  while  this  is  about  0-00045  ^or  each 
degree  between  0°  and  100°,  the  mean  diminution  of  the  height  is  0-00182, 
or  about  four  times  as  much. 

At  the  same  time  that  the  heights  become  less  the  menisci  2a&  flattened, 
so  that  from  a  certain  temperature,  which  varies  with  different  liquids,  the 
capillary  surface  becomes  flat  and  horizontal,  and  its  level  is  that  of  the 


ii6 


On  Liquids. 


[132- 


external  liquid.  Working  in  closed  vessels  Wolff  found  this  temperature  to 
be  191°  for  ether,  and  500°  for  water. 

In  regard  to  the  depression  of  liquids  in  tubes  which  they  do  not 
moisten,  Jurin's  law  has  not  been  found  to  hold  with  the  same  accuracy. 
The  reason  for  this  is  probably  to  be  found  in  the  following  circumstances  : — 
When  a  liquid  moistens  a  capillary  tube,  a  very  thin  layer  of  liquid  is  formed 
against  the  sides,  and  remains  adherent  even  when  the  liquid  sinks  in  the 
tube.  The  ascent  of  the  column  of  liquid  takes  place  then,  as  it  were,  inside 
a  central  tube,  with  which  it  is  physically  and  chemically  identical.  The 
ascent  of  the  liquid  is  thus  an  act  of  cohesion.  It  is  therefore  easy  to 
understand  why  the  nature  of  the  sides  of  the  capillary  tube  should  be 
without  inlluence  on  the  height  of  the  ascent,  which  only  depends  on  the 
diameter. 

With  licjuids,  on  the  contrary,  which  do  not  moisten  the  sides  of  the  tube, 
the  capillary  action  takes  place  between  the  sides  and  the  liquid.  The 
nature  and  structure  of  the  sides  are  never  quite  homogeneous,  and  there  is 
always,  moreover,  a  layer  of  air  on  the  inside,  which  is  not  dissolved  by  the 
liquid.  These  two  causes  undoubtedly  exert  a  disturbing  influence  on  the 
law  of  Jurin. 

133.  Ascent  and  depression  between  parallel  or  inclined  surfaces.^ 
When  two  bodies  of  any  given  shape  are  clipped  in  water,  analogous  phe- 
nomena are  produced,  provided  the  bodies  are  sufficiently  near.  If,  for 
example,  two  parallel  glass  plates  are  immersed  in  water  at  a  very  small 
distance  from  each  other,  water  will  rise  between  the  two  plates  in  the 
inverse  ratio  of  the  distance  which  separates  them.  The  height  of  the 
ascent  for  any  given  distance  is  half  what  it  would  be  in  a  tube  whose  dia- 
meter is  equal  to  the  distance  between  the  plates. 

If  the  parallel  plates  are  immersed  in  mercury,  a  corresponding  depression 
is  produced,  subject  to  the  same  laws. 

If  two  glass  plates  AB  and  AC,  with  their  planes  vertical  and  inclined  to 
one  another  at  a  small  angle,  as  represented  in  fig.    103,  have  their  ends 


Fig.  103. 


Fig.  105. 


dipped  into  a  liquid  which  wets  them-  the  liquid  will  rise  between  them. 
The  elevation  will  be  greatest  at  the  line  of  contact  of  the  plates,  and 
from  hence  gradually  less,  the  surface  taking  the  form  of  an  equilateral 
hyperbola. 

If  a  drop  of  water  be  placed  within  a  conical  glass  tube  whose  angle  is 
small,  and  axis  horizontal,  it  will  have  a  concave  meniscus  at  each  end 


-134]  Tension  of  the  Free  Surface  of  Liquids.  117 

(fig.  104),  and  will  tend  to  move  towards  the  vertex.  But  if  the  drop  be  of 
mercury  it  will  have  a  convex  meniscus  at  each  end  (fig.  105),  and  will  tend 
to  move  from  the  vertex. 

1 34.  Tension  of  the  free  surface  of  liquids. — The  great  mobility  which  is 
characteristic  of  the  liquid  state  undergoes  an  alteration  in  the  neighbour- 
hood of  theyr^^  surface  of  a  liquid,  or  that  which  is  bounded  by  a  gas  or  by 
a  vacuum.  This  surface  has  greater  cohesion  than  any  other.  For,  consider 
any  particle  a  at  the  surface  (fig.  106),  and  let  the  sphere  represent  the 
range  through  which  the  molecular  attraction  is  exerted,  or  what  is  called 
the  radius  of  iiwlecular  activity.  The  attractive  forces  of  the  adjacent 
particles,  which  are  exerted  in  all  directions,  may  be  resolved  into  horizontal 
and  vertical  components  ;  the  attractions  of  the  former  will  compensate  each 
other.  But  the  attractions  represented  by  the  molecules  within  the  hemi- 
sphere beneath  the  surface  ^  ^  j^ 
are  not  so  compensated,  and 
consequently  the  latter  will 
exercise  a  considerable  pull 
towards  the  interior. 

Consider,  again,  a  par- 
ticle b.,  so  much  below  the 
surface  that  the  greater  part 
of  the  sphere  comes  into 
operation.  If  a  plane  de  be 
laid  as  much  below  b  as  the 

surface  is  above  it,  the  attractive  forces  from  the  molecules  within  ghed  will 
neutralise  each  other.  But  the  segment  def  remains  uncompensated,  and 
exerts  a  pull  similar  to,  though  weaker  than,  that  which  acts  on  the  molecule  a. 

The  molecule  c  finally  is  surrounded  uniformly  by  its  adjacent  ones,  and 
their  resultant  action  is  zero. 

The  effect  of  these  actions  is  to  lessen  the  mobility  of  particles  at  or 
veiy  near  the  surface,  while  those  in  the  interior  are  c^uite  mobile  ;  the  sur- 
face, as  it  were,  is  stretched  by  an  elastic  skin,  the  result  being  the  same  as 
if  the  surface  layer  exerted  a  pressure  on  the  interior.  This  surface  tension, 
as  it  is  called,  is  greater,  the  greater  the  cohesion  of  the  liquid. 

When  the  surface  of  a  liquid  increases,  more  particles  enter  into  the 
condition  of  the  surface  layer,  to  effect  which  a  certain  amount  of  work  is 
required.  On  the  other  hand,  when  the  surface  is  diminished,  the  molecules 
pass  into  the  state  of  the  internal  layer,  and  they  perform  work.  The  work 
clone  when  a  sc|uare  mm.  of  surface  passes  into  the  interior  is  called  the 
coefficient  of  surface  tension. 

The  existence  of  this  surface  tension  may  be  illustrated  by  several  inter- 
esting experiments.  In  that  of  Dupre  (fig.  107),  a  quadrangular  flat  vessel 
ABCD  is  used,  of  which  one  side 
CD  is  movable  about  a  hinge. 
By  means  of  a  string  this  side 
is  pressed  against  a  wedge,  and 

the  vessel  is  filled  with    water.  Fig.  107. 

On  burning  the  wire  the  side  CD' 
reverts  to  its  original  position  CD.    Now,  as  the  hydrostatic  pressure  would 


ii8 


On  Liquids. 


[134- 


have  kept  it  pressed  against  the  wedge,  there  must  be  a  tangential  force  at 
work  restoring  it  to  the  vertical,  which  is  an  effect  of  the  surface  tension. 

Another  experiment  by  Mensbrugghe  is  made  by  means  of  a  wire  frame 
(fig.  io8  a\  which  is  immersed  in  a  solution  of  soap,  such  as  is  used  for  blow- 
ing soap  bubbles.  On  removing  this  a  thin 
film  is  formed.  A  loop  of  fine  silk  thread 
moistened  with  the  liquid  in  question  is  care- 
fully placed  on  the  film  and  assumes  any 
shape  (fig.  1 08  a).  By  means  of  a  spill  of  blot- 
ting paper,  the  liquid  is  carefully  removed 
from  inside  the  loop,  and  the  contour  is  then 
seen  to  stretch  and  assume  a  circular  form 
(fig.  108  b),  which  is  owing  to  the  lateral  pull 
exerted  uniformly  on  the  edge  of  the  loop. 

The  surface  tension  depends  on  the  form 
of  the  surface.  Its  value  has  been  determined 
in  the  case  of  spheroidal  bodies.    If  the  pres- 
sure which  is  exerted  on  a  plane  surface  be  called  P,  the  pressure  /,  on  a 

spherical  surface  of  radius  p,  is  /  =  P  -h  ^  for  convex,  and  /  =  P  —    "-liox 


20 
P 


concave  surfaces. 

Hence  for  a  spheroidal  shell,  the  internal  radius  OA  (fig.  109)  of  which  is 

/J,  and  its  thickness  AB  =  (r/,  the  pressure  of  the  outer  layer  is/-P-t-    ~^,, 

p  +  a 

^-,  and  the  resultant  is 
P 

a  pressure  exerted  inwards. 


and  of  the  inner  layer  /i  =  P 

2(/.      20 


their  differences 

p  +  a      p 

since/  >/j.  This  is  well  illustrated  by  blowing  a  soap 
bubble  on  a  glass  tube.  So  long  as  the  other  end  of 
the  tube  is  closed,  the  bubble  remains,  the  elastic  force 
of  the  enclosed  air  counterbalancing  the  tension  of 
the  surface  ;  but  when  the  tube  is  opened,  the  tension 
of  the  surface  being  unchecked,  the  bubble  gradually  contracts  and  finally 
disappears. 

Insects  can  often  move  on  the  surface  of  water  without  sinking.  This 
phenomenon  is  caused  by  the  fact  that,  as  their  feet  are  not  wetted  by  the 
water,  a  depression  is  produced,  and  the  elastic  reaction  of  the  surface  layer 
keeps  them  up  in  spite  of  their  weight.  Similarly  a  sewing-needle,  gently 
placed  on  water,  does  not  sink,  because  its  surface,  being  covered  with  an 
oily  layer,  does  not  become  wetted.  The  pressure  of  the  needle  brings 
about  a  concavity,  the  surface  tension  of  which  acts  in  opposition  to  the 
weight  of  the  needle.  But  if  washed  in  alcohol  or  in  potash,  the  metal  is 
wetted  and  at  once  sinks  to  the  bottom. - 

Among  the  phenomena  due  to  surface  tension  may  be  mentioned  the  well- 
known  one  of  the  '  tears  of  wine.'  The^  surface  tension  of  water  in  contact 
with  air  is  greater  than  that  of  any  othei"  liquid  except  mercury.  It  is  more 
than  three  times  as  great  as  that  of  alcohol.  When  a  wine-glass  is  half  filled 
with  a  strong  wine,  the  wine  rises  up  against  the  sides  like  any  other  liquid ; 


-136]     lufinence  of  Cnrvatuvc  on   Capillary  Phetioinena.         1 1 9 

but  the  alcohol  evaporates  rapidly  from  the  surface,  the  consequence  of  which 
IS  that  the  liquid  layer  becomes  more  watery.  Near  the  surface  of  the 
liquid  the  strength  of  the  liquid  layer  is  kept  up  by  diffusion,  but  higher  up, 
owing  to  the  increased  surface  tension  of  the  more  aqueous  wine,  it  creeps  up 
the  sides  and  draws  with  it  some  of  the  stronger  alcoholic  liquid  below,  the 
increasing  weight  of  which  ultimately  causes  it  to  break  and  run  down  in 
drops. 

If  a  thin  layer  of  water  be  spread  on  a  plate,  and  a  drop  of  ether  be 
placed  upon  it,  the  water  retreats  from  the  drop.  Here,  instead  of  the  surface 
tension  between  water  and  air,  we  have  that  between  water  and  ether,  which 
is  smaller  ;  the  effect  is  much  the  same  as  if  there  were  a  tightly  stretched 
india-rubber  skin,  and  a  portion  of  it  were  softened  or  made  thinner. 

135.  Cause  of  the  curvature  of  liquid  surfaces  in  contact  with  solids. 
The  form  of  the  surface  of  a  liquid  in  contact  with  a  solid  depends  on  the 
relation  between  the  attraction  of  the  solid  for  the  liquid,  and  of  the  mutual 
attraction  between  the  molecules  of  the  liquid. 

Let  111  be  a  liquid  molecule  (fig.  no)  in  contact  with  a  solid.  This 
molecule  is  acted  upon  by  three  forces  :  by  gravity,  which  attracts  it  in  the 
direction  of  the  vertical  mV  ;  by  the  attraction  of  the  hquid  F,  which  acts  in 


the  direction  wF  ;  and  by  the  attraction  of  the  plate  »,  which  is  exerted  in 
the  direction  m)i.  According  to  the  relative  intensities  of  these  forces,  their 
resultant  can  take  three  positions  : — 

i.  The  resultant  is  in  the  direction  of  the  vertical  ;;zR  (fig.  no).  In  this 
case  the  surface  m  is  plane  and  horizontal  ;  for,  from  the  condition  of  the 
equihbrium  of  liquids,  the  surface  must  be  perpendicular  to  the  force  which 
acts  upon  the  molecules. 

ii.  If  the  force  n  increases  or  F  diminishes,  the  resultant  R  is  within  the 
angle  mii?  (fig.  1 1 1)  ;  in  this  case  the  surface  takes  a  direction  perpendicular 
to  7«R,  and  becomes  concave. 

iii.  If  the  force  F  increases  or  11  diminishes,  the  resultant  R  takes  the 
direction  ;«R  (fig.  112)  within  the  angle  PwF,  and  the  surface,  becoming 
perpendicular  to  this  direction,  is  convex. 

136.  Influence  of  curvature  on  capillary  phenomena. — The  elevation 
or  depression  of  a  liquid  in  a  capillaiy  tube  depends  on  the  concavity  or 
convexity  of  the  meniscus.  In  a  concave  meniscus,  abed  (fig.  113),  the  liquid 
molecules  are  sustained  in  equilibrium  by  the  forces  acting  on  them,  and  they 
exert  no  downward  pressure  on  the  inferior  layers.  On  the  contrary,  in  virtue 
of  molecular  attraction,  they  act  on  the  nearest  inferior  layers,  from  which  it 
follows  that  the  pressure  on  any  layer  mn,  in  the  interior  of  the  tube,  is  less 


I20 


On  Liqiiids. 


[136- 


than  if  there  were  no  meniscus.  The  consequence  is  that  the  Hquid  rises 
in  the  tube  until  the  internal  pressure  on  the  layer  ;//;/  is  equal  to  the  pressure 
op^  which  acts  externally  on  a  point  p  of  the  same  layer. 

Where  the  meniscus  is  convex  (fig.  114),  equilibrium  exists  in  virtue  of 
the  molecular  forces  acting  on   the   liquid  :   but   as   the    molecules  which 


would  occupy  the  same  space  ghik^  if  there  were  no  molecular  action,  do 
not  exist,  they  exert  no  attraction  on  the  lower  layers.  Consequently,  the 
pressure  on  any  layer  w;?,  in  the  interior  of  the  tube,  is  greater  than  if  the 
space  gJiik  were  filled,  for  the  molecular  forces  are  more  powerful  than 
gravity.  The  liquid  ought,  therefore,  to  sink  in  the  tube  until  the  internal 
pressure  on  a  layer,  inn,  is  equal  to  the  external  pressure  on  any  point,  p,  of 
this  layer. 

137.  Various  capillary  phenomena. — The  attractions  and  repulsions 
observed  between  bodies  floating  on  the  surface  of  liquids  find  their  expla- 
nation in  the  concave  or  convex  curvature  which  the  liquid  assumes  in  con- 
tact with  the  solid.     The  following  are  some  of  them. 

When  two  floating  balls  both  moistened  by  the  liquid — for  example,  cork 
upon  water — are  so  near  that  the  liquid  surface  between  them  is  not  level, 
an  attraction  takes  place.  The  same  effect  is  produced  when  neither  of  the 
balls  is  moistened,  as  is  the  case  with  balls  of  wax  on  water. 

Lastly,  if  one  of  the  balls  is  moistened  and  the  other  not,  as  a  ball  of  cork 
and  a  ball  of  wax  in  water,  they  repel  each  other  if  the  curved  surfaces  of  the 
liquid  in  their  respective  neighbourhoods  intersect. 

A  drop  of  mercury  on  a  table  has  a  spherical  shape,  which,  like  that  of 
the  heavenly  bodies,  is  due  to  attraction.  The  globule  of  mercury  behaves 
as  if  its  molecules  had  no  weight,  since  it  remains  spherical.  That  is,  the 
molecular  attraction  is  far  greater  than  the  weight,  which  only  alters  the 
shape  of  the  globule  if  the  quantity  of  mercury  is  much  greater  ;  it  then 
flattens,  but  always  retains  at  its  edge  the  convex  form  which  molecular 
attraction  imparts  to  it.  A  liquid  immersed  in  another,  with  which  it  does 
not  mix,  of  exactly  the  same  specific  gravity,  such  as  olive  oil  in  a  mixture 
of  alcohol  and  water,  assumes  the  spherical  form  (fig.  60). 

To  this  cause  also  is  due  the  spherical  form  acquired  by  small  masses  of 
liquid  which  fall  through  great  heights,  such  as  raindrops,  and  molten  lead  in 
casting  small  shot. 

When  a  capillary  tube  is  immersed  in  a  liquid  which  moistens  it,  and 
IS  then  carefully  removed,  the  column  of  liquid  in  the  tube  is  seen  to  be  twice 
as  long  as  while  the  tube  was  immersed  in  the  liquid.  This  arises  from 
the  fact  that  a  drop  adheres  to  the  lower  extremity  of  the  tube  and  forms  a 


-138]        Determination  of  the   Constant  of  Capillarity.  12 1 

convex  meniscus,  which  concurs  with  that  of  the  upper  meniscus  to  form  a 
longer  column  (131). 

For  the  same  reason  a  liquid  does  not  overflow  in  a  capillary  tube, 
although  the  latter  may  be  shorter  than  the  liquid  column  which  would 
otherwise  be  formed  in  it.  For  when  the  liquid  reaches  the  top  of  the  tube, 
its  upper  surface,  though  previously  concave,  becomes  convex,  and,  as  the 
downward  pressure  becomes  greater  than  if  the  surface  were  plane  the 
ascending  motion  ceases. 

It  is  from  capillarity  that  oil  ascends  in  the  wicks  of  lamps,  that  water 
rises  in  woods,  sponge,  bibulous  paper,  sugar,  sand,  and  in  all  bodies  which 
possess  pores  of  a  perceptible  size.  In  the  cells  of  plants  the  sap  rises  with 
great  force,  for  here  we  have  to  do  with  vessels  whose  diameter  is  less  than 
o-oi  mm.  Efflorescence  of  salts  is  also  due  to  capillarity  ;  a  solution  rising 
against  the  side  of  a  vessel,  the  water  evaporates,  and  the  salt  forms  on  the 


Fig.  IIS. 


side  a  means  of  furthering  still  more  the  ascent  of  a  liquid.  Capillarity  is, 
moreover,  the  cause  of  the  following  phenomenon  : — When  a  porous  sub- 
stance, such  as  gypsum,  or  chalk,  or  even  earth,  is  placed  in  a  porous  vessel 
of  unbaked  porcelain,  and  the  whole  is  dipped  in  water,  the  water  penetrates 
into  the  pores,  and  the  air  is  driven  inwards,  with  such  force,  so  that  it  is 
under  four  or  five  times  its  usual  pressure  and  density.  Jamin  has  proved 
this  by  cementing  a  manometer  into  blocks  of  chalk,  gypsum,  &c.,  and  he 
has  made  it  probable  that  a  pressure  of  this  kind,  exerted  upon  the  roots, 
promotes  the  ascent  of  sap  in  plants. 

138.  Determination  of  the  constant  of  capillarity .^ — This  determina- 
tion may  be  effected  in  various  ways,  of  which  the  simplest  and  perhaps  the 
most  accurate  is  that  of  the  measuring  the  ascent  of  a  liquid  in  capillary 
tubes.      For  this  purpose  capillary  tubes  of  glass  are  used,  the  diameter  of 


122 


On  Liquids. 


[138- 


which  is  determined  by  introducing  a  thread  of  mercury  into  the  tube  and 

ascertaining  the  weight  of  a  given  length  (125). 

The  height  to  which  the  Hquid  rises  in  the  capillary  tube  may  be  read 

oft"  by  a  cathetometer  (fig.  115).     The  capillary  tube  is  fixed  to  a  cross-piece 

of  wood,  which  is  placed  on  the  edges  of  a  glass  tube  ee  half  filled  with  the 
liquid.  In  order  that  the  liquid  may  properly  moisten  the 
tube  it  is  sucked  up  by  means  of  a  caoutchouc  tube  beyond 
the  height  at  which  it  finally  stands.  The  cathetometer  is 
then  raised  to  the  level  1 1  n  oi  the  lowest  point  of  the 
meniscus.  The  pointed  screw  b  is  then  screwed  until  its  point 
just  grazes  the  liquid,  and  the  position  of  the  point  is  read 
off".  The  difference  of  these  two  readings  gives  the  desired 
height. 

A  simpler  arrangement  is  the  following  (fig.  116).  The 
capillary  tube  is  fixed  to  a  strip  of  opaque  glass,  graduated  in 
millimetres.  The  lower  end  of  the  tube,  which  is  fixed  in 
a  suitable  support,  is  first  dipped  in  a  small  vessel  of  the 
liquid,  and  then  the  movable  steel  point  p,  being  placed 
opposite  the  zero  of  the  graduation,  liquid  is  added  drop 
by  drop  until  its  level  just  grazes  the  point.  This  height 
may  be  read  off"  by  a  lens. 

In  the  case  of  a  liquid  which  wets  the  tube,  the  force 
which  holds  up  the  liquid  in  the  tube  is  the  surface  tension, 
a  acting  along  the  cross-section  of  the  tube  ;  that  is  27rra, 
where  r  is  the  diameter  of  the  tube.  This  force  is  equal 
to  the  weight  of  the  column  of  liquid,  which  is  tvr-hs,  where 
h  is  the  height  of  the  column  of  liquid,  and  j'  its  specific 
hrs, 


m 


gravity. 


J-  is  unity 


From  this  we  get 
/ir. 


and   for   water,   where 


Fig. 


This,  which  is  known  as  the  capillary 

constant,  gives  the  weight  supported  by  the  unit  of  length, 
which  is  usually  taken  at  a  millimetre.     The  following  are 
some  of  the  values  expressed  in  milligrammes  : — 
Water  ....     7"24   '      Turpentine  ....     277 
Hydrochloric  acid         .     7-15  Petroleum     ....     2-57 

Olive  oil        .         .         .     3'27         Alcohol         ....     2-27 

Quincke  determined  the  capillary  constant  of  such  metals  as  gold  and 
silver  by  fusing  the  ends  of  their  wires  and  weighing  the  drops  which  detached 
themselves.  The  constant,  as  can  be  shown,  is  equal  to  the  quotient  of  the 
weight  of  the  drop  by  the  cross-section  of  the  wire. 

139.  Endosmose  and  exosmose. — When  two  different  liquids  are  sepa- 
rated by  a  thin  porous  partition,  either  inorganic  or  organic,  a  current  sets 
in  from  each  liquid  to  the  other  ;  to  these  currents  the  names  endosmose 
and  exosmose  are  respectively  given.  These  terms,  which  signify  impulse 
from  within  and  impulse  from  without,  were  originally  introduced  by 
Dutrochet,  who  first  drew  attention  to  these  phenomena.  The  general 
phenomenon  may  be  termed  diosmose.     They  may  be  well  illustrated  by 


-139J 


Eudosmosc  and  Exosniosc. 


123 


means  of  the  endosmo>neter.  This  consists  of  a  long  tube,  at  the  end  of 
which  a  membranous  bag  is  firmly  bound  (fig.  117).  The  bag  is  then  filled 
with  a  strong  syrup,  or  some  other  solution  denser  than  water,  such  as  milk 
or  albumen,  and  is  immersed  in  water.  The  liquid  is  found  gradually  to 
rise  in  the  tube  to  a  height  which  may  attain 
several  inches  ;  at  the  same  time  the  level 
of  the  liquid  in  which  the  endosmometer  is 
immersed  becomes  lower.  It  follows,  there- 
fore, that  some  of  the  external  liquid  has 
passed  through  the  membrane  and  has 
mixed  with  the  internal  liquid.  The  ex- 
ternal liquid,  moreover,  is  found  to  contain 
some  of  the  internal  liquid.  Hence  two 
currents  have  been  produced  in  opposite 
directions.  The  flow  of  the  liquid  towards 
that  which  increases  in  volume  is  endosiiiose^ 
and  the  current  in  the  opposite  direction  is 
exosmose.  If  water  is  placed  in  the  bag, 
and  immersed  in  the  syrup,  endosmose  is 
produced  from  the  water  towards  the  syrup, 
and  the  liquid  in  the  interior  diminishes  in 
volume  while  the  level  of  the  exterior  is 
raised. 

The  phenomena  ot  endosmose  are  ex- 
plained as  follows  : — The  diaphragm  is  made 
up  of  numerous  capillary  apertures,  and 
according  to  the  difference  in  the  molecular 
attraction  of  its  material  for  different  liquids 
it  absorbs  different  quantities  of  them.  Thus 
Liebig  found  that  in  24  hours  100  grammes  of  dry  ox-bladder  absorbed  268 
^Tammes  of  water,  or  133  grammes  of  solution  of  chloride  of  sodium.  If, 
therefore,  such  a  bladder  separates  water,  and  solution  of  salt,  it  v/ill  absorb 
both,  but  water  in  larger  quantities.  These  liquids  will  now  be  withdrawn 
from  the  bladder  by  the  different  liquids  on  the  two  sides,  but  in  unequal 
quantities,  for  the  quantities  present  in  the  bladder  are  different.  Hence 
more  water  will  pass  in  one  direction  than  in  the  other. 

The  height  of  the  ascent  in  the  endosmometer  varies  with  different 
liquids.  Of  all  vegetable  substances,  sugar  is  that  which,  for  the  same 
density,  has  the  greatest  power  of  endosmose,  while  albumen  has  the 
highest  power  of  all  animal  substances.  In  general  it  may  be  said  that 
endosmose  takes  place  towards  the  denser  liquid.  Alcohol  and  ether  form 
an  exception  to  this  ;  they  behave  like  liquids  which  are  denser  than  water. 
With  acids,  according  as  they  are  more  or  less  dilute,  the  endosmose  is  from 
the  water  towards  the  acid,  or  from  the  acid  towards  the  water. 

It  is  necessary  for  the  production  of  endosmose — (i.)  that  the  liquids  be 
different  but  capable  of  mixing,  as  alcohol  and  water — there  is  no  dios- 
mose,  for  instance,  with  water  and  oil;  (ii.)  that  the  liquids  be  of  different 
densities  ;  and  (iii.)  that  the  membrane  must  be  permeable  to  at  least  one  of 
the  substances. 


Fig.  117. 


124  ^^^  Liquids.  [139- 

The  current  through  thin  inorganic  plates  is  feeble,  but  continuous,  while 
organic  membranes  are  rapidly  decomposed,  and  diosmose  then  ceases. 

If  a  tube  filled  with  water  be  closed  at  both  ends  by  bladder  (fig.  ii8), 
and  one  end  is  placed  in  a  vessel  of  water,  the  other  being  in  contact  with 
the  air,  the  water  gradually  evaporates  through  the  bladder. 
This  water,  however,  is  as  rapidly  replaced,  so  that,  in  con- 
sequence of  evaporation,  water  moves  towards  the  place 
where  this  takes  place.  Hence  endosmose  plays  a  part  in 
the  motion  of  the  fluids  in  animals  and  vegetables.  The 
evaporation  from  the  skin  of  animals  brings  about  a  motion 
of  liquids  from  the  interior  towards  the  evaporating  sur- 
face. In  like  manner  the  passage  of  water  to  the  rootlets  of 
plants,  as  well  as  the  ascent  of  sap  to  the  highest  points 
of  the  trees,  is  favoured  by  evaporation  from  branchlets. 
leaves,  flowers,  and  fruit. 

The  well-known  fact  that  dilute  alcohol  kept  in  a  porous 
vessel  becomes  concentrated  depends  on  endosmose.  If  a 
mixture  of  alcohol  and  water  be  kept  for  some  time  in  a  bladder,  the  volume 
diminishes,  but  the  alcohol  becomes  much  more  concentrated.  The  reason 
doubtless  is  that  the  bladder  absorbs  water  more  readily  than  alcohol,  and 
accordingly  water  evaporates  on  the  surface,  and  thus  brings  about  a  con- 
centration of  the  residue. 

Dutrochefs  method  is  not  adapted  for  quantitative  measurements,  for  it 
does  not  take  into  account  the  hydrostatic  pressure  produced  by  the  column. 
Jolly  has  examined  the  endosmose  of  various  liquids  by  determining  the 
weights  of  the  bodies  diffused.  He  calls  the  cndosmotic  equivalent  of  a  sub- 
stance the  number  which  expresses  how  many  parts  by  weight  of  water  pass 
through  the  bladder  in^exchange  for  one  part  by  weight  of  the  substance.  The 
following  are  some  of  the  endosmotic  equivalents  which  he  determined  : — 

Sulphate  of  copper  .         .         9-5 

„  magnesium  .       117 

Caustic  potass  .         .     216-0 


He  also  found  that  the  endosmotic  equivalent  increases  with  the  temperature, 
and  that  the  quantities  of  substances  which  pass  in  equal  times  through  the 
bladder  are  proportional  to  the  strengths  of  the  solutions. 

140.  diffusion  of  liquids. — If  oil  be  poured  on  water,  no  tendency  to 
intermix  is  observed,  and  even  if  the  two  liquids  be  violently  agitated  to- 
gether, on  allowing  them  to  stand,  two  separate  layers  are  formed.  With 
alcohol  and  water  the  case  is  different ;  if  alcohol,  which  is  specifically 
lighter,  be  poured  upon  water,  the  liquids  gradually  intermix,  in  spite  of  the 
difference  of  the  specific  gravities  :  they  diffuse  into  one  another. 

This  point  may  be  illustrated  by  the  experiment  represented  in  fig.  119. 
A  tall  jar  contains  w^ater  coloured  by  solution  of  blue  litmus  ;  by  means  of 
a  funnel  some  dilute  sulphuric  acid  is  carefully  poured  in,  so  as  to  form  a 
layer  at  the  bottom  ;  the  colour  of  the  solution  is  changed  into  red,  pro- 
gressing upwards,  and  after  forty-eight  hours  the  change  is  complete — a 


Sulphuric  acid 

0-4 

Alcohol  . 

4-2 

Chloride  of  sodium 

4-3 

Sugar      . 

7-1 

-140]  Diffusion  of  Liquids.  125 

result  of  the  action  of  the  acid,  and  a  proof,  therefore,  that  it  has  diffused 
throughout  the  entire  mass. 

The  laws  of  this  diffusion,  in  which  no  porous  diaphragm  is  used,  were 
completely  investigated  by  Graham.  The  method  by  which  his  latest 
experiments  were  made  was  the  following  : — A  small  wide-necked  bottle  A 
(fig.  120)  filled  with  the  liquid  whose  rate  of  diffusion  was  to  be  examined 
was  closed  by  a  thin  glass  disc  and  placed  in  a  larger  vessel  B,  in  which 
water  was  poured  to  a  height  of  about  an  inch  above  the  top  of  the  bottle. 
The  disc  was  carefully  removed,  and  then  after  a  given  time  successive 
layers  were  carefully  drawn  off  by  means  of  a  siphon  or  pipette,  and  their 
contents  examined. 

The  general  results  of  these  investigations  may  be  thus  stated  : — 

i.  When  solutions  of  the  same  substance,  but  of  different  strengths,  are 
taken,  the  quantities  diffused  in  equal  times  are  proportional  to  the  strengths 
of  the  solutions. 

ii.  In  the  case  of  solutions  containing  equal  weights  of  different  substances 
the  quantities  diffused  vary  with  the  nature  of  the    substances.      Saline 


Fig.  119. 


substances  may  be  divided  into  a  number  of  cqiddiffiisive  groups,  the  rates 
of  diffusion  of  each  group  being  connected  with  the  others  by  a  simple 
numerical  relation. 

iii.  The  quantity  diffused  varies  with  the  temperature.  Thus,  taking  the 
rate  of  diffusion  of  hydrochloric  acid  at  15°  C.  as  unity,  at  49°  C.  it  is  2-18. 

iv.  If  two  substances  which  do  not  combine  be  mixed  in  solution,  they 
may  be  partially  separated  by  diffusion,  the  more  diffusive  one  passing  out 
most  rapidly.  In  some  cases  chemical  decomposition  even  may  be  effected 
by  diffusion.  Thus,  bisulphate  of  potassium  is  decomposed  into  free  sulphuric 
acid  and  neutral  sulphate  of  potassium. 

v.  If  liquids  be  dilute,  a  substance  will  diffuse  into  water  containing 
another  substance  dissolved,  as  into  pure  water  ;  but  the  rate  is  materially 
reduced  if  a  portion  of  the  same  diffusing  substance  be  already  present. 

The  following  table  gives  the  approximate  times  of  equal  diffusion  : — 


126 


On  Liquids. 


[140- 


Hydrochloric  acid  .  .  ro  Sulphate  of  magnesium  .  7-0 
Chloride  of  sodium  .  •  2-3  Albumen.  .  .  .  49-0 
Sugar 7'o         Caramel  .         .         .         .98-0 

It  will  be  seen  from  the  above  table  that  the  difference  between  the  rates 
of  diffusion  is  very  great.  Thus  sulphate  of  magnesium,  one  of  the  least 
diffusible  saline  substances,  diffuses  7  times  as  rapidly  as  albumen  and  14 
times  as  rapidly  as  caramel.  These  last  substances,  like  hydrated  silicic 
acid,  starch,  dextrine,  gum,  &c.,  constitute  a  class  of  substances  which  are 
characterised  by  their  incapacity  for  taking  the  crystalline  form,  and  by  the 
mucilaginous  character  of  their  hydrates.  Considering  gelatine  as  the  type 
of  this  class,  Graham  has  proposed  to  call  them  colloids  (ko'AXt/,  glue),  in  con- 
tradistinction to  the  far  more  easily  diffusible  cryslalloid  substances.  Colloids 
are  for  the  most  part  bodies  of  high  molecular  weight,  and  it  is  probably  the 
larger  size  of  their  molecules  which  hinders  their  passing  through  minute 
apertures. 

Graham  devised  a  method  of  separating  bodies  based  on  their  un- 
ecjual  dififusibility,  which  he  called  dialysis.  His  dialyser  (fig.  121)  consists  of 
a  ring  of  gutta-percha,  over  which  is  stretched  while  wet  a  sheet  of  parch- 
ment paper,  forming  thus  a  vessel  about  two  inches  high  and  ten  inches  in 


Fig.  121 


Fig. 


diameter,  the  bottom  ot  which  is  01  parchment  paper.  After  pouring  in  the 
mixed  solution  to  be  dialysed,  the  whole  is  floated  on  a  vessel  containing  a 
very  large  quantity  of  water  (fig.  122).  In  the  course  of  one  or  two  days  a 
more  or  less  complete  separation  will  have  been  effected.  Thus  a  solution 
of  arsenious  acid  mixed  with  various  kinds  of  food  readily  diffuses  out.  The 
process  has  received  important  applications  to  laboi-atory  and  pharmaceutical 
purposes. 

Eimilsions  such  as  are  of  frequent  use  in  medicine  are  prepared  by  mix- 
ing intimately  oil  with  a  solution  of  gum,  albumen,  or  some  other  colloid,  and 
water.  As  stated  above,  the  reason  of  difficulty  with  which  a  colloid  diffuses 
through  the  membrane  of  another  colloid  is  probably  that  its  molecules  are 
too  large  and  too  near  each  other— in  other  words  that  the  pores  are  too 
small.  With  an  ordinary  emulsion,  the  minute  droplets  of  oil  are  dispersed 
among  the  large  and  difficult  mobile  particles  of  the  colloid,  which  thus 
hinder  their  motion,  and  thereby  prevent  them  from  uniting  and  forming  a 
coherent  layer. 

Diosmose  plays  a  most  important  part  in  organic  life  ;  the  cell-walls  are 
diaphragms,  through  which  the  liquids  in  the  cells  set  up  diosmotic  com- 
munications. 


-143]  Velocity  of  Effiux.      TorricellV s   Theorem.  127 


CHAPTER    III. 

HYDRODYNAMICS. 

141.  Hydrodynamics. — The  science  which  treats  of  the  motion  of  Hquids 
is  called  hydrodyftamics  ;  and  the  application  of  the  principles  of  this  science 
to  conducting  and  raising  water  in  pipes  and  to  the  use  of  water  as  a  motive 
power  is  known  by  the  name  of  Jiydraiilics. 

142.  Velocity  of  efflux.  Torricelli's  theorem. — Let  us  imagine  an 
aperture  made  in  the  bottom  of  any  vessel,  and  consider  the  case  of  a  par- 
ticle of  liquid  on  the  surface,  without  reference  to  those  which  are  beneath. 
If  this  particle  fell  freely,  it  would  have  a  velocity  on  reaching  the  orifice 
equal  to  that  of  any  other  body  falling  through  the  distance  between  the 
level  of  the  liquid  and  the  orifice.  This,  from  the  laws  of  falling  bodies,  is 
\/2gk,  in  which  g  is  the  accelerating  force  of  gravity,  and  h  the  height.  If 
the  liquid  be  maintained  at  the  same  level,  for  instance  by  a  stream  of  water 
running  into  the  vessel  sufficient  to  replace  what  has  escaped,  the  particles 
will  follow  one  another  with  the  same  velocity,  and  will  issue  in  the  form  of 
a  stream.  Since  pressure  is  transmitted  equally  in  all  directions,  a  liquid 
would  issue  from  an  orifice  in  the  side  with  the  same  velocity,  provided  the 
depth  were  the  same. 

The  law  of  the  velocity  of  efflux  was  discovered  by  Torricelli.  It  may  be 
enunciated  as  follows  : — The  velocity  of  efflux  is  the  velocity  which  a  freely 
falling  body  would  have  on  reaching  the  orifice  after  having  started  fro)n 
a  state  of  rest  at  the  surface.  It  is  algebraically  expressed  by  the  formula 
v=^2gh. 

It  follows  directly  from  this  law  that  the  velocity  of  efflux  depends  on  the 
depth  of  the  orifice  below  the  surface,  and  not  on  the  nature  of  the  liquid. 
Through  orifices  of  equal  size  and  of  the  same  depth,  water  and  mercury 
would  issue  with  the  same  velocity,  for  although  the  density  of  the  latter 
liquid  is  greater,  the  weight  of  the  column,  and  consequently  the  pressure,  are 
greater  too.  It  follows  further  that  the  velocities  of  efflux  are  directly  pro- 
portional to  the  square  roots  of  the  depth  of  the  orifices.  Water  would  issue 
from  an  orifice  100  inches  below  the  surface  with  ten  times  the  velocity  with 
which  it  would  issue  from  one  an  inch  below  the  surface. 

The  quantities  of  water  which  issue  from  orifices  of  different  areas  are 
very  nearly  proportional  to  the  size  of  the  orifice,  provided  the  level  remains 
constant. 

143.  Direction  of  the  jet  from  lateral  orifices. — From  the  principle  of 
the  equal  transmission  of  pressui^e,  water  issues  from  an  orifice  in  the  side  of 
a  vessel  with  the  same  velocity  as  from  an  aperture  in  the  bottom  of  a  vessel 
at  the  same  depth.     Each  particle  of  a  jet  issuing  from  the  side  of  a  vessel 


128  On  Liquids.  [143- 

begins  to  move  horizontally  with  the  velocity  above  mentioned,  but  it  is  at 
once  drawn  downward  by  the  force  of  gravity  in  the  same  manner  as  a  bullet 

fired  from  a  gun,  with  its  axis  hori- 
zontal. It  is  well  known  that  the 
bullet  describes  a  parabola  (51) 
with  a  vertical  axis,  the  vertex 
being  the  muzzle  of  the  gun.  Now, 
since  each  particle  of  the  jet  moves 
in  the  same  curve,  the  jet  itself 
takes  the  parabolic  form  (123). 

In    every  parabola   there    is    a 
certain  point  called  the  focus,  and 
the  distance  from  the  vertex  to  the 
Fig.  123.  focus    fixes    the    magnitude    of    a 

parabola  in  much  the  same  manner 
as  the  distance  from  the  centre  to  the  circumference  fixes  the  magnitude 
of  a  circle.  Now  it  can  easily  be  proved  that  the  focus  is  as  much  below 
as  the  surface  of  the  water  is  above  the  orifice.  Accordingly,  if  water  issues 
through  orifices  which  are  small  in  comparison  with  the  contents  of  the  vessel, 
the  jets  from  orifices  at  different  depths  below  the  surface  take  diiTerent 
forms  as  shown  in  fig.  123.  If  these  are  traced  on  paper  held  behind  the  jet, 
then,  knowing  the  horizontal  distance  and  the  vertical  height,  it  is  easy  to 
demonstrate  that  the  jet  forms  a  parabola. 

144.  Height  of  the  jet. — If  a  jet  issuing  from  an  orifice  in  a  vertical 
direction  has  the  same  velocity  as  a  body  would  have  which  fell  from  the 
surface  of  the  liquid  to  that  orifice,  the  jet  ought  to  rise  to  the  level  of  the 
liquid.  It  does  not,  however,  reach  this  ;  for  the  particles  which  fall  hinder 
it,  But  by  inclining  the  jet  at  a  small  angle  with  the  vertical,  it  reaches 
about  j^^  of  the  theoretical  height,  the  difference  being  due  to  friction  and 
to  the  resistance  of  the  air.  By  experiments  of  this  nature  the  truth  of 
Torricelli's  law  has  been  demonstrated. 

145.  Quantity  of  efflux.  Vena  contracta.- — If  we  suppose  the  sides  of 
a  vessel  containing  water  to  be  thin,  and  the  orifice  to  be  a  small  circle  whose 

area  is  A,  we  might  think  that  the  quantity  of  water  E  dis- 
charged in  a  second  would  be  given  by  the  expression 
A.\/2gh,  since  each  particle  has,  on  the  average,  a  velocity 
equal  to  \/2gh,  and  particles  issue  from  each  point  of  the 
orifice.  But  this  is  by  no  means  the  case.  This  may  be 
explained  by  reference  to  fig.  124,  in  which  AB  represents  an 
orifice  in  the  bottom  of  a  vessel — what  is  true  in  this  case 
being  equally  true  of  an  orifice  in  the  side  of  the  vessel. 
Every  particle  above  AB  endeavours  to  pass  out  of  the 
vessel,  and  in  so  doing  exerts  a  pressure  on  those  near  it. 
Those  that  issue  near  A  and  B  exert  pressures  in  the 
directions  MM  and  NN  ;  those  near  the  centre  of  the  orifice  in  the  direction 
RQ,  those  in  the  intermediate  parts  in  the  directions  PQ,  PQ.  In. conse- 
quence, the  water  within  the  space  PQP  is  unable  to  escape,  and  that  which 
does  escape,  instead  of  assuming  a  cylindrical  form,  at  first  contracts,  and 
takes    the   form  of  a   truncated  cone.      It    is   found  that  the  escaping  jet 


M| 


Fig.  124. 


-146]        Influence  of  Tubes  on  the  Quantity  of  Efflux.  i  29 

continues  to  contract,  until  at  a  distance  from  the  orifice  about  equal  to  the 
diameter  of  the  orifice.  This  part  of  the  jet  is  called  the  vena  contracta.  \x 
is  found  that  the  area  of  its  smallest  section  is  about  §  or  0-625  of  that  of  the 
orifice.  Accordingly,  the  true  value  of  the  efiflu.x  per  second  is  given  approxi- 
mately  by  the  formula  ^  ^  o-62A^2-/., 

or  the  actual  value  of  E  is  about  0-62  of  its  theoretical  amount. 

146.  Influence  of  tubes  on  the  quantity  of  efflux. — The  ixsult  given 
in  the  last  article  has  reference  to  an  aperture  in  a  thin  wall.  If  a  cylindrical 
or  conical  efflux  tube,  or  ajutage,  is  fitted  to  the  aperture,  the  amount  of  the 
efflux  is  considerably  increased,  and  in  some  cases  falls  but  a  little  short  of 
its  theoretical  amount. 

A  short  cylindrical  ajutage,  whose  length  is  from  two  to  three  times  its  dia- 
meter, has  been  found  to  increase  the  efflux  per  second  to  about  0-82 A  ^/2_^/^. 
In  this  case  the  water  on  entering  the  ajutage  forms  a  contracted  vein  (fig. 
126),  just  as  it  would  do  on  issuing  freely  into  the  air  ;  but  afterwards  it  ex- 
pands, and,  in  consequence  of  the  adhesion  of  the  water  to  the  interior  surface 
of  the  tube,  has,  on  leaving  the  ajutage,  a  section  greater  than  that  of  the 
contracted  vein.  The  contraction  of  the  jet  within  the  ajutage  causes  a  par- 
tial vacuum.  If  an  aperture  is  made  in  the  ajutage,  near  the  point  of  greatest 
contraction,  and  is  fitted  with  a  vertical  tube,  the 
other  end  of  which  dips  into  water  (fig.  126),  it  is 
found  that  water  rises  in  the  vertical  tube,  thereby 
proving  the  formation  of  a  partial  vacuum. 

If  the  ajutage  has  the  form  of  a  conic  frustum 
whose  larger  end  is  at  the  aperture,  the  efflux  in 
a  second  maybe  raised  to  o-<^2p^^  igh,  provided 
the  dimensions  are  properly  chosen.  If  the 
smaller  end  of  a  frustum  of  a  cone  of  suitable 
dimensions  be  fitted  to  the  orifice,  the  efflux 
may  be  still  further  increased,  and  fall  very  little 
short  of  the  theoretical  amount. 

When  the  ajutage  has  more  than  a  certain 
length,  a  considerable  diminution  takes  place  in 
the  amount  of  the  efflux  :  for  example,  if  its  length 
is  48  times  its  diameter,  the  efflux  is  reduced  to  o-6'},K\/2gh.  This  arises  from 
the  fact  that,  when  water  passes  along  cylindrical  tubes,  the  resistance  in- 
creases with  the  length  of  the  tube  ;  for  a  thin  layer  of  liquid  is  attracted  to 
the  walls  by  adhesion,  and  the  internal  flowing  liquid  rubs  against  this. 
The  resistance  which  gives  rise  to  this  result  is  called  hydraidic  friction  :  it 
is  independent  of  the  material  of  the  tube,  provided  it  be  not  roughened  ; 
but  depends  in  a  considerable  degree  on  the  viscosity  of  the  liquid  ;  for 
instance,  ice-cold  water  experiences  a  greater  resistance  than  lukewarm  water. 

According  to  Prony,  the  mean  velocity  v  of  water  in  a  cast-iron  pipe  of 
the  length  /,  and  the  diameter  d.,  under  the  pressure^,  is  in  metres 

This  is  on  the  assumption  that  the  tubes  are  straight.  An)-  angle  or 
curvature  of  the  tube  diminishes  it,  seeing  that  part  of  the  motion  is  used  up 

K 


I30 


On  Liquids. 


[146- 


in  pressure  against  the  sides.  Thus  Venturi  found  the  time  requisite  to  fill 
a  small  vessel  by  means  of  a  tube  38  inches  in  length  by  3-3  in  diameter,  was 
45,  50,  or  70  seconds,  according  as  the  tube  was  straight,  curved,  or  bent  at 
a  right  angle. 

By  means  of  hydraulic  pressure  Tresca  submitted  solids  such  as  silver, 
lead,  iron  and  steel,  powders  like  sand,  soft  plastic  substances  such  as  clay, 
and  brittle  bodies  like  ice,  to  such  enormous  pressures  as  100,000  kilo- 
grammes, and  has  found  that  they  then  behave  like  fluid  bodies.  His  ex- 
periments show  also  that  these  bodies  transmit  pressure  equally  in  all 
directions  when  the  pressure  is  considerable  enough. 

147.  Efflux  throug-h  capillary  tubes. — This  was  in\estigated  by 
Poisseuille  by  means  of  the  apparatus  represented  in  fig.  127,  in  which  the 
capillary  tube  AB  is  sealed  to  a  glass  tube  on  which  a  bulb  is  blown.  The 
volume  of  the  space  between  the  marks  M  and  N  is  accurately  determined, 
and  the  apparatus,  having  been  filled  with  the  liquid  under  examination 
by  suction,  is  connected  at  the  end  M  with  a  reservoir  of  compressed 
air,  in  which  the  pressure  is  measured  by  means  of  a  mercury  mano- 
meter (183).  The  time  is  then  noted  which  is  required  for  the  level  of  the 
liquid  to  sink  from  M  to  N,  the  pressure  remaining  constant.  It  is  thus  found 
that  V,  the  volume  which  flows  out  in  a  given  time,  is  represented  by  the 

foi'mula  ,,x 

_TTpr_ 

^'  ~  8  el 

where  /  is  the  length,  and  r  the  diameter  of  the  tube,  p  the  pressure,  and  e  the 
coefficient  of  internal frictioti  (48)  ;  which  may  be  defined  as  the  resistance  to 

motion  offered  by  two  layers 
of  the  liquid  of  unit  surface, 
at  unit  distance,  and  moving 
away  from  each  other  with 
unit  velocity.  Knowing  the 
dimensions,  a  determination 
of  the  volume  which  flows 
out  in  a  given  time  is  a  ready 
means  of  obtaining  this  coeffi- 
cient. If  the  experiment  be 
made  with  water,  which  is 
taken  as  standard,  then,  using 
the  same  apparatus,  other 
liquids  may  be  compared  with 
it,  which  has  thus  the  advan- 
tage of  dispensing  with  a  sepa- 
rate determination  of  the  diameter  of  the  tube.  This  is  a  matter  of  importance, 
as  its  fourth  power  occurs  in  the  formula,  and  any  error  in  its  determination 
greatly  affects  the  result.  Bodies  with  a  high  coefficient  of  internal  friction  are 
said  to  be  viscous  (96).  The  liquids  ether,  water,  sulphuric  acid,  linseed  oil, 
Venice  turpentine  represent,  for  instance,  a  series  with  increasing  viscosity. 
The  coefficient  of  internal  friction  is  greater  in  the  case  of  solution  of  salts 
than  with  water,  and  increases  with  the  strength  of  the  solution.  It  greatly 
diminishes  with  the  temperature,  and  at  60°  is  one-third  what  it  is  at  zero. 


-149j 


Hydra u lie   Touni  iqiic t. 


148.  Porm  of  the  jet.— After  the  contracted  vein,  the  jet  has  the  form 
of  a  sohd  I'od  for  a  short  distance,  but  then  begins  to  separate  into  drops, 
which  present  a  pecuHar  appearance.  They  seem  to  form  a  series  of  ventral 
and  nodal  segments  (fig.  128).  The  ventral  segments  consist  of  drops  extended 
in  a  horizontal  direction,  and  the  nodal  segments  in  a  longitudinal  dii^ection. 
And  as  the  ventral  and  nodal  segments  have  respectively  a  fixed  position, 
each  drop  must  alternately  become  elongated  and  flattened  while  it  is 
falling  (fig.  129).  Between  any  two  drops  there  are  smaller  ones,  so  that  the 
whole  jet  has  a  tube-like  appearance. 

These  alterations  in  form  have  been  explained  as  being  due  to  vibrations 
in  the  mouth  of  the  vessel  itself  Their  position  is  modified  by  extraneous 
influences  such  as  musical  and  other  sounds,  but  only  when  these  influences 
afi'ect  the  edges  themselves. 

If  the  jet  is  momentarily  illuminated  by  the  electric  spark,  its  structure  is 
well  seen  ;  the  drops  appear  then  to  be  stationary,  and  separate  from  each 
other.  If  the  aperture  is  not  circular,  the  form  of  the  jet  undergoes  curious 
changes. 

149.  HydratElic  tourniquet. — If  water  be  contained  in  a  vessel,  and  an 
aperture  be  made  in  one  of  the  sides,  the  pressure  at  this  point  is  removed. 


3* 


'■0, 


Fig.  128.  Fig.  129. 

for  it  is  expended  in  sending  out  the  water  ;  but  it  remains  on  the  other  side  ; 
and  if  the  vessel  were  movable  in  a  horizontal  direction,  it  would  move  in  a 
direction  opposite  to  that  of  the  issuing  jet.  This  is  illustrated  by  the  appa- 
ratus known  as  the  hydraulic  tourniquet  or  Barker's  mill  (fig.  130).  It  con- 
sists of  a  glass  vessel,  M,  containing  water,  and  capable  of  moving  about  its 
^•ertical  axis.  At  the  lower  part  there  is  a  tube,  C,  bent  horizontally  in  oppo- 
site directions  at  the  two  ends.     If  the  vessel  were  full  of  water  and  the  tubes 

K  2 


132  On   Liquids.  [149- 

closed,  the  pressure  on  the  sides  of  C  would  balance  each  other,  being  equal 
and  acting  in  contrary  directions  ;  but,  being  open,  the  water  runs  out,  and  the 
pressure  is  not  exerted  on  the  open  part,  but  only  on  the  opposite  side,  as 
shown  in  the  figure  A.  And  this  pressure,  not  being  neutralised  by  an 
opposite  pressure,  imparts  a  rotatory  motion  in  the  direction  of  the  arrow, 
the  velocity  of  which  increases  with  the  height  of  the  liquid  and  the  size  of 
the  aperture. 

The  same  principle  may  be  illustrated  by  the  following  experiment.  A 
tall  cylinder  containing  water,  and  provided  with  a  lateral  stop-cock  near  the 
bottom,  is  placed  on  a  light  shallow  dish  on  water,  so  that  it  easily  floats. 
On  opening  the  stop-cock  so  as  to  allow  water  to  flow  out,  the  vessel  is 
observed  to  move  in  a  direction  diametrically  opposite  to  that  in  which  the 
water  is  issuing.  Similarly,  if  a  vessel  containing  water  be  suspended  by  a 
string,  on  opening  an  aperture  in  one  of  the  sides,  the  water  will  jet  out,  and 
the  vessel  be  deflected  away  from  the  vertical  in  the  opposite  direction. 

Segner's  water-wheel  and  the  reaction  machine  depend  on  this  principle. 
So  also  do  rotating  fireworks  ;  that  is,  an  unbalanced  reaction  from  the 
heated  gases  which  issue  from  openings  in  them  gives  them  motion  in  the 
opposite  direction. 

1 50.  "Water- wheels.  Turbines. — When  water  is  continuously  flowing 
from  a  higher  to  a  lower  level,  it  may  be  made  use  of  as  a  motive  power. 
The  motive  power  of  water  is  generally  utilised  either  by  means  of  water- 
wheels,  turbines,  rams,  or  hydraulic  engines. 

Water-wheels  are  wheels  provided  with  buckets  or  float-boards  at  the 
circumference,  and  on  which  the  water  acts  either  by  pressure  or  by  impact. 
They  are  made  to  turn  in  a  vertical  plane  round  a  horizontal  axis,  and  are 
of  two  principal  kinds,  undershot  and  overshot.  In  imdershot  wheels  the 
float-boards  are  placed  radially,  that  is,  at  right  angles  to  the  circumference 
of  the  wheel.  The  lowest  float-boards  are  immersed  in  the  water,  which 
flows  with  a  velocity  depending  on  the  height  of  the  fall.  Such  wheels  are 
applicable  where  the  quantity  of  water  is  great,  but  the  fall  inconsiderable. 
Overshot  wheels  are  used  with  a  small  quantity  of  water  which  has  a  high 
fall,  as  with  small  mountain  streams.  On  the  circumference  of  the  wheel 
there  are  buckets  of  a  peculiar  shape.  The  water  falls  into  the  buckets  on 
the  upper  part  of  the  wheel,  which  is  thus  moved  by  the  weight  of  the  water, 
and  as  each  bucket  arrives  at  the  lowest  point  of  revolution  it  discharges  all 
the  water,  and  ascends  empty. 

An  overshot  wheel  driven  by  an  extraneous  force  may  be  used  for  raising 
water,  as  in  dredging  machines  ;  and  an  undershot  one  for  moving  a  vessel 
to  which  its  axis  is  fixed,  as  in  the  paddles  of  steam-vessels. 

The  turbine  is  a  horizontal  water-wheel,  and  is  similar  in  principle  to  the 
hydraulic  tourniquet  or  reaction  wheel  (149).  It  consists  of  a  pair  of  discs, 
one  above  the  other,  connected  together  by  a  number  of  specially  shaped  thin 
arms  or  blades,  which  divide  the  space  between  the  discs  into  an  equal 
number  of  curved  radial  chambers.  The  wheel  works  generally  upon  a 
vertical  axis,  and  one  of  the  discs  is  cut  away  at  the  centre.  In  an  outward 
flow  turbine,  the  water  enters  through  the  opening  so  made  into  the  space 
between  the  discs,  and  passes  outwards  radially  through  the  chambers  above 
mentioned,  causing  the  wheel  to  rotate  by  its  reaction  upon  their  curved 


150a] 


The  Hydraulic  Ram. 


133 


walls.  In  order  to  prevent  waste  of  energy  in  giving  useless  rotation  to  the 
water,  the  peripheral  openings  of  the  wheel  are  surrounded  by  a  series  of 
corresponding  fixed  chambers,  whose  sides  (guide-blades)  are  so  curved  that 
the  water  when  it  leaves  them  has  lost  all  its  rotational  motion,  and  simplj' 
flows  away  at  right  angles  to  the  axis.  In  an  inward  flow  turbine  the  water 
enters  the  peripheral  opening  of  the  wheel  through  the  guide-blades,  and 
leaves  the  wheel  at  the  centre. 

The  total  theoretical  effect  of  a  fall  of  water  is  never  realised  ;  for  the 
water,  after  acting  on  the  wheel,  still  retains  some  velocity,  and  therefore 
does  not  impart  the  whole  of  its  velocity  to  the  wheel.  In  many  cases  water 
flows  past  without  acting  at  all  ;  if  the  water  acts  by  impact,  vibrations  are 
produced  which  are  transmitted  to  the  earth  and  lost ;  the  same  effect  is 
produced  by  the  friction  of  water  over  an  edge  of  the  sluice,  in  the  channel 
which  conveys  it,  or  against  the  wheel  itself,  as  well  as  by  the  friction  of 
this  latter  against  the  axle.  A  wheel  working  freely  in  a  stream,  as  with  the 
corn-mills  on  the  Rhine  near  Mainz,  does  not  utilise  more  than  20  per  cent, 
of  the  theoretical  effect.  One  of  the  more  perfect  forms  of  turbines  will 
\\ork  up  to  over  (So  per  cent.  Turbines  also,  when  properly  designed,  may 
be  made  to  have  a  very  high  efficiency  either  with  high  or  low  falls  ;  while,  on 
account  of  the  great  speed  at  which  they  run,  they  are  very  much  smaller 
than  water-wheels  in  proportion  to  their  power.  They  are  thus  more  '  effi- 
cient '  motors  than  steam-engines,  which,  even  if  perfect,  can  only  transform 
into  work  from  25  to  30  per  cent,  of  the  energy  represented  by  the  coal  they 
burn,  and  seldom  in  practice  utilise  more  than  half  of  this  percentage. 

150c?.  The  Hydraulic  Ram. — If  a  quantity  of  water  flow  through  a  pipe 
open  at  one  end,  and  if  this  aperture  be  cjuickly  closed,  a  sudden  impact  will  be 
exerted  on  the  closure  as  well  as  on  the  sides  of  the  pipe.  Some  of  the 
energy  of  the  falling  water  is  thereby  converted  into  heat,  and  some  exerts  a 
dangerous  pressure  on  the  pipe.  The  existence  of  this  pressure  may  be  readily 
observed  in  any  town  with  a  high-pressure  water  supply,  by  the  sharp  click 
heard  if  the  tap,  through  which  water  is  flowing,  is  suddenly  closed. 

The  hydraulic  ram  invented  by  Montgolfier  is  an  arrangement  by  which 
the  energy  of  falling 
water    is  applied    so    I 
as  to  raise  a  portion    || 
of    it    to    a     greate 
height    than    the    re-    j 
servoir  from  which  it 
is  fed.  I 

The  principle  of  j 
such  an  arrangement  ( 
is  represented  in  fig.  ! 
1 3 1 ,  in  which  E  is  the  L 
reservoir,  A  the  pipe 
in  which  the  water 
falls,  B  the  channel,  which  should  be  long  and  straight,  a  and  b  the  valves, 
C  the  windchest,  and  D  the  rising  main.  Water  first  flows  out  in  quantity 
through  the  valve  a,  and  as  soon  as  it  has  acquired  a  certain  velocity  it  raises 
that  valve,  and  the  aperture  is  shut.     The  impact  thus  produced  acting  on 


134  On  Liquids.  [150a- 

the  sides  of  the  pipe  and  on  the  valve  b  raises  this  valve,  and  a  quantity  of  water 
passes  into  the  windchest  shutting  off  air,  and  compressing"  it  in  the  space 
above  the  mouth  d  of  the  rising  main  D.  This  air  by  its  elastic  force  closes 
the  valve  b,  and  the  water  which  has  entered  is  raised  in  the  main  pipe  D. 

As  soon  as  the  impulsive  action  is  over,  and  the  water  in  the  channel  is 
at  rest,  the  valve  a  falls  again  by  its  own  weight,  the  flow  begins  afresh, 
and  when  it  has  acquired  sufficient  velocity  the  valve  b  is  again  closed, 
and  the  whole  process  is  repeated. 

In  this  way  water  can  be  raised  to  a  height  several  times  as  great  as  the 
difference  in  level  from  E  to  the  valve  b.  If  no  energy  were  lost  in 
friction,  and  in  raising  the  valves,  the  height  of  ascent  would  be  to  the  fall 
as  the  quantity  of  water  which  flows  out  at  a  is  to  that  which  is  raised. 
Thus  \  of  the  water  flowing  out  of  the  channel  could  be  raised  to  5  times  the 
height  of  the  available  fall. 

151.  Hydraulic  Eng-ine. — Historically,  falling  water  was  one  of  the 
earliest  sources  of  power  ;  but  it  is  only  in  recent  times  that  attention  has  been 
called  (first  by  Lord  Armstrong)  to  the  advantage  of  using  hydraulic  power  in 


.  / ...  ",:j 


towns  and  other  places  where  there  is  no  natural  fall  of  water  for  driving- 
certain  classes  of  machines,  in  those  cases  more  especially  where  the  use  of 
the  machinery  is  only  intermittent. 

For  this  purpose  the  most  important  docks  and  large  warehouses  are 
now  generally  furnished  with  means  of  obtaining  a  water-supply  at  a  very 
high  pressure,  generally  about  700  pounds  to  the  square  inch.  Steam- 
jDumping  engines  are  employed  to  pump  water  more  or  less  continuously 
into  what  are  practically  large  cylinders  with  immensely  heavy  pistons  loaded 
to  the  required  pressure.  These  vessels  are  called  accumulators,  and  pipes 
from  them  are  led  away  to  the  various  places  (lock  gates,  sluice  valves, 
cranes,  capstans,  &c.)  where  power  maybe  wanted.  At  each  of  these  places 
there  is  some  kind  of  hydraulic  motor  suitable  to  the  particular  work  to  be 


-151]  Hydraulic  Engine.  135 

done,  and  this  motor  can  be  instantaneously  set  to  work  by  opening  the 
communication  between  it  and  the  high-pressure  water  in  the  accumulator. 
The  motor  used  is  not  uncommonly  a  small  engine  similar  in  principle  to  a 
steam-engine,  and  one  of  the  best  of  these  engines  is  that  illustrated  in 
fig.  132,  which  is  the  invention  of  Schmidt  of  Ziirich.  It  consists  of  a 
cylinder  fitted  with  a  piston  c  whose  rod  is  connected  diirectly  to  a  crank 
upon  a  horizontal  shaft.  The  cylinder  has  two  ports  or  passages,  a  and  b, 
one  at  each  end,  both  terminating  below  in  openings  upon  a  convex  curved 
face,  which  is  kept  continually  pressed  against  a  similar  concave  face  upon 
the  framing  of  the  engine.    In  this  fixed  face  are  also  an  inlet  port  or  passage 

A,  and  outlet  passages  B.  "When  the  cylinder  is  in  the  position  shown 
in  the  figure,  the  high-pressure  water  is  passing  through  A  and  b,  forcing 
the  piston  along,  and  driving  out  the  already  used  water  through  a   and 

B.  As  the  piston  moves  and  turns  the  crank,  the  cylinder  oscillates  on 
its  bearings,  and  by  the  time  the  piston  has  got  to  the  end  of  its  stroke, 
the  cylinder  then  being  horizontal,  the  process  is  just  being  reversed,  water 
passing  in  through  A  and  a,  and  out  through  b  and  B.  W  is  an  air-vessel 
for  preventing  shocks. 

The  chief  drawback  about  the  use  of  water  power,  except  where  there  is 
a  large  natural  supply  under  pressure,  is  its  expense.  For  each  revolution 
of  the  crank  shaft,  two  complete  cylinders  full  of  water  must  be  passed 
through  such  an  engine,  as,  whether  the  power  be  wanted  or  not,  the  water 
cannot  be  expanded  like  steam. 

With  any  given  pressure  it  is  easy  to  find  out  how  much  water  will  be 
required  for  a  given  power.  At  a  pressure  of  30  pounds  per  square  inch, 
for  instance,  one  horse-power  will  require,  supposing  the  efficiency  of  the 

machine  to  be  70  per  cent.  (472),  — 33ooo  x    o   ^  about  855  cubic  feet  or  4,000 

"30X  144x07 
gallons  per  hour,  a  quantity  the  cost  of  which  would  in  most  cases  put  the  use 
of  this  power  out  of  the  question.  The  pressure  in  town  mains  generally 
lies  between  20  and  40  pounds  per  square  inch,  and  it  is  therefore  only  in 
cases  where  a  special  high-pressure  supply  is  available  that  the  power  can  be 
economically  used. 

In  London,  water  is  supplied  to  consumers  by  the  Hydraulic  Power  Company 
under  a  pressure  of  700  pounds  ;  and  the  quantity  required  for  one  horse- 
power would  be  about  175  gallons.  The  cost  of  power  supplied  in  this  way 
is  about  fourpence  per  horse-power  per  hour,  which,  although  expensive  for 
continuous  working,  is  not  so  when  it  is  intermittently  used,  and  when 
only  the  quantity  consumed  is  paid  for. 

Water-power  is  usually  represented  by  the  weight  of  the  water  multiplied 
mto  the  height  of  the  available  fall  ;  or  it  may  also  be  represented  by  half 
the  product  of  the  mass  into  the  square  of  the  velocity.  Both  measurements 
give  the  same  result  (60).  The  water-power  of  the  Niagara  Falls  is  calcu- 
lated to  be  equal  to  four  and  a  half  millions  of  horse-power. 


136  On   Gases.  [152- 


BOOK    IV. 

ON    GASES. 


CHAPTER    I. 

PROPERTIES  OF   GASES.      ATMOSPHERE.      BAROMETERS. 

152.  Physical  properties  of  gases. — Gases  are  bodies  which,  unHke 
solids,  have  no  independent  shape,  and,  unhke  hquids,  have  no  independent 
volume.  Their  molecules  possess  almost  perfect  mobility  ;  they  are  con- 
ceived as  darting  about  in  all  directions,  and  are  continually  tending  to 
occupy  a  greater  space.  This  property  of  gases  is  known  by  the  names 
expansibility,  tension,  or  clastic  force,  from  which  they  arc  often  cdW&d.  elastic 
fluids. 

Gases  and  liquids  have  several  properties  in  common,  and  some  in  which 
they  seem  to  differ  are  in  reality  only  different  degrees  of  the  same  property. 
Thus,  in  both,  the  particles  are  capable  of  moving  ;  in  gases  with  almost 
perfect  freedom  ;  in  liquids  not  quite  so  freely,  owing  to  a  greater  degree  of 
viscosity.  Both  are  compressible,  though  in  very  different  degrees.  If  a 
lit|uid  and  a  gas  both  exist  under  the  pressure  of  one  atmosphere,  and  then 
the  pressure  be  doubled,  the  water  is  compressed  by  about  the  j-,^-^  part, 
while  the  gas  is  compressed  by  one-half  In  density  there  is  a  great  differ- 
ence :  water,  which  is  the  type  of  liquids,  is  770  times  as  heavy  as  air,  the 
type  of  gaseous  bodies,  while  under  the  pressure  of  one  atmosphere.  A 
spiral  spring  only  shows  elasticity  when  it  is  compressed ;  it  loses  its  tension 
wl^en  it  has  returned  to  its  primitive  condition.  A  gas  has  no  original  volume  ; 
it  is  always  clastic,  or  in  other  words  it  is  always  striving  to  attain  a  greater 
volume  ;  this  tendency  to  indefinite  expansion  is  the  chief  property  by  which 
gases  are  distinguished  from  liquids. 

Matter  assumes  the  solid,  liquid,  or  gaseous  form  according  to  the  rela- 
tive strength  of  the  cohesive  and  repulsive  forces  exerted  between  their 
molecules.    In  liquids  these  forces  balance  ;  in  gases  repulsion  preponderates. 

By  the  aid  of  pressure  and  of  low  temperatures,  the  force  of  cohesion 
may  loe  so  far  increased  in  many  gases  that  they  are  readily  converted  into 
liquids,  and  we  know  now  that  with  sufficient  pressure  and  cold  they  may  all 
be  liquefied.  On  the  other  hand,  heat,  which  increases  the  vis  viva  of  the 
molecules,  converts  liquids,  such  as  water,  alcohol,  and  ether,  into  the  aeriform 


155] 


Weight  of  Gases. 


^37 


state  in  which  they  obey  all  the  laws  of  gases.  The  aeriform  state  of  liquids 
is  known  by  the  name  oi  vapour ;  while  gases  are  bodies  which,  under  ordi- 
nary temperature  and  pressure,  remain  in  the  aeriform  state. 

In  describing  exclusively  the  properties  of  gases  we  shall,  for  obvious 
reasons,  refer  to  atmospheric  air  as  their  type. 

153.  acxpansibility  of  gases. — This  property  of  gases,  their  tendency  to 
assume  continually  a  greater  volume,  is  exhibited  by  means  of  the  following 
experiment  : — A  bladder,  closed  by  a  stop-cock  and  about  half  full  of  air,  is 
placed  under  the  receiver  of  the  air-pump  (fig.  133),  and  a  vacuum  is  produced, 
on  which  the  bladder  immediately  distends. 
This  arises  from  the  fact  that  the  molecules 
of  air  flying  about  in  all  directions  (293) 
press  against  the  sides  of  the  bladder.  Under 
ordinary  conditions,  this  internal  pressure  is 
counterbalanced  by  the  air  in  the  receiver, 
which  exeits  an  equal  and  contrary  pressure. 
But  when  this  pressure  is  removed,  by  ex- 
hausting the  receiver,  the  internal  pressure 
becomes  evident.  When  air  is  admitted  into 
the  receiver,  the  bladder  resumes  its  original 
form. 

154.  Compressibility  of  g-ases. — The 
compressibility  of  gases  is  readily  shown  by 
the  pneumatic  syringe  (fig.  134).  This  con- 
sists of  a  stout  glass  tube  closed  at  one  end, 
and  provided  with  a  tight-fittmg  sohd  piston. 
When  the  rod  of  the  piston  is  pressed  it  Fi-.  133. 
moves  down  in  the  tube,  and  the  air  becomes 

compressed  into  a  smaller  volume  ;  but  as  soon  as  the  force  is  removed  the 
air  regains  its  original  volume,  and  the  piston  rises  to  its  former  position. 


i:;:!' 


155.  "Weig-ht  of  gases. — From  their  extreme  fluidity  and  expansibility, 
gases  seem  to  be  uninfluenced  by  the  force  of  gravity  :  they  nevertheless 
possess  weight  like  solids  and  liquids.  To  show  this,  a  glass  globe  of  3  or  4 
ciuarts  capacity  is  taken  (fig.  135),  the  neck  of  which  is  provided  with  a  stop- 
cock, which  hermetically  closes  it,  and  by  which  it  can  be  screwed  to  the 
plate  of  the  air-pump.  The  globe  is  then  exhausted,  and  its  weight  deter- 
mined by  means  of  a  delicate  balance.  Air  is  now  allowed  to  enter,  and  the 
globe  again  weighed.     The  weight  in  the  second  case  will  be  found  to  be 


138 


On   Gases. 


[155- 


greater  than  before,  and  if  the  capacity  of  the  vessel  is  known,  the  increase 
will  obviously  be  the  weight  of  that  volume  of  air. 

By  a  modification  of  this  method,  and  with  the  adoption  of  certain  pre- 
cautions, the  weight  of  air  and  of  other  gases  has  been  determined.  Perhaps 
the  most  accurate  are  those  of  Regnault,  who  found  that  a  litre  of  dry  air  at 
o"  C,  and  under  a  pressure  of  760  millimetres,  weighs  i  •293 187  grammes. 
Since  a  litre  of  water  (or  1,000  cubic  centimetres)  at  0°  weighs  o*999877 
gramme,  thedensity  of  air  is  o'ooi29334  that  of  water  under  the  same  circum- 
stances ;  that  is,  water  is  ']']'}>  tinies  as  heavy  as  air.  Expressed  in  English 
measures,  100  cubic  inches  of  dry  air  under  the  ordinary  at- 
^  mospheric  pressure  of  30  in.  and  at  the  temperature  of  16°  C. 

weigh  31  grains  ;  the  same  volume  of  carbonic  acid  gas  under 
the  same  circumstances  weighs  47-25  grains ;  100  cubic 
inches  of  hydrogen,  the  lightest  of  all  gases,  weigh  2*  14 
grains  ;  and  100  cubic  inches  of  hydriodic  acid  gas  weigh 
146  grains. 

156.  Pressure  exerted  toy  g-ases. — Gases  exert  on  their 
own  molecules,  and  on  the  sides  of  vessels  which  contain 
them,  pressures  which  may  be  regarded  from  two  points 
of  view.  First,  we  may  neglect  the  weight  of  the  gas  ; 
secondly,  we  may  take  account  of  its  weight.  If  we  neglect 
the  weight  of  any  gaseous  mass  at  rest,  and  only  consider  its 
expansive  force,  it  will  be  seen  that  the  pressures  due  to  this 
force  act  with  the  same  strength  on  all  points,  both  of  the 
mass  itself  and  of  the  vessel  in  which  it  is  contained.  For 
it  is  a  necessary  consequence  of  the  elasticity  and  fluidity 
of  gases,  that  the  repulsive  force  between  the  molecules  is 
the  same  at  all  points,  and  acts  equally  in  all  directions. 
This  principle  of  the  equality  of  the  pressure  of  gases  in 
all  directions  may  be  shown  experimentally  by  means  of  an  apparatus  re- 
sembling that  by  which  the  same  principle  is  demonstrated  for  liquids  (fig.  68). 
If  we  consider  the  weight  of  any  gas,  we  shall  see  that  it  gives  rise  to 
pressures  which  obey  the  same  laws  as  those  produced  by  the  weight  of 
liquids.  Let  us  imagine  a  cylinder,  with  its  axis  vertical,  several  miles  high, 
closed  at  both  ends  and  full  of  air.  Let  us  consider  any  small  portion  of 
the  air  enclosed  between  two  horizontal  planes.  This  portion  must  sustain 
the  weight  of  all  the  air  above  it,  and  transmit  that  weight  to  the  air  beneath 
it,  and  likewise  to  the  curved  surface  of  the  cylinder  which  contains  it,  and 
at  each  point  in  a  direction  at  right  angles  to  the  surface.  Thus  the  pressure 
increases  from  the  top  of  the  column  to  the  base  ;  at  any  given  layer  it 
acts  equally  on  equal  surfaces,  and  at  right  angles  to  them,  whether  they 
are  horizontal,  vertical,  or  inclined.  ■  The  pressure  acts  on  the  sides  of 
the  vessel,  and  on  any  small  surface  it  is  equal  to  the  weight  of  a  column 
of  gas  whose  base  is  this  surface,  and  whose  height  its  distance  from  the 
summit  of  the  column.  The  pressure  is  also  independent  of  the  shape  and 
dimensions  of  the  supposed  cylinder,  provided  the  height  remain  the  same. 
For  a  small  quantity  of  gas  the  pressures  due  to  its  weight  are  quite  in- 
significant, and  may  be  neglected  ;  but  for  large  quantities,  like  the  atmo- 
sphere, the  pressures  are  considerable,  and  must  be  allowed  for. 


Fig.  135. 


-158]  AtuiospJieric  Pressure.  139 

157.  The  atmosphere  :  its  composition. — ^The  atmosphere  is  the  layer 
of  air  which  surrounds  our  globe  in  every  part.  It  partakes  of  the  rotatory 
motion  of  the  globe,  and  would  remain  fixed  relatively  to  terrestrial  objects 
but  for  local  circumstances,  which  produce  winds,  and  are  constantly  dis- 
turbing its  equilibrium. 

It  is  essentially  a  mixture  of  oxygen  and  nitrogen  gases  ;  its  average  com- 
position by  volume  being  as  follows  : — 

Nitrogen          .         .         . 78"49 

Oxygen 20-63 

Aqueous  vapour 0-84 

Carbonic  acid 0-04 

I  GO-GO 

The  carbonic  acid  arises  from  the  respiration  of  animals  from  the  pro- 
cesses of  combustion,  and  from  the  decomposition  of  organic  substances. 
Boussingault  estimated  that  in  Paris  the  following  quantities  of  carbonic 
acid  are  produced  every  24  hours  : — 

By  the  population  and  by  animals.         .     1 1,895,000  cubic  feet 
By  processes  of  combustion    ,         .         .     92,101,000        ,, 

103,996,000        „ 

Notwithstanding  this  enormous  continual  production  of  carbonic  acid 
the  composition  of  the  atmosphere  does  not  vary  ;  for  plants  in  the  process 
of  vegetation  decompose  the  carbonic  acid,  assimilating  the  carbon,  and 
restoring  to  the  atmosphere  the  oxygen,  which  is  being  continually  consumed 
in  the  processes  of  respiration  and  combustion. 

158.  Atmospheric  pressure. — If  we  neglect  the  perturbations  to  which 
the  atmosphere  is  subject,  as  being  inconsiderable,  we  may  consider  it 
as  a  fluid  sea  of  a  certain  depth,  surrounding  the  earth  on  all  sides,  and 
exercising  the  same  pressure  as  if  it  were  a  liquid  of  very  small  density. 
Consequently,  the  pressure  on  the  unit  of  area  is  constant  at  a  given  level, 
being  equal  to  the  weight  of  the  column  of  atmosphere  above  that  level 
whose  horizontal  section  is  the  unit  of  area  (99).  It  will  act  at  right  angles 
to  the  surface,  whatever  be  its  position.  It  will  diminish  as  we  ascend,  and 
increase  as  we  descend  from  that  level.  Consequently,  at  the  same  height, 
the  atmospheric  pressures  on  unequal  plane  surfaces  will  be  proportional  to 
the  areas  of  those  surfaces,  provided  they  be  small  'in  proportion  to  the 
height  of  the  atmosphere. 

In  virtue  of  the  expansive  force  of  the  air,  it  might  be  supposed  that  the 
molecules  would  expand  indefinitely  into  the  planetaiy  spaces.  But,  in  pro- 
portion as  the  air  expands,  its  expansive  force  decreases,  and  is  further 
weakened  by  the  low  temperature  of  the  upper  regions  of  the  atmosphere,  so 
that,  at  a  certain  height,  equilibrium  is  established  between  the  expansive 
force  which  separates  the  molecules,  and  the  action  of  gravity  which  draws 
them  towards  the  centre  of  the  earth.  It  is  therefore  concluded  that  the 
atmosphere  is  limited. 

From  the  weight  of  the  atmosphere,  and  its  increase  in  density,  and  from 
the  observation  of  certain  phenomena  of  twilight,  its  height  has  been  esti- 
mated at  from  30  to  40  miles.  Above  that  height  the  air  is  extremely  rarefied. 


140  On   Gases.  [168- 

and  at  a  height  of  60  miles  it  is  assumed  that  there  is  a  perfect  vacuum.  On 
the  other  hand,  meteorites  have  been  seen  at  a  height  of  200  miles,  and,  as 
their  luminosity  is  undoubtedly  due  to  friction  against  air,  there  must  be  air 
at  such  a  height.  This  higher  estimate  is  supported  by  observations  made 
at  Rio  Janeiro  on  the  twilight  arc,  by  M.  Liais,  who  estimated  the  height 
of  the  atmosphere  at  between  198  and  212  miles.  The  question  as  to  the 
exact  height  of  the  atmosphere  must  therefore  be  considered  as  still  awaiting 
settlement. 

As  it  has  been  previously  stated  that  100  cubic  inches  of  air  weigh  31 
grains,  it  will  readily  be  conceived  that  the  whole  atmosphere  exercises  a 
considerable  pressure  on  the  surface  of  the  earth.  The  existence  of  this 
pressure  is  shown  by  the  following  experiments. 

1 59.  Crusliingr  force  of  the  atmosphere. — On  one  end  of  a  stout  glass 
cylinder,  about  5  inches  high,  and  open  at  both  ends,  a  piece  of  bladder  is 
tied  quite  airtight.  The  other  end,  the  edge  of  which  is  ground  and  well 
greased,  is  pressed  on  the  plate  of  the  air-pump  (fig.  136).  As  soon  as  the 
air  in  the  vessel  is  rarefied  by  working  the  air-pump,  the  bladder  is  depressed 
by  the  weight  of  the  atmosphere  above  it,  and  finally  bursts  with  a  loud 
report  caused  by  the  sudden  entrance  of  the  air. 


lir 


160.  IWag'deburg'  hemispheres. — The  preceding  experiment  only  serves 
to  illustrate  the  downward  pressure  of  the  atmosphere.  By  means  of  the 
Magdeburg  hemispheres  (figs.  137  and  138),  the  invention  of  Avhich  is  due  to 
Otto  von  Guericke,  burgomaster  of  Magdeburg,  it  can  be  shown  that  the 
pressure  acts  in  all  directions.  This  apparatus  consists  of  two  hollow  brass 
hemispheres  of  4  to  4^^  inches  diameter,  the  edges  of  which  ai-e  made  to  fit 
tightly,  and  are  well  greased.  One  of  the  hemispheres  is  provided  with  a 
stop-cock,  by  which  it  can  be  screwed  on  to  the  air-pump,  and  on  the  other  there 
is  a  handle.     As  long  as  the  hemispheres  contain  air  they  can  be  separated 


-162] 


Pascal's  Experiments. 


141 


without  any  difficulty,  for  the  external  pressure  of  the  atmosphere  is  counter- 
balanced by  the  elastic  force  of  the  air  in  the  interior.  But  when  the  air  in 
the  interior  is  pumped  out  by  means  of  the  air-pump,  the  hemispheres 
cannot  be  separated  without  a  powerful  effort  ;  and  as  this  is  the  case  in 
whatever  position  they  are  held,  it  follows  that  the  atmospheric  pressure  is 
transmitted  in  all  directions. 


DETERMINATION    OF   THE   ATMOSPHERIC    PRESSURE.      BAROMETERS. 

161.  Torricelli's  experiment. — The  above  experiments  demonstrate  the 
existence  of  the  atmospheric  pressure,  but  they  give  no  precise  indication 
as  to  its  amount.  The  following  experiment,  which  was  first  made,  in  1643, 
by  Torricelli,  a  pupil  of  Galileo,  gives  an 
exact  measure  of  the  weight  of  the  atmo- 
sphere. 

A  glass  tube  is  taken,  about  a  yard 
long  and  a  quarter  of  an  inch  internal 
diameter  (fig.  139).  It  is  sealed  at  one 
end,  and  is  quite  filled  with  mercury. 
The  aperture  C  being  closed  by  the 
thumb,  the  tube  is  inverted,  the  open  end 
placed  in  a  small  mercury  trough,  and 
the  thumb  removed.  The  tube  being  in 
a  vertical  position,  the  column  of  mercury 
sinks,  and,  after  oscillating  some  time,  it 
finally  comes  to  rest  at  a  height  A,  which 
at  the  level  of  the  sea  is  about  30  inches 
above  the  mercury  in  the  trough.  The 
mercury  is  raised  in  the  tube  by  the 
pressure  of  the  atmosphere  on  the  mer 
cury  in  the  trough.  There  is  no  contrary 
pressure  on  the  mercury  in  the  tube, 
because  it  is  closed  ;  but,  if  the  end  of 
the  tube  be  opened,  the  atmosphere  will 
press  equally  inside  and  outside  the  tube, 
and  the  mercury  will  sink  to  the  level  of 
that  in  the  trough.  It  has  been  shown  in 
hydrostatics  (107)  that  the  heights  of 
two  columns  of  liquid  in  communication 
with   each   other   are    inversely  as    their  Fig.  1^9. 

densities,  and   hence   it  follows  that  the 

pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  mercury,  the 
height  of  which  is  30  inches.  If,  however,  the  weight  of  the  atmosphere 
diminishes,  the  height  of  the  column  which  it  can  sustain  must  also  diminish. 
162.  Pascal's  experiments. — Pascal,  who  wished  to  ascertain  whether 
the  force  which  sustained  the  mercury  in  the  tube  was  really  the  pressure  of 
the  atmosphere,  made  the  following  experiments,  (i.)  If  it  were  the  case, 
then  the  column  of  mercury  ought  to  be  lower  in  proportion  as  we  ascend  in 
the  atmosphere.     He  accordingly  requested  one  of  his  relatives  to  repeat 


142  On   Gases.  [162- 

Torricelli's  experiment  on  the  summit  of  Puy  de  Dome  in  Auvergne. 
This  was  done,  and  it  was  found  that  the  mercurial  cokimn  was  about  3 
inches  lower,  thus  proving  that  it  is  really  the  weight  of  the  atmosphere 
which  supports  the  mercury,  since,  when  this  weight  diminishes,  the  height 
of  the  column  also  diminishes,  (ii.)  Pascal  repeated  Torricelli's  experiment 
at  Rouen,  in  1646,  with  other  liquids.  He  took  a  tube  closed  at  one  end 
nearly  50  feet  long,  and,  having  filled  it  with  water,  placed  it  vertically  in  a 
vessel  of  water,  and  found  that  the  water  stood  in  the  tube  at  a  height  of 
34  feet ;  that  is,  13-6  times  as  high  as  mercury.  But,  since  the  mercury  is  13-6 
times  as  heavy  as  water,  the  height  of  the  column  of  water  was  exactly 
equal  to  that  of  a  column  of  mercury  in  Torricelli's  experiment,  and  it  was 
consequently  the  same  force,  the  pressui'e  of  the  atmosphere,  which  succes- 
sively supported  the  two  liquids.  Pascal's  other  experiments  with  oil  and 
with  wine  gave  similar  results. 

163.  Amount  of  the  atmospheric  pressure. — Let  us  assume  that  the 
tube  in  the  above  experiment  is  a  cylinder,  the  section  of  which  is  equal  to  a 
square  inch  ;  then,  since  the  height  of  the  mercurial  column  in  round  num- 
bers is  30  inches,  the  column  will  contain  -^^^  cubic  inches  ;  and  as  a  cubic 
inch  of  mercury  weighs  3433'5  grains  =  0-49  of  a  pound,  the  pressure  of  such 
a  column  on  a  square  inch  of  surface  is  equal  to  147  pounds.  In  round 
numbers  the  pressure  of  the  atmosphere  is  taken  at  15  pounds  on  the  square 
inch.  A  surface  of  a  foot  square  contains  144  square  inches,  and  therefore 
the  pressure  upon  it  is  equal  to  2,160  pounds,  or  nearly  a  ton.  Expressed 
in  the  metrical  system,  the  standard  atmospheric  pressure  at  0°  and  the  sea- 
level  is  760  millimetres,  which  is  equal  to  29-9217  inches  ;  and  a  calculation 
similar  to  the  above  shows  that  the  pressure  on  a  square  centimetre  is 
=  I  -032896  kilogrammes. 

A  gas  or  liquid  which  acts  in  such  a  manner  that  a  square  inch  of  surface 
is  exposed  to  a  pressure  of  1 5  pounds,  is  called  a  pressure  of  one  atniospha-c. 
If,  for  instance,  the  elastic  force  of  the  steam  of  a  boiler  is  so  great  that  each 
square  inch  of  the  internal  surface  is  exposed  to  a  pressure  of  90  pounds 
(  =  6  X  15),  we  say  it  is  under  a  pressure  of  six  atmospheres. 

The  surface  of  the  body  of  a  man  of  middle  size  is  about  16  square  feet  ; 
the  pressure,  therefore,  which  a  man  supports  on  the  surface  of  his  body  is 
35,560  pounds,  or  nearly  16  tons.  Such  an  enormous  pressure  might  seem 
impossible  to  be  borne  ;  but  it  must  be  remembered  that,  in  all  directions, 
there  are  equal  and  contrary  pressures  which  counterbalance  one  another. 
It  might  also  be  supposed  that  the  effect  of  this  force,  acting  in  all  directions, 
would  be  to  press  the  body  together  and  crush  it.  But  the  solid  parts  of  the 
skeleton  could  resist  a  far  greater  pressure  ;  and  as  to  the  air  and  licjuids 
contained  in  the  organs  and  vessels,  the  air  has  the  same  density  as  the 
external  air,  and  cannot  be  further  compressed  by  the  atmospheric  pressure  ; 
and  from  what  has  been  said  about  liquids  (97),  it  is  clear  that  they  are  vir- 
tually incompressible.  When  the  external  pressure  is  removed  from  any  part 
of  the  body,  either  by  means  of  a  cupping  vessel  or  by  the  air-pump,  the 
pressure  from  within  is  seen  by  the  distension  of  the  surface. 

164,  Different  kinds  of  barometers. — The  instruments  used  for  measur- 
ing the  atmospheric  pressure  are  called  barometers.  In  ordinary  barometers 
the  pressure  is  measured  by  the  height  of  a  column  of  mercury,  as  in  Torri- 


-164] 


Cistern  Barovieter. 


143 


celli's  experiment  :  the  barometers  which  we  are  about  to  describe  are  of  this 
kind.  But  there  are  barometers  without  any  hquid,  one  of  which,  the  aneroid 
(187),  is  remarkable  for  its  simplicity  and  portability. 

165.  Cistern  barometer. — The  dslern  barometer  consists  of  a  straight 
glass  tube  closed  at  one  end,  about  -^l,  inches  long,  filled  with  mercuiy,  and 
dipping  into  a  cistern  containing  the  same  metal.  In  order  to  render  the 
barometer  more  portable,  and  the  variations  of  the  level  in  the  cistern  [,less 
perceptible  when  the  mercury  rises  or  falls  in  the  tube,  several  different 


liliiiliiliiliilliiillliiii       ^ 


Fig.  14 


forms  have  been  constructed.  Fig.  140  represents  one  form  of  the  cistern 
barometer.  The  apparatus  is  fixed  to  a  m.ahogany  stand,  on  the  upper  part 
of  which  there  is  a  scale  graduated  in  millimetres  or  inches  from  the  level 
of  the  mercury  in  the  cistern  :  a  movable  index,  z",  shows  on  the  scale  the 
level  of  the  mercury.  A  thermometer  on  one  side  of  the  tube  indicates  the 
temperature. 

There  is  one  fault  to  which  this  barometer  is  liable,  in  common  with  all 


144  On   Gases.  [165- 

others  of  the  same  kind.  The  zero  of  the  scale  does  not  always  correspond 
to  the  level  of  the  mercury  in  the  cistern.  For,  as  the  atmospheric  pressure 
is  not  always  the  same,  the  height  of  the  mercurial  column  varies  ;  some- 
times mercury  is  forced  from  the  cistern  into  the  tube,  and  sometimes  from 
the  tube  into  the  cistern,  so  that  in  the  majority  of  cases  the  graduation  of 
the  barometer  does  not  indicate  the  true  height.  If  the  diameter  of  the 
cistern  is  large,  relatively  to  that  of  the  tube,  the  error  from  this  source,  which 
is  known  as  the  error  of  capacity,  is  lessened. 

The  height  of  the  barometer  is  the  distance  between  the  levels  of  the 
mercury  in  the  tube  and  in  the  cistern.  Hence  the  barometer  should 
always  be  perfectly  vertical,  for  if  not,  the  tube  being  inclined,  the  column  of 
mercuiy  is  elongated  (fig.  141),  and  the  number  read  off  on  the  scale  is  too 
great.  As  the  pressure  which  the  mercury  exerts  by  its  weight  at  the  base 
of  the  tube  is  independent  of  the  form  of  the  tube  and  of  its  diameter  (loi), 
provided  it  is  not  capillary,  the  height  of  the  barometer  is  independent  of 
the  diameter  of  the  tube  and  of  its  shape,  but  is  inversely  as  the  density  of 
the  liquid.  With  mercury  the  mean  height  at  the  level  of  the  sea  is  29"92, 
or  in  round  numbers  30,  inches  ;  in  a  water  barometer  it  would  be  about  34 
feet,  or  10-33  metres. 

In  marine  barometers  the  error  of  capacity  is  got  rid  of  by  graduating  the 
scale  not  in  the  true  measurements,  but  by  an  empirical  correction  depending 
on  the  relative  diameters  of  the  tube  and  cistern.  Thus  if  a  rise  of  10  mm. 
in  the  tube  produced  a  fall  of  i  mm.  in  the  cistern,  the  true  change  would  not 
be  10  mm.  but  11  mm.  This  is  obviously  allowed  for  by  dividing  the  space 
of  10  mm.  on  the  scale  into  1 1  mm.  The  correctness  of  such  an  instrument 
depends  on  the  accuracy  with  which  the  scale  is  laid  off. 

166.  rortin's  toarometer. — Fortin^s  barometer  differs  in  the  shape  of 
the  cistern  from  that  just  described.  The  base  of  the  cistern  is  made  of 
leather,  and  can  be  raised  or  lowered  by  means  of  a  screw  ;  this  has  the 
advantage  that  a  constant  level  can  be  obtained,  and  also  that  the  instru- 
ment is  made  more  portable.  For,  in  travelling,  it  is  only  necessary  to 
raise  the  leather  until  the  mercury,  which  rises  with  it,  quite  fills  the  cistern  ; 
the  barometer  may  then  be  inclined,  and  even  inverted,  without  any  fear 
that  a  bubble  of  air  may  enter,  or  that  the  shock  of  the  mercury  may  crack 
the  tube. 

Fig.  142  represents  the  arrangement  of  the  barometer,  the  tube  of  which 
is  placed  in  a  brass  case.  At  the  top  of  this  case  there  are  two  longitudinal 
slits  on  opposite  sides,  so  that  the  level  of  the  mercury,  B,  is  seen.  The 
scale  on  the  case  is  graduated  in  millimetres.  An  index  A,  moved  by  the 
hand,  gives,  by  means  of  a  vernier,  the  height  of  the  mercury  to  j-th  of  a  milli- 
metre.    At  the  bottom  of  a  case  there  is  a  cistern  b,  containing  mercury  0. 

Fig.  143  shows  the  details  of  the  cistern  on  a  larger  scale  It  consists  of 
a  glass  cylinder  b,  through  which  the  mercury  can  be  seen  ;  this  is  closed  at 
the  top  by  a  boxwood  disc  fitted  on  the  under  surface  of  the  brass  cover  M. 
Through  this  passes  the  barometer  tube  E,  which  is  drawn  out  at  the  end, 
and  dips  in  the  mercury  ;  the  cistern  and  the  tube  are  connected  by  a  piece 
of  buckskin,  ce,  which  is  firmly  tied  at  ^  to  a  contraction  in  the  tube,  and  at  e 
to  a  brass  tubulure  in  the  cover  of  the  cistern.  This  mode  of  closing 
prevents  the  mercury  from  escaping  when  the  barometer  is  inverted,  while 


167] 


Gay-Liissacs  Syphon  Barometer. 


145 


the  pores  of  the  leather  transmit  the  atmospheric  pressure.     The  bottom  of 

the  cyhnder  b  is  cemented  on  a  boxwood  cyHnder  sz,  on  a  contraction  in 

which,  ii,  is  firmly  tied  the  buckskin,  vtjt,  which  forms  the  base  of  the  cistern. 

On  this  skin  is  fastened  a  wooden  button  x,  which  rests  against  the  end  of 

a  screw  C.     According  as  this  is  turned  in  one  direction  or  the  other,  the 

skin  mtt  is  raised  or  lowered,  and  with  it  the  mercury.     In  using  this  baro- 
meter, the  mercury  is  first  made  exactly  level  with  the  point  a,  which   is 

effected  by  turning  the  screw  C  either  in  one  direction  or  the  other.     The 

graduation  of  the  scale  is 

counted  from  this  point  «, 

and    thus   the    distance    of 

the  top  B  of  the  column  of 

mercury  from  a  gives  the 

height    of    the    barometer. 

The  bottom  of  the  cistern 

is    surrounded    by   a   brass 

case,  which  is  fastened  to 

the  cover  M  by  screws,  k, 

k,    k.      We    have    already 

seen  (165)   the  importance 

of   having    the    barometer 

quite     vertical,     which     is 

effected    by    the   following 

plan,   known    as    Cardajis 

suspoision. 

The  metal  case  contain- 
ing the  barometer  is  fixed 

in  a  copper  sheath    X   by 

two   screws   a   and    b   (fig. 

144).       This     is     provided 

with  two  axles  (only  one  of 

which,   o,   is    seen    in    the 

figure),  which  turn  freely  in 

two  holes  in  a  ring  Y.     In 

a  direction  at  right  angles 

to  that  of  the  axles,  00^  the 
ring   has   also   two  similar 

axles,  in  and  «,  resting  on 

a  support  Z.  By  means  of  this  double  suspension  the  barometer  can 
oscillate  freely  about  the  axes,  imi  and  00.,  in  two  directions  at  right  angles  to 
each  other.  But  as  care  is  taken  that  the  point  at  which  these  axes  cross 
corresponds  to  the  tube  itself,  the  centre  of  gravity  of  the  system,  which 
must  always  be  lower  than  the  axis  of  suspension,  is  below  the  point  of  inter- 
section, and  the  barometer  is  thus  perfectly  vertical. 

167.  Cay.Iiussac's  syphon  barometer. — -The  syphon  barometer  is  a 
bent  glass  tube,  one  of  the  branches  of  which  is  much  longer  than  the  other. 
The  longer  branch,  which  is  closed  at  the  top,  is  filled  \\\\\\  mercury  as  in  the 
cistern  baro.meter,  while  the  shorter  branch,  which  is  open,  serves  as  a 
cistern.     The  difference  between  the  two  levels  is  the  height  of  the  barometer. 

L 


146 


On   Gases. 


[167- 


Fig.  145  represents  the  syphon  barometer  as  modified  by  Gay-Lussac. 
In  order  to  render  it  more  available  for  travelling,  by  preventing  the  entrance 
of  air,  he  joined  the  two  branches  by  a  capillary  tube  (fig.  146);  when  the 
instrument  is  inverted  (fig.  147)  the  tube  always  remains  full  in  virtue  of  its 
capillarity,  and  air  cannot  penetrate  into  the  longer  branch.  A  sudden 
shock,  however,  might  separate  the  mercury  and  admit  some  air.  To  avoid 
this,  Bunten  introduced  an  ingenious  modification  into  the  apparatus.     The 


Fig.  147. 


longer  branch  is  drawn  out  to  a  fine  point,  and  is  joined  to  a  tube  B  of  the 
form  represented  in  fig.  148.  This  arrangement  forms  an  air-trap  ;  for  if  air 
passes  through  the  capillary  tube  it  cannot  penetrate  the  drawn-out  extremity 
of  the  longer  branch,  but  lodges  in  the  upper  part  of  the  enlargement  B. 
In  this  position  it  does  not  affect  the  observations,  since  the  vacuum  is 
always  at  the  upper  part  of  the  tube  ;  it  is,  moreover,  easily  removed. 

In  the  syphon  barometer  the  shorter  branch  is  closed,  but  there  is  a 


-169J  Correction  for  Capillarity.  147 

capillary  aperture  in  the  side  /,  through  which  the  atmospheric  pressure  is 
transmitted. 

The  barometric  height  is  determined  by  means  of  two  scales,  which  have 
a  common  zero  at  O,  towards  the  middle  of  the  longer  branch,  and  are  gra- 
duated in  contrary  directions,  the  one  from  O  to  E,  and  the  other  from  O  to 
B,  either  on  the  tube  itself,  or  on  brass  rules  fixed  parallel  to  the  tube.  Two 
sliding  verniers,  in  and  «,  indicate  tenths  of  a  millimetre.  The  total  height  of 
the  barometer,  AB,  is  the  sum  of  the  distances  from  O  to  A  and  from  O  to  B. 

Fig.  149  represents  a  very  convenient  mode  of  arranging  the  open  end  of 
a  syphon  barometer  for  transport.  The  quantity  of  mercury  is  so  arranged 
that  when  the  Torricellian  space  is  quite  filled  with  mercury,  by  inclining  the 
tube  the  enlargement  is  just  filled  to  d.  This  is  closed  by  a  carefully  fitted 
cork  fixed  on  the  end  of  a  glass  tube  about  a  millimetre  in  the  clear,  which 
allows  for  the  expansion  of  mercury  by  heat.  When  the  barometer  is  to  be 
used,  the  cork  and  tube  are  raised. 

168.  Precautions  in  reference  to  barometers. — In  constructing  baro- 
meters mercuiy  is  chosen  in  preference  to  any  other  liquid,  for,  being  the 
densest  of  all  liquids,  it  stands  at  the  least  height.  When  the  mercurial 
barometer  stands  at  30  inches,  the  water  barometer  would  stand  at  about 
34  feet  (165).  It  also  deserves  preference  because  it  does  not  moisten  the 
glass.  It  is  necessary  that  the  mercury  be  pure  and  free  from  oxide,  other- 
wise it  adheres  to  the  glass  and  tarnishes  it.  Moreover,  if  it  is  impure,  its 
density  is  changed,  and  the  height  of  the  barometer  is  too  great  or  too  small. 
Mercury  is  purified,  before  being  used  for  barometers,  by  treatment  with 
dilute  nitric  acid,  and  by  distillation. 

The  space  at  the  top  of  the  tube  (figs.  140  and  145),  which  is  called  the 
Torricellian  vacuum.,  must  be  quite  free  from  air  and  from  aqueous  vapour, 
for  otherwise  either  would  depress  the  mercurial  column  by  its  elastic  force. 
To  obtain  this  result,  a  small  quantity  of  pure  mercury  is  placed  in  the  tube 
and  boiled  for  some  time.  It  is  then  allowed  to  cool,  and  a  further  quantity, 
previously  warmed,  added,  which  is  boiled,  and  so  on,  until  the  tube  is  quite 
full  ;  in  this  manner  the  moisture  and  the  air  which  adhere  to  the  sides  of  the 
tube  (193)  pass  off  with  the  mercurial  vapour.  A  barometer  tube  should  not 
be  too  narrow,  for  otherwise  the  mercury  is  moved  with  difiiculty  ;  and  before 
reading  off,  the  barometer  should  be  tapped  so  as  to  get  rid  of  the  adhesion 
to  the  glass. 

A  barometer  is  free  from  air  and  moisture  if,  when  it  is  inclined,  the 
mercury  strikes  with  a  sharp  metallic  sound  against  the  top 
of  the  tube.     If  there  is  air  or  moisture  in  it,  the  sound  is     |||||  i '        j|| 
deadened.  |ll'i  '  j    ,'' 

169.  Correction  for  capillarity. — In  cistern  barometers 
there  is  always  a  certain  depression  of  the  mercurial  column 
due  to  capillarity,  unless  the  internal  diameter  of  the  tube 
exceeds  o-8  inch.  To  make  the  correction  due  to  this 
depression,  it  is  not  enough  to  know  the  diameter  of  the 
tube ;  we  must  also  know  the  height  of  the  meniscus  od  (fig. 
150),  which  varies  according  as  the  meniscus  has  been 
formed  during  an  ascending  or  descending  motion  of  the  mercury  in  the 
tube.     Consequently,  the  height  of  the  meniscus  must  be  determined    by 

L  2 


148 


On  Gases. 


[169- 


bringing  the  pointer  to  the  level  ab,  and  then  to  the  level  d,  when  the  differ- 
ence of  the  readings  will  give  the  height  od  required.  These  two  terms — 
namely,  the  internal  diameter  of  the  tube  and  the  height  of  the  meniscus — 
being  known,  the  resulting  correction  can  be  taken  out  of  the  following- 
table  : 


Internal 
diameter 
in-inches 

Height  of  sag 

itta  of  meniscus  in  inches 

1 

O'OIO 

0-015 

0-020 
0-0555 

0-025 

0030 
0-0780 

0-035 

0-040 

0-I57 

0-0293 

0-0431 

0-0677 

0-0870 

0-0948 

0-236 

0-0119 

0-0176 

0-0231 

0-0294 

0-0342 

0-0398 

0-0432 

0-315 

0-0060 

0-0088 

O-OI18 

0-0144 

0-0175 

0-0196 

0-0221 

0-394 

0-0039 

0-0048 

0-0063 

0-0078 

0-0095 

o-oiio 

00125 

0-472 

0-0020 

0-0029 

0-0036 

0-0045 

0-0053 

0-0063 

0-00T2, 

.0-550 

0-00 10 

0-0017 

0-0024 

0-0029 

0-0034 

0-0039 

0-0044 

In  the  syphon  barometer  the  two  tubes  are  of  the  same  diameter,  so 
that  the  error  caused  by  the  depression  in  the  one  tube  very  nearly  corrects 
that  caused  by  the  depression  in  the  other.  As,  however,  the  meniscus  in 
the  one  tube  is  formed  by  a  column  of  mercury  with  an  ascending  motion, 
while  that  in  the  other  is  formed  by  a  column  with  a  descending  motion, 
their  heights  will  not  be  the  same,  and  the  reciprocal  correction  will  not  be 
quite  exact. 

170.  Correction  for  temperature. — In  all  observations  with  barometers, 
whatever  be  their  construction,  a  correction  must  be  made  for  temperature. 
Mercury  contracts  and  expands  with  different  temperatures,  hence  its 
density  changes,  and  consequently  the  barometric  height,  for  this  height  is 
inversely  as  the  density  of  the  mercury,  so  that  for  different  atmospheric 
pressures  the  mercurial  column  might  have  the  same  height.  Accordingly, 
in  each  observation  the  height  observed  must  be  reduced  to  a  determinate 
temperature.  The  choice  of  this  is  quite  arbitrary,  but  that  of  melting  ice  is 
always  adopted  in  practice.  It  will  be  seen,  in  the  Book  on  Heat,  how  this 
correction  is  made. 

171.  Variations  in  tlie  height  of  the  barometer. — When  the  barometer 
is  observed  for  several  days,  its  height  is  found  to  vary  in  the  same  place, 
not  only  from  one  day  to  another,  but  also  during  the  same  day. 

The  extent  of  these  variations — that  is,  the  difference  between  the  greatest 
and  the  least  height — is  different  in  different  places.  It  increases  from  the 
equator  towards  the  poles.  Except  under  extraordinary  circumstances,  the 
greatest  variations  do  not  exceed  six  millimetres  under  the  equator,  30  under 
the  tropic  of  Cancer,  40  in  France,  and  60  at  25  degrees  from  the  pole.  The 
greatest  variations  are  observed  in  winter. 

The  7nccm  daily  height  is  the  height  obtained  by  dividing  the  sum  of  24 
successive  hourly  observations  by  24.  In  our  latitudes  the  barometric  height 
at  noon  corresponds  to  the  mean  daily  height. 

The  77iean  monthly  height  is  obtained  by  adding  together  the  mean  daily 
heights  for  a  month,  and  dividing  by  30.  The  mean  yearly  height  \^  simi- 
larly obtained. 

Under  the   equator,  the  mean  annual  height  at  the  level  of  the  sea  is 


-173]       Relation  of  Barometric   Variations  to    WeatJier.         149 

o'"758,  or  29-84  inches.  It  increases  from  the  equator,  and  between  the 
latitudes  30°  and  40°  it  attains  a  maximum  of  o™763,  or  30-04  inches.  In 
lower  latitudes  it  decreases,  and  in  Paris  it  does  not  exceed  o'^-7568. 

The  general  mean  at  the  level  of  the  sea  is  o™-76i,  or  29-96  inches. 

The  mean  monthly  height  is  greater  in  winter  than  in  summer,  in  conse- 
quence of  the  cooler  atmosphere. 

Two  kinds  of  variations  are  observed  in  the  barometer  : — ist,  the  acci- 
dental 7Jariatio?is,  which  present  no  regularity  ;  they  depend  on  the  seasons, 
the  direction  of  the  winds,  and  the  geographical  position,  and  are  common 
in  our  climates  ;  2nd,  the  daily  variations,  which  are  produced  periodically 
at  certain  hours  of  the  day. 

At  the  equator,  and  between  the  tropics,  no  accidental  variations  are 
observed  ;  but  the  daily  variations  take  place  with  such  regularity  that  a 
barometer  may  serve  to  a  certain  extent  as  a  clock.  The  barometer  sinks 
from  midday  till  towards  four  o'clock ;  it  then  rises,  and  reaches  its  maximum 
at  about  four  o'clock  in  the  evening.  It  then  again  sinks,  and  reaches  a 
second  minimum  towards  four  o'clock  in  the  morning,  and  a  second  maxi- 
mum at  ten  o'clock.  In  the  temperate  zones  there  are  also  daily  variations, 
but  they  are  detected  with  difficulty,  since  they  occur  in  conjunction  with 
accidental  variations. 

The  hours  of  the  maxima  and  minima  appear  to  be  the  same  in  all 
climates,  whatever  be  the  latitude  ;  they  merely  vary  a  little  with  the  seasons. 

172.  Causes  of  barometric  variations. — It  is  observed  that  the  course 
of  the  barometer  is  generally  in  the  opposite  direction  to  that  of  the  thermo- 
meter ;  that  is,  that  when  the  temperature  rises,  the  barometer  falls,  and  vice 
versa  ;  which  indicates  that  the  barometric  variations  at  any  given  place  are 
produced  by  the  expansion  or  contraction  of  the  air,  and  therefore  by  its 
change  in  density.  If  the  temperature  were  the  same  throughout  the  whole 
extent  of  the  atmosphere,  no  currents  would  be  produced,  and  at  the  same 
height,  atmospheric  pressure  would  be  everywhere  the  same.  But  when 
any  portion  of  the  atmosphere  becomes  warmer  than  the  neighbouring  parts, 
its  specific  gravity  is  diminished,  and  it  rises  and  passes  away  through 
the  upper  regions  of  the  atmosphere,  whence  it  follows  that  the  pressure 
is  diminished,  and  the  barometer  falls.  If  any  portion  of  the  atmosphere 
retains  its  temperature,  while  the  neighbouring  parts  become  cooler,  the  same 
effect  is  produced  ;  for  in  this  case,  too,  the  density  of  the  first-mentioned 
portion  is  less  than  that  of  the  others.  Hence,  also,  it  usually  happens  that 
an  extraordinary  fall  of  the  barometer  at  one  place  is  counterbalanced  by  an 
extraordinary  rise  at  another  place.  The  daily  variations  appear  to  result 
from  the  expansions  and  contractions  which  are  periodically  produced  in 
the  atmosphere  by  the  heat  of  the  sun  during  the  rotation  of  the  earth. 

173.  Relation  of  barometric  variations  to  the  state  of  the  weather. — 
It  has  been  observed  that,  in  our  climate,  the  barometer  in  fine  weather  is 
generally  above  30  inches,  and  is  below  this  point  when  there  is  rain,  snow, 
wind,  or  storm  ;  and  also,  that  for  any  given  number  of  days  at  which  the 
barometer  stands  at  30  inches,  there  are  as  many  fine  as  rainy  days.  From 
this  coincidence  between  the  height  of  the  barometer  and  the  state  of  the 
weather,  the  following  indications  have  been  marked  on  the  barometer 
counting  by  thirds  of  an  inch  above  and  below  30  inches  ; — 


I50 


On   Gases. 


[173- 


Height 

31  inches 
3o|  „ 
30^  „ 
30  „ 
29I  » 
29i    „ 

29    » 

In  using  the  ba 


State  of  the  weather 

.     Very  dry. 

.     Settled  weather. 

.     Fine  weather. 

.     Variable. 

.     Rain  or  wind. 

Much  rain. 
.  Tempest. 
rometer  as  an  indicator  of  the  state  of  the  weather,  we 
must  not  forget  that  it  really  only  serves  to  measure  the  weight  of  the  atmo- 
sphere, and  that  it  only  rises  or  falls  as  the  weight  increases  or  diminishes  ; 
and  although  a  change  of  weather  frequently  coincides  with  a  change  in  the 
pressure,  they  are  not  necessarily  connected.  This  coincidence  arises  from 
meteorological  conditions  peculiar  to  our  climate,  and  does  not  occur  every- 
where. That  a  fall  in  the  barometer  usually  precedes  rain  in  our  latitudes  is 
caused  by  the  position  of  Europe.  The  prevailing  winds  here  are  the  south- 
west and  north-east.  The  former,  coming  to  us  from  the  equatorial  regions, 
are  warmer  and  lighter.  They  often,  therefore,  blow  for  hours  or  even  days 
in  the  higher  regions  of  the  atmosphere  before  manifesting  themselves  on  the 
surface  of  the  earth.  The  air  is  therefore  lighter,  and  the  pressure  lower. 
Hence  a  fall  of  the  barometer  is  a  probable  indication  of  the  south-west 
winds,  which  gradually  extend  downwards,  and  reaching  us,  after  having 
traversed  large  tracts  of  water,  are  charged  with  moisture,  and  bring  us  rain. 
The  north-east  blows  simultaneously  above  and  below,  but  the  hindrances 
to  the  motion  of  the  current  on  the  earth,  by  hills,  forests,  and  houses,  cause 
the  upper  current  to  be  somewhat  in  advance  of  the 
lower  ones,  though  not  so  much  so  as  the  south-west 
wind.  The  air  is  therefore  somewhat  heavier  even 
before  we  perceive  the  north-east,  and  a  rise  of  the 
barometer  affords  a  forecast  of  the  occurrence  of  this 
wind,  which,  as  it  reaches  us  after  having  passed  over 
the  immense  tracts  of  dry  land  in  Central  and  Northern 
Europe,  is  mostly  dry  and  fine. 

When  the  barometer  rises  or  sinks  slowly,  that  is, 
for  two  or  three  days,  towards  fine  weather  or  towards 
rain,  it  has  been  found  from  a  great  number  of  observa- 
tions that  the  indications  are  then  extremely  probable. 
Sudden  variations  in  either  direction  indicate  bad 
weather  or  wind. 

174.  "Wheel  barometer. — The  ivlieel  barometer, 
which  was  invented  by  Hooke,  is  a  syphon  barometer, 
and  is  especially  intended  to  indicate  good  and  bad 
weather  (fig.  151).  In  the  shorter  leg  of  the  syphon 
there  is  a  float  which  rises  and  falls  with  the  mercury. 
A  string  attached  to  this  float  passes  round  a  pulley, 
and  at  the  other  end  there  is  a  weight  somewhat  lighter 
than  the  float.  A  needle  fixed  to  the  pulley  moves 
round  a  graduated  circle,  on  which  is  marked  stormy,  rain,  set  fair,  &c. 
When  the  pressure  varies  the  float  sinks  or  rises,  and  moves  the  needle  round 
to  the  correspondmg  points  on  the  scale. 


Fig.  151- 


-176]  Glycerine  Barometer.  151 

The  barometers  ordinarily  met  with  in  houses,  and  which  are  called 
^cueatker-glasses,  are  of  this  kind.  They  are,  however,  of  little  use,  for  two 
reasons.  The  first  is,  that  they  are  neither  very  delicate  nor  very  accurate 
in  their  indications.  The  second,  which  applies  equally  to  all  barometers,  is 
that  those  commonly  in  use  in  this  country  are  made  in  London,  and  the 
indications,  if  they  are  of  any  value,  are  only  so  for  a  place  of  the  same  level 
and  of  the  same  climatic  conditions  as  London.  Thus  a  barometer  standing 
at  a  certain  height  in  London  would  indicate  a  certain  state  of  weather,  but 
if  removed  to  Shootei-'s  Hill  it  would  stand  half  an  inch  lower,  and  would 
indicate  a  different  state  of  weather.  As  the  pressure  differs  with  the  level 
and  with  geographical  conditions,  it  is  necessary  to  take  these  into  account 
if  exact  data  are  wanted. 

175.  Fixed  barometer. — For  accurate  observa- 
tions Regnault  uses  a  barometer  the  height  of  which 
he  measures  by  means  of  a  cathetometer  (88).  The 
cistern  (fig.  152)  is  of  cast  iron  ;  against  the  frame  on 
which  it  is  supported  a  screw  is  fitted,  which  is  pointed 
at  both  ends,  and  the  length  of  which  has  been  deter- 
mined, once  for  all,  by  the  cathetometer.  To  mea- 
sure the  barometric  height,  the  screw  is  turned  until 
its  point  grazes  the  surface  of  the  mercury  in  the 
bath,  which  is  the  case  when  the  point  and  its  image 
are  in  contact.  The  distance  then  from  the  top  of 
the  point  to  the  level  of  the  mercury  in  the  tube  b  is 
measured  by  the  cathetometer,  and  this,  together  with 
the  length  of  the  screw,  gives  the  barometric  height 
with  great  accuracy.  This  barometer  has,  moreover, 
the  advantage  that,  as  a  tube  an  inch  in  diameter 
may  be  used,  the  influence  of  capillarity  becomes 
inappreciable.  Its  construction,  moreover,  is  very 
simple,  and  the  position  of  the  scale  leads  to  no  kind 
of  error,  since  this  is  transferred  to  the  cathetometer. 
Unfortunately,  the  latter  instrument  requires  great 
accuracy  in  its  construction,  and  is  expensive. 

176.  Glycerine  barometer. — Jordan  constructed 
a  barometer  in  which  the  liquid  used  is  pure  glycerine. 
This  has  the  specific  gravity  1*26,  and  therefore  the 
length  of  the  column  of  liquid  is  rather  more  than 
ten  times  that  of  mercury  ;  hence  small  alterations 
in  the  atmospheric  pressure  produce  considerable 
oscillations  in  the  height  of  the  liquid.  The  tube 
consists  of  ordinary  composition  gas-tubing  about 
I  of  an  inch  in  diameter  and  28  feet  or  so  in  length  ; 
the  lower  end  is  open  and  dips  in  the  cistern,  which 
may  be  placed  in  a  cellar  ;  the  top  is  sealed  to  a  Fig-  152. 
closed  glass    tube  an  inch   in  diameter,  in  which  the 

fluctuations  of  the  column  are  observed.  This  may  be  arranged  in  an  upper 
storey,  and  the  tubing,  being  easily  bent,  lends  itself  to  any  adjustment 
which  the  locality  requires. 


15: 


On   Gases. 


[176- 


The  vapour  of  glycerine  has  very  low  tension  at  ordinary  temperatures, 
and  is  therefore  not  so  exposed  to  such  back  pressures,  varying  with  the 
temperature,  as  is  water.  On  the  other  hand,  it  readily  attracts  moisture 
from  the  air,  whereby  the  density  and  therewith  the  height  of  the  liquid 
column  vary.  This  is  prevented  by  covering  the  liquid  in  the  cistern  with  a 
layer  of  paraffine  oil. 

The  '  Philosophical  Magazine,'  vol.  xxx.  Fourth  series,  page  349,  contains 
a  detailed  account  of  a  method  of  constructing  a  water  barometer. 

177.  Huygrhens'  barometer. — The  desire  to  amplify  the  small  variations 
which  take  place  in  the  barometer  has  led  to  a  number  of  contrivances,  one 
of  the  best  known  of  which  was  invented  by  Huyghens  (fig.  153). 

The  barometer  tube  a  is  wider  at  the  closed  end  b,  and  also  at  c,  where  a 
liquid  of  smaller  specific  gravity  than  mercury,  such  .as  coloured  water,  is 
poured  on  the  mercury  ;  it  fills  the  rest  of  the  tube  c  and  a  portion  of  d. 

Suppose  b  and  c  to  have  the  same  diameter,  which  is  n  times  that  of  d. 
When  the  column  of  mercury  in  b  sinks  through  x  millimetres,  the  level  of 
the  mercury  in  c  rises  just  as  much,  while  the  coloured  liquid  rises  7ix-  milli- 
metres, and  therefore  its  level  is  {n  —  i)x  millimetres  higher.  A  column  of 
this  hquid  {n  —  i)x  in  height  has  the  same  pressure  as  a  column  of  mercury 


{n. 


in  height,  where  .y  is  the  number  expressing  the  ratio  of  the  specific 


gravities  of  mercury  and  the  liquid. 

Accordingly,  when  the  mercury  in  b  sinks  x  milli 
metres. 


y  =  2x+  ■ X 

s 

is  the  height  of  the  column  of  mercury,  which  corre- 
sponds to  the  decrease  of  atmospheric  pressure.  From 
this  we  have 

2S  +  }l-\ 

Thus,  if  the  section  of  the  tubes  b  and  c  is  20  times 
that  of  d,  and  if  the  coloured  liquid  be  water,  we 
have 

\y6y       _i3"6y. 


46- 


=  0-2947. 


27-2-1-20- 

Accordingly,  when  an  ordinary  barometer  sinks 
through  J/  millimetres,  the  mercury  in  b  sinks  0-294;!/  mil- 
limetres, while  the  coloured  liquid  in  Arises  20  x  o-294jk 
=  5-88jK.  Whenever,  that  is,  an  ordinary  barometer 
sinks  or  rises  i  millimetre,  the  coloured  liquid  rises  or 
sinks  5-98  millimetres,  or  nearly  six  times  as  much. 

Such  barometers  are  useful  in  cases  where  the 
\'ariations  in  the  height  of  the  barometer,  rather  than 
its  actual  height,  are  to  be  observed.  The  scale 
should  be  placed  behind  the  tube  d,  and  two  points,  fixed,  near  the  top  and 
bottom,  by  comparison  with  standard  barometers  ;  the  inter\al  between  the 
two  is  then  suitably  divided. 


-178]  Dctcfiiiination  of  Heights  by  the  Barometer.  1 5  3 

178.  Determination  of  beigrhts  by  tbe  barometer. — Since  the  atmo- 
spheric pressure  decreases  as  we  ascend,  it  is  obvious  that  the  barometer 
will  keep  on  falling  as  it  is  taken  to  a  greater  and  greater  height. 
On  this  depends  a  method  of  determining  the  difference  between 
the  heights   of  two   stations,  such  as   the  base  and   summit  of  a 
mountain.     The  method  may  be  explained  as  follows. 

According  to  Boyle's  law  (180),  if  the  temperature  of  an  enclosed 
portion  of  air  continues  constant,  its  volume  will  vary  inversely  as 
the  pressure  ;  that  is  to  say,  if  we  double  the  pressure  we  shall  halve  -"-Q 
the  volume.  But  if  we  halve  the  volume  we  manifestly  double  the  tP 
quantity  of  air  in  each  cubic  inch — that  is  to  say,  we  double  the 
density  of  the  air  ;  and  so  on  in  any  proportion.  Consequently,  the 
law  is  equivalent  to  this  : — That  for  a  constant  temperature  the 
density  of  air  is  proportional  to  the  pressure  which  it  sustaifts. 

Now  suppose  A  and  B  (fig.  1 54)  to  represent  two  stations,  and 
that  it  is  required  to  determine  the  vertical  height  of  B  above  A,  it  .  _^j 
being  borne  in  mind  that  A  and  B  are  not  necessarily  in  the  same  Fig.  154. 
vertical  line.  Take  P,  any  point  in  AB,  and  Q,  a  point  at  a  small 
distance  above  P.  Suppose  a  pressure  on  a  square  inch  of  the  atmosphere 
at  P  to  be  denoted  by^,  and  at  Q  let  it  be  diminished  by  a  quantity  denoted 
by  dp.  It  is  clear  that  this  diminution  equals  the  weight  of  the  column  of 
air  between  P  and  Q,  whose  section  is  one  square  inch.  But,  since  the 
density  of  the  air  is  directly  proportional  to  p,  the  weight  of  a  cubic  inch  of 
air  will  equal  kgp,  where  k  denotes  a  certain  quantity  to  be  determined 
presently,  and  g  the  accelerating  force  of  gravity  (79).  Hence,  if  we  denote 
PQ  in  inches  by  <r/.i-,  the  pressure  will  be  diminished  by  kpg  .  dx\  and  we 
may  represent  this  algebraically  by  the  equation 

kpg .  dx  =  dp. 

By  a  certain  algebraical  process  this  leads  to  the  conclusion  that 

4-X  =  log|-, 

where  X  denotes  the  height  of  AB,  and  P  and  V-^  the  atmospheric  pressures 
at  A  and  B  respectively,  the  logarithms  being  what  are  called  '  Napierian ' 
logarithms.'  Now,  if  H  and  H^  are  the  heights  of  the  barometer  at  A  and 
B  respectively,  the  temperature  of  the  mercury  being  the  same  at  both 
stations,  their  ratio  equals  that  of  P  to  P,,  and  therefore 

It  remains  to  determine  k  and^. 

(i)  Since  the  force  of  gravity  is  different  for  places  in  different  latitudes, 
g  will  depend  upon  the  latitude  (82).  It  is  found  that  if  ^  is  the  accelerating 
force  of  gravity  in  latitude  (^,  and/that  force  in  latitude  45°,  then 

,^ f 

•^        I  +0-00256  cos  2(^  ' 

where /has  a  definite  numerical  value. 


154  On  Gases.  [178- 

(2)  If  o-  is  the  density  of  air  at  a  temperature  of /°  C,  under  Q,  the  pres- 
sure exerted  by  29-92  inches  of  mercury,  we  shall  have 

But  it  will  be  afterwards  shown  (332)  that  if  p^  is  the  density  of  air  under 
the  same  pressure  Q  at  0°  C,  we  shall  have 

I  +  af 
where  a  represents  the  coefficient  of  expansion  of  gases.     Therefore 

^Q  =  _Pp_ 
i-vaf 

Now  if  a-  is  the  density  of  mercury,  and  if  the  latitude  is  45°,  we  shall 
have 

Q  =  29-92  .  (t/; 
and  therefore 

kf=  P-SL  .    ! 

o-        29-92  (I  +<:;/) 

But  p„-^cr  is  the  ratio  which  the  density  of  dry  air  at  a  temperature  0°  C, 
in  latitude  45°,  under  a  pressure  of  29-92  inches   of  mercury,  bears  to  the 
density  of  mercury  at  0°  C,  and  therefore  Po-^or  is  a  determinate  number. 
Substituting,  we  have 

P  =  29-92  in.  .-^(i  +0-00256  cos  2(p)  (i  ■+ at)  log--. 
Po  ^1 

The  value  of  a  is  0-003665,  which  is  nearly  equal  to  3IJ-J.  If  we  substitute 
the  proper  values  for  a-i-p,,,  and  change  the  logarithms  into  common  loga- 
rithms, and  instead  of  /  use  the  mean  of  T  and  T^,  the  temperatures  at  the 
upper  and  lower  stations,  it  will  be  found  that 

X  (in  feet)  =  60346  (1+0-00256  cos  2(b)  (  1  +^STjLIiI)  log  ^-, 

\  1000     /  Hi 

which  is  La  Place's  barometric  formula.  In  using  it,  we  must  remember 
that  T  and  Tj  are  temperatures  on  the  Centigrade  thermometer,  and  that  H 
and  Hj  are  the  heights  of  the  barometer  reduced  to  0°  C.  Thus  if  A  is  the 
measvn-ed  height  of  the  barometer  at  the  lower  station  we  have 

H. ;,(■-/  ). 

V         6500/ 

If  the  height  to  be  measured  is  not  great,  one  observer  is  enough.  For 
greater  heights  the  ascent  takes  some  time,  and  in  the  interval  the  pressure 
may  vary.  Consequently,  in  this  case  there  must  be  two  observers,  one  at 
each  station,  who  make  simultaneous  observations. 

Let  us  take  the  following  example  of  the  above  formula  : — Suppose  that 
in  latitude  65°  N.  at  the  lower  of  the  two  stations  the  height  of  the  barometer 
was  30-025  inches,  and  the  temperature  of  air  and  mercury  i7°-32  C,  while 
at  the  upper  the  height  of  the  barometer  was  28-230  inches,  and  the  tempera- 
ture of  air  and  mercury  was  io°-55  C.  What  is  the  height  of  the  upper 
station  above  the  lower? 


-179]  Ruhhnanns  Observations.  1 5  5 

.(I)  Find  H  and  H^  :  viz. 

H  ^30-025(1 -^^-3^)  =  39-945. 

H, = 28-230(1 -;^^;55)= 28-184. 

\       6500/ 

TT 

Hence  log       =1-4763243-1-4500026  =  0-0263217. 

(2)  Find  I  +  ^^     "^     'J  viz.  1-05574. 

1000 

(3)  Find  I  +0-00256  cos  20. 

Since  0-00256  cos  130°=  —0-00256  cos  50°=  —0-001645, 

therefore  i  +0-00256  cos  20=  -0-998355. 

Hence  the  required  height  in  feet  equals 

60346  X  0-998355  X  1-05574  X  0-0063217  =  1674. 
If  H  and  H^  do  not  greatly  differ,  the  Napierian  logarithm  of 
H  ^^H-H, 
h;     "H  +  Hi' 

If,  for  instance,  H  =  30  and  Hj  =  29  inches,  the  resulting  error  would  not 
exceed  the  i^--^-^  part  of  the  whole.  Accordingly  for  heights  not  exceeding 
2,000  ft.  we  may,  without  much  error,  use  the  formula 

X  (in  feet)  =  52500(1  +  ^^'^  ^  ^A\  x  ^-^. 
V  1000     /     H  +  Hj 

179.  Ruhlmann's  observations. — The  results  obtained  for  the  difference 
in  height  of  places  by  using  the  above  formula  often  differ  from  the  true 
heights  as  measured  trigonometrically,  to  an  extent  which  cannot  be  ascribed 
to  errors  in  observation.  The  numbers  thus  found  for  the  heights  of  places 
are  influenced  by  the  time  of  day,  and  also  by  the  season  of  year,  at  which 
they  are  made.  Ruhlmann  has  investigated  the  cause  of  this  discrepancy 
by  a  series  of  direct  barometric  and  thermometric  observations  made  at  two 
different  stations  in  Saxony,  and  also  by  a  comparison  of  the  continuous 
series  of  observations  made  at  Geneva  and  on  the  St.  Bernard. 

Ruhlmann  thus  ascertained  that  the  cause  of  the  discrepancy  is  to  be 
found  in  the  fact  that  the  mean  of  the  temperatures  indicated  by  the  ther- 
mometer at  the  two  stations  is  not  an  accurate  measure  of  the  actual  mean 
temperature  of  the  column  of  air  between  the  two  stations,  a  condition  which 
is  assumed  in  the  above  formula.  The  variations  in  the  temperature  of  the 
column  of  air  are  not  of  the  same  extent  as  those  indicated  by  the  thermo- 
meter, nor  do  they  follow  them  so  rapidly  ;  they  drag  after  them  as  it  were. 
If  the  mean  monthly  temperatures  at  the  two  fixed  stations  are  introduced 
into  the  formula,  they  give  in  winter  heights  which  are  somewhat  too  low, 
and  in  summer  such  as  are  too  high.  The  results  obtained  by  introducing 
the  mean  yearly  temperature  of  the  two  stations  are  very  near  the  true  ones. 

This  influence  of  temperature  is  most  perceptible  in  individual  observa- 
tions of  low  heights.    Thus,  using  the  observed  temperatures  in  the  barometric 


156  On  Gases.  [179- 

formula,  the  error  in  height  of  the  Uetliberg  above  Ziirich  (about  1,700  feet) 
was  found  to  be  ~  of  the  total,  while  the  height  of  the  St.  Bernard  above 
Geneva  was  found  within  ^§3  of  the  true  height. 

The  reason  why  the  thermometers  do  not  indicate  the  true  temperature 
of  the  air  is  undoubtedly  that  they  are  too  much  influenced  by  radiation 
from  the  earth  and  surrounding  bodies.  The  earth  is  highly  absorbent,  and 
becomes  rapidly  heated  under  the  influence  of  the  sun's  rays,  and  becomes 
as  rapidly  cooled  at  night  ;  the  air,  as  a  very  diathermanous  body,  is  but 
little  heated  by  the  sun's  rays,  and  on  the  contrary  is  little  cooled  by  radia- 
tion during  the  night. 


-180]  Boyle  s  Laiv.  157 


CHAPTER    II 

MEASUREMENT  OF  THE  ELASTIC    FORCE   OF   GASES. 

180.  Boyle's  law. — The  law  of  the  compressibility  of  gases  was  dis- 
covered by  Boyle  in  1662,  and  afterwards  independently  by  Mariotte  in  1679. 
It  is  in  England  commonly  called  '  Boyle's  Law,'  and,  on  the  Continent, 
'  Mariotte's  Law.'     It  is  as  follows  : — 

The  iouperatiire  remaining  the  same,  the  volume  of  a  given  quantity  of 
gas  is  inversely  as  the  pressure  which  it  bears. 

This  law  may  be  verified  by  means  of  an  apparatus  devised  by  Boyle 
(fig.  155).  It  consists  of  a  long  glass  tube  fixed  to  a  vertical  support  ;  it  is 
open  at  the  upper  part,  and  the  other  end,  which  is  bent  into  a  short  vertical 
leg,  is  closed.  On  the  shorter  leg  there  is  a  scale  which  indicates  equal 
capacities  ;  the  scale  against  the  long  leg  gives  the  heights.  The  zero  of 
both  scales  is  in  the  same  horizontal  line. 

A  small  quantity  of  mercury  is  poured  into  the  tube,  so  that  its  level  in 
both  branches  is  at  zero,  which  is  effected  without  much  difficulty  after  a  few 
trials  (fig.  155).  The  air  in  the  short  leg  is  thus  under  the  ordinary  atmo- 
spheric pressure  which  is  exerted  through  the  open  tube.  Mercury  is  then 
poured  into  the  longer  tube  until  the  volume  of  the  air  in  the  smaller  tube  is 
reduced  to  one-half ;  that  is,  until  it  is  reduced  from  10  to  5,  as  shown  in 
fig.  156.  If  the  height  of  the  mercurial  column,  CA,  be  measured,  it  will  be 
found  exactly  equal  to  the  height  of  the  barometer  at  the  time  of  the  experi- 
ment. The  pressure  of  the  column  CA  is  therefore  equal  to  an  atmosphere 
which,  with  the  atmospheric  pressure  acting  on  the  surface  of  the  column  at 
C,  makes  two  atmospheres.  Accordingly,  by  doubling  the  pressure,  the 
volume  of  the  gas  has  been  diminished  to  one-half. 

If  mercury  be  poured  into  the  longer  branch  until  the  volume  of  the  air 
is  reduced  to  one-third,  it  will  be  found  that  the  distance  betv.een  the  level 
of  the  two  tubes  is  equal  to  two  barometric  columns.  The  pressure  is  now 
three  atmospheres,  while  the  volume  is  reduced  to  one-third.  Dulong  and 
Petit  have  verified  the  law  for  air  up  to  27  atmospheres,  by  means  of  an 
apparatus  analogous  to  that  which  has  been  described. 

The  law  also  holds  good  in  the  case  of  pressures  of  less  than  one  atmo- 
sphere. To  establish  this,  mercury  is  poured  into  a  graduated  tube  until  it 
is  about  two-thirds  full,  the  rest  being  air.  It  is  then  inverted  in  a  deep 
trough  M  containing  meixury  (fig.  157),  and  lowered  until  the  levels  of  the 
mercury  inside  and  outside  the  tube  are  the  same,  and  the  volume  AB  noted. 
The  tube  is  then  raised,  as  represented  in  the  figure,  until  the  volume  of  air 
AC  is  double  that  of  AB  (fig.  158).  The  height  of  the  mercury  in  the  tube 
above  the  mercury  in  the  trough  CD  is  then  found  to  be  exactly  half  the 


158 


On   Gases. 


[180- 


height  of  the  barometric  column.  The  air  whose  volume  is  now  doubled  is 
now  only  under  the  pressure  of  half  an  atmosphere  ;  for  it  is  the  elastic  force 
of  this  air  which,  added  to  the  weight  of  the  column  CD,  is  equivalent  to  the 
atmospheric  pressure.     Accordingly  the  volume  is  inversely  as  the  pressure. 


llllllliB> 


Fig.  155- 


Fig.  is6. 


Fig.  157.         Fig.  158. 


In  general,  if  V  be  the  original  volume  of  a  gas  under  the  pressure  P,  and 
V  the  volume  of  the  same  gas  under  another  pressure  P',  we  have  the  ratio 
V  :  V  =  P'  :  P  or  VP  =  V'P'. 

This  may  be  expressed  by  saying  that  the  tcmpcratufe  of  a  gh'en  mass  of 

gas  being  constant,  the  product  of  pressure  and  volume  is  constant  ;  that  is, 

PV  =  const. 

In  the  experiment  with  Boyle's  tube,  as  the  mass  of  air  remains  the 
same,  its  density  must  obviously  increase  as  its  volume  diminishes,  and  vice 
versa.  The  law  may  thus  be  enunciated  : — '  For  the  same  temperature  the 
density  of  a  gas  is  proportional  to  its  pressure.^  Hence,  as  watei  is  T]'^  times 
as  heavy  as  air,  under  a  pressure  of  TJi  atmospheres  air  would  be  as  dense 
as  water. 


-181] 


Boyle's  Lazv. 


159 


Boyle's  law  must  not  be  understood  to  mean  that  gases  of  equal  density 
have  equal  elastic  force  ;  different  gases  of  various  densities  have  the  same 
tension  when  they  are  under  the  same  pressure.  A  given  volume  of  hydrogen 
under  the  ordinary  atmospheric  pressure  has  the  same  elastic  force  as  the 
same  volume  of  air,  although  the  latter  is  14  times  as  heavy  as  the  former. 
Since,  for  the  same  volume,  there  are  the  same  number  of  atoms  in  all  gases, 
the  lighter  atoms  must  possess  a  greater  velocity  in  order  to  exert  the  same 
pressure  as  the  same  number  of  atoms  of  greater  mass. 

181.  Boyle's  law  is  only  approximately  true. — Until  within  the  last 
few  years  Boyle's  law  was  supposed  to  be  absolutely  true  for  all  gases  at  all 
pressures,  but  Despretz 
obtained  results  incom- 
patible with  the  law.  He 
took  two  graduated  glass 
tubes  of  the  same  length, 
and  filled  one-  with  air 
and  the  other  with  the 
gas  to  be  examined. 
These  tubes  were  placed 
in  the  same  mercury 
trough,  and  the  whole 
apparatus  immersed  in  a 
strong  glass  cylinder  filled 
with  water.  By  means 
of  a  piston  moved  by  a 
screw  which  worked  in  a 
cap  at  the  top  of  a  cylin- 
der the  liquid  could  be 
subjected  to  an  increasing 
pressure,  and  it  could  be 
seen  whether  the  com- 
pression of  the  two  gases 
was  the  same  or  not.  The 
apparatus  resembled  that 
used  for  examining  the 
compressibility  of  liquids 
(fig.  64).  In  this  manner 
Despretz  found  that  car- 
bonic acid,  sulphuretted 
hydrogen,  ammonia,  and 
cyanogen  are  more  com- 
pressible than  air  :  hydro- 
gen, which  has  the  same 
compressibility  as  air  up  to  15  atmospheres,  is  then  less  compressible.  From 
these  experiments  it  was  concluded  that  the  law  of  Boyle  was  not  general. 

In  some  experiments  on  the  elastic  force  of  vapours,  Dulong  and  Arago 
had  occasion  to  test  the  accuracy  of  Boyle's  law.  The  method  adopted  was 
exactly  that  of  Boyle,  but  the  apparatus  had  gigantic  dimensions. 

The  gas  to  be  compressed  was  contained  in  a  strong  glass  tube,  GF  (fig. 


Fig-  159- 


i6o  On   Gases.  [181- 

1 59),  about  six  feet  long  and  closed  at  the  top,  G.  The  pressure  was  pro- 
duced by  a  column  of  mercury,  which  could  be  increased  to  a  height  of  65 
feet,  contained  in  a  long  vertical  tube,  KL,  formed  of  a  number  of  tubes 
firmly  joined  by  good  screws,  so  as  to  be  perfectly  tight. 

The  tubes  KL  and  GF  were  hermetically  fixed  in  a  hoi'izontal  iron  pipe, 
DE,  which  fonned  part  of  a  mercurial  reservoir,  A.  On  the  top  of  this 
reservoir  there  was  a  force-pump,  BC,  by  which  mercury  could  be  forced  into 
the  apparatus. 

At  the  commencement  of  the  experiment  the  volume  of  the  air  in  the 
manometer  (183)  was  observed,  and  the  initial  pressure  determined,  by 
adding  to  the  pressure  of  the  atmosphere  the  height  of  the  mercury  in  K 
above  its  level  in  H.  If  the  level  of  the  mercury  in  the  manometer  had 
been  above  the  level  in  KL,  it  would  have  been  necessary  to  subtract  the 
difference. 

By  means  of  the  pump,  water  was  injected  into  A.  The  mercury,  being 
then  pressed  by  the  water,  rose  in  the  tube  GF,  where  it  compressed  the 
air,  and  in  the  tube  KL,  where  it  rose  freely.  It  was  only  then  necessary 
to  measui^e  the  volume  of  the  air  in  GF  ;  the  height  of  the  mercury  in  KL 
above  the  level  in  GF,  together  with  the  pressure  of  the  atmosphere,  was 
the  total  pressure  to  which  the  gas  was  exposed.  These  were  all  the  elements 
necessary  for  comparing  different  volumes  and  the  corresponding  tempera- 
tures. The  tube  GF.was  kept  cold  during  the  experiment  by  a  stream  of 
cold  water. 

The  long  tube  was  attached  to  a  long  mast  by  means  of  staples.  The 
individual  tubes  were  supported  at  the  junction  by  cords,  which  passed 
round  pulleys  R  and  R\  and  were  kept  stretched  by  small  buckets,  P,  con- 
taining shot.  In  this  manner  each  of  the  thirteen  tubes  having  been  sepa- 
rately counterpoised,  the  whole  column  was  perfectly  free  notwithstanding  its 
weight. 

Dulong  and  Arago  experimented  with  pressures  up  to  27  atmospheres, 
and  observed  that  the  volume  of  air  always  diminished  a  little  more  than  is 
required  by  Boyle's  law.  But  as  these  differences  were  very  small,  they 
attributed  them  to  errors  of  observation,  and  concluded  that  the  law  was 
perfectly  exact,  at  any  rate  up  to  27  atmospheres. 

Regnault  investigated  the  same  subject  with  an  apparatus  resembling 
that  of  Dulong  and  Arago,  but  in  which  all  the  sources  of  error  were  taken 
into  account,  and  the  observations  made  with  remarkable  precision.  Thus, 
starting  with  a  unit  volume  of  gas  under  a  pressure  of  i  metre  of  mercury,  in 
order  to  reduce  this  volume  to  one-half,  the  pressure  should  be  two  metres, 
whereas  the  following  were  the  pressures  actually  required  ;  air  i  "9978  metre  ; 
nitrogen  r9985  ;  carbonic  acid,  1-9829  ;  and  hydrogen  2-oii.  Similar  results 
were  obtained  at  higher  pressures  ;  thus  to  reduce  air  to  ^^  of  its  original 
volume,  a  pressure  of  197 199  m.  was  required  instead  of  20;  and  while  car- 
bonic acid  only  required  16705,  hydrogen  required  20-269  metres. 

It  thus  appears  that  with  increasing  pressures  hydrogen  has  a  greater,  and 
the  other  gases  a  smaller,  volume  than  is  required  by  Boyle's  law. 

Very  much  higher  pressures  have  been  employed  in  similar  experiments 
by  Natterer  and  by  Andrews.  Cailletet  used  a  special  apparatus  by 
which  the  pressure   could    be    raised  to  600  atmospheres.      Amagat  made 


-182]  Van  der   Waals^  Formula.  i6i 

a  remarkable  series  of  experiments  by  a  method  based  on  Boyle's  experiment. 
The  pressure  could  be  applied  directly  by  means  of  mercury  in  a  steel  tube 
about  i,ooo  feet  in  length,  arranged  in  the  shaft  of  a  deep  coal  pit,  and 
suitably  connected  at  the  bottom  with  a  carefully  calibrated  glass  tube.  In 
this  way  pressures  of  as  much  as  400  atmospheres  could  be  applied,  and  the 
temperatures  remained  constant. 

The  general  result  of  these  experiments  is  to  show  that  at  high  pressures 
the  volume  is  greater  than  that  required  by  Boyle's  law,  agreeing  in  this  respect 
with  hydrogen  at  ordinary  pressures.  This  is  well  illustrated  by  the  deport- 
ment of  ethylene  as  given  in  the  following  table,  where  P  is  the  pressure 
in  oietres  of  mercury,  and  PV  the  product  of  pressure  into  volume,  which 
according  to  Boyle's  law  should  be  constant. 

Pressure     24        34-8     45-1     55-4     64      72       84     134      214      303 
PV     21-5     i8-4     12-3       9-8       9-4     97     lo?    iS'i     22-1     29-3 

It  will  thus  be  seen  that  the  product  PV  decreases  with  increasing 
pressure  to  a  minimum,  and  then  increases  agam  with  the  pressure. 

The  pressure  at  which  this  7nimmu7?i  of  compressibility  occurs  is  different 
with  different  gases,  as  is  also  the  extent  of  the  deviation  from  the  law. 

At  a  temperature  of  20°  this  minimum  occurs  at  the  following  pressures 
in  metres  of  mercury  :  nitrogen  and  carbonic  oxide  50,  air  and  ethylene  65, 
oxygen  100,  and  marsh  gas  120. 

182.  Van  der  "VW^aals'  Formula. — Under  high  pressures  gases  do  not,  as 
we  have  seen,  follow  Boyle's  law  with  strictness.  In  order  to  account  for  these 
discrepancies  Van  der  Waals  has  introduced  a  modification  into  the'formula 
PV  =  const.  (180)  which  is  based  on  the  following  considerations.  We  shall 
afterwards  see  (293)  that  Boyle's  law  may  be  deduced  from  the  dynamical 
theory'  of  gases,  which  assumes  that  they  are  made  up  of  infinitely  small 
particles  moving  with  great  velocities  ;  it  is  also  assumed  that  these  particles 
have  no  cohesion  or  specific  attraction  for  each  other,  and  also  that  they  are 
mere  mathematical  points.  Van  der  Waals  takes  account  of  these  limitations. 
He  considers  that  the  cohesion  a,  which  the  particles  possess,  though  small,  has 
a  certain  value,  the  effect  of  which  is  to  add  itself  to  the  pressure  ;  its  force 
will  be  proportional  to  the  number  of  acting  and  attracting  particles,  and 
will  be  directly  proportional  to  the  square  of  the  density,  or  inversely  propor- 
tional to  the  square  of  the  volume.  The  other  correction  is  for  the  volume 
of  the  particles  themselves,  b.,  which,  though  exceedingly  small,  has  a  certain 
value.  The  pressure  of  a  given  mass  of  gas  being  due  to  the  number  of 
impacts  which  take  place  in  a  given  time,  it  is  clear  that  if  the  particles  have 
a  certain  magnitude  they  must  collide  against  each  other  more  frequently  than 
if  they  are  mere  mathematical  points  ;  the  influence  on  the  formula  will  be 
that  the  volume  V  will  be  diminished  by  an  amount  which  represents  a  multiple 
of  the  molecular  volume,  or  the  space  actually  occupied  by  the  particles. 

The  formula  of  Boyle's  law,  as  thus  modified  by  Van  der  Waals,  becomes 


(P+  ^-^iy-b)^  const. 


It  will  thus  be  seen  that  the  two  influences  mentioned  affect  Boyle's  law 
in  opposite  directions.     With  hydrogen,  where  the  molecules  have  little  or 

M 


l62 


On  Gases. 


[182- 


no  attraction,  there  is  no  cohesion,  and  accordingly  the  product  PV  increases 
continuously  with  the  pressure,  and  there  is  no  maximum  of  compressibility. 


With  other  gases  a  has  a  definite  value  ;  at  low  pressures  the  product 
PV  is  less  than  that  required  by  Boyle's  law,  and  the  influence  of  a  pre- 
ponderates ;  but  as  the  pressure  continuously  increases  this  diminishes  in 
comparison  with  the  influence  of  b.,  and  the  product  now  increases,  and  at 
high  pressures  the  gases  behave  as  does  hydrogen  at  low  ones.  Between 
these  a  maximum  compressibility  is  seen,  which  varies  with  different  gases 
according  to  the  values  of  a  and  b  in  each  case. 

^  Van  der  Waals  deduced  from  the  experimental  results 

obtained  by  Regnault  for  the  condensation  of  various  gases 
and  for  their  expansion  by  heat,  values  for  a  and  b  for  the 
respective  gases,  which  when  introduced  into  the  formula 
satisfactorily  represent  the  numbers  obtained. 

183.  iMtanometers.  —  Manometers  are  instruments  for 
measuring  the  tension  of  gases  or  vapours.  In  all  such  in- 
struments the  unit  chosen  is  the  pressure  of  one  atmosphere, 
or  30  inches  of  mercury  at  the  standard  temperature,  which, 
as  we  have  seen,  is  nearly  15  lbs.  to  the  square  inch. 

The  open-air  manometer  consists  of  a  bent  glass  tube  BD 
(fig.  160),  fastened  to  the  bottom  of  a  reservoir  AC,  of  the 
same  material,  containing  mercury,  which  is  connected  with 
the  closed  recipient  containing  the  gas  or  vapour  the  pres- 
sure of  which  is  to  be  measured.  The  whole  is  fixed  on  a 
long  plank  kept  in  a  vertical  position. 

In  graduating  this  manometer,  C  is  left  open,  and  the 
number  i  marked  at  the  level  of  the  mercury,  for  this  repre- 
sents one  atmosphere.  From  this  point  the  numbers  2,  3,  4, 
5,  6,  are  marked  at  each  30  inches,  indicating  so  many  atmo- 
spheres, since  a  column  of  mercury  30  inches  represents  a 
pressure  of  one  atmosphere.  The  intervals,  from  i  to  2,  and 
from  2  to  3,  &c.,  are  divided  into  tenths.  C  being  then 
placed  in  connection  with  a  boiler,  for  example,  the  mercury 
rises  in  the  tube  BD  to  a  height  which  measures  the  tension 
of  the  vapour.  In  the  figure  the  manometer  marks  2  atmo- 
spheres, which  represents  a  height  of  30  inches,  plus  the 
atmospheric  pressure  exerted  at  the  top  of  the  column 
through  the  aperture  D. 

This  manometer  is  only  used  when  the  pressures  do  not 
exceed  5  to  6  atmospheres.  Beyond  this,  the  length  of  tube 
necessary  makes  it  very  inconvenient,  and  the  following  ap- 
paratus is  commonly  used. 

184.  Manometer  with  compressed  air. — The  mano- 
meter with  co7npressed  air  is  founded  on  Boyle's  law  :  one 
form  is  represented  in  fig.  161,  which  may  be  screwed  into 

a  boiler  or  steam-pipe  where  pressure  is  to  be  measured.  The  pressure  is 
transmitted  through  the  opening  a  into  the  closed  space  b.  In  this  is  an 
iron  vessel  containing  mercury,  in  which  dips  the  open  end  of  the  mano- 
meter tube,  which  is  screwed  airtight  in  the  tubulure. 


— '^ — 

Fig.  160. 


-185J 


Volumonieter. 


163 


In  the  graduation  of  this  manometer,  the  quantity  of  air  contained  in  the 
tube  is  such  that  when  the  aperture  A  communicates  freely  with  the  atmo- 
sphere, the  level  of  the  mercury  is  the  same  in  the  tube  and  in  the  tubulure. 
Consequently,  at  this  level,  the  number  i  is  marked  on  the 
scale  to  which  the  tube  is  affixed.  As  the  pressure  acting 
through  the  tubulure  A  increases,  the  mercury  rises  in  the 
tube,  until  its  weight,  added  to  the  tension  of  the  compressed 
air,  is  equal  to  the  external  pressure.  It  would  consequently 
be  incorrect  to  mark  two  atmospheres  in  the  middle  of  the 
tube  ;  for,  since  the  volume  of  the  air  is  reduced  to  one-half, 
its  tension  is  equal  to  two  atmospheres,  and,  together  with 
the  weight  of  the  mercury  raised  in  the  tube,  is  therefore 
more  than  two  atmospheres.  The  position  of  the  number  is 
at  such  a  height  that  the  elastic  force  of  the  compressed  air, 
together  with  the  weight  of  the  column  of  mercuiy  in  the 
tube,  is  equal  to  two  atmospheres.  The  exact  position  of 
the  numbers  2,  3,  4,  &c.,  on  the  manometer  scale  can  only 
be  determined  by  calculation.  Sometimes  this  manometer 
is  made  of  one  glass  tube  ;  the  principle  is  obviously  the 
same. 

185.  Volumometer.— An  interesting  application  of  Boyle's 
law  is  met  with  in  the  volumonieter,  which  is  used  in  deter- 
minations of  the  specific  gravity  of  solids  which  cannot  be 
brought  into  contact  with  water  or  other  liquids.  A  simple 
form  consists  of  a  glass  tube  with  a  cylinder  G  at  the  top 
(fig.  162),  the  edges  of  which  are  carefully  ground,  and  which 
can  be  closed  hermetically  by  means  of  a  ground-glass  plate 
D.  The  top  being  open,  the  tube  is  immersed  until  the 
level  of  the  mercury  inside  and  outside  is  the  same  ;  this  is 
represented  by  the  mark  Z.  The  apparatus  is  then  closed 
airtight  by  the  plate,  and  is  raised  until  the  mercury  stands 
at  a  height  /?,  above  the  level  Q  in  the  bath.  The  original 
volume  of  the  enclosed  air  V,  which  was  under  the  pressure  of 
the  atmosphere,  is  now  increased  to  V  +  2/,  since  the  pressure 
has  diminished  by  the  height  of  the  column  of  mercury  h. 
Calling  the  pressure  of  the  atmosphere  at  the  time  of  obser- 
vation b,  we  shall  have  V  :  Y  +  v  =  b-h  :  b. 

Placing  now  in  the  cylinder  a  body  K,  whose  volume  x  is 
unknown,  the  same  operations  are  repeated  ;  the  tube  is  raised 
until  the  mercury  again  stands  at  the  same  mark  as  before,  but 
its  height  above  the  bath  is  now  different  :  a  second  reading 
h^  is  obtained,  and  we  have  (V  -  or)  :    {Y  -  x)  w  =  b-h^:  b. 

Combining  and  reducing,  we  get  ;f  =  (V  +  7/)(i  — -^).      The 

^'■\ 
volume  V-i-z/  is  constant,  and  is   determined  numerically, 
once  for  all,  by  making  the  experiment  with  a  substance  of 
known  volume,  such  as  a  glass  bulb. 

This  apparatus,  which  is  also  known  as  the  steromefer,  is  of  great  value 
in  determining  the  gravimetrical  density  of  gunpowder  ;  this  averages  from 


Fig.  161 


164 


On   Gases. 


[185- 


I  -67  to  I  '84,  and  is  thus  materially  different  from  its  apparoit  density,  or 
the  weight  of  a  given  volume  compared  with  that  of  an  equal  volume  of 
water,  which  is  from  0-89  to  0-94. 

186.  Reg-nault's  barometric  manometer. — For  measuring  pressures  of 
less  than  one  atmosphere,  Regnault  devised  the  following  arrangement, 
which  is  a  modification  of  his  fixed  barometer  (fig.  152).  In  the  same  cistern 
dips  a  second  tube  a  of  the  same  diameter,  open  at  both  ends,  and  provided 
at  the  top  with  a  three-way  cock,  one  of  which  is  connected  with  an  air-pump 
and  the  other  with  the  space  to  be  exhausted.  The  further  the  exhaustion 
is  carried  the  higher  the  mercury  rises  in  the  tube  a.  The  differences 
of  level  in  the  tubes  b  and  a  give  the  pressures.  Hence,  by  measuring  the 
height  ab,  by  means  of  the  cathetometer,  the  pressure  in  the  space  that  is 
being  exhausted  is  accurately  given.  This  apparatus  is  also  called  the 
diffcre?itial  barometer. 

187.  Aneroid  barometer. — This  instrument  derives  its  name  from  the 
circumstance  that  no  liquid  is  used  in  its  construction  (a,  without  ;  vr\pos, 
moist).    Fig.  163  represents  one  of  the  forms  of  these  instruments,  constructed 


Fig.  163. 


Fig.  164. 


by  Casella  ;  it  consists  of  a  cylindrical  metal  box,  exhausted  of  air,  the  top 
of  which  is  made  of  thin  corrugated  metal,  so  elastic  that  it  readily  yields  to 
alterations  in  the  pressure  of  the  atmosphere. 

When  the  pressure  mcreases,  the  top  is  pressed  inwards  ;  when,  on  the 
contrary,  it  decreases,  the  elasticity  of  the  lid,  aided  by  a  spring,  tends  to 
move  it  in  the  opposite  direction.  These  motions  are  transmitted  by  delicate 
multiplying  levers  to  an  index  which  moves  on  a  scale.  The  instrument  is 
graduated  empirically  by  comparing  its  indications,  under  different  pressures^ 
with  those  of  an  ordinary  mercurial  barometer. 

The  aneroid  has  the  advantage  of  being  portable,  and  can  be  constructed 
of  such  dehcacy  as  to  indicate  the  difference  in  pressure  between  the  height 


-188] 


Laivs  of  the  Mixture  of  Gases. 


165 


of  an  ordinary  table  and  the  ground.  It  is  hence  much  used  in  determining 
heights  in  mountain  ascents.  But  it  is  somewhat  Hable  to  get  out  of  order, 
especially  when  it  has  been  subjected  to  great  variations  of  pressure  ;  and 
its  indications  must  from  time  to  time  be  compared  with  those  of  a  standard 
barometer. 

The  errors  arising  from  the  use  of  the  aneroid  are  mainly  due  to  the  trans- 
mission of  the  motion  of  the  lid  by  the  multiplying  arrangement.  Goldschmid 
of  Zurich  devised  a  form  in  which  the  motion  of  the  lid  is  directly  observed. 

Like  that  of  other  aneroids,  the  lid  of  a  box  a  (fig.  164),  in  which  the 
alterations  of  pressure  are  determined,  is  of  fine  corrugated  sheet  metal.  To 
this  is  fixed  a  horizontal  metal  strip  b^  on  the  front  end  of  which  is  a  small 
square  e,  acting  as  index.  This  rises  and  falls  with  the  movement  of  the  lid, 
and  indicates  on  a  scale  ff\  on  the  sides  of  the  slit  dd'.,  alterations  of 
pressure  in  centimetres.  To  this  strip  a  second  and  more  delicate  one,  c,  is 
fixed  on  the  front  end  of  which  is  also  fixed  an  index  e'.  Before  making  an 
observation,  the  horizontal  line  of  this  index  is  made  to  coincide  with  that  of 
e  ;  this  is  effected  by  means  of  a  micrometer  screw  7;/,  which  is  raised  or 
lowered  by  the  movable  ring  Ji  ;  on  the  corresponding  scale  millimetres  and 
tenths  of  a  millimetre  are  read  off.  To  do  this  the  instrument  is  provided 
with  a  lens,  not  represented  in  the  figure.  There  is  also  a  small  thermo- 
meter / ;  from  its  indications  a  correction  is  made  for  temperature  according 
to  an  empirical  scale  specially  constructed  for  each  instrument. 

188.  Iiaws  of  the  mixture  of  g-ases. — If  a  communication  is  opened 
between  two  closed  vessels  containing  gases,  they  at  once  begin  to  mix, 
whatever  be  their  density,  and  in  a  longer  or 
shorter  time  the  mixture  is  complete,  and  will 
continue  so,  unless  chemical  action  is  set  up. 
The  laws  which  govern  the  mixture  of  gases 
may  be  thus  stated  : — 

I.  The  mixture  takes  place  rapidly  and  is 
homogetieous ;  that  is,  each  portion  of  the  mix- 
ture contains  the  two  gases  in  the  sa7ne  propor- 
tion. 

II.  If  the  gases  severally  and  the  inixture 
have  the  same  temperature,  and  if  the  gases 
severally  and  the  mixture  occupy  the  same 
volume,  then  the  pressure  on  the  unit  of  area 
exerted  by  the  mixture  will  equal  the  sum  of 
pressures  on  the  unit  of  area  exerted  by  the 
gases  severally. 

From  the  second  law  a  very  convenient 
formula  can  be  easily  deduced. 

Let  v^,  7'o,  ■z'o  .  .  .  .  be  the  volumes  of 
several  gases  under  pressure  of  py,p..,p,,  .... 
respectively.  Suppose  these  gases  when  mixed 
to  have  a  volume  V,  under  a  pressure  P,  the  temperatures  being  the  same. 
By  Boyle's  law  we  know  that  v^  will  occupy  a  volume  V  under  a  pressure//, 
provided  that 

V//  =  vp^  ;  similarly,  Wp./  =  v.-f^ 


Fig.  165. 


1 66  On  Gases.  [188- 

and  so  on.     But  from  the  above  law 

P=A'+A'+    •  •  • 

therefore  VP  =  v^p^  +  v.^p.^  +  v.^p.^  +    .  .  . 

It  obviously  follows  that  if  the  pressures  are  all  the  same,  the  volume  of  the 
mixture  equals  the  sum  of  the  separate  volumes. 

The  first  law  was  shown  experimentally  by  BerthoUet,  by  means  of  an 
apparatus  represented  in  fig.  165.  It  consists  of  two  glass  globes  provided 
with  stopcocks,  which  can  be  screwed  one  on  the  other.  The  upper  globe 
was  filled  with  hydrogen,  and  the  lower  one  with  carbonic  acid,  which 
has  22  times  the  density  of  hydrogen.  The  globes  having  been  fixed  to- 
gether were  placed  in  the  cellars  of  the  Paris  Observatory  and  the  stopcocks 
then  opened,  the  globe  containing  hydrogen  being  uppermost.  BerthoUet 
found  after  some  time  that  the  pressure  had  not  changed,  and  that,  in 
spite  of  the  difference  in  density,  the  two  gases  had  become  uniformly  mixed 
in  the  two  globes.  Experiments  made  in  the  same  manner  with  other 
gases  gave  the  same  results,  and  it  was  found  that  the  diffusion  was  more 
rapid  in  proportion  as  the  difference  between  the  densities  was  greater. 

The  second  law  may  be  demonstrated  by  passing  into  a  graduated  tube, 
over  mercury,  known  volumes  of  gas  at  known  pressures.  The  pressure  and 
volume  of  the  whole  mixture  are  then  measured,  and  found  to  be  in  accord- 
ance with  the  law. 

Gaseous  mixtures  follow  Boyle's  law,  like  simple  gases,  as  has  been 
proved  for  air  (180),  which  is  a  mixture  of  nitrogen  and  oxygen. 

189.  Absorption  of  gases  by  liquids.— Water  and  many  liquids  possess 
the  property  of  absorbing  gases.  Under  the  same  conditions  of  pressure  and 
temperature  a  liquid  does  not  absorb  equal  volumes  of  different  gases. 
At  the  temperature  0°  C.  and  pressure  760  mm.,  one  volume  of  water  dissolves 
the  following  volumes  of  gas  : — 

Nitrogen       .         .     o'02o         Sulphuretted  hydrogen  .         4-37 

Oxygen         .         .     0-041         Sulphurous  acid    .         .         .       7979 
Carbonic  acid       .     J79  Ammonia       ....   1046-63 

From  the  very  great  condensation,  to  which  the  latter  correspond,  it  may  be 
inferred  that  the  gases  in  solution  are  in  the  liquid  state. 

Gases  are  more  soluble  in  alcohol ;  thus  at  0°  C.  alcohol  dissolves  4-33 
volumes  of  carbonic  acid  gas. 

The  whole  subject  of  gas  absorption  has  been  investigated  by  Bunsen. 
The  general  laws  are  the  following  : — 

I.  For  the  same  gas,  the  same  liquid,  attd  the  same  temperature,  the 
weight  of  gas  absorbed  is  proportional  to  the  pressure.  This  may  also  be 
expressed  by  saying  that  at  all  pressures  the  volume  dissolved  is  the  same  ; 
or  that  the  density  of  the  gas  absorbed  is  in  a  constant  relation  with  that  of 
the  external  gas  which  is  not  absorbed. 

Accordingly,  when  the  pressure  diminishes,  the  quantity  of  dissolved 
gas  decreases.  If  a  solution  of  gas  be  placed  under  the  air-pump  and 
a  vacuum  created,  the  gas  obeys  its  expansive  force,  and  escapes  with 
effervescence. 


-190] 


Diffusion  of  Gases. 


167 


II.  T/ie  quantity  of  gas  absorbed  decreases  with  the  temperature;  that  is 
to  say,  when  the  elastic  force  of  the  gas  is  greater.  Thus  at  15°  water 
absorbs  only  i-oo  of  carbonic  acid. 

III.  The  quantity  of  gas  ivhich  a  liquid  can  dissolve  is  independent  oj 
the  nature  and  of  the  quantity  of  other  gases  which  it  may  already  hold  in 
solution. 

In  every  gaseous  mixture  each  gas  exercises  the  same  pressure  as  it 
would  if  its  volume  occupied  the  whole  space  ;  and  the  total  pressure  is 
equal  to  the  suiii  of  the  individual  pressures.  When  a  liquid  is  in  contact 
with  a  gaseous  mixture,  it  absorbs  a  certain  part  of  each  gas,  but  less  than 
it  would  if  the  whole  space  were  occupied  by  each  gas.  The  quantity  of 
each  gas  dissolved  is  proportional  to  the  pressure  which  the  unabsorbed 
gas  exercises  alone.  For  instance,  oxygen  forms  only  about  \  the  quantity 
of  air  ;  and  water,  under  ordinary  conditions,  absorbs  exactly  the  same 
quantity  of  oxygen  as  it  would  if  the  atmosphere  were  entirely  formed  of  this 
gas  under  a  pressure  equal  to  \  that  of  the  atmosphere. 

190.  Diffusion  of  gases. —Phenomena  analogous  to  those  of  endosmose 
(139)  are  seen  in  a  high  degree  in  the  case  of  gases.  When  two  different 
gases  are  separated  by  a  porous  diaphragm,  an  interchange  takes  place 
between  them,  and  ultimately  the  composition  of  the  gas  on  both  sides  of  the 


Fig.  166.  Fig    167. 

diaphragm  is  the  same  ;  but  the  rapidity  with  which  different  gases  diffuse 
into  each  other  under  these  circumstances  varies  considerably.  There  is, 
however,  an  essential  difference  between  the  phenomena  of  endosmose  and 
those  of  diffusion  ;  for  while  the  inequality  in  the  curi"ents  in  the  former  case 
is  due  to  the  different  attraction  of  the  material  of  the  diaphragm  for  the  con- 
stituents, in  the  diffusion  of  gases  this  nature  has  no  influence  ;  from  the 
smallness  of  the  pores  the  actions  are  molecular,  and  not  molar,  and  the 
rate  of  interchange  depends  only  on  the  size  of  the  molecules,  that  is,  on  the 
specific  gravities  of  the  gases.  The  laws  of  the  diffusion  of  gases  were  in\esti- 
gated  by  Graham.  Numerous  experiments  illustrate  it,  some  of  the  most 
interesting  of  which  are  the  following  : — 

A  glass  cylinder  closed  at  one  end  is  filled  with  carbonic  acid  gas,  its 
open  end  tied  over  with  a  bladder,  and  the  whole  placed  under  a  jar  of 
hydrogen.     Diffusion  takes  place  between  them  through  the    porous  dia- 


1 68  On   Gases.  [190- 

phragm,  and  after  the  lapse  of  a  certain  time  hydrogen  has  passed  through 
the  bladder  into  the  cylindrical  vessel  in  much  greater  quantity  than  the 
carbonic  acid  which  has  passed  out,  so  that  the  bladder  becomes  very  much 
distended  outwards  (fig.  i66).  If  the  cylinder  be  filled  with  hydrogen  and 
the  bell-jar  with  carbonic  acid,  the  reverse  phenomenon  will  be  produced 
— the  bladder  will  be  distended  inwards  (fig.  167). 

A  tube  about  12  inches  long,  closed  at  one  end  by  a  plug  of  dry  plaster 
of  Paris,  is  filled  with  dry  hydrogen,  and  its  open  end  then  immersed  in  a 
mercury  bath.  Diffusion  of  the  hydrogen  towards  the  air  takes  place  so 
rapidly  that  a  partial  vacuum  is  produced,  and  mercury  rises  in  the  tube  to 
a  height  of  se\eral  inches  (fig.  168).  If  several  such  tubes  are  filled  with 
different  gases,  and  allowed  to  diffuse  into  the 
air  in  a  similar  manner,  in  the  same  time, 
different  quantities  of  the  various  gases  will 
diffuse,  and  Graham  found  that  the  law  regu- 
lating these  diffusions  is  that  the  force  of  diffu- 
sion is  inversely  as  the  square  roots  of  the 
densities  of  gases.  Thus,  if  two  A'essels  of  equal 
capacity,  containing  oxygen  and  hydrogen,  be 
separated   by    a   porous   plug,    diffusion   takes 

1 [|r  place  ;   and  after  the  lapse  of  some  time,   for 

(HJ ' '" '^^^  every  one  part  of  oxygen  which  has  passed  into 

the  hydrogen,  four  parts  of  hydrogen  have 
passed  into  the  oxygen.  Now,  the  density  of 
hydrogen  being  i,  that  of  oxygen  is  16,  hence 
the  force  of  diffusion  is  inversely  as  the  square 
roots  of  these  numbers.  It  is  four  times  as 
great  in  the  one  which  has  ^ij  the  density  of  the 
other. 

Let  the  stem  of  an  ordinary  tobacco  pipe  be 
cemented,  so  that  its  ends  project,  in  an  outer 
glass  tube,  which  can  be  connected  with  an  air- 
pump  and  thus  exhausted.  On  allowing  then  a 
slow  current  of  air  to  enter  one  end  of  the  pipe, 
its  nitrogen  diffuses  more  rapidly  on  its  way 
through  the  porous  pipe  than  the  heavier  o.xy- 
gen,  so  that  the  gas  which  emerges  at  the  other 
end  of  the  porous  pipe,  and  which  can  be  col- 
lected, is  richer  in  oxygen,  and  by  repeating  the 
operation  on  the  gas  which  has  passed  through, 
the  proportion  of  oxygen  is  so  much  increased 
that  the  gas  can  relight  a  semi-extinguished  taper.  To  this  process,  in 
which  one  gas  can  be  separated  from  another  by  diffusion,  the  term  atmolysis 
is  given. 

Fig.  169  is  an  excellent  illustration  of  the  action  of  diffusion.  A  porous 
pot  A,  such  as  is  used  for  voltaic  cells,  is  fixed  by  means  of  a  cork  to  the 
glass  tube,  which  contains  water  up  to  the  bulb  C,  the  upper  part  con- 
taining air.  When  a  beaker  containing  hydrogen,  B,  is  placed  over  the  pot, 
the  diffusion  of  the  hydrogen  into  it  is  so  rapid  that  the  water  is  at  once 


-191] 


Effusion  of  Gases. 


169 


driven  down  and  jets  out.  When  the  beaker  is  removed,  the  gas  inside  the 
pot  being  richer  in  hydrogen  now  diffuses  out  with  great  rapidity,  and  the 
water  rises  in  the  tube  much  higher  than  its  original  level. 

191.  Effusion  of  g-ases. — A  gas  can  only  flow  from  one  space  to  another 
space  occupied  by  the  same  gas,  when  the  pressure  in  the  one  is  greater 
than  in  the  other.  Effusion  is  the  term  applied  to  the  phenomenon  of  the 
passage  of  gases  into  vacuum,  through  a  minute  aperture  not  much  more 
or  less  than  0-013  millimetre  in  diameter,  in  a  thin  plate  of  metal  or  of 
glass  ;  for  in  a  tube  we  are  dealing  with  masses  of  gases,  and  friction  comes 
into  play,  and  in  a  larger  aperture  the  particles  would  strike  against  one 
another,  and  form  eddies  and  whirlpools.  The  velocity  of  the  efflux  is  mea- 
sured by  the  formula  v=  '\/2gh,  in  which  h  re- 
presents the  pressure  under  which  the  gas 
flows,  expressed  in  terms  of  the  height  of  a 
column  of  the  gas  which  would  exert  the  same 
pressure  as  that  of  the  effluent  gas.  Thus  for 
air  under  the  ordinary  pressure  flowing  into  a 
vacuum  the  pressure  is  equivalent  to  a  column 
of  mercury  76  centimetres  high  ;  and  as  mer- 
cury is  approximately  10,500  times  as  dense 
as  air,  the  equivalent  column  of  air  will  be 
76  X  10,500  =  7,980  metres.  Hence  the  velocity 
of  efflux  of  air  into  vacuum  is  =  ^2  x  9'8  x  7980 
=  395-5  metres.  This  velocity  into  vacuum 
only  holds,  however,  for  the  first  moment,  for 
the  space  contains  a  continually  increasing  quan- 
tity of  air,  so  that  the  velocity  becomes  con- 
tinually smaller,  and  is  null  when  the  pressure 
on  each  side  is  the  same.  If  the  height  of  the 
column  of  air  hh,  corresponding  to  the  ex- 
ternal pressure,  is  known,  the  velocity  may  be 
calculated  by  the  formula  v=  sjT.g  {h-Ji^. 

For  gases  hghter  than  air  a  greater  height 
must  be  inserted  in  the  formula,  and  for 
heavier  gases  a  lower  height ;  and  this  change 
must  be  inversely  as  the  change  of  density. 
Hence  the  velocities  of  efflux  of  various  gases 
must  be  inversely  as  the  square  roots  of  their 
densities.  A  simple  inversion  of  this  statement 
is  that  the  deftsities  of  two  gases  are  inversely 
as  the  squares  of  their  velocities   of  cff'usion. 

On  this  law  Bunsen  has  based  an  interesting  method  of  determining  the 
densities  of  gases  and  vapours,  which  is  of  great  service  where  only  small 
quantities  of  the  substances  are  available. 

The  gas  in  question  is  contained  (fig.  170)  in  a  glass  tube  A,  closed  at  the 
top  with  a  stopper  s,  in  the  neck  B.  In  a  little  enlargement  here  a  platinum 
plate  V  is  fixed,  in  which  is  a  fine  capillary  aperture.  The  tube  is  inserted 
in  a  deep  mercury  trough,  CC,  so  that  the  top  r  of  a  glass  swimmer  D  is  level 
with  the  mercury.      The  stopper  s  having  been  removed,  the  gas  issues 


I/O  On   Gases.  [191- 

throLigh  the  capillary  aperture,  and  the  time  is  noted  which  elapses  until  a 
mark  t  in  the  swimmer  is  level  with  the  mercury.  Working  in  this  way  with 
different  gases,  it  is  found  that  the  ratios  of  the  times  of  effusion  are  directly 
as  the  squares  of  the  densities,  which  is  another  form  of  the  above  statement. 
By  this  method  it  may  often  be  ascertained  whether  a  gas  is  a  mixture 
or  not.  Thus  marsh  gas  (CHJ  has  the  same  specific  gravity  (o"554)  as  a 
mixture  in  equal  volumes  of  dimethyl  ''C.^H^  sp.  gr.  1-039)  ^"d  hydrogen 
(sp.  gr.  0-069),  ai'id  would  furnish  the  same  results  on  chemical  analysis. 
But  if  the  composition  of  the  gas  which  had  been  subjected  to  diffusion 
were  examined  in  the  two  cases,  it  would  be  found  that  the  residual  marsh 
gas  would  retain  the  same  composition,  while  that  of  the  mixture  would  be 
different,  for  a  larger  volume  of  the  specifically  lighter  hydrogen  would  have 
diffused  out. 

192.  Transpiration  of  grases. — If  gases  issue  through  long,  fine  capillary 
tulles  into  a  vacuum,  the  phenomenon  is  called  tj'anspiration  ;  and  the  rate 
of  efflux,  or  the  velocity  of  transpiration,  is  independent  of  the  rate  of 
diffusion. 

i.  For  the  same  gas,  the  rate  of  transpiration  increases,  other  things 
being  equal,  directly  as  the  pressure ;  that  is,  equal  volumes  of  air  of  different 
densities  require  times  inversely  proportional  to  their  densities. 

ii.  With  tubes  of  equal  diameters,  the  volume  transpired  in  equal  times 
is  inversely  as  the  length  of  the  tube. 

iii.  As  the  temperature  rises  the  transpiratioii  becomes  slozuer. 

iv.    The  rate  of  transpiration  is  independent  of  the  material  of  the  tube. 

193.  Absorption  of  gases  by  solids. — The  surfaces  of  all  solid  bodies 
exert  an  attraction  on  the  molecules  of  gases  with  which  they  are  in  contact, 

of  such  a  nature  that  they  become  covered  with  a 
more  or  less  thick  layer  of  co?idensed  gas.  When  a 
porous  body,  such  as  a  piece  of  charcoal,  which  conse- 
quently presents  an  immensely  increased  surface  in 
proportion  to  its  size,  is  placed  in  a  vessel  of  ammonia 
gas  over  mercury  (fig.  171),  the  great  diminution  of 
volume  which  ensues  indicates  that  considerable  quan- 
tities of  gas  are  absorbed. 

Now,  although  there  is  no  absorption  such  as  arises 
from  chemical  combination  between  the  solid  and  the 
gas  (as  with  phosphorus  and  oxygen),  still  the  quan- 
tity of  gas  absorbed  is  not  entirely  dependent  on  the 
physical  conditions  of  the  solid  body  ;  it  is  influenced 
in  some  measure  by  the  chemical  nature  both  of  the 
solid  and  the  gas.  Boxwood  charcoal  has  very  great 
absorptive  power.  The  following  table  gives  the 
volumes  of  gas,  under  standard  conditions  of  tempera- 
ture and  pressure,  absorbed  by  one  volume  of  boxwood  charcoal  and  of  meer- 
schaum respectively  : — 

Charcoal         Meerschaum 

Ammonia 90  15 

Hydrochloric  acid  ......         85  — 

Sulphurous  acid      ......        65  — 


Fig.  171. 


-194]  Occlusion  of  Gases.  171 


Charcoal 

Meerschaur 

Sulphuretted  hydr 

ogen   . 

55 

II 

Carbonic  acid 

35 

5-3 

Carbonic  oxide 

9-4 

1-2 

Oxygen 

9-2 

1-5 

Nitrogen 

7-5 

1-6 

Hydrogen 

175 

0-5 

The  absorption  of  gases  is  in  general  greatest  in  the  case  of  those  which  are 
most  easily  liquefied. 

Cocoa-nut  charcoal  is  even  more  highly  absorbent  ;  it  absorbs  171  of 
ammonia,  72)  of  carbonic  acid,  and  108  of  cyanogen  at  the  ordinary  pressure  ; 
the  amount  of  absorption  increases  with  the  pressure.  The  absorptive 
power  of  pine  charcoal  is  about  half  as  much  as  that  of  boxwood.  The 
charcoal  made  from  cork  wood,  which  is  very  porous,  is  not  absorbent, 
neither  is  graphite.  Platinum,  in  the  finely  divided  form  known  as  platinum 
sponge,  is  said  to  absorb  250  times  its  volume  of  oxygen  gas.  Many  other 
porous  substances,  such  as  meerschaum,  gypsum,  silk,  &c.,  are  also  highly 
absorbent. 

If  a  coin  be  laid  on  a  plate  of  glass  or  of  metal,  after  some  time,  when 
the  plate  is  breathed  on,  an  image  of  the  coin  appears.  If  a  figure  is  traced 
on  a  glass  plate  with  the  finger,  nothing  appears  until  the  plate  is  breathed 
on,  when  the  figure  is  at  once  seen.  Indeed,  the  traces  of  an  engraving 
which  has  long  lain  on  a  glass  plate  may  be  produced  in  this  way. 

These  phenomena  are  known  as  Moser^s  linages,  for  he  first  investigated 
them,  although  he  explained  them  erroneously.  The  correct  explanation 
was  given  by  Waidele,  who  ascribed  them  to  alterations  in  the  layer  of  gas, 
^'apour,  and  fine  dust  which  is  condensed  on  the  surface  of  all  solids.  If 
this  layer  is  removed  by  wiping,  on  afterwards  breathing  against  the  surface 
more  vapour  is  condensed  on  the  marks  in  question,  which  then  present  a 
different  appearance  from  the  rest. 

■  If  a  die  or  a  stamp  is  laid  on  a  freshly  polished  metal  plate,  and  one 
therefore  which  has  been  deprived  of  its  atmosphere,  the  layer  of  vapour 
from  the  coin  will  diffuse  on  to  the  metal  plate,  which  thereby  becomes 
altered  ;  so  that  when  this  is  breathed  on  an  impression  is  seen. 

Conversely,  if  a  coin  be  polished  and  placed  on  an  ordinary  glass  plate, 
it  will  partially  remove  the  layer  of  gas  from  the  parts  in  contact,  so  that  on 
breathing  on  the  plate  the  image  is  visible. 

194.  Occlusion  of  g:ases Graham  found  that  at  a  high  temperature 

platinum  and  iron  allow  hydrogen  to  traverse  them  even  more  readily  than 
does  caoutchouc  in  the  cold.  Thus  while  a  square  metre  of  caoutchouc  o"oi4 
millimetre  in  thickness  allowed  129  cubic  centimetres  of  hydrogen  at  20°  to 
traverse  it  in  a  minute,  a  platinum  tube  i-i  millimetre  in  thickness  and  of  the 
same  surface  allowed  489  cubic  centimetres  to  traverse  it  at  a  bright  red  heat. 

This  is  probably  connected  with  the  property  which  some  metals,  though 
destitute  of  physical  pores,  possess  of  absorbing  gases  either  on  their  surface 
or  in  their  mass,  and  to  which  Graham  has  applied  the  term  occlusion.  It 
is  best  observed  by  allowing  the  heated  metal  to  cool  in  contact  with  the 
gas.  The  gas  cannot  then  be  extracted  by  the  air-pump,  but  is  disengaged 
on  heating.     In  this  way  Graham  found  that  platinum  occluded  four  times 


i;: 


On   Gases. 


[194- 


its  volume  of  hydrogen  ;  iron  wire  0*44  its  volume  of  hydrogen,  and  4-15 
volumes  of  carbonic  oxide  ;  silver,  reduced  from  the  oxide,  absorbed  about 
seven  volumes  of  oxygen,  and  nearly  one  volume  of  hydrogen  when  heated 
to  dull  redness  in  these  gases.  This  property  is  most  remarkable  in  palla- 
dium, which  absorbs  hydrogen,  not  only  in  cooling  after  being  heated,  but 
also  in  the  cold.  When,  for  instance,  a  palladium  electrode  is  used  in  the 
decomposition  of  water,  one  volume  of  the  metal  can  absoi"b  980  times  its 
volume  of  the  gas.  This  gas  is  again  driven  out  on  being  heated,  in  which 
respect  there  is  a  resemblance  to  the  solution  of  gases  in  liquids.  By  the 
occlusion  of  hydrogen  the  volume  of  palladium  is  increased  by  0-09827  of 
its  original  amount,  from  which  it  follows  that  the  hydrogen,  which  under 
ordinary  circumstances  has  a  density  of  0-000089546  that  of  water,  has  here  a 
density  nearly  9,868  times  as  great,  or  about  o-88  that  of  water.  Hence  the 
hydrogen  must  be  in  the  liquid  or  even  solid  state  ;  it  probably  forms  thus 
an  alloy  with  palladium,  like  a  true  metal—  a  view  of  this  gas  which  is 
strongly  supported  by  independent  chemical  considerations.  The  physical 
properties  too,  in  so  far  as  they  have  been  examined,  support  this  \-iew  of  its 
being  an  alloy. 

The  phenomenon  of  occlusion  may  be  illustrated  by  the  following  experi- 
ment (fig.  172).  A  platinum  wire  be  is  stretched  between  supports  on  a 
glass  plate  ;  one  end  of  a  palladium 
:  wire  fg  is  also  fixed,  of  which  the  other 
end  is  attached  to  the  short  arm  of  a  light 
lever  movable  about  o,  the  long  arm  of 
which  is  loaded  with  a  weight  (not  repre- 
sented in  the  figure)  to  keep  the  wire  tight. 
The  platinum  wire  is  connected  with  the 
positive  pole  a,  and  the  palladium  with  the 
negative  pole  d,  of  a  voltaic  battery,  and 
the  apparatus  is  partially  immersed  in 
acidulated  water  ;  the  water  is  thereby- 
decomposed  into  its  constituent  gases  ; 
oxygen  is  liberated  in  bubbles  from  the 
platinum  wire,  but  there  is  no  visible  dis- 
Fig.  172.  engagement  at  the  palladium.     It  becomes 

longer,  however,  as  is  seen  by  the  lever 
moving  downwards.  If  the  current  is  reversed,  the  wire  again  contracts,  and 
the  lever  resumes  its  original  position. 


195] 


ArcJiimcdes'  Principle  applied  to  Gases. 


17; 


CHAPTER  III. 

PRESSURE   OF   BODIES    IN   AIR.       BALLOONS. 


195.  Archimedes'  principle  applied  to  g^ases. — The  pressure  exerted 
by  gases,  on  bodies  immersed  in  them,  is  transmitted  equally  in  all  directions, 
as  has  been  shown  by  the  experiment 
with  the  Magdeburg  hemispheres.  It 
therefore  follows  that  all  which  has 
been  said  about  the  equilibrium  of 
bodies  in  liquids  applies  to  bodies  in 
air  ;  they  lose  a  part  of  their  weight 
equal  to  that  of  the  air  which  they  dis- 
place. 

The  loss  of  weight  in  air  is  demon- 
strated by  means  of  the  baroscope, 
which  consists  of  a  scalebeam,  at  one 
of  whose  extremities  a  small  leaden 
weight  is  supported,  and  at  the  other 
there  is  a  hollow  copper  sphere  (fig. 
163).  In  the  air  they  exactly  balance 
each  other ;  but  when  they  are  placed 
under  the  receiver  of  an  air-pump, 
and  a  vacuum  is  produced,  the  sphere 
sinks,  thereby  showing  that  in  reality 
it  is  heavier  than  the  smaller  leaden 
weight.  Before  the  air  is  exhausted,  each  body  is  buoyed  up  by  the  weight 
of  the  air  which  it  displaces.  But  as  the  sphere  is  much  the  larger  of  the 
two,  its  weight  undergoes  most  apparent  diminution,  and  thus,  though  in 
reality  the  heavier  body,  it  is  balanced  by  the  small  leaden  weight.  It  may 
be  proved  by  means  of  the  same  apparatus  that  this  loss  is  equal  to  the 
weight  of  the  displaced  air.  Suppose  the  volume  of  the  sphere  is  10  cubic 
inches.  The  weight  of  this  volume  of  air  is  3-1  grains.  If  now  this  weight 
be  added  to  the  leaden  weight,  it  will  overbalance  the  sphere  in  air,  but  will 
exactly  balance  it  in  vacuo. 

The  principle  of  Archimedes  is  true  for  bodies  in  air ;  all  that  has  been 
said  about  bodies  immersed  in  liquids  applies  to  them  ;  that  is,  that  when  a 
body  is  heavier  than  air,  it  will  sink,  owing  to  the  excess  of  its  weight  over 
the  buoyancy.  If  it  is  as  heavy  as  air,  its  weight  will  exactly  counterbalance 
the  buoyancy,  and  the  body  will  float  in  the  atmosphere.  If  the  body  is 
lighter  than  air,  the  buoyancy  of  the  air  will  prevail,  and  the  body  will  rise 
in  the  atmosphere  until  it  reaches  a  layer  of  the  same  density  as  its  own. 


Fig.  173- 


174  On   Gases.  [195- 

The  force  of  the  ascent  is  equal  to  the  excess  of  the  buoyancy  over  the  weight 
of  the  body.  This  is  the  reason  why  smoke,  vapours,  clouds,  and  air-balloons 
rise  in  the  air. 

AIR-BALLOONS. 

196.  Air-balloons. — Air-balloons  are  hollow  spheres  made  of  some  light 
impermeable  material,  which,  when  filled  with  heated  air,  with  hydrogen 
gas,  or  with  coal  gas,  rise  in  the  air  by  virtue  of  their  relative  lightness. 

They  were  invented  by  the  brothers  Montgolfier  of  Annonay,  and  the 
first  experiment  was  made  at  that  place  in  June  1783.  Their  balloon  was  a 
sphere  of  forty  yards  in  circumference,  and  weighed  500  pounds.  At  the 
lower  part  there  was  an  aperture,  and  a  sort  of  boat  was  suspended,  in  which 
fire  was  lighted  to  heat  the  internal  air.  The  balloon  rose  to  a  height  of 
2,200  yards,  and  then  descended  without  any  accident. 

Charles,  a  professor  of  physics  in  Paris,  substituted  hydrogen  for  hot  air. 
He  himself  ascended  in  a  balloon  of  this  kind  in  December  1783.  The  use 
of  hot-air  balloons  was  entirely  given  up  in  consec^uence  of  the  serious 
accidents  to  which  they  were  liable. 

Since  then  the  art  of  ballooning  has  been  greatly  extended,  and  many 
ascents  have  been  made.  That  which  Gay-Lussac  made  in  1804  was  the 
most  remarkable  for  the  facts  with  which  it  has  enriched  science,  and  for  the 
height  which  he  attained — 23,000  feet  above  the  sea-level.  At  this  height 
the  barometer  sank  to  12-6  inches,  and  the  thermometer,  which  was  31°  C. 
on  the  ground,  was  9  degrees  below  zero. 

In  these  high  regions  the  dryness  was  such  on  the  day  of  Gay-Lussac's 
ascent,  that  hygrometric  substances,  such  as  paper,  parchment,  &c.,  became 
dried  and  crumpled  as  if  they  had  been  placed  near  the  fire.  The  respira- 
tion and  circulation  of  the  blood  were  accelerated  in  consequence  of  the 
great  rarefaction  of  the  air.  Gay-Lussac's  pulse  made  120  pulsations  in  a 
minute  instead  of  66,  the  normal  number.  At  this  great  height  the  sky  had 
a  very  dark  blue  tint,  and  an  absolute  silence  prevailed. 

One  of  the  most  remarkable  of  ascents  was  made  by  Mr.  Glaisher  and 
Mr.  Coxwell,  in  a  large  balloon  belonging  to  the  latter.  This  was  filled  with 
90,000  cubic  feet  of  coal  gas  (sp.  gr.  0-37  to  0-33) ;  the  weight  of  the  load 
was  600  pounds.  The  ascent  took  place  at  i  P.M.  on  September  5,  1861  ;  at 
1.28  they  had  reached  a  height  of  15,750  feet,  and  in  eleven  minutes  after  a 
height  of  21,000  feet,  the  temperature  being— 10*4°;  at  1.50  they  were  at 
26,200  feet,  with  the  thermometer  at— 1 5*2°.  At  1.52  the  height  attained 
was  29,000  feet,  and  the  temperature  —  16°  C.  At  this  height  the  rarefaction 
of  the  air  was  so  great,  and  the  cold  so  intense,  that  Mr.  Glaisher  fainted, 
and  could  no  longer  observe.  According  to  an  approximate  estimation  the 
lowest  barometric  height  they  attained  was  7  inches,  which  would  correspond 
to  an  elevation  of  from  36,000  to  37,000  feet. 

197.  Construction  and  manag-ement  of  balloons. — A  balloon  (fig.  174) 
is  made  of  long  bands  of  silk  sewed  together  and  covered  with  caoutchouc 
varnish,  which  renders  it  airtight.  At  the  top  there  is  a  safety-valve  closed 
by  a  spring,  which  the  aeronaut  can  open  at  pleasure  by  means  of  a  cord. 
A  light  wickerwork  boat  is  suspended  by  means  of  cords  to  a  network  which 
entirely  covers  the  balloon. 


-197]  Construction  and  Management  of  Balloons.  175 

A  balloon  of  the  ordinary  dimensions,  which  can  carry  three  persons,  is 
about  16  yards  high,  12  yards  in  diameter,  and  its  volume,  when  it  is  quite 
full,  is  about  680  cubic  yards.  The  bal- 
loon itself  weighs  200  pounds  ;  the  ac- 
cessories, such  as  the  rope  and  boat,  100 
pounds. 

The  balloon  is  filled  either  with  hy- 
drogen or  with  coal  gas.  Although  the 
latter  is  heavier  than  the  former,  it  is 
generally  preferred,  because  it  is  cheaper 
and  more  easily  obtained.  It  is  passed 
into  the  balloon  from  the  gas  reservoir 
by  means  of  a  flexible  tube.  It  is  im- 
portant not  to  fill  the  balloon  quite 
full,  for  the  atmospheric  pressure  dimi- 
nishes as  it  rises,  and  the  gas  inside, 
expanding  in  consequence  of  its  elastic 
force,  tends  to  burst  it.  It  is  suffi- 
cient for  the  ascent  if  the  weight  of 
the  displaced  air  exceeds  that  of  the 
balloon  by  8  or  10  pounds.  And  this 
force  remains  constant  so  long  as  the 
balloon  is  not  quite  distended  by  the 
dilatation  of  the  air  in  the  interior.  If 
the  atmospheric  pressure,  for  example, 
has  diminished  to  one-half,  the  gas  in  the 
balloon,  according  to  Boyle's  law,  has 
doubled  its  volume.  The  volume  of  the 
air  displaced  is  therefore  twice  as  great  ; 
but  since  its  density  has  become  only 
one-half,  the  weight  and  consequently 
the  upward  buoyancy  are  the  same. 
When  once  the  balloon  is  completely 
dilated,  if  it  continues  to  rise,  the  force  of 
the  ascent  decreases,  for  the  volume  of 
the  displaced  air  remains  the  same,  but 
its  density  diminishes,  and  a  time  arrives 
at  which  the  buoyancy  is   equal   to    the 

weight  of  the  balloon.  The  balloon  can  now  only  take  a  horizontal  direction, 
carried  by  the  currents  of  air  which  prevail  in  the  atmosphere.  The  aero- 
naut knows  by  the  barometer  whether  he  is  ascending  or  descending,  and 
by  the  same  means  he  determines  the  height  which  he  has  reached.  A  long 
flag  fixed  to  the  boat  would  indicate,  by  the  position  it  takes  either  above  or 
below,  whether  the  balloon  is  descending  or  ascending. 

When  the  aeronaut  wishes  to  descend,  he  opens  the  valve  at  the  top  of 
the  balloon  by  means  of  the  cord,  which  allows  gas  to  escape,  and  the 
balloon  sinks.  If  he  wants  to  descend  more  slowly,  or  to  rise  again,  he 
empties  out  bags  of  sand,  of  which  there  is  an  ample  supply  in  the  car.  The 
descent  is  facilitated  by  means  of  a  grappling  iron  fixed  to  the  boat.     When 


a»k. 


176 


On   Gases. 


[197- 


once   this    is   fixed  to  any  obstacle,  the  balloon  is  lowered  by  pulling  the 
cord. 

The  only  practical  applications  which  air-balloons  have  hitherto  had 
have  been  in  military  reconnoitring.  At  the  battle  of  Fleurus,  in  1794,  a 
captive  balloon — that  is,  one  held  by  a  rope — was  used,  in  which  there  was 
an  observer  who  reported  the  movements  of  the  enemy  by  means  of  signals. 
At  the  battle  of  Solferino  the  movements  and  dispositions  of  the  Austrian 
troops  were  watched  from  a  captive  balloon  ;  and  in  the  war  in  America 
balloons  were  frequently  used,  while  their  importance  during  the  siege  of 
Paris  will  not  have  been  forgotten.  The  whole  subject  of  military  ballooning 
was  treated  in  two  papers  by  Col.  Grover  and  by  Col.  Beaumont,  in  a 
volume  of  the  Professional  Papers  of  the  Royal  Engineers  ;  and  experiments 
are  in  progress  at  Woolwich  and  at  Aldershot,  with  a  view  of  ascertaining 
the  most  practical  means  of  inflating  balloons,  and  the  best  form  and 
equipment  for  service  in  the  field.  It  has  been  proposed  to  use  captive 
balloons  for  observations  on  the  changes  of  temperature  in  the  air,  &c.  Air- 
balloons  can  only  be  truly  useful  when  they  can  be  guided,  and  as  yet  all 
attempts  made  with  this  view  have  completely  failed.  There  is  no  other 
course  at  present  than  to  rise  in  the  air  until  there  is  a  current  which  has 

more  or  less  the  desired  direc- 
tion. Unfortunately,  the  currents 
in  the  higher  regions  of  the 
atmosphere  are  variable  and 
irregular. 

1 98.  Paracbute. — The  ob- 
ject of  the  parachute  is  to  allow 
the  aeronaut  to  leave  the  bal- 
loon, by  giving  him  the  means 
of  lessening  the  rapidity  of  his 
descent.  It  consists  of  a  large 
circular  piece  of  cloth  (fig.  175), 
about  16  feet  in  diameter,  and 
which  by  the  resistance  of  the 
air  spreads  out  like  a  gigantic 
umbrella.  In  the  centre  there 
is  an  aperture,  through  which 
the  air  compressed  by  the 
rapidity  of  the  descent  makes 
its  escape  ;  for  otherwise  os- 
cillations might  be  produced, 
which,  when  communicated  to 
the  boat,  would  be  dangerous. 

In  fig.   174  there  is  a  para- 
chute  attached   to  the  network 
1,^,  ,_^  of  the   balloon  by  means    of  a 

cord  which  passes  round  a 
pulley,  and  is  fixed  at  the  other  end  to  the  boat.  When  the  cord  is  cut 
the  parachute  sinks,  at  first  very  rapidly,  but  more  slowly  as  it  becomes  dis- 
tended, as  represented  in  the  figure. 


-199J     Calculation  of  the  Weight  zvhich  a  Balloon  can  raise.     177 

199.    Calculation    of  the    weight    which   a   balloon   can  raise. — To 

calculate  the  weight  which  can  be  raised  by  a  balloon  of  given  dimensions, 
let  us  suppose  it  perfectly  spherical,  and  premise  that  the  formuh^  which 

express  the  volume  and  the  superficies  in  terms  of  the  radius  are  V  =  ^^ 

S  =  47rR-  ;  TT  being  the  ratio  of  the  circumference  to  the  diameter.  The 
radius  R  being  measured  in  feet,  let  p  be,  in  pounds,  the  weight  of  a 
square  foot  of  the  material  of  which  the  balloon  is  constructed  ;  let  P 
be  the  weight  of  the  car  and  the  accessories,  a  the  weight  in  pounds  of 
a  cubic  foot  of  air  at  zero,  and  under  the  pressure  076'",  and  a'  the  weight 
of  the  same  volume,  under  the  same  conditions,  of  the  gas  with  which 
the  balloon  is  inflated  (155).     Then    the   total   weight   of  the  envelope  in 

pounds  will  be  ^Tx'K-p  ;  that  of  the  gas  will  be  ^~ ^;  and  that  of  the  dis- 
placed air  ^^ — -•  If  X  be  the  weight  which  the  balloon  can  support,  we 
have 


Whence 


47rR^_47rR!a'_      j^.^_.p_ 
:  =  4^(«  _  a!)  -  47rR-/  -  P. 


But,  as  we  have  before  seen  (197),  in  order  that  the  balloon  may  rise,  the 
weight  must  be  less  by  8  or  10  pounds  than  that  given  by  this  equation. 


178 


On  Gases. 


[200- 


CHAPTER    IV. 

APPARATUS    WHICH    DEPEND    ON    THE   PROPERTIES    OF   AIR. 

200.  Air-pump. — The  air-pump  is  an  instrument  by  which  a  vacuum  can 
be  produced  in  a  given  space,  or  rather  by  which  air  can  be  greatly  rarefied, 
for  an  absokite  vacuum  cannot  be  produced  by  its  means.     It  was  invented 


Fig.  176. 

by  Otto  von  Guericke  in  1650,  a  few  years  after  the  invention  of  the  baro- 
meter. 

The  air-pump,  as  now  usually  constructed,  may  be  described  as  follows. 
Fig.  176  represents  a  general  view  ;  177  a  section,  and  figs.  178-183 
various  parts  ;  the  letters  in  all  the  figures  having  eveiywhere  the  same 
meaning. 

The  base  VGL  is  of  stout  metal,  and  is  firmly  fixed  on  a  table.     At  one 


200] 


A  ir-pninp. 


179 


end  two  glass  cylinders  or  barrels  are  firmly  cemented,  and  the  two  leather 
pistons  P  and  P',  work  airtight  in  them.  To  these  pistons  are  attached 
racks  H,  K  and  by 
means  of  a  handle 
M  N,  working  about 
a  pinion  X,  the  pis- 
tons P  and  P'  are 
moved  alternately 
up  and  down.  On 
the  plate  V  is  fitted 
a  thick  glass  plate 
with  a  very  true 
surface.  In  its 
centre  is  a  screw 
tubulure«,  fixed  into 
a  conduit  nc  in  the 
base  of  the  pump, 
and  which  connects 
the  receiver  and 
the  barrels. 

Fig.  178  gives  a 
vertical  section  of 
one  of  the  pistons 
on  a  larger  scale. 
It  consists  of  two 
brass  discs,  A  and 
B,     the     latter     ot 

which  is  provided  with  a  tubulure  in  which  is  a  screw  D  ;  this  presses 
together  a  number  of  leather  washers,  very  slightly  larger  than  the  disc. 
The  leather  is  thoroughly  soaked  with  oil,  and  slides  airtight  in  the  barrels, 
but  with  slight  friction.  D  is  pierced  by  a  channel  which  connects  it  with 
the  outer  air.  In  the  centre  of  the  disc  B  is  a  hole  /,  closed  by  a  metal  valve 
Z,  which  is  shod  with  cork,  and  by  means  of  a  rod  e  is  kept  in  position  in 
the  channel. 

A  valve  s  opens  and  closes  the  orifice  of  the  channel  c  which  is  in  con- 
nection with  the  receiver.  It  is  fixed  to  the  end  ofa  rod  a  which  moves,ibut 
with  friction,  through  the  piston.  Then  when  the  piston  sinks  it  carries  with 
it  the  rod  <;?,  and  closes  the  orifice.  As  the  piston  rises  it  lifts  the  rod,  but 
only  for  a  small  distance,  for  the  rod  strikes  against  the  top  of  the  barrel,  and 
the  piston,  continuing  its  upward  motion,  slides  along  the  rod. 

The  stopcock  T  connects  the  receiver  R  with  the  air-pump  gauge  E  (201), 
while  S  connects  the  receiver  with  the  barrels.  When  the  receiver  has  been 
exhausted,  S  is  turned  through  a  quarter,  and  the  vacuum  is  thus .  preserved. 
Air  can  be  admitted  by  opening  a  screw  r,  at  the  top  of  a  channel  in  the 
stopcock  itself. 

The  piston  P^  being  at  the  bottom  of  the  barrel  (fig.  179),  as  the 
handle  is  worked,  the  piston  rises,  and  with  it  the  rod  a  and  the  valve  j-, 
while  Z  is  closed  by  its  own  weight  and  the  pressure  of  the  air.  A  partial 
vacuum  is  created  under  the  piston,  but  the  valve  s  having  opened  up  con- 

N  2 


Fig.  177. 


i8o  On   Gases.  [200- 

nection  with  the  receiver  R,  the  air  in  this  expands  and  fills  both  the  receiver 
and  the  barrel.  When  P'  begins  to  descend,  the  valve  s  is  closed  by  the 
descent  of  the  rod  a,  the  rarefied  air  in  the  barrel  can  no  longer  return  to 
the  receiver,  it  gets  more  and  more  condensed,  and  its  elastic  force  is  ulti- 
mately so  great  as  to  open  the  valve  Z,  and  the  air  under  the  piston  escapes 
by  the  channel  D  into  the  outer  air,  and  thus  the  rarefaction  produced 
in  the  receiver  is  permanent.  At  the  second  stroke  of  the  piston  the 
same  phenomenon  is  repeated,  until  a  limit  is  reached  at  which,  although 
there  is  air  in  the  receiver,  its  elastic  force  is  insufficient  to  raise  the 
valve  Z. 

It  is  clear  that  when  the  rarefaction  has  proceeded  to   a   considerable 
extent,  the  atmospheric  pressure  on  the  top  of  P  will  be  very  great,  but  it  will 


be  very  nearly  balanced  by  the  atmospheric  pressure  on  the  top  of  the  other 
piston.  Consequently,  the  experimenter  will  have  to  overcome  only  the 
difference  of  the  two  pressures.  This  is  the  reason  why  two  barrels  are 
employed,  a  plan  first  adopted  by  Hawksbee. 

20I.  Air-pump  g-augre. — When  the  pump  has  been  worked  some. time, 
the  pressure  in  the  receiver  is  indicated  by  the  difference  of  level  of  the 
mercury  in  the  two  legs  of  a  glass  tube  bent  like  a  syphon,  one  of  which  is 
opened,  and  the  other  closed  like  the  barometer.  This  little  apparatus, 
which  is  called  the  gauge,  is  fixed  to  an  upright  scale,  and  placed  under  a 
small  bell-jar,  which  communicates  with  the  receiver  E  by  a  stopcock  A, 
inserted  in  the  tube  leading  from  the  orifice  G  to  the  cylinders — (fig.  177). 

Before  commencing  to  exhaust  the  air  in  the  receiver,  its  elastic  force 
exceeds  the  weight  of  the  column  of  mercury  which  is  in  the  closed  branch, 


-202]  Doubk-exhaustion  Stopcock.  i8i 

and  which  consequently  remains  full.  But  as  the  pump  is  worked,  the 
elastic  force  soon  diminishes,  and  is  unable  to  support  the  weight  of  the 
mercury,  which  sinks  and  tends  to  stand  at  the  same  level  in  both  legs.  It 
an  absolute  vacuum  could  be  produced,  they  would  be  exactly  on  the  same 
level,  for  there  would  be  no  pressure  either  on  the  one  side  or  the  other.  But 
with  the  very  best  machines  the  level  is  always  about  a  thirtieth  of  an  inch 
higher  in  the  closed  branch,  which  indicates  that  the  vacuum  is  not  absolute, 
for  the  elastic  force  of  the  residue  is  ec[ual  to  the  pressure  of  a  column  of 
mercury  of  that  height. 

Theoretically  an  absolute  vacuum  is  impossible  ;  for,  since  the  volume 
of  each  cylinder  is,  say,  ~  that  of  the  receiver,  only  ~  of  the  air  in  the 
receiver  is  extracted  at  each  stroke  of  the  piston,  and  consequently  it  is  im- 
possible to  exhaust  all  the  air  which  it  contains.  The  theoretical  degree  of 
exhaustion  after  a  given  number  of  strokes  is  easily  calculated  as  follows  : — 
Let  a  denote  the  volume  of  the  receiver,  including  in  that  term  the  pipe ; 
b  the  volume  of  the  cyhnder  between  the  highest  and  lowest  positions  of 
the  piston  ;  and  assume,  for  the  sake  of  distinctness,  that  there  is  only  one 
cylinder  :  then  the  air  which  occupied  a  before  the  piston  is  lifted  occupies 
a  +  b  after  it  is  lifted  ;  and  consequently  if  ^^  is  the  density  at  the  end  of  the 
first  stroke,  and  d  the  original  density,  we  must  have 

a  +  b 
If  ^,  is  the  density  at  the  end  of  the  second  stroke,  we  have 

a  +  b  \a  +  bJ 

Now  this  reasoning  will  apply  to  n  strokes  ; 
consequently,  d^  =  d(  -^, ) 

If  there  are  two  equal  cylinders,  the  same  formula  holds  ;  but  in  this 
case,  in  counting  ;/,  upstrokes  and  downstrokes  ecjually  reckon  as  ojie. 

It  is  obvious  that  the  exhaustion  is  never  complete,  since  d  ca.n  be  zero 
only  when  «  is  infinite.  However,  no  very  great  number  of  strokes  is  re- 
quired to  render  the  exhaustion  virtually  complete,  even  if  a  is  several  times 
greater  than  b.  Thus  if  «=  lod  a  hundred  strokes  will  reduce  the  density 
from  ^to  0-0004^^;  that  is,  if  the  initial  pressure  is  30  inches,  the  pressure  at 
the  end  of  100  strokes  is  0-012  of  an  inch. 

Practically,  however,  a  limit  is  placed  on  the  rarefaction  that  can  be  pro- 
duced by  any  given  air-pump ;  for,  as  we  have  seen,  the  air  becomes  ulti- 
mately so  rarefied  that,  when  the  pistons  are  at  the  bottom  of  the  cylinder, 
its  elastic  force  cannot  overcome  the  pressure  in  the  valves  on  the  inside  of 
the  piston  ;  they  therefore  do  not  open,  and  there  is  no  further  action  of  the 
pump. 

202.  Bouble-exbaustion  stopcock. — By  means  of  this  device  the  ex- 
haustion of  the  air  can  be  carried  to  a  very  high  degree.  Fig.  180  gives  a 
horizontal  section  of  the  stopcock  Q,  which  by  means  of  a  central  channel 
and  two  lateral    ones  forms  a  communication   with  the  receiver  and  the 


On   Gases. 


[202- 


barrels.  When  the  working  ceases,  that  is  when  Z  no  longer  rises,  a  quarter- 
turn  is  given  to  Q  (fig.  182).  The  connections  are  now  altered,  as  is  seen  from 
the  horizontal  sections  in  figs.  180  and  182,  and  the  vertical  sections  in  figs. 
181  and  183.  The  new  channels  correspond  now  with  those  of  the  base,  and 
the  right  barrel  is  alone  connected  with  the  receiver  by  the  channel  nmc, 
while  the  left  is  connected  by  an  oblique  channel  in  the  stopcock  with  a 
central  aperture  s  in  the  base  of  the  right  barrel. 

The  right  piston  as  it  rises  exhausts  air  from  the  receiver  ;  but  when  it 
sinks  the  exhausted  air  is  drawn  into  the  left  barrel  by  the  apertures  o  and 
d,  this  latter  being  always  open,  for  the  corresponding  conical  valve  is  raised. 


When  the  right  piston  rises,  that  of  the  left  sinks  ;  but  the  air  below  does 
not  return  to  the  right  barrel,  for  the  orifice  is  now  closed  by  the  conical 
valve.  As  the  right  cylinder  continues  to  exhaust  the  air  in  the  receiver, 
and  to  force  it  into  the  left  cylinder,  the  air  accumulates  here  and  ultimately 
acquires  sufficient  pressure  to  raise  the  valve  of  the  piston  Q,  which  was 
impossible  before  the  stopcock  was  turned,  for  it  is  only  when  the  valves  in 
the  piston  no  longer  open  that  a  quarter  of  a  turn  is  given  to  the  stopcock. 
In  this  way  a  rarefaction  of  half  a  millimetre  has  been  attained. 

203.  Bianchi's  air-pump. — Bianchi  invented  an  air-pump  which  has 
several  advantages.  It  is  made  entirely  of  iron,  and  it  has  only  one  cylinder, 
which  oscillates  on  a  horizontal  axis  fixed  at  its  base,  as  seen  in  fig.  184. 
A  horizontal  shaft,  with  heavy  fly-wheel  V,  works  in  a  frame,  and  is  turned 
by  a  handle,  M.     A  crank,  in,  which  is  joined  to  the  top  of  the  piston  rod,  is 


-203] 


BiancJii 's  A  ir-pii uip. 


183 


fixed  to  the  same  shaft,  and  consequently  at  every  revohition  of  the  wheel 
the  cyHnder  makes  two  oscillations. 

In  some  cases,  as  in  that  shown  in  the  figure,  the  crank  and  the  fly-wheel 
are  on  parallel  axes  connected  by  a  pair  of  cog-wheels.  The  modification 
in  the  action  produced  by  this  arrangement  is  as  follows  :  — If  the  cog- 
wheel on  the  former  axis  has  twice  as  many  teeth  as  that  on  the  latter  axis, 


f  %'^'x^ 


Fig.  184. 

the  pressure  which  raises  the  piston  is  doubled  ;  an  advantage  which  is 
counterbalanced  by  the  inconvenience  that  now  the  piston  will  make  one 
oscillation  for  one  revolution  of  the  fly-wheel. 

The  machine  is  double-acting;  that  is,  the  piston  PP  (fig.  185)  produces 
a  vacuum,  both  in  ascending  and  descending.  This  is  effected  by  the  fol- 
lowing arrangements: — In  the  piston  there  is  a  valve,  ^,  opening  upwards 


'^i  Jr 


(h 


't 


184  On  Gases.  [203- 

as  in  the  ordinary  machine.     The  piston  rod  AA  is  hollow,  and  in  the  inside 
there  is  a  copper  tube,  X,  by  which  the  air  makes  its  escape  through  the  valve 

b.  At  the  top  of  the  cylinder  there 
is  a  second  valve,  a^  opening  up- 
wards. An  iron  rod,  D,  works  with 
gentle  friction  in  the  piston,  and 
terminates  at  its  ends  in  two  conical 
valves  s  and  s\  which  fit  into  the 
openings  of  the  tube  BB  leading  to 
the  receiver. 

Let  us  suppose  the  piston  de- 
scends. The  valve  s'  is  then  closed, 
and,  the  valve  s  being  open,  the  air 
of  the  receiver  passes  into  the  space 
above  the  piston,  while  the  air  in 
the  space  below  the  piston  under- 
goes compression,  and,  raising  the 
valve,  escapes  by  the  tube  X,  which 
communicates  with  the  atmosphere. 
When  the  piston  ascends,  the  ex- 
haustion takes  place  through  s',  and 
the  valve  s  being  closed,  the  com- 
pressed air  escapes  by  the  valve  a. 
The  machine  has  a  stopcock  for 
double  exhaustion,  similar  to  that 
already  described  (202).  It  is  also 
oiled  in  an  ingenious  manner.  A 
cup,  E,  round  the  rod  is  filled  with 
oil,  which  passes  into  the  annular 
space  between  the  rod  AA  and  the 
tube  X  ;  it  passes  then  into  a  tube 
00  in  the  piston,  and,  forced  by  the 
atmospheric  pressure,  is  uniformly 
distributed  on  the  surface  of  the 
piston. 

The  apparatus,  being  of  iron,  may  be  made  of  much  greater  dimensions 
than  the  ordinary  air-pump.  A  vacuum  can  also  be  produced  with  it  in  far 
less  time  and  in  apparatus  -of  greater  size  than  usual. 

204.  Deleuil's  air-pump. — In  this  air-pump  the  main  peculiarity  is  its 
piston,  which  is  of  considerable  length,  and  consists  of  a  series  of  accurately 
constructed  metal  discs  bolted  together.  This  works  easily  and  smoothly  in 
the  barrel,  and  no  packing  or  lubricator  is  used  ;  or  rather,  the  lubricator 
is  the  air  in  the  space  between  the  piston  and  the  barrel.  The  internal 
friction  of  the  air  in  this  narrow  space  is  so  great  that  the  rate  at  which  it 
leaks  into  the  barrel  is  far  inferior  to  the  rate  at  which  the  pump  is  exhaust- 
ing air  from  the  receiver.  And  Maxwell  showed  that  the  internal  friction 
is  not  diminished  even  when  its  density  is  greatly  reduced.  Hence  the 
pump  works  very  satisfactorily  up  to  a  considerable  degree  of  exhaustion — to 
a  millimetre  of  mercury,  for  instance. 


Fig.  185 


-205] 


SprengeVs  A  ir-punip. 


185 


205.  Sprengrel's  air-pump. — Sprengel  has  devised  a  form  of  air-pump 
which  depends  on  the  principle  of  converting  the  space  to  be  exhausted  into 
a  TorriceHian  vacuum. 

If  an  aperture  be  made  in  the  top  of  a  barometer  tube,  the  mercury  sinks 
and  draws  in  air  ;  if  the  experiment  be  so  arranged  as  to  allow  air  to  enter 
along  with  mercury,  and  if  the  supply 
of  air  be  limited  while  that  of  mercury 
is  unlimited,  the  air  will  be  carried 
away  and  a  vacuum  produced.  The 
following  is  the  simplest  form  of  the 
apparatus  in  which  this  action  is  real- 
ised. In  fig.  186,  cd  is  a  glass  tube 
longer  than  a  barometer,  open  at  both 
ends,  and  connected  by  means  of  india- 
rubber  tubing  with  a  funnel,  A,  filled 
with  mercury  and  supported  by  a  stand. 
Mercur}^  is  allowed  to  fall  in  this  tube 
at  a  rate  regulated  by  a  clamp  at  c ; 
the  lower  end  of  the  tube  cd  fits  in  the 
flask  B,  which  has  a  spout  at  the  side 
a  little  higher  than  the  lower  end  of 
cd ;  the  upper  part  has  a  branch  at  x, 
to  which  a  receiver  R  can  be  tightly 
fixed  When  the  clamp  at  c  is  opened, 
the  first  portions  of  mercury  which 
run  out  close  the  tube  and  prevent  air 
from  enterin_g  below.  As  the  mercury 
is  allowed  to  run  down,  the  exhaustion 
begins,  and  the  whole  length  of  the 
tube  from  ;r  to  ^  is  filled  with  cylinders 
of  air  and  mercury  having  a  downward 
motion.  Air  and  mercury  escape 
through  the  spout  of  the  flask  B  which 
is  above  the  basin  H,  where  the  mer- 
cury is  collected.  It  is  poured  back 
from  time  to  time  into  the  funnel  A,  to 
be  re-passed  through  the  tube  until 
the  exhaustion  is  complete.  As  this 
point  is  approached,  the  enclosed  air  between  the  mercury  cyHnders  is  seen 
to  diminish,  until  the  lower  part  of  reforms  a  continuous  column  of  mercury 
about  30  inches  high.  Towards  this  stage  of  the  process  a  noise  is  heard 
like  that  of  a  water-hammer  when  shaken  ;  the  operation  is  completed  when 
the  column  of  mercury  encloses  no  air,  and  a  drop  of  mercury  falls  on  the 
top  of  the  column  without  enclosing  the  slightest  air-bubble.  The  height  of 
the  column  then  represents  the  height  of  the  column  of  mercury  in  the 
barometer  ;  in  other  words,  it  is  a  barometer  whose  Torricellian  vacuum 
is  the  receiver  R.  This  apparatus  has  been  used  with  great  success  in 
experiments  in  which  a  very  complete  exhaustion  is  required,  as  in  the 
preparation  of  Geissler's  tubes  and  in  incandescent  electrical  lamps.     It 


1 86 


On   Gases. 


[205- 


may  be  advantageously  combined  with  an  exhausting  syringe,  which  first 

removes  the  greater  part  of  the  air,  the  exhaustion  being  then  completed  as 

above. 

The  most  perfect  vacua  are  obtained  by  absorbing'  the  residual  gas,  after 

the  exhaustion  has  been  pushed  as  far  as  possible,  either  mechanically  or 

by  some  substance  with  which 
it  combines  chemically.  Thus 
Dewar  has  produced  a  vacuum 
which  he  estimates  at  — ^  of  a 
millimetre,  by  heating  charcoal 
to  redness,  in  a  vessel  from 
which  air  had  been  exhausted 
by  the  Sprengel  pump,  and  then 
allowing  it  to  cool.  Finkener 
filled  a  vessel  with  oxygen,  then 
exhausted  as  far  as  possible, 
and  finally  heated  to  redness 
some  copper  contained  in  the 
vessel.  This  absorbed  the 
minute  quantity  of  gas  left,  with 
the  formation  of  cupric  oxide. 
In  some  of  his  experiments 
Crookes  obtained  by  chemical 
means  a  vacuum  of  -^-^,060  of  a 
millimetre.  In  these  highly 
rarefied  gases  the  pressure  is  so 
low  that  it  is  veiy  difficult  to 
measure  minute  differences. 
For  such  cases  McLeod  has 
devised  a  very  valuable  gauge, 
the  principle  of  which  is  to  con- 
dense  a   measured  volume   ot 

the  highly  rarefied  gas  to  a  much  smaller  volume,  and  then  to  measure  its 

pressure  under  the  new  conditions. 

206.  Bunsen's  Sprengel  pump. — This  is  a  very  convenient  arrangement 
for  producing  a  vacuum  in  cases  where  a  good  supply  of  water  is  available, 
as  in  laboratories.  A  composition  tube  a  (fig.  187),  connected  with  the  ser- 
vice-pipe of  a  water-supply,  is  joined  by  means  of  a  caoutchouc  tube  to  a 
glass  tube,  cdf,  to  which  is  attached  at  /  a  leaden  tube  about  10  to  12  yards 
long.  The  tube  sr  is  connected  with  the  space  to  be  exhausted.  The  water 
enters  by  a,  and  in  falling  down  the  tube  carries  with  it  air  from  the  space 
to  be  exhausted.  The  supply  of  water,  and  therewith  the  rate  of  exhaustion, 
can  be  regulated  by  the  stopcock  b  ;  the  bent  tube  pq,  which  contains  mer- 
cury, measures  the  degree  of  exhaustion,  which  may  be  reduced  to  a 
pressure  of  10  to  15  millimetres. 

207.  Aspirating-  action  of  currents  of  air. — When  a  jet  of  liquid  or  of 
a  gas  passes  through  air,  it  carries  the  surrounding  air  along  with  it,  fresh 
air  rushes  in  to  supply  its  place,  comes  also  in  contact  with  the  jet,  and  is 
in  like  manner  caiTied  away.     Thus,  then,  there  is  a  continual  rarefaction 


-207j  Aspii'atiiig  Action  of  Currents  of  Air.  187 

of  the  air  round  the  jet,  in  consequence  of  which  it  exerts  an  aspiratory 
action. 

This  phenomenon  may  be  well  illustrated  by  means  of  an  apparatus  re- 
presented in  fig.  188,  the  analogy  of  which  to  the  experiment  described  (146) 
will  be  at  once  evident.  It  consists  of  a 
wide  glass  tube,  in  the  two  ends  of  which  are 
fitted  two  small  tubes,  nd  and  B  ;  in  the 
bottom  is  a  manometer  tube  containing  a 
coloured  liquid.  On  blowing  through  the 
narrow  tube  the  liquid  at  o  is  seen  to  rise. 
If,  on  the  contraiy,  the  wide  tube  is  blown 
into,  a  depression  is  produced  at  o. 

To  this  class  of  phenomena  belongs  the 
following  experiment,  which  is  a  simple  modi- 
fication of  one  originally  described  by  Cle- 
ment and  Desormes.  A  tube  is  fixed  in  a 
metal  disc  (fig.  189),  its  end  bemg  flush  with 
the  surface.  A  light  disc  is  held  at  a  little 
distance  by  means  of  three  metal  studs. 
Holding  the  tube  vertically  with  the  discs 
downwards,  and  blowing  into  it,  the  movable 
disc  is  seen  to  rise  until  it  comes  in  contact 
with  the  upper  one.  The  current  of  air 
spreads  out  from  the  centre  of  the  plate 
towards  the  circumference,  and  in  doing  so 
it  is  rarefied  ;  in  consequence  of  this  lessened 
pressure  in  the  space,  the  lower  disc  is  lifted 
by  the  external  pressure  against  the  upper 
one,  where  it  remains  as  long  as  the  blowing 
continues.  The  simplest  plan  of  making  this 
experiment  was  devised  by  Faraday.  Hold- 
ing one  hand  horizontal,  the  palm  down- 
wards and  the  fingers  closed,  the  space  between  the  index  and  middle  finger 
is  blown  through.  If  a  piece  of  light  paper,  of  2  or  3  square  inches,  is  held 
against  the  aperture,  it  does  not  fall  as  long  as  the  blowing  continues. 

The  old  water-bellows.,  still  used  in  mountainous  places  where  there  is  a 
continuous  fall,  is  a  further  application  of  the  principle.  Water  falling  from 
a  reservoir  down  a  narrow  tube  divides  and  carries  air  along  with  it ;  and,  if 
there  are  apertures  in  the  side  through  which  air  can  enter,  this  also  is 
carried  along,  and  becomes  accumulated  in  a  reservoir  placed  below,  from 
which  by  means  of  a  lateral  tube  it  can  be  directed  into  the  hearth  of  a 
forge. 

This  may  be  illustrated  by  the  simple  apparatus  represented  in  fig.  190,  the 
construction  of  which  from  glass  tubes  and  corks  will  be  readily  intelligible.  It 
may  be  remarked  that  the  outer  tube  at  b  is  represented  in  section,  and  that 
the  part  of  the  tubes  ofd  and  ghk  outside  the  cork  are  relatively  much  longer 
horizontally  and  vertically  than  is  here  represented. 

If  the  vertical  tube  fd  is  fitted  to  a  vessel  of  boiling  water,  as  soon  as 
steam  issues  through  f,  it  not  only  raises  water  from  a  vessel  in  which  the 


i88 


On   Gases. 


[207- 


Fig.  190. 


bottom  of  the  tube  gh  dips,  but  drives  it  through  the  aperture  o.     And  if  a 
bent  tube,  with  a  narrow  opening  Hke  <?,  be  fitted  at  n,  and  directed  upwards, 

a    continuous    jet    of 
^  water     is     produced, 

often  reaching  to  the 
ceihng. 

This  apparatus 
serves  well  to  illus- 
trate the  principle  of 
Giffard's  t?jjector,  an 
extremely  ingenious 
and  important  appa- 
ratus by  which  steam-boilers  are  kept  supplied  with  water. 

The  principle  is  also  applied  in  a  series  of  machines  for  moving  and 
lifting  liquids,  and  even  solids  such  as  corn  ;  in  pumping,  in  blowers, 
exhausters,  air-pumps,  etc.  An  interesting  application  is  that  of  the  well- 
known  spray  producer ;  this  principle  has  further  been  utilised  by  Sprengel 
in  supplying  water  to  sulphuric  acid  chambers. 

By  the  locomotive  steampipe  a  jet  of  steam  entering  the  chimney  of  the 
locomotive  carries  the  air  away,  so  that  fresh  air  must  arrive  through  the 
fire,  and  thus  the  draught  be  kept  up. 

208.  DCorren's  mercury  pump. — Figs.  191  and  192  represent  a  mercu- 
rial air-pump,  constructed  by  Alvergniat.  It  consists  of  two  reservoirs,  A 
and  B,  connected  by  a  barometer  tube  T,  and  a  long  caoutchouc  tube  C. 
The  reservoir  B  and  the  tube  T  are  fixed  to  a  vertical  support  A,  which  is 
movable  and  open,  and  can  be  alternately  raised  and  lowered  through  a 
distance  of  nearly  4  feet.  This  is  effected  by  means  of  a  long  wire  rope, 
which  is  fixed  at  one  end  to  the  reservoir  A,  and  passes  over  two  pulleys,  a 
and  b,  the  latter  of  which  is  turned  by  a  handle.  Above  the  reservoir  B  is  a 
three-way  cock  n  ;  to  this  is  attached  a  tube  </,  for  exhaustion,  and  on  the 
left  is  an  ordinary  stopcock  ni^  which  communicates  with  a  reservoir  of 
mercury  t/,  and  with  the  air.  The  exhausting  tube  d  is  not  in  direct  com- 
munication with  the  receiver  to  be  exhausted  ;  it  is  first  connected  with  a 
reservoir  0^  partially  filled  with  sulphuric  acid,  and  designed  to  dry  the  gases 
which  enter  the  apparatus.  A  caoutchouc  tube,  <;,  makes  communication 
with  the  receiver  which  is  to  be  exhausted.  On  the  reservoir  <?  is  a  small 
mercury  manometer^. 

These  details  being  understood,  suppose  the  reservoir  A  at  the  top  of  its 
course  (fig.  191),  the  stopcock  m  open,  and  the  stopcock  n  turned  as  seen  in 
Z  ;  the  caoutchouc  tube  C,  the  tube  T,  the  reservoir  B,  and  the  tube  above 
are  filled  with  mercury  as  far  as  v  ;  closing  then  the  stopcock  w,  and  lower- 
ing the  reservoir  A  (fig.  192),  the  mercury  sinks  in  the  reservoir  B,  and  in 
the  tube  T,  until  the  difference  of  levels  in  the  two  tubes  is  equal  to  the  baro- 
metric height,  and  there  is  a  vacuum  in  the  reservoir  B.  Turning  now  the 
stopcock  «,  as  shown  in  fig.  X,  the  gas  from  the  space  to  be  exhausted  passes 
into  the  barometric  chamber  B  by  the  tubes  c  and  d,  and  the  level  again 
sinks  in  the  tube  T.  The  stopcocks  are  now  replaced  in  the  first  position 
(fig.  Z),  and  the  reservoir  A  is  again  lifted,  the  excess  of  pressure  of  mercury 
in  the  caoutchouc  tube  expels,  through  the  stopcocks  n  and  w,  the  gas  which 


-209] 


Conciensing  Pump. 


189 


had  passed  into  the  chamber  B,  and,  if  a  few  droplets  of  mercury  are  carried 
along  with  them,  they  are  collected  in  the  vessel  v.  The  process  is  repeated 
until  the  mercury  is  virtually  at  the  same  level  in  both  legs. 

Like  Sprengel's  pump,  this  is  very  slow  in  its  working,  and,  like  it,  is  best 
employed  in  completing  the  exhaustion  of  a  space  which  has  already  been  par- 
tially rarefied ;  for  a  vacuum  of  j-  of  a  millimetre  may  be  obtained  by  its  means. 


Fig.  iQi. 


Fig.  192. 


209.  Condensing-  pump. — The  condensing  pump  is  an  apparatus  for 
compressing  air  or  any  other  gas.  The  form  usually  adopted  is  the  follow- 
ing : — In  a  cyHnder,  A,  of  small  diameter  (fig.  194),  there  is  a  solid  piston, 
the  rod  of  which  is  moved  by  the  hand.  The  cylinder  is  provided  with  a 
screw  which  fits  into  the  receiver  K.  Fig.  193  shows  the  arrangement  of 
the  valves,  which  are  so  constructed  that  the  lateral  valve  o  opens  from  the 
outside,  and  the  lower  valve  j-  from  the  inside. 

When  the  piston  descends  the  valve  0  closes,  and  the  elastic  force  of  the 


190 


On   Gases, 


[209- 


compressed  air  opens  the  valve  s,  which  thus  allows  the  compressed  air  to 
pass  into  the  receiver.     When  the  piston  ascends,  s  closes  and  o  opens,  and 

permits  the  entrance  of  fresh  air,  which 
in  turn  becomes  compressed  by  the 
descent  of  the  piston,  and  so  on.  This 
apparatus  is  chiefly  used  for  charging 
liquids  with  gases.  For  this  purpose 
the  stopcock  B  is  connected  with  a  re- 
servoir of  the  gas  by  means  of  the  tube 
D.  The  pump  exhausts  this  gas,  and 
forces  it  into  the  vessel  K,  in  which 
the  liquid  is  contained.  The  artificial 
gaseous  waters  are  made  by  means  of 
analogous  apparatus. 

The  applications  of  condensed  air  are 
both  numerous  and  important.  In  a 
certain  sense  condensed  air  plays  the 
part  of  a  metal  spring  in  which  is  stored 
up  a  greater  or  less  provision  of  work, 
and  which  can  then  be  utilised  by  ex- 
panding the  air  at  a  given  moment,  and 
at  a  given  point  in  the  most  favourable 
condition  for  its  being  applied.  In  some 
cases  the  expansion  is  sudden  and  inter- 
'^^  mittent,  as  in  the  air-gun,  the  pneumatic 
post,  or  in  air-brakes,  and  in  some  cases 
\—  slow,    gradual,    and    continuous     as    in 

boring  machines. 

One  of  the  most  important  applica- 

jer  boring  machines  used  in  tunnelling  through  the 

where  steam    power  would  be   objectionable 


Fig.  194. 


tions  is  that  to  the  lar 

Alps  and  elsewhere.     There, 

owing  to  the  steam  produced,  compressed  air  is  of  great  service,  for  it  not  only 

supplies  the  power,  but  it  ventilates  the  underground  spaces. 

The  principal  parts  of  such  machines,  which  were  first  employed  on  a 
large  scale  in  the  Mont  Cenis  tunnel,  are  as  follows  : — A  sheaf  of  borers  or 
iron  rods  with  punches  on  the  ends  are  mounted  on  a  framework.  Each  of 
these  .borers  is  susceptible  of  three  simultaneous  motions,  one  backward  and 
forward  producing  repeated  shocks  against  the  rock  ;  a  second  analogous  to 
that  of  a  gimlet  ;  while  a  third  moves  the  whole  framework  backwards  and 
forwards. 

This  triple  motion  is  effected  by  a  machine  like  a  steam  engine,  but 
driven  by  compressed  air  ;  the  first  motion  by  a  piston,  the  action  of  which 
is  regulated  by  a  slide  valve  (469) ;  the  other  two  motions  are  effected  by 
means  of  a  separate  machine.  The  air  is  under  a  pressure  of  five  atmo- 
spheres, the  compression  being  effected  by  special  machines  worked  by  water 
power.  The  air  by  which  all  this  is  effected  on  expanding  serves  to  cool 
and  ventilate  the  mine. 

The  j)?teiimatic  post  is  of  great  service  in  London  and  other  large  towns 
in  forwarding  the  actual  written  telegraphic  messages  from  the  several  re- 


-210] 


Uses  of  the  Air-pump. 


191 

ceiving  stations  to  a  central  telegraph  station.  The  messages  are  placed  in 
a  carrier  (fig.  195),  which  is  a  guttapercha  cylinder  7  in.  long  by  2  in. 
in  diameter,  closed  at  one  end  ;  it  is  covered  with  felt,  and  there  is  a  welt  of 
that  material  at  one  end  ;  the  felt  projects  at  the  other,  so  that  it  can  be 
folded  down,  and  held  in  position  by  an  india- 
rubber  band,  so  as  to  keep  the  contents  in 
their  place. 

Such  carriers  move  air-tight  in  carefully 
turned  leaden  tubes  polished  internally  and 
protected  by  being   incased   in    iron  tubes.  Fig.  195. 

The  propulsion  is  effected  either  by  pressure 

or  by  exhaustion  ;  and  by  suitable  valves  the  tubes  can  be  placed  in  con- 
nection with  compressed  or  rarefied  air,  so  that  the  carriers  may  either  be 
shot  in  one  direction  by  compressed  air,  or  drawn  in  the  other  by  rarefied  air. 
The  compression  and  rarefaction  are  produced  by  means  of  powerful  steam 
engines  to  a  pressure  of  about  ten  pounds,  or  a  vacuum  of  eight  pounds  to  the 
inch.  By  this  means  a  speed  of  nearly  a  mile  in  a  minute  may  be  obtained 
in  tubes  not  more  than  a  mile  in  length. 

Other  applications  of  compressed  air  are  in  the  small  pumps  used  by 
plumbers  for  testing  and  for  clearing  gas-pipes,  in  ventilating  mines,  in 
supplying  air  to  blast-furnaces,  in  the  air- 
brakes used  in  railway  trains,  and  so  forth. 

210.  Uses  of  the  air-pump. — A  great 
many  experiments  with  the  air-pump  have 
been  already  described.  Such  are  the  mer- 
curial rain  (13),  the  fall  of  bodies  in  vacuo 
(76),  the  bladder  (153),  the  bursting  of  a 
bladder  (159),  the  Magdeburg  hemispheres 
(160),  and  the  baroscope  (195). 

The  fountain  in  vacuo  (fig.  196)  is  an  ex-' 
periment  made  with  the  air-pump,  and  shows 
the  elastic  force  of  the  air.  It  consists  of  a 
glass  vessel.  A,  provided  at  the  bottom  with 
a  stopcock,  and  a  tubulure  which  projects 
into  the  interior.  Having  screwed  this 
apparatus  to  the  air-pump,  it  is  exhausted, 
and,  the  stopcock  being  closed,  it  is  placed 
in  a  vessel  of  water,  R.  Opening  then  the 
stopcock,  the  atmospheric  pressure  upon  the 
water  in  the  vessel  makes  it  jet  through  the 
tubulure  into  the  interior  of  the  vessel,  as 
shown  in  the  drawing. 

Fig.  197  represents  an  experiment  illus- 
trating the  effect  of  atmospheric  pressure  on 
the  human  body.  A  glass  vessel,  open  at 
both  ends,  being  placed  on  the  plate  of  the  machine,  the  upper  end  of  the 
cylinder  is  closed  by  the  hand,  and  a  vacuum  is  made.  The  hand  then 
becomes  pressed  by  the  weight  of  the  atmosphere,  and  can  only  be  taken 
away  by  a  great  effort.     And  as  the  elasticity  of  the  fluids  contained  in  the 


192 


On   Gases.  [210- 

organs  is  not  counterbalanced  by  the  weight 
of  the  atmosphere,  the  pahn  of  the  hand 
swells,  and  blood  tends  to  escape  from  the 
pores. 

By  means  of  the  air-pump  it  may  be 
shown  that  air,  by  reason  of  the  oxygen  it 
contains,  is  necessary  for  the  support  of 
combustion  and  of  life.  For  if  we  place  a 
lighted  taper  under  the  receiver,  and  begin 
to  exhaust  the  air,  the  flame  becomes  weaker 
as  rarefaction  proceeds  and  is  finally  extin- 
guished. Similarly  an  animal  faints  and  dies 
if  a  vacuum  is  formed  in  a  receiver  under 
which  it  is  placed.  Mammalia  and  birds 
soon  die  in  vacuo.  Fish  and  reptiles  sup- 
port the  loss  of  air  for  a  much  longer  time. 
Insects  can  live  several  days  in  vacuo. 

Substances  liable  to  ferment  may  be 
kept  in  vacuo  for  a  long  time  without 
alteration,  as  they  are  not  in  contact  with  oxygen,  which  is  necessary  for 
fermentation.  Food  kept  in  airtight  cases,  from  which  the  air  had  been  ex- 
hausted, has  been  found  as  fresh  after  years 
as  on  the  first  day. 

211.  Hero's  fountain. — Hero's  fountain, 
which  derives  its  name  from  its  inventor, 
Hero,  who  lived  at  Alexandria,  120  B.C., 
depends  on  the  elasticity  of  the  air.  It 
consists  of  a  brass  dish,  D  (fig.  198),  and  of 
two  glass  globes,  M  and  N.  The  dish  com- 
municates with  the  lower  part  of  the  globe  N 
by  a  long  tube,  B  ;  and  another  tube.  A, 
connects  the  two  globes.  A  third  tube 
passes  through  the  dish  D  to  the  lower  part 
of  the  globe  M.  This  tube  having  been 
taken  out,  the  globe  M  is  partially  filled  with 
water,  the  tube  is  then  replaced  and  water 
is  poured  into  the  dish.  The  water  flows 
through  the  tube  B  hito  the  lower  globe, 
and  expels  the  air,  which  is  forced  into  the 
upper  globe  ;  the  air,  thus  compressed,  acts 
upon  the  water,  and  makes  it  jet  out  as  re- 
presented in  the  figure.  If  it  were  not  for 
the  resistance  of  the  atmosphere  and  friction, 
the  liquid  would  rise  to  a  height  above  the 
water  in  the  dish  equal  to  the  difference  of 
the  level  in  the  two  globes. 

212.  Intermittent  fountain. — The  in- 
termittent fountain  depends  partly  on  the 
elastic  force  of  the  air,  and  partly  on   the 


-213] 


TJie  SipJion. 


193 


atmospheric  pressure.  It  consists  of  a  stoppered  glass  globe  (C,  fig.  190), 
provided  with  two  or  three  capillary  tubulures,  D.  A  glass  tube  open  at 
both  ends  reaches  at  one  end  to  the 
upper  part  of  the  globe  C  ;  the  other  end 
terminates  just  above  a  little  aperture  in 
the  dish  B  which  supports  the  whole  ap- 
paratus. 

The  water  with  which  the  globe  C  is 
nearly  two-thirds  filled  runs  out,  by  the 
tubes  D,  as  shown  in  the  figure,  the  in- 
ternal pressure  at  D  being  equal  to  the 
atmospheric  pressure  together  with  the 
weight  of  the  column  of  water  CD,  while 
the  external  pressure  at  that  point  is  only 
that  of  the  atmosphere.  These  condi- 
tions prevail  so  long  as  the  lower  end  of 
the  glass  tube  is  open  ;  that  is,  so  long  as 
air  can  enter  C  and  keep  the  air  in  C  at 
the  same  density  as  the  external  air  ;  but 
the  apparatus  is  arranged  so  that  the 
orifice  in  the  dish  B  does  not  allow  so 
much  water  to  flow  out  as  it  receives  from 
the  tubes  D,  in  consequence  of  which 
the  level  gradually  rises  in  the  dish,  and 
closes  the  lower  end  of  the  glass  tube. 
As  the  external  air  cannot  now  enter  the 
globe  C,  the  air  becomes  rarefied  in  pro- 
portion as  the  flow  continues,  until  the 
pressure  of  the  column  of  water  CD,  togethei  with  that  of  the  air  contained 
in  the  globe,  is  equal  to  this  external  pressure  at  D  ;  the  flow  consequently 
stops.  But  as  water  continues  to  flow 
out  of  the  dish  B,  the  tubes  D  become 
open  again,  air  enters,  and  the  flow  recom- 
mences, and  so  on,  as  long  as  there  is 
water  in  the  globe  C. 

213.    The    siphon.  —  The    siphon    is 
a    bent    tube    open    at   both    ends,   and 
with  unequal  legs  (fig.  200).      It  is  used 
in   transferring   liquids    in    the   following 
manner  : — The  siphon  is  filled  with  some 
Hquid,  and,  the  two  ends  being  closed, 
the  shorter  leg  is   dipped  in  the  liquid, 
as     represented     in     fig.     200  ;    or,     the 
shorter  leg  having   been    dipped  in  the    ■ 
liquid,  the  air  is  exhausted  by  applying 
the  mouth  at  B.     A  vacuum  is  thus  pro- 
duced, the  liquid  in  C  rises  and  fills  the  ^'^-  ^°°- 
tube  in  consequence  of  the  atmospheric  pressure.       It   will   then   run    out 
through  the  siphon  as  long  as  the  shorter  end  dips  in  the  liquid. 


194  On  Gases.     \  [213- 

To  explain  this  flow  of  water  from  the  siphon,  let  us  suppose  it  filled  and 
the  short  leg  immersed  in  the  liquid.  The  pressure  then  acting  on  C,  and 
tending  to  raise  the  liquid  in  the  tube,  is  the  atmospheric  pressure  minus 
the  height  of  the  column  of  liquid  DC.  In  like  manner,  the  pressure  on 
the  end  of  the  tube  B  is  the  weight  of  the  atmosphere  less  the  pressure  of 
the  column  of  liquid  AB.  But  as  this  latter  column  is  longer  than  CD,  the 
force  acting  at  B  is  less  than  the  force  acting  at  C,  and  consequently  a  flow 
takes  place  proportional  to  the  difference  between  these  two  forces.  The 
flow  will  therefore  be  more  rapid  in  proportion  as  the  difference  of  level 
between  the  aperture  B  and  the  surface  of  the  liquid  in  C  is  greater. 

It  follows  from  the  theory  of  the  siphon  that  it  would  not  work  in  vacuo, 
nor  if  the  height  CD  were  greater  than  that  of  a  column  of  liquid  which 
counterbalances  the  atmospheric  pressure. 

214.  The  intermittent  sipbon. — In  the  interinitte)it  siphon  the  flow  is 
not  continuous.     It  is  arranged  in  a  vessel,  so  that  the  shorter  leg  is  near  the 

bottom  of  the  vessel,  while  the  longer  leg  passes 

through  it  (fig.  201).     Being  fed  by  a  constant 

supply  of  water,  the  level  gradually  rises  both 

in  the  vessel  and  in  the  tube  to  the  top  of  the 

siphon,  which  it  fills,  and  water  begins  to  flow 

out.     But  the  apparatus  is  arranged  so  that  the 

flow  of  the  siphon  is  more  rapid  than  that  of  the 

tube  which  supplies  the  vessel,  and  consequently 

the  level  sinks  in  the  vessel  until  the  shorter 

branch  no  longer  dips  in  the  liquid  ;  the  siphon 

"^  .  is  then  empty,  and  the  flow  ceases.     But  as  the 

'^'  "°^"  vessel  is  continually  fed  from  the  same  source 

the  level  again  rises,  and  the  same  series  of  phenomena  is  reproduced. 

The  theory  of  the  intermittent  siphon  explains  the  natural  intermittent 
springs  which  are  found  in  many  countries,  and  of  which  there  is  an  excel- 
lent example  near  Giggleswick  in  Yorkshire.  Many  of  these  springs  fur- 
nish water  for  several  days  or  months,  and  then,  after  stopping  for  a  certain 
interval,  again  recommence.  In  others  the  flow  stops  and  recommences 
several  times  in  an  hour. 

These  phenomena  are  explained  by  assuming  that  there  are  subterranean 
fountains,  which  are  more  or  less  slowly  filled  by  springs,  and  which  are  then 
emptied  by  fissures  so  occurring  in  the  ground  as  to  form  an  intermittent 
siphon. 

215.  Different  kinds  of  pumps. — Pumps  are  machines  which  serve  to 
raise  water  either  by  suction,  by  pressure,  or  by  both  efforts  combined  ;  they 
are  consequently  divided  into  sitctiofi  or  lift pumps^fo?-cc  piu)ips,  and  suction 
and  forcing  pumps. 

The  various  parts  entering  into  the  construction  of  a  pump  are  the  barrel, 
the  piston,  the  valves,  and  the  pipes.  The  barrel  is  a  cylinder  of  metal  or 
of  wood,  in  which  is  the  pisto?i.  The  latter  is  a  metal  or  wooden  cylinder 
wrapped  with  tow,  and  working  with  gentle  friction  the  whole  length  of  the 
barrel. 

The  valves  are  discs  of  metal  or  leather,  which  alternately  close  the 
apertures  which  connect  the  barrel  with  the  pipes.     The  most  usual  valves 


-216] 


Suction-piiDip. 


195 


_■ 


are  the  clack  valve  (fig.  202)  and  the  conical  valve  (fig.  203).     The  former  is 
a  metal  disc  fixed  to  a  hinge  on  the  edge  of  the  orifice  to  be  closed.     In  order 
more  effectually  to  close  it,  the  lower  part  of  the  disc  is  covered  with  thick 
leather.  Sometimes  the  valve 
consists  merely  of  a  leather       '^i||||l||!|f'll'' 
disc,  of  larger  diameter  than 
the    orifice,    nailed    on    the 
edge  of  the  orifice.     Its  flexi- 
bility enables  it  to  act  as  a 

The    conical   valve    con- 
sists of  a  metal  cone  fitting  in  an  aperture  of  the  same  shape.     Below  this 
is  an  iron  hoop,  through  which  passes  a  bolt-head  fixed  to  the  valve.     The 
object  of  this  is  to  limit  the  play  of  the  valve  when  it  is  raised  by  the  water, 
and  to  prevent  its  removal. 

216.  Suction-pump. — Fig.  204  represents  a  model  of  a  suction-pump 
such  as  is  used  in  lectures,  but  which  has  essentially  the  same  arrangement 
as  the  pumps  in  common  use.  It  con- 
sists, 1st,  of  a.  glass  cylinder  B,  at  the 
bottom  of  which  there  is  a  valve  S 
opening  upwards  ;  2nd,  of  a  suctiott- 
tiibe  A,  which  dips  into  the  reservoir 
from  which  water  is  to  be  raised  ;  3rd, 
of  a  piston,  which  is  moved  up  and 
down  by  a  rod  worked  by  a  handle 
P.  The  piston  is  perforated  by  a  hole  ; 
the  upper  aperture  is  closed  by  a 
\alve  O,  opening  upwards. 

When  the  piston  rises  from  the 
bottom  of  the  cylinder  B,  a  vacuum  is 
produced  below,  and  the  valve  O  is 
kept  closed  by  the  atmospheric  pres- 
sure, while  the  air  in  the  pipe  A,  in 
consequence  of  its  elasticity,  raises  the 
valve  S,  and  partially  passes  into  the 
cylinder.  The  air  being  thus  rarefied, 
water  rises  in  the  pipe  until  the  pres- 
sure of  the  liquid  column,  together 
with  the  pressure  of  the  rarefied  air 
which  remains  in  the  tube,  counter- 
balances the  pressure  of  the  atmo- 
sphere on  the  water  of  the  reservoir. 

When  the  piston  descends,  the 
valve  S  closes  by  its  own  weight,  and 
prevents  the  return  of  the  air  from  the 
cylinder  into  the  tube  A.  The  air  compressed  by  the  piston  opens  the  valve 
O,  and  escapes  into  the  atmosphere  by  the  pipe  C.  With  a  second  stroke 
of  the  piston  the  same  series  of  phenomena  is  produced,  and  after  a  few- 
strokes  the  water  reaches  the  cylinder.     The  effect  is  now  somewhat  modi- 

o  2 


Fig.  204. 


196 


071   Gases. 


[216- 


fied  ;  during  the  descent  of  the  piston  the  valve  S  closes,  and  the  water 
raises  the  valve  O,  and  passes  above  the  piston  by  which  it  is  lifted  into 
the  upper  reservoir  D.  There  is  now  no  more  air  in  the  pump,  and  the 
water  forced  by  the  atmospheric  pressure  rises  with  the  piston,  provided 
that,  when  it  is  at  the  summit  of  its  course,  it  is  not  more  than  34  feet  above 
the  level  of  the  water  in  which  the  tube  A  dips,  for  we  have  seen  (163)  that 
a  column  of  water  of  this  height  is  equal  to  the  pressure  of  the  atmosphere. 

In  practice  the  height  of  the  tube  A  does  not  exceed  26  to  28  feet,  for 
although  the  atmospheric  pressure  can  supJDort  a  higher  column,  the  vacuum 
produced  in  the  barrel  is  not  perfect,  owing  to  the  fact  that  the  piston  does 
not  fit  exactly  on  the  bottom  of  the  barrel.  But  when  the  water  has  passed  the 
piston,  it  is  the  ascending  force  of  the  latter  which  raises  it,  and  the  height 
to  which  it  can  be  brought  depends  on  the  power  which  works  the  piston. 

217.  Suction  and  force  pump. — The  action  of  this  pump,  a  model  of 
which  is  represented  in  fig.  205,  depends  both  on  exhaustion  and  on  pres- 
sure. At  the  base  of  the  barrel,  where  it  is  connected  with  the  tube  A,  there 
is  a  valve  S,  which  opens  upwards.  Another  valve  O,  opening  in  the  same 
direction,  closes  the  aperture  of  a  conduit,  which  passes  from  a  hole  <?,  near 
the  valve  S,  into  a  vessel   M,  which  is  called  the  air-chamber.     From  this 

chamber  there  is  another 
tube  D,  up  which  the 
water  is  forced. 

At  each  ascent  of  the 
piston  B,  which  is  solid, 
the  water  rises  through 
the  tube  A  into  the  barrel. 
When  the  piston  sinks, 
the  valve  S  closes,  and 
the  water  is  forced  through 
the  valve  O  into  the  reser- 
voir M,  and  thence  into 
the  tube  D.  The  height 
to  which  it  can  be  raised 
in  this  tube  depends 
solely  on  the  motive  force 
which  works  the  pump. 

If  the  tube  D  were  a 
prolongation  of  the  tube 
]ao,  the  flow  would  be  in- 
termittent ;  it  would  take 
place  when  the  piston  de- 
scended, and  would  cease 
as  soon  as  it  ascended. 
But  between  these  tubes 
there  is  an  interval, 
which,  by  means  of  the 
air  in  the  reservoir  M, 
ensures  a  continuous  flow.  The  water  forced  into  the  reservoir  M  divides 
into  two  parts,  one  of  which,  rising  in  D,  presses  on  the  water  in  the  reser- 


-219]  Fire-engine.  1 97 

voir  by  its  weight  ;  while  the  other,  in  virtue  of  this  pressure,  rises  in  the 
reservoir  above  the  lower  orifice  of  the  tube  D,  compressing  the  air  above. 
Consequently,  when  the  piston  ascends,  and  no  longer  forces  the  water  into 
M,  the  air  of  the  reservoir,  by  the  pressure  it  has  received,  reacts  on  the 
liquid,  and  raises  it  in  the  tube  D,  until  the  piston  again  descends,  so  that 
the  jet  is  continuous. 

218.  Xioad  which  the  piston  supports. — In  the  suction-pump,  when 
once  the  water  fills  the  pipe,  and  the  barrel,  as  far  as  the  spout,  the  effort 
necessary  to  raise  the  piston  is  equal  to  the  weight  of  a  column  of  water, 
the  base  of  which  is  this  piston,  a7id  the  height  the  vertical  distance  oti  the 
spout  from  the  level  of  the  water  i?i  the  reservoir ;  that  is,  the  height  to 
which  the  water  is  raised.  For  if  H  is  the  atmospheric  pressure,  h  the 
height  of  the  water  above  the  piston,  and  fi'  the  height  of  the  column 
which  fills  the  suction-tube  A  (fig.  205),  and  the  lower  part  of  the  barrel,  the 
pressure  above  the  piston  is  obviously  H  + //,  and  that  below  is  H-/;',  since 
the  weight  of  the  column  h'  tends  to  counterbalance  the  atmospheric  pressure. 
But  as  the  pressure  H  -  h'  tends  to  raise  the  piston,  the  effective  resistance 
is  equal  to  the  excess  of  H  -1-  >%  over  H  -h',  that  is  to  say,  to  //  +  h'. 

In  the  suction  and  force  pump  it  is  readily  seen  that  the  pressure  which 
the  piston  supports  is  also  equal  to  the  weight  of  a  column  of  water  the  base 
of  which  is  the  section  of  the  piston,  and  the  height  that  to  which  the  water 
is  raised. 


Fig.  206. 


219.  Fire-engrine. — Thefre-engine  is  a  force-pump  in  which  a  steady  jet 
is  obtained  by  the  aid  of  an  air-chamber,  and  also  by  two  pumps  working 
alternately  (fig.  206).  The  two  pumps  fn  and  n,  worked  by  the  same  lever 
PQ,  are  immersed  in  a  tank,  which  is  kept  filled  with  water  as  long  as  the 


198  On   Gases.  [219- 

pump  works.  P'rom  the  arrangement  of  the  valves  it  will  be  seen  that  when 
one  pump,  «,  draws  water  from  the  tank,  the  other,  in,  forces  it  into  the  air- 
chamber  R  ;  whence,  by  an  orifice  Z,  it  passes  into  the  delivery  tube,  by 
which  it  can  be  sent  in  any  direction. 

Without  the  air-chamber  the  jet  would  be  mtermittent.  But  as  the  velo- 
city of  the  water  on  entering  the  reservoir  is  less  than  on  emerging,  the  level 
of  the  water  rises  above  the  orifice  Z,  compressing  the  air  which  fills  the 
reservoir.  Hence,  whenever  the  piston  stops,  the  air  thus  compressed,  re- 
acting on  the  liquid,  forces  it  out  during  its  momentary  stoppage,  and  thus 
keeps  up  a  constant  flow. 


-222]  199 


BOOK   V. 

ON     SOUND. 


CHAPTER    I. 

PRODUCTION,   PROPAGATION,   AND   REFLECTION   OF   SOUND. 

220.  Province  of  acoustics. — The  study  of  sounds,  and  that  of  the 
vibrations  of  elastic  bodies,  form  the  province  of  the  science  of  sounds^  or 
acoustics. 

Music  considers  sounds  with  reference  to  the  pleasurable  feeling  they  are 
calculated  to  excite.  Acoustics  is  concerned  with  the  questions  of  the  pro- 
duction, transmission,  and  comparison  of  sounds  ;  to  which  may  be  added 
the  physiological  question  of  the  perception  of  sounds. 

221.  Sound  and  noise. — Sound  is  the  peculiar  sensation  excited  in  the 
organ  of  hearing  by  the  vibratory  motion  of  bodies,  when  this  motion  is 
transmitted  to  the  ear  through  an  elastic  medium. 

Sounds  are  distinguished  from  noises.  Sound  properly  so  called,  or 
musical  soujid,  is  that  which  produces  a  continuous  sensation,  and  the 
musical  value  of  which  can  be  estimated  ;  while  noise  is  either  a  sound 
of  too  short  a  duration  to  be  determined,  like  the  report  of  a  cannon  ;  or 
else  it  is  a  confused  mixture  of  many  discordant  sounds,  like  the  rolling 
of  thunder  or  the  noise  of  the  waves.  Nevertheless  the  difference  between 
sound  and  noise  is  by  no  means  precise  ;  Savart  showed  that  there  are 
relations  of  height  in  the  case  of  noise,  as  well  as  in  that  of  sound  ;  and 
there  are  said  to  be  certain  ears  sufficiently  well  organised  to  determine 
the  musical  value  of  the  sound  produced  by  a  carriage  rolling  on  the 
pavement. 

222.  Cause  of  sound. — Sound  is  always  the  result  of  rapid  oscillations 
imparted  to  the  molecules  of  elastic  bodies,  when  the  state  of  equilibrium  of 
these  bodies  has  been  disturbed  either  by  a  shock  or  by  friction.  Such  bodies 
tend  to  regain  their  first  position  of  equilibrium,  but  only  reach  it  after  per- 
forming, on  each  side  of  that  position,  very  rapid  vibratory  movements,  the 
amplitude  of  which  quickly  decreases.  A  body  which  produces  a  sound  is 
called  a  sonorous  or  sounding  body. 

As  understood  in  England  and  Germany,  a  vibration  comprises  a  motion 
to  and  fro  ;  in  France,  on  the  contrary,  a  vibration  means  a  movement  to  or 


200 


On  Sound. 


[222- 


Fig.  207. 


fro.  The  French  vibrations  are  with  us  semi-vibrations,  an  oscillation  or 
vibration  is  the  movement  of  the  vibrating  molecule  in  only  one  direction  ; 
a  double  or  complete  vibration  comprises  the  oscillation  both  backwards  and 
forwards.  Vibrations  of  sounding  bodies  are  very  readily  observed.  If  a 
light  powder  is  sprinkled  on  a  body  which  is  in  the  act  of  yielding  a  musical 

sound,  a  rapid  motion  is  imparted 
to  the  powder,  which  renders  visible 
the  vibrations  of  the  body  ;  and,  in 
the  same  manner,  if  a  stretched 
cord  be  smartly  pulled  and  let  go, 
its  vibrations  are  apparent  to  the 
eye. 

A  bell-jar  is  held  horizontally 
in  one  hand  (fig.  207),  and  made 
to  vibrate  by  being'  struck  with  the 
other  ;  if  then  a  piece  ot  metal  is  placed  in  it,  it  is  rapidly  raised  by  the 
vibrations  of  the  side ;  touching  the  bell-jar  with  the  hand,  the  sound  ceases, 
and  with  it  the  motion  of  the  metal. 

223.  Sounds  not  propag-ated  in  v  acuo. — The  vibrations  of  elastic  bodies 
can  only  produce  the  sensation  of  sound  in  us  by  the  intervention  of  a 
medium  mterposed  between  the  ear  and  the 
sonorous  body  and  vibrating  with  it.  This 
medium  is  usually  the  air  ;  but  all  gases, 
vapours,  liquids,  and  sohds  also  transmit 
sounds. 

The  following  experiment  shows  that  the 
presence  of  a  ponderable  medium  is  neces- 
sary for  the  propagation  of  sound.  A  small 
metal  bell,  which  is  continually  struck  by  a 
small  hammer  by  means  of  clockwork,  or 
else  an  ordinaiy  musical  box,  is  placed  under 
the  receiver  of  an  air-pump  (fig.  208).  As 
long  as  the  receiver  is  full  of  air  at  the  ordi- 
nary pressure  the  sound  is  transmitted,  but 
in  proportion  as  the  air  is  exhausted  the 
sound  becomes  feebler,  and  cannot  be  heard 
in  a  vacuum. 

To  ensure  the  success  of  the  experiment, 
the   bellwork   or  the   musical  box  must  be 
placed  on  wadding  ;  for  otherwise  the  vibra- 
tions would  be  transmitted  to  the  air  through 
the  plate  of  the  pump. 
224.   Sound    is   propag-ated   in  all   elastic   bodies. — If,   in   the  above 
experiment,  any  vapour  or  gas  be  admitted  after  the  vacuum  has  been  made, 
the  sound  of  the  bell  will  be  heard,  showing  that  sound  is  propagated  in  this 
medium  as  in  air. 

Sound  is  also  propagated  in  liquids.  When  two  stones  are  struck  against 
each  other  under  water,  the  shock  is  distinctly  heard  ;  and  a  diver  at  the 
bottom  of  the  water  can  hear  the  sound  of  voices  on  the  bank.     The  sound 


Fig.  208. 


-225j  Propagation  of  Sound  in  Air.  201 

is,  however,  enfeebled,  as  a  considerable  portion  is  reflected  at  the  boundary 
of  the  two  media. 

The  conductibility  of  solids  is  such  that  the  faint  scratching  of  a  pen  or 
the  ticking  of  a  watch  at  one  end  of  a  long  horizontal  wooden  rod  is  heard 
much  more  distinctly  when  the  ear  is  directly  applied  against  the  other  end 
of  the  rod,  than  when  it  is  at  the  same  distance  in  the  air.  Sound  may  even 
reach  the  ear  through  solids  alone  without  passing  through  the  air,  for  if  the 
ears  be  closed,  and  the  rod  be  put  between  the  teeth,  the  ticking  is  distinctly 
heard.  The  earth  conducts  sound  so  well  that  at  night,  when  the  ear  is 
applied  to  the  ground,  the  stepping  of  horses,  or  any  other  noise  at  a  great 
distance,  is  heard. 

225.  Propagation  of  sound  in  air. — In  order  to  simplify  the  theory  of 
the  propagation  of  sound  in  air,  we  shall  first  consider  the  case  in  which  it 
is  propagated  in  a  cylindrical  tube  of  indefinite  length.  Let  MN,  fig.  209, 
be  a  tube  filled  with  air  at  a  constant  pressure  and  temperature,  and  let  P 
be  a  piston  oscillating  rapidly  from  A  to  a.  When  the  piston  passes  from 
A  to  «  it  compresses  the  air  in  the  tube.     But  in  consequence  of  the  great 


Fig.  205. 

compressibility,  the  condensation  of  the  air  does  not  take  place  at  once 
throughout  the  whole  length  of  the  tube,  but  solely  within  a  certain  length, 
rtH,  which  is  called  the  co7idensed  wave. 

If  the  tube  MN  be  supposed  to  be  divided  into  lengths  ecjual  to  aW,  and 
each  of  these  lengths  divided  into  layers  parallel  to  the  piston,  it  may  be 
shown  by  calculation  that,  when  the  first  layer  of  the  wave  aYi  comes  to  rest, 
the  motion  is  communicated  to  the  first  layer  of  the  second  wave  HH',  and 
so  on  from  layer  to  layer  in  all  parts  of  H'H",  WW".  The  condensed  wave 
advances  in  the  tube,  each  of  its  parts  having  successively  the  same  degree 
of  velocity  and  condensation. 

When  the  piston  returns  in  the  direction  aA,  a  vacuum  is  produced 
behind  it,  which  causes  an  expansion  of  the  air  in  contact  with  its  posterior 
face.  The  next  layer  expanding  in  turn  brings  the  first  to  its  original  state 
of  condensation,  and  so  on  from  layer  to  layer.  Thus  when  the  piston  has 
returned  to  A,  an  expanded  wave  is  produced  of  the  same  length  as  the  con- 
densed wave,  and  directly  following  it  in  the  tube  where  they  are  propagated 
together,  the  corresponding  layers  of  the  two  waves  possessing  equal  and 
contrary  velocities. 

The  whole  of  a  condensed  and  expanded  wave  forms  an  undulation; 
that  is,  an  undulation  comprehends  that  part  of  the  column  of  air  affected 
during  the  backward  and  forward  motion  of  the  piston.  The  length  of  an 
U7idulation  is  the  space  which  sound  traverses  during  a  complete  \ibration 
of  the  body  which  produces  it.  This  length  is  less  in  proportion  as  the 
vibrations  are  more  rapid. 


202  On  Sound.  [225- 

It  is  important  to  remark  that  if  we  consider  a  single  row  of  particles, 
which  when  at  rest  occupy  a  line  parallel  to  the  axis  of  the  cylinder,  for 
instance,  those  along  AH'^  (fig.  209),  we  shall  find  they  will  have  respectively 
at  the  same  instant  all  the  various  velocities  which  the  piston  has  had  suc- 
cessively while  oscillating  from  A  to  a  and  back  to  A.  So  that  if  in  fig.  38 
AH'  represents  the  length  of  one  undulation,  the  curved  line  H'PQA  will 
represent  the  various  velocities  which  all  the  points  in  the  line  AH'  have 
sinmltancously  :  for  instance,  at  the  instant  the  piston  has  returned  to  A, 
the  particle  at  M  will  be  moving  to  the  right  with  a  velocity  represented  by 
QM,  the  particle  at  N  will  be  moving  to  the  left  with  a  velocity  represented 
by  PN,  and  so  on  of  the  other  particles. 

When  an  undulatory  motion  is  transmitted  through  a  medium,  the 
motions  of  any  two  particles  are  said  to  be  in  the  smne  phase  when  those 
particles  move  with  equal  velocities  in  the  same  direction  ;  the  motions  are 
said  to  be  in  opposite  phases  \i\i'exv  the  particles  move  with  the  same  velocities 
in  opposite  directions.  It  is  plain  from  an  inspection  of  fig.  38  that  when 
any  two  particles  are  separated  by  a  distance  equal  to  half  an  undulation, 
their  motions  are  always  in  opposite  phases,  but  if  their  distance  equals  the 
length  of  a  complete  undulation  their  motions  are  in  the  same  phase.  A 
little  consideration  will  show  that  in  the  condensed  wave  the  condensation 
will  be  gi^eatest  at  the  middle  of  the  wave,  and  likewise  that  the  expanded 
wave  will  be  most  rarefied  at  its  middle. 

It  is  an  easy  transition  from  the  explanation  of  the  motion  of  sound- 
waves in  a  cylinder  to  that  of  their  motion  in  an  unenclosed  medium.  It  is 
simply  necessary  to  apply  in  all  directions,  to  each  molecule  of  the  vibrating 
body,  what  has  been  said  about  a  piston  movable  in  a  tube.  A  series  of 
spherical  waves  alternately  condensed  and  rarefied  is  produced  around  each 
centre  of  disturbance.  As  these  waves  are  contained  within  two  concentrical 
spherical  surfaces,  whose  radii  gradually  increase,  while  the  length  of  the 
undulation  remains  the  same,  their  mass  increases  with  the  distance  from 
the  centre  of  disturbance,  so  that  the  amplitude  of  the  vibration  of  the  mole- 
cules gradually  lessens,  and  the  intensity  of  the  sound  diminishes. 

It  is  these  spherical  waves,  alternately  condensed  and  expanded,  which 
in  being  propagated  transmit  sound.  If  many  points  are  disturbed  at  the 
same  time,  a  system  of  waves  is  produced  around  each  point.  But  all  these 
waves  are  transmitted  one  through  the  other  without  modifying  either 
their  lengths  or  their  velocities.  Sometimes  condensed  or  expanded  waves 
coincide  with  others  of  the  same  nature  to  produce  an  effect  equal  to  their 
sum  ;  sometimes  they  meet  and  produce  an  effect  equal  to  their  difference. 
If  the  surface  of  still  water  is  disturbed  at  two  or  more  points,  the  co-exist- 
ence of  waves  becomes  sensible  to  the  eye. 

226.  Causes  which  influence  the  intensity  of  sound. — Many  causes 
modify  the  force  or  the  intensity  of  sound.  These  are  the  distance  of  the 
sounding  body,  the  amplitude  of  the  vibrations,  the  density  of  the  air  at  the 
place  where  the  sound  is  produced,  the  direction  of  the  currents  of  air,  and, 
lastly,  the  neighbourhood  of  other  sounding  bodies. 

i.  The  i/iteftsity  of  souftd  is  inversely  as  the  square  of  the  distance  of  the 
sonorous  body  from  the  ear.  This  law  has  been  deduced  by  calculation,  but 
it  may  be  also  demonstrated  experimentally.    Let  us  suppose  several  sounds 


-227J  Apparatus  to  Strengthen  Sound.  203 

of  equal  intensity — for  instance,  bells  of  the  same  kind,  struck  by  hammers 
of  the  same  weight,  falling  from  equal  heights.  If  four  of  these  bells  are 
placed  at  a  distance  of  20  yards  from  the  ear,  and  one  at  a  distance  of  10 
yards,  it  is  found  that  the  single  bell  produces  a  sound  of  the  same  intensity 
as  the  four  bells  struck  simultaneously.  Consequently,  for  double  the  dis- 
tance the  intensity  of  the  sound  is  only  one-fourth.  A  method  of  com- 
paring the  intensities  of  different  sounds  will  be  described  afterwards  (289). 
The  distance  at  which  sounds  can  be  heard  depends  on  their  intensity. 
The  report  of  a  volcano  at  St.  Vincent  was  heard  at  Demerara,  300  miles 
off,  and  the  firing  at  Waterloo  was  heard  at  Dover. 

ii.  The  intenstiy  of  the  soundiiicreases  with  the  amplitude  of  the  vibrations 
of  the  so?toroiis  body.  The  connection  between  the  intensity  of  the  sound 
and  the  amplitude  of  the  vibrations  is  readily  observed  by  means  of  vibrating 
cords.  For,  if  the  cords  are  somewhat  long,  the  oscillations  are  perceptible 
to  the  eye,  and  it  is  seen  that  the  sound  is  feebler  in  proportion  as  the  am- 
plitude of  the  oscillations  decreases. 

iii.  The  i?itensity  of  sound  depe7tds  on  the  density  of  the  air  in  the  place  in 
which  it  is  produced.  As  we  have  already  seen  (222),  when  an  alarum  moved 
by  clockwork  is  placed  under  the  bell-jar  of  an  air-pump,  the  sound  becomes 
weaker  in  proportion  as  the  air  is  rarefied. 

In  hydrogen,  which  is  about  ^i  ^^  density  of  air,  sounds  are  much 
feebler,  although  the  pressure  is  the  same.  In  carbonic  acid,  on  the  con- 
trary, whose  density  is  i"529,  sounds  are  more  intense.  On  high  mountams, 
where  the  air  is  much  rarefied,  it  is  necessary  to  speak  with  some  effort  in 
order  to  be  heard,  and  the  discharge  of  a  gun  produces  only  a  feeble  sound. 
The  ticking  of  a  watch  is  heard  in  water  at  a  distance  of  23  feet,  in  oil  of  16^, 
in  alcohol  of  13,  and  in  air  of  only  10  feet. 

iv.  The  inte/tsity  of  sound  is  modified  by  the  motion  of  the  atmosphere 
and  the  directio/t  of  the  wind.  In  calm  weather  sound  is  always  better 
propagated  than  when  there  is  wind  ;  in  the  latter  case,  for  an  equal  distance, 
sound  is  more  intense  in  the  direction  of  the  wind  than  in  the  contrary 
direction. 

V.  Lastly,  sound  is  strengthened  by  the  neighbourhood  of  a  sonorous  body. 
A  string  made  to  vibrate  in  free  air  has  but  a  very  feeble  sound  ;  but  when  it 
vibrates  above  a  sounding-box,  as  in  the  case  of  the  violin,  guitar,  or  violon- 
cello, its  sound  is  much  stronger.  This  arises  from  the  fact  that  the  box  and 
the  air  which  it  contains  vibrate  in  unison  with  the  string.  Hence  the  use  of 
sounding-boxes  in  stringed  instruments. 

Attempts  have  been  made  to  get  a  measure  of  the  loudness  of  sound 
which  should  serve  as  a  standard,  by  allowing  leaden  pellets  to  fall  from 
various  heights  on  an  iron  plate  of  some  size.  It  appears  that  within 
certain  limits  the  loudness  is  nearly  proportional  to  the  square  root  of  the 
height  from  which  the  pellet  falls,  and  not  to  the  height  itself.  It  thus 
appears  that  only  a  portion  of  the  energy  of  the  falling  body  is  expended  in 
producing  vibrations  of  the  plate. 

227.  Apparatus  to  strengthen  sound. — The  apparatus  represented  in 
fig.  210  was  used  by  Savart  to  show  the  influence  of  boxes  in  strengthening 
sound.  It  consists  of  a  hemispherical  brass  vessel,  A,  which  is  set  in  vibra- 
tion by  means  of  a  violin  bow.     Near  it  there  is  a  hollow  cardboard  cylinder 


204 


On  Sound. 


[227- 


B,  closed  at  the  further  end.  By  means  of  a  handle  this  cylinder  can  be  turned 
on  its  support,  so  as  to  be  inclined  at  any  given  degree  towards  the  vessel. 
The  cylinder  is  fixed  on  a  slide  C,  by  which  means  it  can  be  placed  at  any 
distance  from  A.  When  the  vessel  is  made  to  vibrate,  the  strengthening  of 
the  sound  is  very  remarkable.     But  the  sound  loses  almost  all  its  intensity  if 

the  cylinder  is  turned 
away,  and  it  becomes 
gradually  weaker  when 
the  cylinder  is  removed  to 
a  greater  distance,  show- 
ing that  the  strengthen- 
ing is  due  to  the  vi- 
bration of  the  air  in  the 
cylinder. 

The  cylinder  B  is 
made  to  vibrate  in  unison 
with  the  bi^ass  vessel  by 
adjusting  it  to  a  certain 
depth,  which  is  effected 
by  making  one  part  slide 
into  the  other. 

Vitruvius    states  that, 
in    the    theatres    of    the 
ancients,   resonant   brass 
^'S-  210-  vessels    were    placed    to 

strengthen  the  \-oices  of  the  actors. 

228.  Influence  of  tubes  on  the  transmission  of  sound. — The  law 
that  the  intensity  of  sound  decreases  in  proportion  to  the  square  of  the 
distance  does  not  apply  to  the  case  of  tubes,  especially  if  they  are  straight 
and  cylindrical.  The  sound-waves  in  that  case  are  not  propagated  in  the 
form  of  increasing  concentrical  spheres,  and  sound  can  be  transmitted  to  a 
great  distance  without  any  perceptible  alteration.  Biot  found  that  in  one 
of  the  Paris  water-pipes,  1,040  yards  long,  the  voice  lost  so  little  of  its  inten- 
sity that  a  conversation  could  be  kept  up  at  the  ends  of  a  tube  in  a  very  low 
tone.  The  weakening  of  sound  becomes,  however,  perceptible  in  tubes  of 
large  diameter,  or  where  the  sides  are  rough.  This  property  of  transmitting  • 
sounds  was  first  used  in  England  for  speaking  tubes.  They  consist  of  caout- 
chouc or  metal  tubes  of  small  diameter  passing  from  one  room  to  another. 
If  a  person  speaks  at  one  end  of  the  tube,  he  is  distinctly  heard  by  a  person 
with  his  ear  at  the  other  end. 

From  Biot's  experiments  it  is  evident  that  a  communication  might  be 
made  between  two  towns  by  means  of  speaking  tubes.  The  velocity  of 
sound  is  1,125  feet  in  a  second  at  i6°-6  C,  so  that  a  distance  of  50  miles 
would  be  traversed  in  four  minutes. 

229.  Reg-nault's  experiments.— Theoretically,  a  sound-wave  should  be 
propagated  in  a  straight  cylindrical  tube  with  a  constant  intensity.  Regnault 
found,  however,  that  in  these  circumstances  the  intensity  of  sound  gradually 
diminishes  with  the  distance,  and  that  the  distance  at  which  it  ceases  to  be 
audible  is  nearly  proportional  to  the  diameter  of  the  tube. 


-230]  Velocity  of  Sound  in  Air.  205 

He  produced  sound-waves  of  equal  strength  by  means  of  a  small  pistol 
charged  with  a  gramme  of  powder,  and  fired  at  the  open  ends  of  tubes  of 
various  diameters  ;  and  he  then  ascertained  the  distance  at  which  the  sound 
could  no  longer  be  heard,  or  at  which  it  ceased  to  act  on  what  he  calls  a 
sensitive  membrane.  This  was  a  very  flexible  membrane  which  could  be 
fixed  across  the  tube  at  various  distances,  and  was  provided  with  a  small 
metal  disc  in  its  centre.  When  the  membrane  began  to  vibrate,  this  disc 
struck  against  a  metallic  contact,  and  thereby  closed  a  voltaic  circuit,  which 
traced  on  a  chronograph  the  exact  moment  at  which  the  membrane  received 
the  sound-wave. 

Experimenting  in  this  manner,  Regnault  found  that  the  report  of  a  pistol 
charged  as  stated  is  no  longer  audible  at  a  distance  of 

1,159  metres  in  a  tube  of o™- 108  diameter 

3,810         „  ,,  o'"-3oo       „ 

9,540         ,,  „  .....     i™-ioo        „ 

These  numbers  represent  the  limit  of  distance  at  which  the  sound-wave 
is  no  longer  heard,  but  it  still  acts  on  the  membrane  at  the  distances  of 
4,156,  11,430,  and  19,851  metres  respectively. 

According  to  Regnault  the  principal  cause  of  this  diminution  of  intensity 
is  the  loss  of  7//^  7/zV(^  against  the  sides  of  the  tube:  he  found  also  that  sounds 
of  high  pitch  are  propagated  in  tubes  less  easily  than  those  of  low  ones;  a 
bass  would  be  heard  at  a  greater  distance  than  a  treble  voice. 

230.  Velocity  of  sound  In  air. — Since  the  propagation  of  sound-waves 
is  gradual,  sound  requires  a  certain  time  for  its  transmission  from  one  place 
to  another,  as  is  seen  in  numerous  phenomena.  For  example,  the  sound 
of  thunder  is  only  heard  some  time  after  the  flash  of  lightning  has  been  seen, 
although  both  the  sound  and  the  light  are  produced  simultaneously;  and  in  like 
manner  we  see  a  mason  in  the  act  of  striking  a  stone  before  hearing  the  sound. 

The  velocity  of  sound  in  air  has  often  been  the  subject  of  experimental 
determination.  The  most  accurate  of  the  direct  measurements  was  made 
by  Moll  and  Van  Beck  in  1823.  Two  hills,  near  Amsterdam,  Kooltjesberg 
and  Zevenboomen,  were  chosen  as  stations  :  their  distance  from  each  other 
as  determined  trigonometrically  was  57,971  feet,  or  nearly  eleven  miles. 
Cannons  were  fired  at  stated  intervals  simultaneously  at  each  station,  and  the 
time  which  elapsed  between  seeing  the  flash  and  hearing  the  sound  was 
noted  by  chronometers.  This  time  could  be  taken  as  that  which  the  sound 
required  to  travel  between  the  two  stations;  for  it  will  be  subsequently  seen 
that  light  takes  an  inappreciable  time  to  traverse  the  above  distance.  In- 
troducing corrections  for  the  barometric  pressure,  temperature,  and  hygro- 
metric  state,  and  eliminating  the  influence  of  the  wind,  Moll  and  Van  Beck's 
results  as  recalculated  by  Schroder  van  der  Kolk  give  1,09278  feet  as  the 
velocity  of  sound  in  one  second  in  dry  air  at  0°  C.  and  under  a  pressure  of 
760  mm.  Kendall,  in  a  North  Pole  expedition,  found  that  the  velocity  of 
sound  at  a  temperature  of  -40°  was  314  metres. 

The  velocity  of  sound  at  zero  may  be  taken  at  1,093  feet,  or  2>'i'})  metres. 
This  velocity  increases  with  the  increase  of  temperature;  it  may  be  calcu- 
lated for  a  temperature  t°  from  the  formula 

7/=  1,093  v'  (i  +  0-003665/) 


2o6  On  Sound.  [230- 

where  1,093  is  the  velocity  in  feet  at  0°  C,  and  0-003665  the  coefficient  of  ex- 
pansion for  1°  C.  This  amounts  to  an  increase  of  nearly  two  feet  for  every 
degree  Centigrade.  For  the  same  temperature  it  is  independent  of  the  density 
of  the  air,  and  consequently  of  the  pressure.  It  is  the  same  for  the  same 
temperature  with  all  sounds,  whether  they  be  strong  or  weak,  deep  or  acute. 
Biot  found,  in  his  experiments  on  the  conductivity  of  sound  in  tubes,  that 
when  a  well-known  air  was  played  on  a  flute  at  one  end  of  a  tube  1,040  yards 
long,  it  was  heard  without  alteration  at  the  other  end,  from  which  he  con- 
cluded that  the  velocity  of  cHfFerent  sounds  is  the  same.  For  the  same 
reason  the  tune  played  by  a  band  is  heard  at  a  great  distance  without  altera- 
tion, except  in  intensity,  which  could  not  be  the  case  if  some  sounds  travelled 
more  rapidly  than  others. 

This  cannot,  however,  be  admitted  as  universally  true.  Earnshaw,  by  a 
mathematical  investigation  of  the  laws  of  the  propagation  of  sound,  concludes 
that  the  velocity  of  a  sound  depends  on  its  strength  ;  and,  accordingly,  that 
a  violent  sound  ought  to  be  propagated  with  greater  velocity  than  a  gentler 
one.  This  conclusion  is  confirmed  by  an  observation  made  by  Captain 
Parry  on  his  Arctic  expedition.  During  artillery  practice  it  was  found,  by 
persons  stationed  at  a  considerable  distance  from  the  guns,  that  the  report 
of  the  cannon  was  heard  before  the  command  to  fire  given  by  the  officer.  And 
more  recently,  Mallet  made  a  series  of  experiments  on  the  velocity  with  which 
sound  is  propagated  in  rocks,  by  observing  the  times  which  elapsed  before 
blastings,  made  at  Holyhead,  were  heard  at  a  distance.  He  found  that  the 
larger  the  charge  of  gunpowder,  and  therefore  the  louder  the  report,  the  more 
rapid  was  the  transmission.  With  a  charge  of  2,000  pounds  of  gunpowder 
the  velocity  was  967  feet  in  a  second,  while  with  a  charge  of  12,000  it  was 
1,210  feet  in  the  same  time. 

Jacques  made  a  series  of  experiments  by  firing  different  weights  of  pow- 
der from  a  cannon,  and  observing  the  velocity  of  the  report  at  different 
distances  from  the  gun  by  means  of  an  electrical  arrangement.  He  thus 
found  that,  nearest  the  gun,  the  velocity  is  least,  increasing  to  a  certain 
maximum  which  is  considerably  greater  than  the  average  velocity.  The 
velocity  is  also  greater  with  the  heavier  charge.  Thus  with  a  charge  of 
\\  pound  the  velocity  was  1,187,  and  with  a  charge  of  ^  pound  it  was  1,032 
at  a  distance  of  from  30  to  50  feet  ;  while  at  a  distance  of  70  to  80  it  was  1,267 
and  1,120  ;  and  at  90  to  100  feet  it  was  1,262  and  1,1 14  respectively. 

Bravais  and  Martins  found,  in  1844,  that  sound  travelled  with  the  same 
velocity  from  the  base  to  the  summit  of  the  Faulhorn,  as  from  the  summit  to 
the  base. 

231.  Calculation  of  the  velocity  of  sound  in  grases. — From  theoretical 
considerations  Newton  gave  a  rule  for  calculating  the  velocity  of  sound  in 
gases,  which  may  be  represented  by  the  formula 


VS 


in  which  v  represents  the  velocity  of  the  sound,  or  the  distance  it  travels  in 
a  second,  e  the  elasticity  of  the  gas,  and  rt'its  density. 

This  formula  expresses  that  the  velocity  of  the  propagation  of  sound  in 
gases  is  directly  as  the  square  root  of  the  elasticity  of  the  gas,  and  inversely 


-231]       Calculation  of  the    Velocity  of  Sound  in   Gases.         207 

as  the  square  root  of  its  density.  It  follows  that  the  velocity  of  sound  is  the 
same  under  any  pressure  ;  for  although  the  elasticity  increases  with  increased 
pressure,  according  to  Boyle's  law,  the  density  increases  in  the  same  ratio. 
At  Quito,  where  the  mean  pressure  is  only  2r8  inches,  the  velocity  is  the 
same  as  at  the  sea-level,  provided  the  temperature  is  the  same. 

Now  the  measure  of  the  elasticity  of  a  gas  is  the  pressure  to  which  it  is 
subjected  ;  hence,  if  g  be  the  force  of  gravity,  h  the  barometric  height 
reduced  to  the  temperature  zero,  and  8  the  density  of  mercury,  also  at  zero, 
then  for  a  gas  under  the  standard  atmospheric  pressure  and  for  zero,  e  =ghh  : 
Newton's  formula  accordingly  becomes 


^-f"" 


d 

Now,  if  we  suppose  the  temperature  of  a  gas  to  increase  from  0°  to  /°,  its. 
volume  will  increase  from  unity,  at  zero,  to  \  +  at  at  /,  a  being  the  coefficient 
of  expansion  of  the  gas.  But  the  density  varies  inversely  as  the  volume, 
therefore  d  becomes  d-^{\  +  at).     Hence 

Substituting  in  this  formula  the  values  in  centimetres  and  grammes, 
^  =  981,  A  =  76,  ^=0-001293,  we  get  for  the  value  v  a  number  29,795  centi- 
metres =297-95  metres,  which  is  about  one-sixth  less  than  the  experimental 
result.  Laplace  assigned  as  a  reason  for  this  discrepancy  the  heat  produced 
by  pressure  in  the  condensed  waves  ;  and,  by  considerations  based  on  this 
idea,  Poisson   and  Biot  found  that    Newton's  formula  ought  to  be  written, 

V  =  f^jSl-ii^at)-/,  <:  being  the  specific  heat  of  the  gas  for  a  constant 
pressure,  and  c'  its  specific  heat  for  a  constant  volume  (460).  The  average 
value  of  the  constant  -  is  1-41,  and  if  the  formula  be  modified  by  the  intro- 
duction of  the  value  ^i-i\\  or  1-1875  the  calculated  numbers  agree  with  the 
experimental  results. 

The  physical  reason  for  introducing  the  constant  x/-  into    the  ecpation 

for  the  velocity  of  sound  may  be  understood  from  the  following  considera- 
tions : — We  have  already  seen  (225)  that  sound  is  propagated  in  air  by  a 
series  of  alternate  condensations  and  rarefactions  of  the  layers.  At  each 
condensation  heat  is  evolved,  and  this  heat  increases  the  elasticity,  and  thus 
the  rapidity  with  which  each  condensed  layer  acts  on  the  next  ;  but  in  the 
rarefaction  of  each  layer  the  same  amount  of  heat  disappears  as  was  deve- 
loped by  the  condensation,  and  its  elasticity  is  diminished  by  the  cooling. 
The  effect  of  this  diminished  elasticity  of  the  cooled  layer  is  the  same  as  if 
the  elasticity  of  an  adjacent  wave  had  been  increased,  and  the  rapidity  with 
which  this  latter  would  expand  upon  the  dilated  wave  would  be  greater. 
Thus,  while  the  average  temperature  of  the  air  is  unaltered,  both  the  heating 
which  increases  the  elasticity,  and  the  chilling  which  diminishes  it,  concur 
in  increasing  the  velocity. 

Knowing  the  velocity  of  sound,  we  can  calculate  approximately  the  dis- 
tance at  which  it  is  produced.     Light  travels  with  such  velocity  that  the 


2o8  On  Sound.  [231- 

rtash  or  the  smoke  accompanying  the  report  of  a  gun  may  be  considered  to 
be  seen  simultaneously  with  the  occurrence  of  the  explosion.  Counting 
then  the  number  of  seconds  which  elapse  between  seeing  the  flash  and 
hearing  the  sound,  and  multiplying  this  number  by  1,125,  we  get  the  distance 
in  feet  at  which  the  gun  is  discharged.  In  the  same  way  the  distance  of 
thunder  may  be  estimated. 

232.  Velocity  of  sound  in  various  gases.— Approximately  the  same 
results  have  been  ol-»tainetl  for  the  \elocity  of  sound  in  air  by  another  method, 
by  wliich  the  velocity  in  other  gases  could  be  determined.  As  the  wave- 
length A  is  the  distance  which  sound  travels  during  the  time  of  one  oscillation, 

that  is,  -  of  a  second,  the  velocity  of  sound  or  the  distance  traversed  in  a 

n 
second  is  v  =  /iK.  Now  the  length  of  an  open  pipe  is  half  the  wave-length 
of  the  fundamental  note  of  that  pipe  ;  and  that  of  a  closed  pipe  is  a  quarter 
of  the  wave-length  (275).  Hence,  if  we  know  the  number  of  vibrations  of 
the  note  emitted  by  any  particular  pipe,  which  can  be  easily  ascertained  by 
means  of  a  sirene,  and  we  know  the  length  of  this  pipe,  -we  can  calculate  v. 
Taking  the  temperature  into  account,  Wertheim  found  in  this  way  1,086  feet 
for  the  velocity  of  sound  in  air  at  zero. 

Further,  since  in  different  gases  which  have  the  same  elasticity,  but  differ 
in  density,  the  velocity  of  sound  varies  inversely  as  the  square  root  of  the 
density,  knowing  the  velocity  of  sound  in  air,  we  may  calculate  it  for  other 
gases;  thus  in  hydrogen  it  will  be 

/'°^A^Q  =4168  feet. 
\/o-o6S8 

This  number  cannot  be  universally  accurate,  for  the  coefficient    ,  differs 

somewhat  in  different  gases.  And  when  pipes  were  sounded  with  different 
gases,  and  the  number  of  vibrations  of  the  notes  multiplied  with  twice  the 
length  of  the  pipe,  numbers  were  obtained  which  differed  from  those  cal- 
culated by  the  above  formula.     \Mien,  however,  the  calculation  was  made 

introducing  for  each  gas  its  special  value  of    ,,  the  theoretical  results  agreed 

very  well  with  the  observed  ones. 

By  the  above  method  the  following  values  hax^e  been  obtained : — 

Chlorine 677  feet  in  a  second. 

Carbonic  acid 856  „ 

Oxygen 1040  „ 

Air 1093  „ 

Carbonic  oxide       ......  1106  ,, 

Hydrogen 4163  „ 

Zjj-  Boppler's  principle. — When  a  sounding  body  approaches  the  car, 
the  tone  percei^■ed  is  somewhat  higher  than  the  true  one  ;  but  if  the  source 
of  sound  recedes  from  the  ear,  the  tone  perceived  is  lower.  The  truth  of 
this,  which  is  known  as  Doppler's  principle^  will  be  apparent  from  the  follow- 
ing considerations  : — When  the  source  of  sound  and  the  ear  are  at  rest,  the 
ear  receives  n  waves  in  a  second;  but  if  the  ear  approaches  the  sound,  or 
the  sound  approaches  the  ear,  it  receives  more;  just  as  a  ship  meets  more 


-234]  Velocity  of  Sound  in  Liquids.  209 

waves  when  it  ploughs  through  them  than  if  it  is  at  rest.  Conversely,  the  ear 
receives  a  smaller  number  when  it  recedes  from  the  source  of  sound.  The 
effect  in  the  first  case  is  as  if  the  sounding  body  emitted  more  vibrations  in 
a  second  than  it  really  does,  and  in  the  second  case  fewer.  Hence  in  the 
first  case  the  note  appears  higher  ;  in  the  second  case  lower. 

If  the  distance  which  the  ear  traverses  in  a  second  towards  the  source  of 
sound  (supposed  to  be  stationary)  is  s  feet,  and  the  wave-length  of  the  par- 
ticular tone  is  X  feet,  then  there  are  -  waves  in  a  second  :  or  also  — ,  for 

A  c 

\  =  ^,  where  c  is  the  velocity  of  sound  (230).     Hence  the  ear  receives  not 
n 

only  the  ;/  original  waves,  but  also  —  in  addition.     Therefore  the  number 

c 

of  vibrations  which  the  ear  actually  receives  is 

,  ns  ,  S-. 

?i'  =  n  +  -  ~  =  ?t  {i  +     ) 

for  an  ear  which  approaches  a  tone  ;  and  by  similar  reasoning  it  is 

n    =  n  -         =  «  ( I ) 

for  an  ear  receding  from  a  tone. 

To  test  Dopplei^s  theory  Buys  Ballot  stationed  trumpeters  on  the  Utrecht 
railways  and  also  upon  locomotives,  and  had  the  height  of  the  approaching- 
or  receding  tones  compared  with  stationaiy  ones  by  musicians.  He  thus 
found  both  the  principle  and  the  formula  fully  confirmed.  Similar  conclu- 
sive experiments  were  made  by  Scott  Russell  on  English  railways.  The 
observation  may  often  be  made  as  a  fast  train  passes  a  station  in  which 
an  electrical  alarum  is  sounding.  Independently  of  the  difference  in  loud- 
ness, an  attentive  ear  can  detect  a  difference  in  pitch  on  approaching,  or  on 
leaving  the  station.  A  speed  of  about  40  miles  an  hour  sharpens  the  note 
of  the  whistle  of  an  approaching  train  by  a  semitone,  and  tlattens  it  to  that 
extent  as  the  train  recedes. 

Dopplefs  principle  may  also  be  established  by  direct  laboratory  ex- 
periments. Rollmann  fixed  a  long  rod  on  a  turning  machine,  at  the  end 
of  which  was  a  large  glass  bulb  with  a  slit  in  it,  which  sounded  like  a 
humming-top  when  a  tangential  current  of  air  was  blown  against  the  slit. 
The  uniform  and  sufficiently  rapid  rotation  of  the  sphere  developed  such 
a  current,  and  produced  a  steady  note,  the  pitch  of  which  was  higher  or 
lower  in  each  rotation  according  as  the  bulb  came  nearer,  or  receded  from, 
the  observer. 

The  principle  may  also  be  illustrated  by  means  of  a  tuning-fork  with  wide 
branches,  and  producing  a  very  high  note  of  2046  vibrations.  When  this  is 
loudly  sounded,  and,  being  held  in  front  of  a  smooth  wall,  is  moved  towards  it 
with  a  velocity  of  a  metre  in  a  second,  the  direct  note  and  that  reflected 
from  the  wall  undergo  opposite  changes,  so  that  an  obsen-er  hears  distinctly 
twelve  beats  in  a  second  (262). 

234.  Velocity  of  sound  in  liquids. — ^The  velocity  of  sound  in  water 
was   experimentally  determined    in    1827  by  CoUadon   and   Sturm.     They 

P 


2IO  On   Sound.  [234- 

moored  two  boats  at  a  known  distance  in  the  Lake  of  Geneva.  The  first 
supported  a  bell  immersed  in  water,  and  a  bent  lever  provided  at  one  end 
with  a  hammer  which  struck  the  bell,  and  at  the  other  with  a  lighted  wick,  so 
arranged  that  it  ignited  some  powder  the  moment  the  hammer  struck  the 
bell.  To  the  second  boat  was  affixed  an  ear-trumpet,  the  bell  of  which  was 
in  water,  while  the  mouth  was  applied  to  the  ear  of  the  observer,  so  that  he 
could  measure  the  time  between  the  flash  of  light  and  the  arrival  of  sound  by 
the  water.  By  this  method  the  velocity  was  found  to  be  4,708  feet  in  a  second 
at  the  temperature  8°-i,  or  four  times  as  great  as  in  air. 

The  velocity  of  sound,  which  is  different  in  different  liquids,  can  be  cal- 
culated by  a  formula  analogous  to  that  given  above  (230)  as  applicable  to 

gases,  that  is,  ^'  =  \/^—,  >  'i^  which  ^,  /?,  and  8  have  their  previous  signi- 
ficance ;  while  ^  is  the  coefficient  of  the  compressibility  for  the  liquid  in  ques- 
tion (97),  that  is,  its  diminution  in  volume  by  a  pressure  of  one  atmosphere — 
and  ^^s  the  density.  In  this  way  were  obtained  the  numbers  given  in  the 
following  table.  As  in  the  case  of  gases,  the  velocity  varies  with  the  tem- 
perature, which  is  therefore  appended  in  each  case. 


River  water  (Seine) 

.     13°  c. 

=    4714: 

feet 

in  a  second. 

Artificial  sea-water 

•     30 

.     20 

=    5013 
-    4761 

Mercury 

Solution  of  common 

salt 

10 
.      18 

=    4866 
=    5132 

Absolute  alcohol     . 

•     23 

=    3854 

Turpentine     . 
Ether     . 

•     24 

=    3976 
=    3801 

It  will  be  seen  how  close  is  the  agreement  between  the  two  values  for 
the  velocity  of  sound  in  water,  the  only  case  in  which  they  have  been 
directly  compared.  There  is  considerable  uncertainty  about  the  values  for 
other  liquids,  owing  to  the  doubt  as  to  the  values  for  their  compressibility. 

235.  Velocity  of  sound  in  solids. — As  a  general  rule,  the  elasticity  of 
solids,  as  compared  with  the  density,  is  greater  than  that  of  liquids,  and 
consequently  the  propagation  of  sound  is  more  rapid. 

The  difference  is  well  seen  in  an  experiment  by  Biot,  who  found  that  when 
a  bell  was  struck  by  a  hammer,  at  one  end  of  an  iron  tube  3,120  feet  long, 
two  sounds  were  distinctly  heard  at  the  other  end.  The  first  of  these  was 
transmitted  by  the  tube  itself  with  a  velocity  x  ;  and  the  second  by  the  en- 
closed air  with  a  known  velocity  a.  The  mterval  between  the  sounds  was 
2-5  seconds.     The  value  of  x  obtained  from  the  equation 

3120_3120^^ 

a  X 

shows  that  the  velocity  of  sound  in  the  tube  is  nearly  9  times  as  great  as  that 
in  air. 

That  the  report  of  the  firing  of  cannon  is  heard  at  far  greater  distances 
than  peals  of  thunder,  is  doubtless  owing  to  the  fact  that  the  sound  in  the 
former  case  is  mainly  transmitted  through  the  earth. 

To  this  class  of  phenomena  belongs  the  fact  that  if  the  ear  is  held  against 


-235]  Velocity  of  Sound  in  Solids.  211 

a  rock  in  which  a  blasting  is  being  made  at  a  distance,  two  distinct  reports 
are  heard — one  transmitted  through  the  rock  to  the  ear,  and  the  other  trans- 
mitted through  the  air.  The  conductivity  of  sound  in  sohds  is  also  well 
illustrated  by  the  fact  that  in  manufacturing  telegraph  wires  the  filing  at  any 
particular  part  can  be  heard  at  distances  of  miles  by  placing  one  end  of  the 
wire  in  the  ear.     The  toy  telephone  also  is  based  on  this  fact. 

The  velocity  of  sound  in  wires  has  also  been  determined  theoretically 

by  Wertheim  and  others,  by  the  formula  v  =  a /^  in  which  /x  is  the  modulus 

of  elasticity  (89),  while  d  is  the  mass  in  unit  volume,  which  is  equal  to  the 

specific  gravity,  or  the  weight  of  unit  volume  divided  by  the  acceleration  of 

s 
gravity,  or     . 

This  may  be  illustrated  from  a  determination  by  Wertheim  of  the  velocity 
of  sound  in  a  specimen  of  annealed  steel  wire,  the  specific  gravity  ^  of  which 
was  7'63i  and  its  modulus  21,000  (88).  That  is,  a  weight  of  21,000  kilo- 
grammes would  double  the  unit  length  of  a  wire  i  sq.  mm.  in  cross  section,  if 
this  were  possible  without  exceeding  the  limit  of  elasticity.  This  is  equal  to 
2,100,000,000,  or  21  X  10®,  grammes  on  a  wire  i  sq.  cm.  in  cross  section. 
Hence 


/2 1 00000000  X  98 1  o 

^'=  V ;763-~-=  519581  cm. 


17047  feet. 


The  following  table  gives  the  velocity  in  various  bodies,  expressed  in  feet 
per  second,  mostly  from  the  experimental  determinations  of  Wertheim  and 
Stefan : — 


Caoutchouc      .         .       100  to  200 

Oak    . 

12622 

Tallow     . 

1 180 

Cedar. 

13120 

Wax 

2394 

Elm    . 

13516 

Paraffine 

4250 

Ash     . 

15314 

Lead        . 

4653 

Fir      . 

15316 

Gold 

7021 

Walnut 

15744 

Silver       . 

8806 

Glass  . 

16057 

Pine 

10900 

Steel  wire  . 

16336 

Copper    . 

1 2 194 

Wrought  ire 

nanc 

istee 

1    16498 

The  numbers  for  caoutchouc  are  of  the  same  order  of  magnitude  as  those 
for  the  propagation  of  a  nervous  impulse,  and  suggest  that  this  impulse  is 
transmitted  by  longitudinal  vibrations  like  those  of  sound. 

In  the  case  of  wood  these  velocities  are  in  the  directions  of  the  fibres, 
and  are  considerably  greater  than  across  the  rings  or  along  the  rings  ;  thus 
with  fir  the  velocities  are  4382  and  2572  for  these  directions  respectively. 

From  a  recent  determination  of  the  elasticity  of  ice,  Trowbridge  and 
Macrae  have  deduced  the  velocity  of  sound  in  it  to  be  9,600  feet  per  second, 
2,900  metres  or  about  9  times  that  of  air. 

Mallet  investigated  the  velocity  of  the  transmission  of  sound  in  various 
rocks,  and  found  that  it  is  as  follows  : — 

p  2 


212 


Ofi  Sound. 


[235- 


Wet  sand  ...... 

Contorted,  stratified  quartz  and  slate  rock 
Discontinuous  granite      .... 

Solid  g-ranite 


825  feet  in  a  second. 
1088 

1306  „ 

1664 


A  direct  experimental  method  of  determining  the  velocity  of  sound  in 
solids,  gases,  and  vapours  will  be  described  subsequently  (277). 

If  a  medium  through  which  sound  passes  is  heterogeneous,  the  waves  of 
sound  are  reflected  on  the  different  surfaces,  and  the  sound  becomes  rapidly 
enfeebled.  Thus  a  soft  earth  conducts  sound  badly,  while  a  hard  ground 
which  forms  a  compact  mass  conducts  it  well.  So  also  we  hear  badly 
through  air  spaces  which  are  filled  with  porous  materials,  such  as  shavings, 
sawdust,  cinders,  and  the  like. 

236.  Reflection  of  sound. — So  long  as  sound-waves  are  not  obstructed 
in  their  motion  they  are  propagated  in  the  form  of  concentric  spheres  ;  but, 
when  they  meet  with  an  olDstacle,  they  follow  the  general  law  of  elastic 
bodies  ;  that  is,  they  return  upon  themselves,  forming  new  concentric  waves, 
which  seem  to  emanate  from  a  second  centre  on  the  other  side  of  the  obstacle. 
This  phenomenon  constitutes  the  reflection  of  sound. 

Fig.  212  represents  a  series  of  incident  waves  reflected  from  an  obstacle 
PQ.  Taking,  for  example,  the  incident  wave  MCDN,  emitted  from  the 
centre  A,  the  corresponding  reflected  wave  is  represented  by  the  arc  CKD, 
of  a  circle  whose  centre  a  is  as  far  behind  the  obstacle  PQ  as  A  is  before  it. 


If  any  point  C  of  the  reflecting  surface  be  joined  to  the  centre  of  sound, 
and  if  the  perpendicular  CH  be  let  fall  on  the  surface  of  this  body,  the  angle 
ACH  is  called  the  a7igle  of  incidence,  and  the  angle  BCH,  formed  by  the 
prolongation  of  czC,  is  the  angle  of  reflection. 

The  reflection  of  sound  is  subject  to  the  two  following  laws  : — 

I.  The  angle  of  reflection  is  equal  to  the  angle  ofificidence. 

II.  The  incident  sonorous  ray  and  the  reflected  7'ay  are  in  the  same  plane 
perpendicular  to  the  reflecting  surface. 

From  these  laws  it  follows  that  the  wave,  which  in  the  figure  is  propa- 


-237]  Echoes  and  Resonances.  213 

yated  in  the  direction  AC,  takes  the  direction  CB  after  reflection,  so  that  an 
observer  placed  at  B  hears  a  second  sound,  which  appears  to  come  from  C, 
besides  the  sound  proceeding  from  the  point  A. 

The  laws  of  the  reflection  of  sound  are  the  same  as  those  for  light  and 
radiant  heat,  and  may  be  demonstrated  by  similar  experiments.  One  of  the 
simplest  of  these  is  made  with  conjugate  mirrors  (see  chapter  on  Radiant 
Heat)  ;  if  in  the  focus  of  one  of  these  mirrors,  which  should  be  rather  large, 
a  watch  is  placed,  the  ear  placed  in  the  focus  of  the  second  mirror  hears  the 
ticking  very  distinctly  even  when  the  mirrors  are  at  a  distance  of  12  or  13 
yards. 

In  like  manner  the  explosion  of  fulminating  mercury  in  the  focus  of  one 
mirror  causes  that  of  iodide  of  nitrogen  placed  in  that  of  the  other. 

237.  Echoes  and  Resonances. — An  echo  is  the  repetition  of  a  sound  in 
the  air,  caused  by  its  reflection  from  some  obstacle. 

A  very  sharp  quick  sound  can  produce  an  echo  when  the  reflecting 
surface  is  55  feet  distant  ;  but  for  articulate  sounds  at  least  double  that 
distance  is  necessary,  for  it  may  be  easily  shown  that  no  one  can  pronounce 
or  hear  distinctly  more  than  five  syllables  in  a  second.  Now,  as  the  velo- 
city of  sound  at  ordinary  temperatures  maybe  taken  at  1,125  ^^^^  i'^^  second, 
in  a  fifth  of  that  time  sound  would  travel  225  feet.  If  the  reflecting  surface 
is  112-5  feet  distant,  in  going  and  returning  sound  would  travel  through  225 
feet.  The  time  which  elapses  between  the  articulated  and  the  reflected 
sound  would,  therefore,  be  a  fifth  of  a  second,  the  two  sounds  would  not 
interfere,  and  the  reflected  sound  would  be  distinctly  heard.  A  person 
speaking  with  a  loud  voice  in  front  of  a  reflector,  at  a  distance  of  ii2"5  feet, 
can  only  distinguish  the  last  reflected  syllable  :  such  an  echo  is  said  to  be 
vioHosy liable .  If  the  reflector  were  at  a  distance  of  two  or  three  times  112-5 
feet,  the  echo  would  be  dissyllabic^  trisyllabic,  and  so  on. 

When  the  distance  of  the  reflecting  surface  is  less  than  112-5  feet,  the 
direct  and  the  reflected  sound  are  confounded.  They  cannot  be  heard 
separately,  but  the  sound  is  strengthened.  This  is  what  is  often  called 
reso7iance,  and  is  frequently  observed  in  large  rooms.  Bare  walls  and  par- 
ticularly wood  work  are  very  resonant ;  they  reflect  the  sound  and  add  to  it 
the  effect  of  their  own  vibrations,  so  that  the  sound  is  prolonged  and 
enforced.  In  a  large  meeting  room  this  may  considerably  aid  a  speakei-'s 
voice  ;  too  great  resonance,  however,  hindeis  the  distinct  perception  of  the 
words.  Tapestry  and  hangings,  on  the  contrary,  which  are  bad  reflectors, 
deaden  the  sound.  To  control  or  eliminate  the  effects  of  resonance  is  a 
difficult  problem  in  the  acoustics  of  the  building  art. 

Multiple  ecJioes  are  those  which  repeat  the  same  sound  several  times  ; 
this  is  the  case  when  two  opposite  surfaces  (for  example  two  parallel  walls) 
successively  reflect  sound.  There  are  echoes  which  repeat  the  same  sound 
20  or  30  times.  An  echo  in  the  chateau  of  Simonetta,  in  Italy,  repeats  a 
sound  30  times.  At  Woodstock  there  is  one  which  repeats  from  17  to  20 
syllables. 

As  the  laws  of  reflection  of  sound  are  the  same  as  those  of  light  and 
heat,  curved  surfaces  produce  acoustic  foci  like  the  luminous  and  calorific 
foci  produced  by  concave  reflectors.  If  a  person  standing  under  the  arch  of 
a  bridge  speaks  with  his  face  turned  towards  one  of  the  piers,  the  sound  is 


214  On  Sound.  [237- 

reproduced  near  the  other  pier  with  such  distinctness  that  a  conversation 
can  be  kept  up  in  a  low  tone,  which  is  not  heard  by  anyone  standing  in  the 
intermediate  spaces. 

There  is  a  square  room  with  an  elhptical  ceihng,  on  the  ground  floor  of  the 
Conservatoire  des  Arts  et  Metiers,  in  Paris,  which  presents  this  phenomenon 
in  a  remarkable  degree  when  persons  stand  in  the  two  foci  of  the  ellipse. 

Whispering  galleries  are  formed  of  smooth  walls  having  a  continuous 
curved  form.  The  mouth  of  the  speaker  is  presented  at  one  point,  and 
the  ear  of  the  hearer  at  another  and  distant  point.  In  this  case,  the 
sound  is  successively  reflected  from  one  point  to  the  other  until  it  reaches 
the  ear. 

In  the  whispering  gallery  of  St.  Paul's,  the  faintest  sound  is  thus  conveyed 
from  one  side  to  the  other  of  the  dome,  but  it  is  not  heard  at  any  intermediate 
points.  Placing  himself  close  to  the  upper  wall  of  the  Colosseum,  a  circular 
building  130  feet  in  diameter,  Wheatstone  found  a  word  to  be  repeated  a 
great  many  times.  A  single  exclamation  sounded  like  a  peal  of  laughter, 
while  the  tearing  of  a  piece  of  paper  resembled  the  patter  of  hail. 

It  is  not  merely  by  solid  surfaces,  such  as  walls,  rocks,  ships'  sails,  &c., 
that  sound  is  reflected.  It  is  also  reflected  by  clouds,  and  it  has  even  been 
shown  by  direct  experiment  that  a  sound  in  passing  from  a  gas  of  one  density 
into  another  is  reflected  at  the  surface  of  separation  as  it  would  be  against 
a  gas  of  solid  surface.  Now,  different  parts  of  the  earth's  surface  are  un- 
equally heated  by  the  sun,  owing  to  the  shadows  of  trees,  evaporation  of  water, 
and  other  causes,  so  that  in  the  atmosphere  there  are  numerous  ascending  and 
descending  currents  of  air  of  different  density.  Whenever  a  sound-wave 
passes  from  a  medium  of  one  density  into  another  it  undergoes  partial  reflec- 
tion, which,  though  not  strong  enough  to  form  an  echo,  distinctly  weakens 
the  direct  sound.  This  is  doubtless  the  reason,  as  Humboldt  remarked,  why 
sound  travels  further  at  night  than  at  daytime,  even  in  the  South  American 
forests  where  the  animals,  which  are  silent  by  day,  fill  the  atmosphere  at 
night  with  thousands  of  confused  sounds.  To  this  may  be  added  that  at 
night  and  in  repose,  when  other  senses  are  at  rest,  that  of  hearing  becomes 
more  acute.     This  is  the  case  with  persons  who  have  become  blind. 

It  has  generally  been  considered  that  fog  in  the  atmosphere  is  a  great 
deadener  of  sound  ;  it  being  a  mixture  of  air  and  globules  of  water,  at  each 
of  the  innumerable  surfaces  of  contact  a  portion  of  the  vibration  is  lost. 
The  evidence  as  to  the  influence  of  this  property  is  conflicting  ;  recent  re- 
searches of  Tyndall  show  that  a  white  fog,  or  snow,  or  hail,  are  not  important 
obstacles  to  the  transmission  of  sound,  but  that  aqueous  vapour  is.  Expe- 
riments made  on  a  large  scale,  in  order  to  ascertain  the  best  form  of  fog 
signals,  gave  some  remarkable  results. 

On  some  days,  which  optically  were  quite  clear,  certain  sounds  could  not 
be  heard  at  a  distance  far  inferior  to  that  at  which  they  could  be  heard  even 
during  a  thick  haze.  Tyndall  ascribes  this  result  to  the  presence  in  the 
atmosphere  of  aqueous  vapour,  which  forms  in  the  air  innumerable  stria; 
that  do  not  interfere  with  its  optical  clearness,  but  render  it  acoustically 
turbid,  the  sound  being  reflected  by  this  invisible  vapour  just  as  light  is  by 
the  visible  cloud. 

These  conclusions  first  drawn  from  observations  have  been  verified  by 


-238] 


Refraction  of  Sound. 


215 


laboratory  experiments.  Tyndall  has  shown  that  a  medium  consisting  of 
alternate  layers  of  light  and  heavy  gas,  such  as  coal  gas  and  carbon 
dioxide,  deadens  sound,  and  also  that  a  medium  consisting  of  alternate  strata 
of  heated  and  ordinary  air  exerts  a  similar  influence.  The  same  is  the  case 
with  an  atmosphere  containing  the  vapours  of  volatile  liquids.  So  long  as 
the  continuity  of  air  is  preserved,  sound  has  great  power  of  passing  through 
the  interstices  of  solids  ;  thus  it  will  pass  through  twelve  folds  of  a  dry  silk 
handkerchief,  but  is  stopped  by  a  single  layer  if  it  is  wetted. 

238.  Refraction  of  sound.— It  will  be  found  afterwards  (536)  that  refrac- 
tion is  the  change  of  direction  which  light  and  heat  experience  on  passing  from 
one  m.edium  to  another.  It  has  been  shown  by  Hajech  that  the  laws  of  the 
refraction  of  sound  are  the  same  as  those  for  light  and  heat  :  he  used  tubes 
filled  with  various  gases  and  liquids,  and  closed  by  membranes  ;  the  mem- 
brane at  one  end  was  at  right  angles  to  the  axis  of  the  tube,  while  the  other 
made  an  angle  with  it.  When  these  tubes  were  placed  in  an  aperture  in  the 
wall  between  two  rooms,  a  sound  produced  in  front  of  the  tube  in  one  room, 
that  of  a  tuning-fork  for  instance,  was  heard  in  directions  in  the  other  vary- 
ing with  the  inclination  of  the  second  membrane,  and  with  the  nature  of  the 
substance  with  which  the  tube  was  filled.     Accurate  measurements  showed 


\/ 


that  the  law  held  that  the  sines  of  the  angle  of  incidence  and  of  refraction 
are  in  a  constant  ratio,  and  that  this  ratio  is  equal  to  that  of  the  velocity  of 
sound  in  the  two  media. 

Thus  the  velocity  of  sound  in  water  is  not  very  different  from  that  in 
hydrogen,  and  they  produce  deviations  which  are  nearly  equal. 

Sondhauss  confirmed  the  analogy  of  the  refraction  of  sound-waves  to 
those  of  light  and  heat.  He  constructed  lenses  of  gas  by  cutting  equal 
segments  out  of  a  large  collodion  balloon,  and  fastening  them  on  the  two 
sides  of  a  sheet  iron  ring  a  foot  in  diameter,  so  as  to  form  a  double  convex 
lens  about  4  inches  thick  in  the  centre  (fig.  212),  This  was  filled  with  car- 
bonic acid,  and  a  watch  A  was  placed  in  the  direction  of  the  axis  :  the  point 
was  then  sought  on  the  other  side  of  the  lens  at  which  the  sound  was  most 
distinctly  heard.  It  was  found  that  when  the  ear  was  removed  from  the 
axis,  the  sound  was  scarcely  perceptible;  but  that  at  a  certain  point  B  on  the 


2i6  On  Soiind.  [238- 

axial  line  it  was  very  distinctly  heard.  Consequently,  the  sound-waves  in 
passing  from  the  lens  had  converged  towards  the  axis,  their  direction  had 
been  changed  ;  in  other  words,  they  had  been  refracted. 

The  refraction  of  sound  may  be  easily  demonstrated  by  means  of  one  of 
the  very  thin  india-rubber  balloons  used  as  children's  toys,  inflated  by 
carbonic  acid.  If  the  balloon  be  filled  with  hydrogen,  no  focus  is  detected  ; 
it  acts  like  a  concave  lens,  and  the  divergence  of  the  rays  is  increased,  instead 
of  their  being  converged  to  the  ear. 

A  direct  proof  of  the  refraction  of  sound  is  given  by  the  experiments  of 
Schellbach  and  Bohm.  The  source  of  sound  was  a  film  of  collodion  stretched 
across  a  ring  ab  (fig.  213),  and  which  was  put  in  vibration  by  electrical  sparks 
at  0.  A  disc  of  paper,  sprinkled  with  fine  charcoal  powder,  was  suspended  in 
the  vessel  BB'.  When  this  vessel  contained  air,  rings  of  dust  were  formed, 
the  centre  of  which  was  at /in  the  direction  of  the  propagation  of  the  sound. 
But  if  the  vessel  was  filled  with  carbonic  acid  the  centre  of  the  rings  was  found 
to  be  at/',  showing  that  the  sound  had  been  refracted  towards  the  perpendi- 
cular on  passing  from  air  into  the  denser  medium  ;  and  measurements  showed 
that  the  position  of  the  point  /'  was  in  accordance  with  the  law  of  refraction 
for  light.  Experiments  showed  that,' when  hydrogen  was  substituted  for  car- 
bonic acid,  the  sound  was  bent  away  from  the  perpendicular. 

It  has  long  been  known  that  sound  is  propagated  in  a  direction  against 
that  of  the  wind  with  less  velocity  than  with  the  wind.  This  is  probably 
due  to  a  refraction  of  sound  on  a  large  scale.  The  velocity  of  wind  along 
the  ground  is  always  considerably  less  than  at  a  greater  height  ;  thus,  the 
velocity  at  a  height  of  8  feet  has  been  observed  to  be  double  what  it  is  at  a 
height  of  one  foot  above  the  ground.  Hence  the  front  of  a  condensed  wave 
(fig.  209),  which  was  originally  vertical,  becomes  tilted  upwards  and  with  the 
lower  part  forward  ;  and,  as  the  direction  of  the  wave-motion  is  at  right 
angles  to  the  front  of  the  wave,  the  effect  of  the  coalescence  of  a  number  of 
these  rays,  thus  directed  upwards,  is  to  produce  an  increase  of  the  sound  in 
the  higher  regions.  The  rays  which  travel  with  the  wind  will,  for  similar 
reasons,  be  refracted  downwards,  and  thus  the  sound  be  better  heard. 

239.  Speaking-  trumpet.  Ear  trumpet. — These  instruments  depend 
both  on  the  reflection  of  sound  and  on  its  conductibility  in  tubes. 

The  speaking  trumpet,  as  its  name  implies,  is  used  to  render  the  voice 
audible  at  great  distances,  more  especially  on  board  ship.     It  consists  of  a 


~^%r~ 


Fig.  214. 

slightly  conical  tin  or  brass  tube  (fig.  214),  very  much  wider  at  one  end  (which 
is  called  the  bell),  and  provided  with  a  mouthpiece  at  the  other.  They  are 
as  much  as  7  feet  in  length,  the  bell  being  i  foot  in  diameter. 

The  larger  the  dimensions  of  this  instrument  the  greater  is  the  distance 
at  which  the  voice  is  heard.     Its  action  is  usually  ascribed  to  the  .successive 


-240] 


Stethoscope. 


217 


reflections  of  sound-waves  from  the  sides  of  the  tube,  by  which  the  waves 
tend  more  and  more  to  pass  in  a  direction  parallel  to  the  axis  of  the 
instrument.  It  has,  however,  been  objected  to  this  explanation  that  the 
sounds  emitted  by  the  speaking  trumpet  are  not  stronger  solely  in  the 
direction  of  the  axis,  but  in  all  directions  ;  that  the  bell  would  not  tend  to 
produce  parallelism  in  the  sound-wave,  whereas  it  certainly  exerts  consider- 
able influence  in  strengthening  the  sound.  According  to  Hassenfratz  the  bell 
acts  by  allowing  a  large  mass  of  air  to  be  set  in  consonant  vibration  before 
it  begins  to  be  diffused.  This  is  probably  also  the  reason  why  sound  travels 
best  in  the  chief  direction  of  the  sounding  body  ;  thus  the  report  of  a  cannon, 
the  sound  of  a  wind  instrument  in  the  line  of  the  tube,  the  voice  in  the 
direction  of  the  mouth,  etc. 

The  ear  trumpet  is  used  by  persons  who  are  hard  of  hearing.  It  is 
essentially  an  inverted  speaking  trumpet,  and  consists  of  a  conical  metallic 
tube,  one  of  whose  extremities,  terminating  in  a  bell^  receives  the  sound,  while 
the  other  end  is  introduced  into  the  ear.  This  instrument  is  the  reverse  of 
the  speaking  trumpet.  The  bell  serves  as  a  mouthpiece  ;  that  is,  it  receives 
the  sound  coming  from  the  mouth  of  the  person  who  speaks.  These  sounds 
are  transmitted  by  a  series  of  reflections  to  the  interior  of  the  trumpet,  so 
that  the  waves,  which  would  become  greatly  diffused,  are  concentrated  on 


Fig.  215.  Fig.  216. 

the  ear,  and  produce  a  far  greater  effect  than  divergent  waves  would  have 
done. 

240.  Stetboscope. — One  of  the  most  useful  applications  of  acoustical 
principles  is  the  stethoscope.  Figs.  215,  216,  represent  an  improved  form  of 
this  instrument  devised  by  Konig.  Two  sheets  of  caoutchouc,  c  and  cz,  are 
fixed  to  the  circular  edge  of  a  hollow  metal  hemisphere;  the  edge  is  provided 
with  a  stopcock,  so  that  the  sheets  can  be  inflated,  and  then  present  the  ap- 
pearance of  a  double  convex  lens,  as  represented  in  section  in  fig.  215.  To 
a  tubulure  on  the  hemisphere  is  fixed  a  caoutchouc  tube  terminated  by  horn 
or  ivory,  (5,  which  is  placed  in  the  ear  (fig.  216). 

When  the  membrane  c  of  the  stethoscope  is  applied  to  the  chest  of  a  sick 
person  the  beating  of  the  heart  and  the  sounds  of  respiration  are  transmitted 
to  the  air  in  the  chamber  «,  and  from  thence  to  the  ear  by  means  of  the 
flexible  tube.  If  several  tubes  are  fixed  to  the  instrument,  as  many  observers 
may  simultaneously  auscultate  the  same  patient. 


2li 


On  Sound. 


[241- 


CHAPTER    II. 

MEASUREMENT   OF   THE   NUMBER   OF   VIBRATIONS. 

241.  Savart's  apparatus. — Satuirfs  toothed  zuheel^  so  called  from  the 
name  of  its  inventor,  is  an  apparatus  by  which  the  absokite  number  of  vibra- 
tions corresponding  to  a  given  note  can  be  determined.  It  consists  of  a 
solid  oak  frame  in  which  there  are  two  wheels,  A  and  B  (fig.  217)  ;  the  larger 


Fig.  217. 

wheel.  A,  is  connected  with  the  toothed  wheel  by  means  of  a  strap  and  a 
multiplying"  wheel,  thereljy  causing  the  toothed  wheel  to  revolve  with  great 
velocity  ;  a  card,  E,  is  fixed  on  the  frame,  and,  in  revolving,  the  toothed 
wheel  strikes  against  it,  and  causes  it  to  vibrate.  The  card,  being  struck  by 
each  tooth,  makes  as  many  vibrations  as  there  are  teeth.  At  the  side  of  the 
apparatus  there  is  an  indicator,  H,  which  gives  the  number  of  revolutions  of 
the  wheel,  and  consequently  the  number  of  vibrations  in  a  given  time. 

When  the  wheel  is  moved  slowly,  the  separate  shocks  against  the  card 
are  distinctly  heard  ;  but  if  the  velocity  is  gradually  increased,  the  sound 
becomes  higher  and  higher.  Having  obtained  the  sound  whose  number  of 
vibrations  is  to  be  determined,  the  revolution  of  the  wheel  is  continued  with 
the  same  velocity  for  a  certain  number  of  seconds.  The  number  of  turns  of 
the  toothed  wheel  B  is  then  read  oft"  on  the  indicator,  and  this  multiplied 
by  the  number  of  teeth  in  the  wheel  gives  the  total  number  of  \'ibrations. 
Dividing  this  by  the  corresponding  number  of  seconds,  the  ciuotient  gives 
the  number  of  vibrations  per  second  for  the  given  sound. 

242.  Syren. — The  syre/i  is  an  apparatus  which,  like  Sa\art's  wheel,  is 
used  to  measure  the  number  of  vibrations  of  a  body  in  a  given  time.     The 


-242] 


Syren. 


219 


name  'syren'  was  given  to  it  by  its  inventor,  Cagniard  Latour,  because  it 
yields  sounds  under  water. 

It  is  made  entirely  of  brass.  Fig.  218  represents  it  fixed  on  the  table  of 
a  bellows,  by  which  a  continuous  current  of  air  can  be  sent  through  it.  Figs. 
219  and  220  show  the  internal  details.  The  lower  part  consists  of  a  cylin- 
drical box,  O,  closed  by  a  fixed  plate,  B.  On  this  plate  a  vertical  rod,  T,  rests, 
to  which  is  fixed  a  disc.  A,  moving  with  the  rod.  In  the  plate  B  there  are 
equidistant  circular  holes,  and  in  the  disc  A  are  an  equal  number  of  holes  of 
the  same  size,  and  the  same  distance  from  the  centre  as  those  of  the  plate. 
These  holes  are  not  perpendicular  to  the  disc  ;  they  are  all  inclined  to  the 
same  extent  in  the  same  direction  in  the  plate,  and  are  inclined  to  the  same 
extent  in  the  opposite  direction  in  the  disc,  so  that  when  they  are  opposite 
each  other  they  have  the  appearance  represented  in  w«,  fig.  219.  Conse- 
quently, when  a  current  of  air  from  the  bellows  reaches  the  hole,  w,  it  strikes 


obliquely  against  the  sides  of  the  hole  ;/,  and  imparts  to  the  disc  A  a  rotatoiy 
motion  in  the  direction  ?/A. 

For  the  sake  of  simplicity,  let  us  first  suppose  that  in  the  movable  disc 
A  there  are  eighteen  holes,  and  in  the  fixed  plate  B  only  one,  which  faces 
one  of  the  upper  holes.  The  wind  from  the  bellows  striking  against  the 
sides  of  the  latter,  the  movable  disc  begins  to  rotate,  and  the  space  between 
two  of  its  consecutive  holes  closes  the  hole  in  the  lower  plate.  But  as  the 
disc  continues  to  turn  from  its  acquired  velocity,  two  holes  are  again  opposite 
each  other,  a  new  impulse  is  produced,  and  so  on.  During  a  complete 
revolution  of  the  disc  the  lower  hole  is  eighteen  times  open  and  eighteen 
times  closed.  A  series  of  effluxes  and  stoppages  is  thus  produced,  which 
makes  the  air  vibrate,  and  ultimately  produces  a  sound  when  the  successive 
impulses  are  sufficiently  rapid.  If  the  fixed  plate,  like  the  moving  disc,  had 
eighteen  holes,  each  hole  would  separately  produce  the  same  effect   as  a 


220  On  Sound.  [242- 

separate  one,  the  sound  would  be  eighteen  times  as  intense,  but  the  number 
of  vibrations  would  not  be  increased. 

In  order  to  know  the  number  of  vibrations  corresponding  to  the  sound 
produced,  it  is  necessary  to  know  the  number  of  revolutions  of  the  disc  A  in 
a  second.  For  this  purpose  an  endless  screw  on  the  rod  T  transmits  the 
motion  to  a  wheel,  «,  with  loo  teeth.  On  this  wheel,  which  moves  by  one 
tooth  for  eveiy  turn  of  the  disc,  there  is  a  catch,  P,  which  at  each  complete 
revolution  moves  one  tooth  of  a  second  wheel,  b  (fig.  220).  On  the  axis  of 
these  wheels  there  are  two  needles,  which  move  round  dials  represented  in 
fig.  218.  One  of  these  indices  gives  the  number  of  turns  of  the  disc  A,  the 
other  the  number  of  hundreds  of  turns.  By  means  of  two  screws,  D  and  C, 
the  wheel  a  can  be  uncoupled  from  the  endless  screw. 

Since  the  pitch  of  the  sound  rises  in  proportion  to  the  velocity  of  the  disc 
A,  the  wind  is  forced  until  the  desired  sound  is  produced  The  same  current 
is  kept  up  for  a  certain  time — two  minutes,  for  example — and  the  number  of 
turns  read  off.  This  number  multiplied  by  18,  and  divided  by  120,  gives 
the  number  of  vibrations  in  a  second.  For  the  same  velocity  of  rotation  the 
syren  gives  the  same  sound  in  air  as  in  water  ;  the  same  is  the  case  with 
all  gases  ;  and  it  appears,  therefore,  that  any  given  sound  depends  on  the 
number  of  vibrations  produced,  and  not  on  the  nature  of  the  sounding  body. 

The  buzzing  and  humming  noise  of  certain  insects  is  not  vocal,  but  is 
produced  by  very  rapid  flapping  of  the  wings  against  the  air  or  the  body. 
The  syren  has  been  ingeniously  applied  to  count  the  velocity  of  the  undu- 
lations thus  produced,  which  is  effected  by  bringing  it  into  unison  with  the 
sound.  It  has  thus  been  found  that  .the  wings  of  a  gnat  flap  at  the  rate  of 
1,500  times  in  a  second.  If  a  report  is  produced  in  a  space  with  two 
parallel  walls  at  no  great  distance  apart,  the  sound  is  reflected  from  one  to 
the  other  and  reaches  the  ear  at  regular  and  frequent  intervals  ;  that  is,  the 
repetition  of  the  echo  acts  as  a  note. 

A  modification  of  the  syren  known  as  Brown's  steam  horn,  in  which  high 
pressure  steam  is  employed  instead  of  compressed  air,  is  used  as  ^fog-signal. 
Its  shrill  and  penetrating  note  is  better  adapted  than  an  ordinary  fog-horn, 
or  even  cannon,  for  being  heard  over  the  noise  of  breakers. 

243.  Bellows. — In  acoustics  a  bellows  is  an  apparatus  by  which  wind 
instruments,  such  as  the  syren  and  organ-pipes,  are  worked.  Between  the 
four  legs  of  a  table  there  is  a  pair  of  bellows,  S  (fig.  221),  which  is  worked 
by  means  of  a  pedal,  P.  D  is  a  reservoir  of  flexible  leather,  in  which  is  stored 
the  air  forced  in  by  the  bellows.  If  this  reservoir  is  pressed  by  means  of 
weights  on  a  rod,  T,  moved  by  the  hand,  the  air  is  driven  through  a  pipe,  E, 
into  a  chest,  C,  fixed  on  the  table.  In  this  chest  there  are  small  holes  closed 
by  leather  valves,  which  can  be  opened  by  pressing  on  keys  in  front  of  the 
box.     The  syren  or  sounding  pipe  is  placed  in  one  of  these  holes. 

244.  X>imit  of  perceptible  sounds. — Previous  to  Savart's  researches, 
physicists  assumed  that  the  ear  could  not  perceive  a  sound  when  the  number 
of  vibrations  was  below  16  for  deep  sounds,  or  above  9,000  for  acute  sounds. 
But  he  showed  that  these  limits  were  too  close,  and  that  the  faculty  of  per- 
ceiving sounds  depends  rather  on  their  intensity  than  on  their  height  ;  so 
that  when  extremely  acute  sounds  are  not  heard,  it  arises  from  the  fact  that 


244] 


Limit  of  perceptible  Soimds 


221 


they  have  not  been  produced  with  sufficient  intensity  to  affect  the  organ  of 
hearing. 

By  increasing  the  diameter  of  the  toothed  wheel,  and  consequently  the 
amplitude  and  intensity  of  the  vibrations,  Savart  pushed  the  limit  of  acute 
sounds  to  24,000  vibrations  in  a  second. 

For  deep  sounds  he  substituted  for  the  toothed  wheel  an  iron  bar  about 
two  feet  long,  which  revolved  on  a  horizontal  axis  between  two  thin  wooden 
plates,  about  o-o8  of  an  inch  from  the  bar.  As  often  as  the  bar  passed,  a 
grave  sound  was  produced,  due  to  the  displacement  of  the  air.  As  the 
motion  was  accelerated,  the  sound  became  continuous,  very  grave  and 
deafening.  By  this  means  Savart  found  that,  with  7  to  8  vibrations  in  a 
second,  the  ear  perceived  a 
distinct  but  very  deep  sound. 

Despretz,  howe\'er,  who 
investigated  the  same  sub- 
ject, disputed  Savart's  results 
as  to  the  limits  of  deep 
sounds,  and  considers  that 
no  sound  is  audible  that  is 
made  by  less  than  16  vibra- 
tions per  second.  Helm- 
holtz  holds  that  the  percep- 
tion of  a  sound  begins  at  30 
vibrations,  and  only  has  a 
definite  musical  value  when 
the  number  is  more  than  40. 
Below  30  the  impression  of 
a  number  of  separate  beats 
is  produced.  On  the  other 
hand,  acute  sounds  are  audi- 
ble up  to  those  correspond- 
ing to  38,000  vibrations  in  a 
second.  Such  sounds,  how- 
ever, are  far  from  pleasur- 
able :  they  affect  the  ear  as  if 
it  had  been  pricked  with  a 
pin  or  needle. 

The  discordant  results  obtained  by  these  and  other  observers  for  the 
limit  of  audibility  of  higher  notes  are  no  doubt  due  to  the  circumstance 
that  different  observers  have  different  capacities  for  the  perception  of 
sounds.  Preyer  has  investigated  this  subject  by  means  of  experimental 
methods  of  greater  precision  than  any  that  have  hitherto  been  applied 
for  this  purpose.  The  minimum  limit  for  the  normal  ear  he  found  to  lie 
between  16  and  24  single  vibrations  in  a  second;  the  maximum  limit  reached 
41,000  ;  but  many  persons  with  average  powers  of  hearing  were  found  to  be 
absolutely  deaf  to  notes  of  16,000,  12,000,  or  even  fewer  vibrations. 

It  appears  that  the  limit  of  audibility  for  any  particular  ear  is  increased 
with  the  strength  of  the  sound.  Paucher  examined  this  by  sounding  a 
powerful  syren  by  steam  ;  he  found  that  with  steam  of  ^  atmosphere  pres- 


222  On  Sound.  [244- 

sure  the  upper  limit  was  at  48,000  vibrations,  with  li  atmospheres  it  was 
60,000,  while  with  steam  of  2.^  atmospheres  it  had  not  been  attained  with 
72,000  vibrations. 

245.  Suhamel's  graphic  method. — When  the  syren  or  Sa\art's  wheel 
is  used  to  determine  the  exact  number  of  vibrations  corresponding  to  a  given 
note,  it  is  necessary  to  bring  the  sounds  which  they  produce  into  unison 
with  the  given  note,  and  this  cannot  be  done  exactly  unless  the  experi- 
menter has  a  practised  ear.  Duhamel's  graphic  method  is  very  simple  and 
exact,  and  free  from  this  difificulty.  It  consists  in  fixing  a  fine  point  to  the 
body  emitting  the  note,  and  causing  it  to  trace  the  vibrations  on  a  properly 
prepared  surface. 

The  apparatus  consists  of  a  wood  or  metal  cylinder,  A  (fig.  222),  fixed  to 
a  vertical  axis,  O,  and  turned  by  a  handle.  The  lower  part  of  the  axis  is  a 
screw  working  in  a  fixed  nut,  so  that,  according  as  the  handle  is  turned  from 
left  to  right,  or  from  right  to  left,  the  cylinder  is  raised  or  depressed.     Round 


Fig.  222. 


the  cylinder  is  rolled  a  sheet  of  paper  covered  with  an  inadhesive  film  of 
lampblack.  On  this  film  the  vibrations  register  themselves.  This  is  effected 
as  follows.  Suppose  the  body  emitting  the  note  to  be  a  steel  rod.  It  is  held 
firmly  at  one  end,  and  carries,  at  the  other,  a  fine  point  which  grazes  the  sur- 
faces of  the  cylinder.  If  the  rod  is  made  to  vibrate  and  the  cylinder  is  at  rest, 
the  point  would  describe  a  short  line;  but,  if  the  cylinder  is  turned,  the  point 
produces  an  tindidatino  Hue.,  containing  as  many  undulations  as  the  point 
has  made  vibrations.  Consequently,  the  number  of  vibrations  can  be  counted.. 
It  remains  only  to  determine  the  time  in  which  the  \'ibrations  were  made. 


-245]  Duhainel's  Graphic  Method.  223 

There  are  several  ways  of  doing  this.  The  simplest  is  to  compare  the 
curve  traced  by  the  vibrating  rod  with  that  traced  by  a  tuning-fork  (251), 
which  gives  a  known  number  of  vibrations  per  second — for  example,  500. 
The  prong  of  the  fork  is  furnished  with  a  point,  which  is  placed  in  contact 
with  the  lampblack.  The  fork  and  the  rod  are  then  set  vibrating  together, 
and  each  produces  its  own  undulating  trace.  When  the  paper  is  unrolled, 
it  is  easy,  by  counting  the  number  of  vibrations  each  has  made  in  the  same 
distance,  to  determine  the  number  of  vibrations  made  per  second  by  the 
elastic  rod.  Suppose,  for  instance,  that  the  tuning-fork  made  150  vibrations 
while  the  rod  made  165  vibrations.  Now  we  already  know  that  the  tuning- 
fork  makes  one  vibration  in  the  ^-^  part  of  a  second,  and  therefore  150 
vibrations  in  \~  of  a  second.     But  in  the  same  time  the  rod  makes   165 

vibrations  ;  therefore  it  makes  one  vibration  in  the     ^     ,    ,  of  a  second, 

500  X  165 

and  hence  it  makes  per  second  ^ ^,  or  550  vibrations. 

^  150 


224  On  Sound.  [246- 


CHAPTER    III. 

THE   PHYSICAL  THEORY   OF   MUSIC. 

246.  Properties  of  musical  notes. — A  simple  musical  note  results  from 
continuous  rapid  isochronous  vibrations,  provided  the  number  of  the  vibra- 
tions falls  within  the  very  wide  hmits  mentioned  in  the  last  chapter  (244). 
Musical  notes  are  in  most  cases  compound.  The  distinction  between  a 
simple  and  a  compound  musical  note  will  be  explained  later  in  the  chapter. 
The  tone  yielded  iDy  a  tuning-fork  furnished  with  a  proper  resonance-box  is 
simple ;  that  yielded  by  a  wide-stopped  organ  pipe,  or  by  a  flute,  is  near/v 
simple ;  that  yielded  by  a  musical  string  is  compotind. 

Musical  notes  have  three  leading  qualities,  namely,  pitcJi.,  intensity.,  and 
timbre  or  quality. 

i.  The  pitch  of  a  musical  note  is  determined  by  the  number  of  vibrations 
per  second  yielded  by  the  body  producing  the  note. 

ii.  The  i?ttensity  of  the  note  depends  on  the  extent  of  the  vibrations.  It 
is  greater  when  the  extent  is  greater,  and  less  when  it  is  less.  It  is,  in  fact, 
proportional  to  the  square  of  the  extent  or  amplitude  of  the  vibrations  which 
produce  the  note. 

iii.  The  timbre  or  stamp  or  quality  is  that  peculiar  property  of  note  which 
distinguishes  a  note  when  sounded  on  one  instrument  from  the  same  note 
when  sounded  on  another,  and  which  by  some  is  called  the  colour.  Thus 
when  the  C  of  the  treble  stave  is  sounded  on  a  violin,  and  on  a  flute,  the  two 
notes  will  have  the  same  pitch  ;  that  is,  they  are  produced  by  the  same  number 
of  vibrations  per  second,  and  they  may  have  the  same  intensity,  and  yet  the 
two  notes  will  have  very  distinct  qualities  ;  that  is,  their  timbre  is  different. 
The  cause  of  the  peculiar  timbre  of  notes  will  be  considered  later  in  the 
chapter. 

247.  IVZusical  intervals. — Let  us  suppose  that  a  musical  note,  which  for 
the  sake  of  future  reference  we  will  denote  by  the  letter  C,  is  produced  by 
7/1  vibrations  per  second  ;  and  let  us  further  suppose  that  any  other  musical 
note,  X,  is  produced  by  ;/  vibrations  per  second,  n  being  greater  than  in  ; 
then  the  interval  from  the  note  C  to  the  note  X  is  the  ratio  ;/ :  m,  the  interval 
between  two  notes  being  obtained  by  division,  not  by  subtraction.  Although 
two  or  more  notes  may  be  separately  musical,  it  by  no  means  follows  that 
when  sounded  together  they  produce  a  pleasant  sensation.  On  the  con- 
trary, unless  they  are  concordant,  the  result  is  harsh,  and  usually  unpleasing. 
We  have,  therefore,  to  inquire  what  7iotes  are  fit  to  be  sounded  together. 
Now,  when  musical  notes  are  compared,  it  is  found  that  if  they  are  separated 
by  an  interval  of  2  :  1,4:  i,  &c.,  they  so  closely  resemble  one  another  that 
they  may  for  most  purposes  of  music  be  considered  as  the  same  note.  Thus, 
suppose  c  to  stand  for  a  musical  note  produced  by  2m  vibrations  per  second, 
then  C  and  c  so  closely  resemble  each  other  as  to  be  called  in  music  by 


-248]  The  Musical  Scale.  225 

the  same  name.  The  interval  from  C  to  c  is  called  an  octave,  and  c  is 
said  to  be  an  octave  above  C,  and  conversely  C  an  octave  below  c.  If  we  now 
consider  musical  sounds  that  do  not  differ  by  an  octave,  it  is  found  that 
if  we  take  three  notes,  X,  Y,  and  Z,  resulting  respectively  from  /,  ^,  and  r 
vibrations  per  second,  these  three  notes  when  sounded  together  will  be  con- 
cordant if  the  ratio  oi  p  :  q  :  r  equals  4:5:6.  Three  such  notes  form  a 
harinojtic  triad,  and  if  sounded  with  a  fourth  note,  which  is  the  octave  of 
X,  constitute  what  is  called  in  music  a  major  chord.  Any  of  the  notes  of  a 
chord  may  be  altered  by  one  or  more  octaves  without  changing  its  distinc- 
tive character  ;  for  instance,  C,  E,  G,  and  c  are  a  chord,  and  C  c,  e,  g  form 
the  same  chord. 

If,  however,  the  ratio/  :  q  :  r  equals  10  :  12  :  15,  the  three  sounds  are 
slightly  dissonant,  but  not  so  much  so  as  to  disqualify  them  from  producing 
a  pleasing  sensation.  When  these  three  notes  and  the  octave  to  the  lower 
are  sounded  together,  they  constitute  what  in  music  is  called  a  mi?tor  chord. 

248.  The  musical  scale. — The  series  of  sounds  which  connects  a  given 
note  C  with  its  octave  c  is  called  the  diatonic  scale  or  gamut.  The  notes 
composing  it  are  indicated  by  the  letters  C,  D,  E,  F,  G,  A,  B.  The  scale 
is  then  continued  by  taking  the  octaves  of  these  notes,  namely,  c,  d,  e,f.,g,  a,  b, 
and  again  the  octaves  of  these  last,  and  so  on. 

The  notes  are  also  known  by  names,  viz.,  do  or  ut,  re,  7ni,fa,  sol,  la,  si, 
do.  The  relations  existing  between  the  notes  are  thiese  : — C,  E,  G  form 
a  major  triad,  G,  B,  d  form  a  major  triad,  and  F,  A,  c  form  a  major  triad. 
C,  G,  and  F  have,  for  this  reason,  special  names,  being  called  respectively 
the  tom'c,  dovmtant,  and  sub-dominant,  and  the  three  triads  the  tonic, 
domiiiant,  and  sub-dominant  triads  or  chords  respecti\ely.  Consequently, 
the  numerical  relations  between  the  notes  of  the  scale  will  be  given  by  the  . 
three  proportions — 


c 

E  : 

G   : 

:  4 

5 

6 

G 

B 

2D   : 

:  4 

5 

6 

F 

A  : 

2C   : 

:  4 

5 

6 

Hence,  if  m  denotes  the  number  of  double  vibrations  corresponding  to 
the  note  C,  the  number  of  vibrations  corresponding  to  the  remaining  notes 
will  be  given  by  the  following  table — 

do  re  mi  fa  sol  la  si  do 
CDEFGAB^ 
m        \m        \m       \m       \m       \m         ^/         2w 

The  intervals  between  the  successive  notes  being  respectively — 
C  to  D     D  to  E     E  to  F     F  to  G     G  to  A    A  to  B     B  to  (T 


It  will  be  observed  here  that  there  are  three  kinds  of  intervals  "  '^^  and 
if  ;  of  these  the  first  two  are  called  a  tone,  the  last  a  semitone,  because  it 
is  about  half  as  great  as  the  interval  of  a  tone.  The  two  tones,  however  are 
not  identical,  but  differ  by  an  interval  of  |^,  which  is  called  a  comma.  Two 
notes  which  differ  by  a  cofn?na  can  be  readily  distinguished  by  a  trained 

Q 


226  On  Sound.  [248- 

ear.  The  interval  between  the  tonic  and  any  note  is  denominated  by  the 
position  of  the  latter  note  in  the  scale  ;  thus  the  interval  from  C  to  G  is  a 
fifth.  The  scale  we  have  now  considered  is  called  the  major  scale,  as  being 
formed  oi  major  VcxdidA.  If  the  minor  triad  were  substituted  for  the  major, 
a  scale  would  be  formed  that  could  be  strictly  called  a  minor  scale.  As 
scales  are  usually  written,  however,  the  ascending  scale  is  so  formed  that 
the  tonic  bears  a  minor  triad,  the  dominant  and  sub-dominant  bear  major 
triads,  while  in  the  descending  scale  they  all  bear  minor  triads.  Practically^ 
in  musical  composition,  the  dominant  triad  is  always  >najor.  If  the  ratios 
given  above  are  examined,  it  will  be  found  that  in  the  major  scale  the 
interval  from  C  to  E  equals  f,  while  in  the  minor  scale  it  equals  f.  The 
former  interval  is  called  a  major  third,  the  latter  a  minor  third.  Hence  the 
major  third  exceeds  the  minor  third  by  an  interval  of  §|.  This  interval  is 
called  a  semitone,  though  very  different  from  the  interval  above  called  by 
that  name. 

249.  On  semitones  and  on  scales  with  different  key-notes. — It  will 
be  seen  from  the  last  article  that  the  term  '  semitone '  does  not  denote  a. 
constant  interval,  being  in  one  case  equivalent  to  \i  and  in  another  to  ||. 
It  is  found  convenient  for  the  purposes  of  music  to  introduce  notes  inter- 
mediate to  the  seven  notes  of  the  gamut  ;  this  is  done  by  raising  or  lowering- 
these  notes  by  an  interval  of  |f.  When  a  note  (say  C)  is  increased  by  this 
mterval,  it  is  said  to  be  sharpened,  and  is  denoted  by  the  symbol  CJI ,  called 
'  C  sharp  ;'  that  is,  Cji-=-C  =  |f.  When  it  is  lowered  by  the  same  interval,  it 
is  said  to  \i&  flattened,  and  is  represented  thus — Bb,  called  '  B  flat  ; '  that  is, 
B-^Bb  =  §f.  If  the  effect  of  this  be  examined,  it  will  be  found  that  the 
number  of  notes  in  the  scale  from  C  up  to  c  has  been  increased  from  seven 
to  twenty-one  notes,  all  of  which  can  be  easily  distinguished  by  the  ear. 
Thus,  reckoning  C  to  equal  i,  we  have — 

C         Cff         Db         D         Dj         Eb         E         &c. 

Hitherto  we  have  made  the  note  C  the  tonic  or  key-note.  Any  other  of 
the  twenty-one  distinct  notes  above  mentioned,  e.g.,  G,  or  F,  or  Cff,  &c., 
may  be  made  the  key-note,  and  a  scale  of  notes  constructed  with  reference 
to  it.  This  will  be  found  to  give  rise  in  each  case  to  a  series  of  notes,  some 
of  which  are  identical  with  those  contained  in  the  series  of  which  C  is  the 
key-note,  but  most  of  them  different.  And  of  course  the  same  would  be  true 
for  the  minor  scale  as  well  as  for  the  major  scale,  and  indeed  for  other  scales 
which  may  be  constructed  by  means  of  the  fundamental  triads. 

250.  On  musical  temperament. — The  number  of  notes  that  arise  from 
the  construction  of  the  scales  described  in  the  last  article  is  so  great  as  to 
prove  quite  unmanageable  in  the  practice  of  music  ;  and  particularly  for 
music  designed  for  instruments  with  fixed  notes,  such  as  the  pianoforte  or 
harp.  Accordingly,  it  becomes  practically  important  to  reduce  the  number 
of  notes,  which  is  done  by  slightly  altering  their  just  proportions.  This 
process  is  called  temperament.  By  tempering  the  notes,  however,  more  or 
less  dissonance  is  introduced,  and  accordingly  several  different  systems  of 
temperament  have  been  devised  for  rendering  this  dissonance  as  slight  as 
possible.    The  system  usually  adopted  is  called  the  system  o^  equal  tempera- 


-251]        The  Number  of  Vibrations  producing  each  Note.         227 

ment.  It  consists  in  retaining  the  octaves  pure,  and  in  substituting  between 
C  and  c  eleven  notes  at  equal  intervals,  each  interval  being,  of  course,  the 
twelfth  root  of  2,  or  1-05946.  By  this  means  the  distinction  between  the 
semitones  is  abolished,  so  that,  for  example,  CJt  and  Db  become  the  same 
note.  The  scale  of  twelve  notes  thus  formed  is  called  the  chroinatic  scale. 
It  of  course  follows  that  major  triads  become  slightly  dissonant.  Thus,  in 
the  diatonic  scale,  if  we  reckon  C  to  be  i,  E  is  denoted  by  1-25000,  and  G  by 
1-50000.  On  the  system  of  equal  temperament,  if  C  is  denoted  by  i,  E  is 
denoted  by  1-25992,  and  G  by  i -49831. 

If  individual  intervals  are  made  pure  while  the  errors  are  distributed  over 
the  others,  such  a  system  is  called  that  of  unequal  temperament.  Of  this 
class  is  Kirnbergcr^s,  in  which  nine  of  the  tones  are  pure. 

Although  the  system  of  equal  temperament  has  the  advantage  of  afford- 
ing the  greatest  variety  of  tones  with  as  small  a  number  of  notes  as  possible, 
yet  it  has  the  drawback  that  no  chord  of  an  equally  tempered  instrument, 
such  as  the  piano,  is  perfectly  pure.  And  as  musical  education  mostly  has 
its  basis  on  the  piano,  even  singers  and  instrumentahsts  usually  give  equally- 
tempered  intervals.  Only  in  the  case  of  string  quartet  players,  who  have 
freed  themselves  from  school  rules,  and  in  that  of  vocal  quartet  singers,  who 
sing  much  without  accompaniment,  does  the  natural  pure  temperament  assert 
itself,  and  thus  produce  the  highest  musical  effect. 

251.  The  number  of  vibrations  producing'  each  note.  The  tuningr- 
fork. — Hitherto  we  have  denoted  the  number  of  vibrations  corresponding  to 
the  note  C  by  w,  and  have  not  assigned  any 
numerical  value  to  that  symbol.  In  the  theory 
of  music  it  is  frequently  assumed  that  the  middle 
C  corresponds  to  256  double  vibrations  in  a 
second.  This  is  the  note  which,  on  a  pianoforte 
of  seven  octaves,  is  produced  by  the  white  key 
on  the  left  of  the  two  black  keys  close  to  the 
centre  of  the  keyboard.  This  number  is  con- 
venient as  being  continually  divisible  by  two, 
and  is  therefore  frequently  used  in  numerical 
illustrations.  If  is,  however,  arbitrary.  An 
instrument  is  in  tune  provided  the  intervals 
between  the  notes  are  correct,  when  c  is  yielded 
by  any  number  of  vibrations  per  second  not 
differing  much  from  256.  Moreover,  two  instru- 
ments are  in  tune  with  one  another,  if,  being 
separately  in  tune,  they  have  any  one  note,  for 
instance  C,  yielded  by  the  same  number  of  vibra- 
tions. Consequently,  if  two  instruments  have 
one  note  in  common,  they  can  then  be  brought 
into  tune  jointly  by  having  their  remaining  notes 
separately  adjusted  with  reference  to  the  funda- 
mental note.  A  tutiing-fork  or  diapason  is  an  instrument  yielding  a  con- 
stant sound,  and  is  used  as  a  standard  for  tuning  musical  instruments.  It 
consists  of  an  elastic  steel  rod,  bent  as  represented  in  fig.  223.  It  is  made 
to  vibrate  either  by  drawing  a  bow  across  the  ends,  or  by  striking  one  of 

Q  2 


Fig.  223. 


228  On  Soimd.  [251- 

the  legs  against  a  small  hammer  covered  with  leather,  or  by  rapidly  sepa- 
rating the  two  prongs  by  means  of  a  steel  rod  as  shown  in  the  figure.  The 
vibration  produces  a  note  which  is  always  the  same  for  the  same  tuning-fork. 
The  note  is  strengthened  by  fixing  the  tuning-fork  on  a  box  open  at  one  end, 
called  a  sounding  or  rcso7tance  box,  adjusted  so  as  to  strengthen  the  special 
note  of  the  tuning-fork.  The  length  of  this  column  of  air  enclosed  in  the 
box  is  a  quarter  that  of  the  wave-length  of  the  note  which  the  tuning-fork 
emits.  The  vibrations  of  the  air  produce  the  same  note  as  the  fork  itself ;  the 
vibrations  of  the  tuning-fork,  being  communicated  to  the  column  of  air  in  the 
box,  set  it  in  vibration,  by  which  a  strong  and  pure  note  is  obtained  (255). 

The  standard  tuning-fork  in  any  countr}^  represents  its  accepted  concert 
pitch. 

It  has  been  remarked  for  some  years  that  not  only  has  the  pitch  of  the 
tuning-fork  been  getting  higher  in  the  large  theatres  of  Europe,  but  also 
that  it  is  not  the  same  in  London,  Paris,  Berlin,  Vienna,  Milan,  &c.  This  is 
a  source  of  great  inconvenience  both  to  composers  and  singers,  and  a  com- 
mission was  appointed  in  1859  to  establish  in  France  a  tuning-fork  of  uniform 
pitch,  and  to  prepare  a  standard  which  would  serve  as  an  invariable  type. 
In  accordance  with  the  recommendations  of  that  body,  a  norma!  tunifig-fork 
has  been  established,  which  is  compulsory  on  all  musical  establishments 
in  France,  and  a  standard  has  been  deposited  in  the  Conservatory  of  Music 
in  Paris.  It  performs  437'5  double  vibrations  per  second,  and  gives  the 
standard  note  a  or  la,  or  the  a  in  the  treble  stave  (252).  Consequently,  with 
reference  to  this  standard,  the  middle  c  or  do  would  result  from  261  double 
vibrations  per  second. 

In  England  a  committee,  appointed  by  the  Society  of  Arts,  recommended 
that  a  standard  tuning-fork  should  be  one  constructed  to  yield  528  double 
vibrations  in  a  second,  and  that  this  should  represent  c'  in  the  treble  stave. 
This  number  has  the  advantage  of  being  divisible  by  2  down  to  2)3^  and  is  in 
fact  the  same  as  the  normal  tuning-fork  adopted  in  Stuttgart  in  1834,  which 
makes  440  vibrations  in  the  second,  and,  like  the  French  one,  corresponds 
to  a  in  the  same  stave. 

In  exact  determinations  of  pitch  the  temperature  must  be  taken  into 
account.  Heat  acts  on  the  tuning-fork  by  expanding  it,  and  also  by 
diminishing  the  elasticity  of  the  metal.  Both  effects  concur  in  lowering 
the  pitch.  Thus  Konig  found  that  a  tuning-fork  which  made  512  vibrations 
at  20°  C.  varied  by  0*0572  for  each  degree  Centigrade.  Stone  and  McLeod 
found  the  number  0-055. 

An  international  conference  at  Vienna  in  1885  adopted  a  tuning-fork 
of  polished  mild  cast-steel  with  prismatic  prongs,  making  435  vibrations  in  a 
second  at  1 5°  C,  as  the  standard  a  note. 

252.  IVXusical  notation.  IMCusical  rangre. — It  is  convenient  to  have 
some  means  of  at  once  naming  any  particular  note  in  the  whole  range  of 
musical  sounds  other  than  by  stating  its  number  of  vibrations.  ^^Perhaps  a 
convenient  practice  is  to  call  the  octave,  of  which  the  C  is  produced  by  an 
eight-foot  organ  pipe,  by  the  capital  letters  C,  D,  E,  F,  G,  A,  B  ;  the  next 
higher  octave  by  the  corresponding  small  letters,  c,  d,  e,f,g,  a,  b  ;  and  to 
designate  the  octaves  higher  than  this  by  the  index  placed  over  the  letter 
thus,  d ,  d',  e',  _/"',  g',  a',  b\  and  the  higher  series  in  a  similar  manner.     The 


-253]  Wave-length  of  a  Given  Note.  229 

same  principle  may  be  applied  to  the  notes  below  C  ;  thus  the  octave  below 
C  is  C^,  and  the  next  lower  one  C^,. 
Hence  we  have  the  series 

C,^  C^  C  c  c'  c"  c"'  c". 

In  musical  writing  the  notes  are  expressed  by  signs  which  indicate  the 
length  of  time  during  which  the  note  is  to  be  played  or  sung,  and  are  written 
on  a  series  of  lines  called  a  stave.     Thus 


stands  for  the  octave  in  the  treble  clef,  of  which  the  top  note  is  the  standard 
c'  and  the  bottom  is  the  middle  c.  When  the  five  lines  are  insufficient  they 
are  continued  above  and  below  the  stave  by  what  are  called  ledger  lines. 
In  order  to  avoid  confusion,  a  bass  clef  is  used  for  the  lower  notes  ;  and  it 


may  be  remarked  that  tff)  l=~  and  s^' r:=  stand  for  the  same  note 

Xf      -¥- 
(251),  which  is  the  middle  c. 

The  deepest  note  of  orchestral  instruments  is  the  E^  of  the  double  bass, 
which  makes  41I  vibrations,  taking  the  key-note  as  making  440  vibrations 
in  a  second.  Some  organs  and  pianofortes  go  as  low  as  C^^^  with  32  vibra- 
tions in  a  second,  some  grand  pianos  even  as  low  as  A^^^  with  27!  vibrations. 
But  the  musical  character  of  all  these  notes  below  E^  is  imperfect,  for  we 
are  near  the  limit  at  which  it  is  possible  for  the  ear  to  combine  the  separate 
vibrations  to  a  musical  note  (244).  These  notes  can  only  be  used  musically 
with  their  next  higher  octave,  to  which  they  impart  a  certain  character  of 
depth  and  richness. 

In  the  other  direction,  pianofortes  go  to  a'^  with  3,520  or  even  c^  with  4,224 
vibrations  in  a  second.  The  highest  note  of  the  orchestra  is  probably  the 
d"  of  the  piccolo  flute,  which  makes  4,752  vibrations.  Although  the  ear  can 
distinguish  sounds  which  are  still  higher,  they  have  no  longer  a  pleasurable 
character.  And  while  the  notes  which  are  distinguishable  by  the  ear  range 
between  16  and  38,000  vibrations,  or  11  octaves,  those  which  are  musically 
available  range  from  about  40  to  4,000  vibrations,  or  within  7  octaves. 

253.  Wave-Iengtb  of  a  given  note.  Amplitude  of  oscillation. — 
Knowing  the  number  of  vibrations  which  a  sounding  body  makes  in  a 
second,  the  corresponding  wave-length  is  easily  calculated.  For  since  sound 
travels  at  about  1,120  feet  in  a  second,  if  a  body  only  made  one  vibration  in 
a  second  its  wave-length  would  be  1,120  feet  ;  if  it  made  two,  the  wave-length 
would  be  half  of  1,120  feet  ;  if  it  made  three,  the  third,  and  so  on — that  is, 
that  the  7vave-le?igth  of  any  note  is  the  quotient  obtained  by  dividing  the 
velocity  of  sound  by  the  number  of  vibrations  ;  and  this  whatever  the  height 
of  the  sound,  since  the  velocity  is  the  same  for  high  and  low  notes. 

Hence,  calling  zi  the  velocity  of  sound,  /  the  wave-length,  n  the  number 

of  vibrations  in  a  second,  we  have  v  =  In,  from  which  n  =  "^  ;  that  is,  that  the 
number  of  vibrations  is  inversely  as  the  wave-length. 


230  On  Sound.  [253- 

The  amplitude  of  oscillation  which  is  required  for  the  production  of 
audible  sounds  is  very  small.  Lord  Rayleigh  determined  it  in  the  case  of 
the  waves  due  to  a  pipe  which  sounded  the  note  _/"',  and  which  could  be 
heard  at  a  distance  of  820  metres.  He  found  that  the  amplitude  of  the  oscil- 
lation of  these  waves  could  not  be  greater  than  o-ooooooi  of  a  millimetre. 

254.  On  compound  musical  tones  and  harmonics. — When  any  given 
note  (say  C)  is  sounded  on  most  musical  instruments,  not  that  tone  alone  is 
produced,  but  a  series  of  tones,  each  being  of  less  intensity  than  the  one 
preceding  it.  If  C,  which  may  be  called  the  primary  tone,  is  denoted  by 
unity,  the  whole  series  is  given  by  the  numbers  i,  2,  3,  4,  5,  6,  7,  &c.  ;  in 
other  words,  first  the  primary  C  is  sounded,  then  its  octave  becomes  audible, 
then  the  fifth  to  that  octave,  then  the  second  octave,  then  the  third,  fifth, 
and  a  note  between  the  sixth  and  seventh  to  the  second  octave,  and  so  on. 
These  secondary  notes  are  called  the  harmonics  of  the  primary  note.  Though 
feeble  in  comparison  with  the  primary  note,  they  may,  with  a  little  practice, 
be  heard  when  the  primaiy  note  is  produced  on  most  musical  instruments  ; 
when,  for  instance,  one  of  the  lower  notes  is  sounded  on  the  pianoforte. 

2  54<:;.  Consonance  and  Resonance. — A  singular  property  of  bodies  in 
a  state  of  vibration  is  that  of  setting  in  vibration  bodies  at  rest.  Thus,  if 
two  tuning-forks,  tuned  so  as  to  give  accurately  the  same  note,  be  at  some 
distance  from  each  other,  and  one  of  them  be  sounded,  the  other  will  be  set 
in  vibration  and  emit  the  same  note.  But,  if  one  of  the  forks  be  put  slightly 
out  of  tune  with  the  other,  by  attaching  a  piece  of  wax  to  one  prong,  for  in- 
stance, then  the  excitation  of  either  one  will  have  no  effect  on  the  other. 

It  is  remarkable  that  the  successive  action  of  a  series  of  impulses  of  small 
mechanical  force  should,  as  in  this  case,  be  able  to  set  a  relatively  very  heavy 
body — such  as  a  tuning-fork — in  vibration  ;  but  for  this  there  are  many  purely 
mechanical  analogies.  Thus,  if  a  series  of  pulls  be  exerted  in  regular  inter- 
vals on  the  rope  of  a  large  church  bell,  the  superposition  of  these  small  mo- 
tions will  ultimately  set  the  bell  swinging.  A  regiment  of  soldiers  marching 
in  step  over  an  iron  bridge  at  Angers  set  it  in  such  powerful  oscillation  as  to 
endanger  its  stability.  In  like  manner  the  position  of  a  ship  in  the  trough  of 
the  sea  is  very  dangerous,  when  the  period  of  vibration  of  the  waves  coincides 
with  that  of  its  own  vibration. 

This  phenomenon,  that  a  body  in  a  state  of  vibration  has  the  power  of 
causing  an  independent  body  at  rest  to  vibrate  in  the  same  period,  is  called 
conso7iance. 

If  a  metal  wire  freely  suspended  in  the  air  be  tightly  stretched  and  then  be 
set  in  vibration,  the  note  which  it  emits  will  be  feeble,  seeing  that  from  its  small 
surface  it  can  set  in  vibration  only  small  masses  of  air.  So,  too,  a  tuning-fork 
when  sounded  gives  but  a  feeble  note,  but  if  its  stem  be  held  on  a  table  the 
note  becomes  far  louder. 

The  reinforcement  of  a  sound  by  attaching  the  sounding  body  to  a  large, 
dry,  elastic,  wooden  plate,  called  a  sound-board,  or  to  a  wooden  box  enclosing 
a  mass  of  air,  is  called  resonance  ;  the  vibrations  of  the  sounding  body  are 
transmitted  to  the  sound-board,  which,  being  set  in  vibration,  communicates 
its  motion  to  large  masses  of  air. 

Although  the  terms  consonance  and  resonance  are  sometimes  used  indis- 
crimmately,  there  are  distinctions  between  them. 


-255]  HehnJioltd's  Analysis  of  Sound.  231 

Consonance  is  the  excitation  of  an  independent  body  to  vibrate  in  unison 
with  the  sounding  body  ;  it  begins  later  than  the  sounding  body,  and  con- 
tinues after  it  has  become  silent.  Resonance  begins  and  ends  with  the  sound 
of  the  exciting  body.  A  sound-board  strengthens  and  imparts  a  general  sono- 
rity to  a  complex  series  of  notes.  The  more  a  body  diverges  from  the 
form  of  a  plate  and  approaches  that  of  a  rod,  the  more  is  its  resonance 
limited  to  strengthening  one  or  two  notes. 

In  resonance,  however,  there  is  a  certain  amount  of  tuning.  For  the  loud 
and  deep  notes  of  the  cello  a  large  resonance-box  is  used,  and  a  smaller 
one  for  the  higher  notes  of  the  violin.  Small  enclosed  volumes  of  air  also 
strengthen  one  note  in  preference. 

255.  Helmholtz's  analysis  of  sound. — For  the  purpose  of  experimentally 
proving  the  presence  of  the  harmonics  as  distinct  tones,  Von  Helmholtz 
devised  an  instrument  which  he  called  a  resonance-globe.  This  may  be 
shown  by  the  following  experiment,  which  is  an  illustration  of  what  has  been 
said  in  the  previous  article,  and  is  indeed  analogous  in  principle  with  that 
described  in  article  227  : — If  an  empty  glass  cylinder  be  taken,  and  a 
vibrating  tuning-fork  be  held  over  the  mouth  of  the  vessel,  the  air  will  not  be 
set  in  vibration  unless  it  be  of  a  certain  definite  length  ;  such,  indeed,  that 


Fig.  224.  Fig.  225. 

the  wave-length  of  the  fundamental  note  corresponds  to  the  wave-length  of 
the  note  produced  by  the  tuning-fork.  Now,  by  pouring  in  water  we  can 
regulate  the  length  of  the  column  of  air,  and  by  trial  can  hit  off  the  exact 
length  ;  when  this  is  attained  the  note  of  the  tuning-fork  will  be  heard  to 
be  powerfully  reinforced  (227).  A  resonance-globe  (fig.  224)  is  a  glass  globe 
tuned  to  a  particular  note,  furnished  with  two  openings,  one  of  which,  a^  is 
turned  towards  the  origin  of  the  sound,  and  the  other,  b,  by  means  of  an 
india-rubber  tube,  is  applied  to  the  eai".  If  the  tone  proper  to  the  resonance- 
globe  exists  among  the  harmonics  of  the  compound  tone  that  is  sounded, 
it  is  strengthened  by  the  globe,  and  thereby  rendered  distinctly  audible. 
Further,  other  things  being  the  same,  the  note  proper  to  a  given  globe 
depends  on  the  diameter  of  the  globe  and  that  of  the  uncovered  opening. 
Consequently,  by  means  of  a  series  of  such  globes,  the  whole  series  of 
harmonics  in  a  given  compound  tone  can  be  rendered  distinctly  audible, 
and  their  existence  put  beyond  a  doubt. 

Konig,  the  eminent  acoustical  instrument  maker,  has  made  an  important 
modification  in  the  resonance-globe,  to  which  he  has  given  the  form  repre- 
sented in  fig.  225.  The  resonator  is  cylindrical,  and  the  end  which  receives 
the  sound  can  be  drawn  out,  so  that  the  volume  maybe  increased  at  pleasure. 


232  On  Sound.  [255- 

As  the  sound  thereby  becomes  deeper,  the  same  resonator  may  be  tuned  to  a 
variety  of  notes.  On  the  tubulure  fits  a  caoutchouc  tube  by  which  the  vibra- 
tions may  be  transmitted  in  any  direction. 

256.  Konigr's  apparatus  for  the  analysis  of  sound. — As  the  successive 
appHcation  to  the  ear  of  various  resonators  is  both  slow  and  tedious,  Konig 
devised  a  remarkable  apparatus  in  which  a  series  of  resonators  act  on  mano- 
metric  flames  (288)  ;  the  sounds  thus,  as  it  were,  become  visible,  and  may 
be  shown  to  a  large  auditory. 


Fig.  226. 


It  consists  of  an  iron  frame  (fig.  226)  on  which  are  fixed  in  two  parallel 
lines  fourteen  resonators  tuned  so  as  to  give  the  notes  from  F^  to  c" — that  is 
to  say,  four  octaves  and  a  half ;  or  notes  of  which  the  highest  give  the  lower 
harmonics  of  the  primary.  On  the  right  is  a  chamber  C,  which  is  supplied 
with  coal  gas  by  the  caoutchouc  tube,  D,  and  on  which  are  placed  eight 
gas  jets,  each  provided  with  a  manometric  capsule  (288).  Each  jet  is  con- 
nected with  the  chamber  C  by  a  special  caoutchouc  tube,  while  behind  the 
apparatus  a  second  tube  connects  the  same  jet  to  one  of  the  resonators. 


-257J 


Synthesis  of  Sounds. 


233 

On  the  right  of  the  jets  is  a  system  of  rotating  mirrors  identical  with  that 
described  in  article  288. 

These  details  being  understood,  suppose  the  largest  resonator  on  the  right 
tuned  to  resound  with  the  note  i,  and  seven  others  with  the  harmonics  of 
this  note.  Let  the  sound  i  be  produced  in  part  of  this  apparatus  ;  if  it  is 
simple,  the  lower  resonator  alone  answers,  and  the  corresponding  flame  is 
alone  dentated  ;  but  if  the  fundamental  note  is  accompanied  by  one  or  more 
of  its  harmonics,  the  corresponding  resonators  speak  at  the  same  time,  which 
is  recognised  by  the  dentation  of  their  flames  ;  and  thus  the  constituents  of 
each  sound  may  be  detected. 

257.  Synthesis  of  sounds. — Not  only  has  Von  Helmholtz  succeeded  in 
decomposing  sounds  into  their  constituents  ;  he  has  verified  the  result  of  his 
analysis  by  performing  the  reverse  operation,  the  synthesis  ;  that  is,  he  has 


Fig.  227. 


reproduced  a  given  sound  by  combining  the  individual  sounds  of  which  his 
resonators  had  shown  that  it  was  composed.  The  apparatus  which  he  used 
for  this  purpose  consists  of  eleven  tuning-forks,  the  first  of  which  yields  the 
fundamental  note  of  256  vibrations,  or  C,  nine  others  its  harmonics,  while  the 
eleventh  serves  as  make  and  break  to  cause  the  diapasons  to  vibrate  by  means 
of  electro-magnets.  Each  diapason  has  a  special  electro-magnet,  and  more- 
over a  resonator,  which  strengthens  it. 

All  these  diapasons  and  their  accessories  are  arranged  in  parallel  lines  of 
five  (fig.  227),  the  first  comprising  the  fundamental  note  and  its  uneven  har- 
monics, 3,  5,  7,  and  9  ;  the  second  the  even  harmonics,  2,  4,  6,  8,  and  10  ; 
beyond,  there  is  the  diapason  break  K  arranged  horizontally.  One  of  its 
prongs  is  provided  with  a  platinum  point  which  grazes  the  surface  of  mercury 


2  34  On  Sound.  [257- 

contained  in  a  small  cup,  the  bottom  of  which  is  connected,  by  a  copper  wire, 
with  an  electro-magnet  placed  in  front  of  the  diapason. 

The  apparatus  being  thus  arranged,  a  wire  from  a  voltaic  battery  is  con- 
nected with  the  binding  screw,  c,  and  this  with  the  electro-magnet  E  ;  which 
in  turn  is  connected  with  those  of  the  nine  following  diapasons,  and  then 
with  the  diapason  K  itself.  So  long  as  the  diapason  does  not  vibrate,  the 
current  does  not  pass,  for  the  platinum  point  does  not  dip  in  the  mercury 
cup  which  is  connected  with  the  other  pole  of  the  battery.  But  when  the 
diapason  is  made  to  vibrate  by  means  of  a  bow,  the  current  passes.  Owing 
to  their  elasticity,  the  limbs  of  the  tuning-fork  soon  revert  to  their  original 
position,  the  point  is  no  longer  in  the  mercury,  the  current  is  broken,  and  so 
on  at  each  double  vibration  of  the  diapason.  This  intermittence  of  the 
current  being  transmitted  to  all  the  other  electro-magnets,  they  are  alternately 
active  and  inactive.  Hence  they  communicate  to  all  the  diapasons  by  their 
attraction  the  same  number  of  vibrations.  This  is  the  case  with  the  diapason 
I,  which  is  tuned  in  unison  with  the  diapason  break  ;  but  the  diapason  3, 
being  tuned  to  make  three  times  as  many  vibrations,  makes  three  vibrations 
at  each  break  of  the  current  ;  that  is  to  say,  the  electro-magnet  only  attracts 
it  at  every  third  vibration  ;  in  like  manner,  diapason  5  only  receives  a  fresh 
impulse  every  five  vibrations,  and  so  on. 

The  following  is  the  working  of  the  apparatus  : — The  resonator  of  each 
■diapason  is  closed  by  a  clapper  O  (fig.  228),  so  that  the  sounds  made  by  the 

diapasons  are  scarcely 
perceptible  when  the  clap- 
pers are  lowered.  Each  of 
these  is  fixed  to  the  end  of 
a  bent  lever,  the  shorter 
arm  of  which  is  worked 
by  a  cord  a,  which  is  con- 
nected with  one  of  the 
keys  of  a  keyboard  placed 
in  front  of  the  apparatus 
(fig.  227).  When  a  key  is 
depressed,  the  cord  moves 
the  le\er,  which  raises  the 
clapper,  and  the  resonator 
then  acts  by  strengthening- 
its  diapason.  Hence  by 
depressing  any  key  we 
may  add  to  the  funda- 
mental sounds  any  of  the  nine  primary  harmonics,  and  thus  reproduce  the 
sounds,  the  composition  of  which  has  been  determined  by  analysis.  Thus  by 
depressing  all  the  keys  at  once  we  obtain  the  sound  of  an  open  pipe  in  unison 
with  the  deepest  diapason.  By  depressing  the  key  of  the  fundamental  note 
and  those  of  its  uneven  harmonics,  we  obtain  the  sound  of  a  closed  pipe. 

258.  Results  of  Von  Helmholtz's  researches. —By  both  his  analytical 
and  synthetical  investigations  into  sounds  of  the  most  varied  kinds — those 
from  various  musical  instruments,  the  human  voice,  and  even  noises — Von 
Helmholtz  has  fully  succeeded  in  explaining  the  different  timbre  or  quality  of 


Fig.  22S 


-259]  Production  of  Vocal  Sounds.  235 

sounds.  It  is  due  to  the  different  intensities  of  the  harmonics  which  accom- 
pany the  primary  tones  of  these  sounds.  The  leading  results  of  these  re- 
searches into  the  colour  (246)  of  sounds  may  be  thus  stated  : — 

i.  Simple  notes,  as  those  produced  by  a  tuning-fork  with  a  resonance-box, 
and  by  wide  covered  pipes,  are  soft  and  agreeable  without  any  roughness, 
but  weak,  and  in  the  deeper  notes  dull. 

ii.  Musical  sounds  accompanied  by  a  series  of  harmonics,  say  up  to  the 
sixth,  in  moderate  strength,  are  full  and  musical.  In  comparison  with  simple 
tones  they  are  grander,  richer,  and  more  sonorous.  Such  are  the  sounds  of 
open  organ-pipes,  of  the  pianoforte,  &c. 

iii.  If  only  the  uneven  harmonics  are  present,  as  in  the  case  of  narrow 
stopped  pipes,  of  pianoforte  strings  struck  in  the  middle,  clarionets,  &c.,  the 
sound  becomes  indistinct  ;  and,  when  a  greater  number  of  harmonics  is 
audible,  the  sound  acquires  a  nasal  character. 

iv.  If  the  harmonics  beyond  the  sixth  and  seventh  are  very  distinct, 
the  sound  becomes  sharp  and  rough.  If  less  strong,  the  harmonics  are  not 
prejudicial  to  the  musical  usefulness  of  the  notes.  On  the  contrary,  they 
are  useful  as  imparting  character  and  expression  to  the  music.  Of  this  kind 
are  most  stringed  instruments,  and  most  pipes  furnished  with  tongues,  &c. 
Sounds  in  which  harmonics  are  particularly  strong  accjuire  thereby  a  pecu- 
.  liarly  penetrating  character  ;  such  are  those  yielded  by  brass  instruments. 

259.  Production  of  vocal  sounds. — The  trachea  or  windpipe  is  a  tube 
which  terminates  at  one  end  in  the  lungs,  and  at  the  other  in  the  tatynx, 
which    is   the   true    organ    of    vocal   sound. 

Fig.    229  represents  a  horizontal  section  of  c  p 

this  organ.  It  consists  of  a  number  of  car- 
tilaginous structures,  bb.,  which  are  connected 
by  various  muscles,  by  which  great  variety  and 
control  in  the  motions  are  attainable.  These 
muscles  are  connected  with,  and  move,  two 
elastic  membranes  or  bands  with  broad  bases 
fixed  to  the  larynx,  and  with  sharp  edges  cc ; 
these  are  called  the  vocal  chords.  Accord- 
ing to  the  pressure  of  the  muscles  these 
chords  are   more  or  less   tightly  stretched,  I 

and  the  space  between  them,  the  vocal  slit, 
is  narrower  or  wider  accordingly.  In  ordi- 
nary breathing,  air  passes  through  the  triangular  aperture  o ;  but  when  in 
singing  this  is  closed,  the  vocal  chords  are  stretched  and  are  put  in  vibration 
by  the  current  of  air,  and  produce  tones  which  are  higher  the  more  tightly 
the  chords  are  stretched,  and  the  narrower  is  the  vocal  slit.  These  changes 
can  be  effected  with  surprising  rapidity,  so  that  in  this  respect  the  human 
voice  far  exceeds  anything  that  can  be  made  artificially. 

The  notes  produced  by  men  are  deeper  than  those  of  women  or  boys, 
because  in  them  the  larynx  is  longer  and  the  vocal  chords  larger  and  thicker  ; 
hence,  though  equally  elastic,  they  vibrate  less  swiftly.  The  vocal  chords 
are  18  miUimetres  long  in  men,  and  12  millimetres  long  in  women.  Chest 
notes  are  due  to  the  fact  that  the  whole  membrane  vibrates,  while  the  fal- 
setto is  produced  by  a  vibration  of  the  extreme  edges  only.     The  ordinary 


!36 


On  Sound. 


[259- 


compass  of  the  individual  voice  is  within  two  octaves,  though  this  is  exceeded 
by  some  celebrated  singers.  Catalani,  for  instance,  is  said  to  have  had  a 
range  of  3|  octaves. 

The  wave-length  of  the  sounds  emitted  by  a  man's  voice  in  ordinary  con- 
versation is  from  8  feet  to  12  feet,  and  that  of  a  woman's  voice  is  from  2  feet 
to  4  feet. 

The  vowel  sounds  can  be  produced  in  any  pitch,  and  the  difference  in 
them  arises  from  the  fact  that  to  form  a  given  vowel  sound  one  or  more 
characteristic  notes,  which  are  always  the  same,  must  be  added.  These 
change  with  the  syllable  pronounced,  but  depend  neither  on  the  height  of 
the  note,  nor  on  the  person  who  emits  them. 

The  form  and  cavity  of  the  mouth  can  be  greatly  modified  by  the  extent 
to  which  it  is  opened,  by  the  altered  position  of  the  tongue,  and  so  forth.  It 
thus  forms  a  resonator  which  can  be  cjuickly  and  completely  controlled. 
When  the  mouth  is  adjusted  so  as  to  produce  the  broad  A,  as  in  father^  it 
has  then  a  sort  of  funnel  shape,  with  the  wide  part  outward  ;  for  O,  as  in 
more,  the  effect  is  like  that  of  a  bottle  with  a  wide  neck  ;  and  for  U,  as  in 
poor,  it  is  that  of  a  similar  bottle  with  a  narrow  neck.  For  the  other  vowels, 
such  as  A,  E,  and  I,  the  effect  is  as  if  the  bottle  were  prolonged  by  a  tube, 
formed  by  contracting  the  tongue  against  the  palate. 

If  now,  while  the  mouth  is  adjusted  for  the  position  in  which  it  could 
utter  the  vowel  U,  on  successively  holding  different  vibrating  tuning-forks  in 
front  of  it,  only  that  emitting  the  note  /  will  be  found  to  be  reinforced  by 
the  enclosed  column  of  air  vibrating  in  unison  with  it.  This  is  accordingly 
the  characteristic  note  of  that  vowel ;  in  like  manner  b'  is  the  note  for  O, 
and  b"  that  for  A.  The  other  vowel  sounds,  such  as  I,  have  a  higher  and 
lower  characteristic  note  ;  thus  those  of  A  as  in  day  are  d  and  a'",  of  I,/ 
and  rf'"'.  In  most  cases,  however,  the  deeper  notes  have  but  little  influence. 
260.  Perception  of  sounds.  The  ear. — The  organ  of  hearing  in  man  con- 
sists of  several  structures  ; 
there  is  first  the  outer  ear 
(fig.  230)  by  which  the 
sound  is  collected  and 
transmitted  through  the 
auditory  passage,  a,  to 
the  drum  or  tympiDtum,  t. 
This  is  a  delicate  tightly 
stretched  membrane  or 
skin  which  separates  the 
outer  ear  from  the  middle 
ear  or  tympanic  cavity. 
This  is  a  cavity  in  the 
temporal  bone  in  which 
are  several  small  bones 
whose  dimensions  are 
'^'  ~^°'  considerably  exaggerated 

in  the  figure.  One  of  these,  the  hammer,  d,  is  attached  at  one  end  to  the 
drum,  and  at  the  other  is  jointed  to  the  attvil,  e;  the  latter  is  connected  by 
means  of  the  stirrup  bone,f,  to  the  oval  tvindow,  an  aperture  closed  by  a 


-262  J  Beats.  237 

fine  membrane  and  which  separates  the  tympanic  cavity  from  the  labyrinth. 
The  tympanic  cavity  is  also  connected  by  the  Eustachian  tube.,  b,  with  the 
cavity  of  the  mouth,  so  that  the  air  in  it  is  always  under  the  same  pressure. 

The  labyrinth  is  a  complicated  structure  filled  with  fluid  ;  it  is  entirely  of 
bone,  with  the  exception  of  the  oval  window  already  mentioned  and  the 
round  window,  o.  The  labyrinth  consists  of  three  parts  :  the  vestibule, 
which  is  closed  by  the  oval  window  ;  the  three  semicircular  canals,  k  ;  and 
the  spiral-shaped  cochlea  or  snail  shell,  s.  This  is  separated  throughout  its 
entire  length  by  a  division  partly  of  bony  projection  and  partly  of  membrane  ; 
the  upper  part  of  this  division  is  connected  with  the  vestibule,  and  therefore 
with  the  oval  window,  while  the  lower  part  is  connected  with  the  round 
window.  In  the  labyrinthine  fluid  of  this  part  the  termination  of  the  auditory 
nerve  is  spread,  the  other  end  leading  to  the  brain. 

The  membranous  part  of  this  diaphragm  is  lined  with  about  3,000 
extremely  minute  fibres,  which  are  the  terminations  of  the  acoustic  nerve,  n. 
Each  of  these,  which  are  called  CortVs  fibres,  seems  to  be  tuned  for  a 
particular  note  as  if  it  were  a  small  resonator.  Thus  when  the  vibrations  of 
any  particular  note  reach  these  fibres,  through  the  intervention  of  the  stirrup 
bone  and  the  fluid  of  the  labyrinth,  one  fibre  or  set  of  fibres  only  vibrates  in 
unison  with  this  note,  and  is  deaf  for  all  others.  Hence  each  simple  note 
only  causes  one  fibre  to  vibrate,  while  compound  notes  cause  several ;  just 
as  when  we  sing  with  a  piano,  only  the  fundamental  note  and  its  harmonics 
vibrate.  Thus,  however  complex  external  sounds  may  be,  these  microscopic 
fibres  can  analyse  them  and  reveal  the  constituents  of  which  they  are  formed. 

261.  Interference  of  sound. — If  two  waves  of  sound  of  the  same  length, 
proceed  in  the  same  direction,  and  if  they  coincide  in  their  phases,  they 
strengthen  one  another  ;  if,  however,  their  phases  differ  by  half  a  wave-length, 
they  neutralise  each  other,  and  silence  is  the  result.  This  is  called  thezV/Z^r- 
ference  of  sound. 

It  may  be  illustrated  by  a  number  of  experiments,  of  which  that  repre- 
sented in  fig.  231  is  one  of  the  simplest  and  most  convenient.  Two  T-shaped 
glass  tubes,  obac  and  nedf,  are 
connected  at  one  end  by  a 
short  india-rubber  tube  ad, 
while  at  the  other  ends  they 
are  connected  by  a  long 
india-rubber  tube,  cqf.  The 
end  0  provided  with  a  caout- 
chouc tube  is  held  in  one 
ear,    the    other    ear     being  „. 

"  r  ig.  231. 

closed,  and  a  tuning-fork  is  • 

sounded  in  front  of  the  long  free  tube,  nrs.  If  the  length  of  the  india-rubber 
tube  c^/be  half  the  wave-length  of  the  note  produced  by  the  fork,  the  sounds 
will  reach  the  ear  in  completely  opposite  phases  ;  they  will  accordingly 
neutralise  each  other  and  no  sound  will  be  heard.  But  if  this  india-rubber 
tube  is  closed  by  pinching  it,  the  note  is  at  once  heard.  If  the  tuning-fork 
gives  the  note  c,  the  note  it  produces  makes  528  vibrations  in  a  second,  and 
the  length  of  the  tube  should  be  34  centimetres. 

262    Beats If  the  notes  are  different  and  are  not  quite  in  the  same 


Fig.  232. 


238  On  Sound.  [262- 

phase,  they  alternately  weaken  and  strengthen  each  other ;  they  are  said  to 
beat  with  one  another.  This  may  be  explained  as  follows  : — Suppose  AB,  in 
fig.  232,  to  be  a  row  of  particles  transmitting  the  sound  :  suppose  the  vibra- 
tions producing  the  one  note  to  be  indicated  by  the  continuous  curved  line  ; 
then,  on  the  one  hand,  the  ordinates  of  the  different  points  of  AB  give  the 
velocities  with  which  those  points  are  simultaneously  moving,  and,  on  the 
other  hand,  each  point  will  have  successively  the  different  velocities  repre- 
sented by  the  successive  ordinates.  In  like  manner  let  the  dotted  line  show 
the  vibrations  which  produce  the  second  note.  And,  for  the  sake  of  distinct- 
ness, suppose  the  number  of  vibrations  in  a  second  producing  the  former 
note  to  be  to  that  producing  the  latter  in  the  ratio  of  3  :  2.  Now.  let  us  con- 
sider any  point  which 
f,  Q  when  at  rest  occupies 

the  position  N  ;  draw 
the  ordinate,  cutting 
the  former  curve  in  P 
and  the  latter  in  Q. 
If  the  notes  were 
sounded  separately, 
the  velocity  of  N  at  a 
given  distance  pro- 
duced by  the  former 
note  would  be  PN,  and  that  of  N  at  the  same  instant  produced  by  the  latter 
note  would  be  QN.  Consequently,  as  they  are  sounded  together,  the  actual 
velocity  of  N  at  the  given  instant  is  the  sum  of  these,  or  PN  +  QN.  If  at 
the  same  instant  we  consider  the  point  «,  its  velocity  will  consist  q{  j)n  and 
nq  jointly,  but,  as  these  are  in  opposite  directions,  its  actual  amount  will  be 
pn-  7jq.  Hence  the  actual  velocity  resulting  from  the  co-existence  of  the  two 
notes  will  be  indicated  by  the  curve  in  fig.  233,  whose  ordinates  equal  the 
(algebraical)  sum  of  the  corresponding  ordinates  of  the  two  curves  in  fig. 
232  ;  that  is,  if  AN,  A«,  .  .  .  represent  equal  distances  in  both  figures,  the 
curve  is  described  by  taking  RN  equal  to  PN  +  QN,  rn  equal  io pn  -  gft, 
and  so  on.  This  curve  shows  by  its  successive  ordinates  the  simultaneous 
velocities  of  the  different  particles  of  AB,  and  the  successive  velocities  com- 
municated to  the  drum  of  the  ear.  An  inspection  of  the  figure  will  shov/ 
that  the  velocities  are  first  great,  then  small,  then  great,  and  so  on,  the  drum 
being  first  moved  rapidly  for  a  short  time,  then  for  a  short  time  nearly  brought 
to  rest,  and  so  on.  In  short,  the  effect  of  the  beating  of  notes  on  the  ear, 
as  compared  with  that  of  a  continuous  note,  is  strictly  analogous  to  the  effect 
produced  on  the  eye  by  a  flickering,  as  compared  with  a  steady,  light. 

,  It  may  be  proved  that  when  two  simple  notes  are  produced  by  ;«  and  n 
double  vibrations  per  second,  they  produce  m-n  beats  per  second  ;  thus,  if 
C  is  produced  by  128,  and  D  by  144,  double  vibrations  per  second,  on  being 
sounded  together  they  will  produce  16  beats  per  second.  It  has  been  ascer- 
tained that  the  beats  produced  by  two  notes  are  not  audible  unless  the  ratio 
m  :  n  is  less  than  the  ratio  6  :  5.  Hence,  in  the  case  represented  by  fig.  232, 
though  the  alternations  of  intensity  exist,  they  would  not  be  audible.  Also, 
if  the  notes  have  very  different  intensities,  the  intensity  of  the  beat  is  very 
much  disguised. 


-263]  Combinational  Notes.  239 

It  IS  found  that  when  beats  are  fewer  than  10  per  second  or  more  than  70 
per  second  they  are  disagreeable,  but  not  to  the  extent  of  producing  discord. 
Beats  from  10  to  70  per  second  may  be  regarded  as  the  source  of  all  discord 
in  music,  the  maximum  of  dissonance  being  attained  when  about  30  beats 
are  produced  in  a  second.  For  example,  if  c  and  B  are  sounded  together 
the  effect  is  very  discordant,  the  interval  between  those  notes  being  16  :  15, 
so  that  the  beats  are  audible,  and  the  number  of  beats  per  second  being  16. 
On  the  other  hand,  if  C,  E,  and  G  are  sounded  together  there  is  no  disso- 
nance ;  but  if  C,  E,  G,  B  are  sounded  together  the  discord  is  very  marked, 
since  C  produces  c,  which  is  discordant  with  B.  It  will  be  remarked  that 
C,  E,  G  is  a  major  triad,  while  E,  G,  B  is  a  minor  triad. 

A  compound  musical  note,  being  composed  of  simple  notes  represented 
by  I,  2,  3,  4,  5,  6,  7,  &c.,  does  not  give  rise  to  any  simple  notes  capable  of 
producing  an  audible  beat  up  to  the  seventh — the  sixth  and  seventh  are  the 
first  that  produce  an  audible  beat.  It  is  for  this  reason  that  there  is  no 
trace  of  roughness  in  a  compound  note,  unless  the  seventh  harmonic  be 
audible. 

If  we  were  to  represent  graphically  a  compound  note,  we  should  proceed 
to  construct  a  curve  out  of  simple  notes  of  different  intensities  in  the  same 
manner  as  fig.  233  is  constructed  from  two  simple  notes  of  equal  intensity 
represented  by  fig.  232.  It  is  evident  that  the  resulting  curve  will  take 
different y»rw.y  according  to  the  presence  or  absence  of  different  harmonics 
and  their  different  intensities  ;  in  other  words,  the  quality  or  timbre  of  the 
notes  produced  by  different  instruments  will  depend  upon  the  form  of  the 
vibrations  producing  the  sound. 

Beats  not  too  fast  to  be  readily  counted  arise  between  adjacent  notes  in 
the  lower  octaves  of  large  organs.  They  are  also  met  with  in  the  sounds 
of  church  bells,  and  in  those  emitted  by  telegraph  wires  when  vibrating 
powerfully  in  a  strong  wind.  They  are  heard  very  distinctly  in  the  latter 
case  by  pressing  one  ear  against  a  telegraph-post  and  closing  the  other. 

By  means  of  beats,  the  notes  emitted  by  two  musical  instruments  may  be 
brought  into  very  accurate  unison,  by  continuing  the  tuning  until  the  beats 
disappear.  In  order  to  make  tuning-forks  produce  the  normal  number  of 
440  vibrations,  an  auxiliary  tuning-fork  is  used  which  makes  436  vibrations  ; 
each  of  the  forks  under  experiment  iiiust  then  make  with  this  4  beats  in  a 
second,  which  can  be  controlled  with  very  great  accuracy. 

263.  Combinational  notes. — Besides  the  beats  produced  when  two 
musical  notes  are  sounded  together,  there  is  another  and  distinct  pheno- 
menon, which  may  be  thus  described  :  —  Suppose  two  simple  notes  to  be 
simultaneously  produced  by  n  and  ;;/  vibrations  per  second.  It  has  been 
shown  by  Helmholtz  that  they  generate  a  series  of  other  notes.  The  prin- 
cipal one  of  these,  which  may  be  called  the  differential  note,  is  produced 
hy  n-tn  vibrations  per  second.  Its  intensity  is  usually  very  small,  but  it  is 
distinctly  audible  in  beats.  It  has  been  called  the  grave  harmonic,  as  its 
pitch  is  generally  much  lower  than  that  of  the  notes  by  which  it  is  generated. 
It  has  been  supposed  to  be  caused  by  the  beats  becoming  too  numerous  to 
be  distinguished,  and  coalescing  into  a  continuous  sound,  and  this  supposition 
was  countenanced  by  the  fact  that  its  pitch  is  the  same  as  the  beat  number. 
The  supposition   is  shown    to  be  erroneous,  first,  by  the  existence  of  the 


240  On  Sound.  [263- 

dififerential  tones  for  intervals  that  do  not  beat  ;  and,  secondly,  by  the  fact 
that,  under  certain  circumstances,  both  the  beats  and  the  dififerential  tones 
may  be  heard  together. 

264.  The  physical  constitution  of  musical  chords. — Let  us  suppose 
two  compound  notes  to  be  sounded  together,  say  C  and  G  ;  then  we  obtain 
two  series  of  notes  each  consisting  of  a  primary  and  its  harmonics,  namely 
denoting  C  by  4,  the  two  series,  4,  8,  12,  16.  .  .  .  and  6,  12,  18,  24,  &c.  Now, 
if,  instead  of  producing  the  two  notes  C  and  G,  we  had  sounded  the  octave 
below  C,  we  should  have  produced  the  series,  2,  4,  6,  8,  10,  12,  14,  16,  18,  &c. 
It  is  plain  that  the  two  former  series  when  joined  differ  from  the  last  in  the 
following  respects  : — {a)  The  primary  note  2  is  omitted.  (<5)  In  the  case  of 
the  last  series,  the  consecutive  notes  continually  decrease  in  intensity  ; 
whereas  in  the  two  foniier  series,  4  and  6  are  of  the  same  intensity,  8  is  of 
lower  intensity,  but  the  two  12's  will  strengthen  each  other,  and  so  on. 
{c)  Certain  of  the  harmonics  of  the  primary  2  are  omitted  ;  for  example,  10,  i^K 
&c.,  do  not  occur  in  either  of  the  two  former  series.  In  spite  of  these  dif- 
ferences, however,  the  two  compound  notes  affect  the  ear  in  a  manner  very 
closely  resembling  a  single  compound  note  ;  in  short,  they  coalesce  into  a 
single  note  with  an  artificial  colour.  It  may  be  added  that  in  the  case  above 
taken  C  and  G  produce  as  a  combination  note  2  (that  is  6  -  4),  so  that, 
strictly  speaking,  the  2  is  not  wanted  in  the  series  produced  by  C  and  G, 
only  it  exists  in  very  diminished  intensity.  The  same  explanation  will 
apply  to  all  possible  chords  ;  for  example,  in  the  case  of  the  major  chord, 
C,  E,  G,  we  have  a  note  of  artificial  colour  expressed  by  the  series  of  simple 
tones,  4,  5,  6,  8,  10,  12,  15,  16,  18,  t&c,  together  with  the  combination  notes, 

I,  I,  2.  It  will  be  remarked  that  in  the  whole  of  this  series  there  are  no  dis- 
sonant notes  introduced,  except  15,  16,  and  16,  18,  and  this  dissonance  will 
be  inappreciably  slight,  since  15  is  the  third  harmonic  of  5,  and  16  the 
fourth  harmonic  of  4,  so  that  their  intensities  will  be  different,  as  also  will  be 
the  intensities  of  16  and  18.  On  the  other  hand,  nearly  all  the  notes  which 
form  a  natural  compound  note  are  present,  namely,  there  are  i,  2,  4,  5,  6,  8, 
10,  12,  &c.,  in  place  of  i,  2,  3,  4, -5,  6,  7,  8,  9,  10,  11,  12,  &c.  In  short,  the 
major  triad  differs  only  from  a  natural  compound  note  in  that  it  consists  of 
a  series  of  simple  notes  of  different  intensities,  and  omits  those  which,  by 
beating  with  the  neighbouring  note,  would  produce  dissonance  ;  for  example 
7,  which  would  beat  with  6  and  8  ;  9,  which  would  beat  with  8  and  10 ;  and 

II,  which  would  beat  with  lo  and  12.  It  is  this  circumstance  which  renders 
the  major  chord  of  such  great  importance  in  harmony.  If  the  constituents 
of  the  minor  chord  are  similarly  discussed,  namely,  three  compound  tones 
whose  primaries  are  proportional  to  10,  12,  15,  it  will  be  found  to  differ  from 
the  major  chord  in  the  following  principal  respects  : — ia)  The  primary  of  the 
natural  tone  to  which  it  approximates'  is  very  much  deeper  than  that  of  the 
corresponding  major  chord,  {b)  It  introduces  the  differential  notes,  2,  3,  5, 
which  form  a  major  chord.  Now  it  has  already  been  remarked  that  when  a 
major  and  minor  chord  are  sounded  together,  they  are  distinctly  dissonant  ; 
for  example,  when  C,  E,  G,  A  are  sounded  together.  Accordingly,  the  fact 
of  the  dififerential  notes  forming  a  major  chord  shows  that  an  elementary 
dissonance  exists  in  every  minor  chord. 


-267j  Transverse  Vibrations  of  Strings.  241 


CHAPTER   IV. 

VIBRATIONS   OF    STRETCHED    STRINGS    AND    OF   COLUMNS    OF   AIR. 

265.  Vibrations  of  strings. — By  a  strmg  is  meant  the  string  of  a 
musical  instrument,  such  as  a  vioHn,  which  is  stretched  by  a  certain  force, 
and  is  commonly  of  catgut,  or  is  a  metal  wire.  The  vibrations  which 
strings  experience  may  be  either  transverse  or  lo?tgitudi?ial,  but  practically 
the  former  are  alone  important.  Transverse  vibrations  may  be  produced 
by  drawing  a  bow  across  the  string,  as  in  the  case  of  the  violin  ;  or  by 
striking  the  string,  as  in  the  case  of  the  pianoforte  :  or  by  pulling  it  trans- 
versely, and  then  letting  it  go  suddenly,  as  in  the  case  of  the  guitar  and  harp. 

266.  Sonometer. — The  sonometer  is  an  apparatus  by  which  the  trans- 
verse vibrations  of  strings  may  be  studied.     It  is  also  called  the  nionochord . 


Fig.  234 

because  it  has  often  only  one  string.  In  addition  to  the  string,  it  consists 
of  a  box  of  thin  wood  which  has  the  effect  of  strengthening  the  sound  ;  this 
it  does  by  presenting  a  far  larger  area  to  the  air  than  the  string  itself. 
On  this  there  are  two  fixed  bridges,  A  and  D  (fig.  234),  over  which  and 
over  the  pulley  ;/,  passes  the  string,  which  is  usually  a  metal  wire.  This 
is  fastened  at  one  end,  and  stretched  at  the  other  by  weights,  P,  which  can 
be  increased  at  will.  By  means  of  a  third  movable  bridge,  B,  the  length  of 
that  portion  of  the  wire  which  is  to  be  put  in  vibration  can  be  altered  at 
pleasure. 

267.  laws  of  the  transverse  vibrations  of  strings. — If  /  be  the 
length  of  a  string— that  is,  the  vibrating  part  between  two  bridges,  A  and  B 
(fig.  234) — r  the  radius  of  the  string,  d  its  density,  P  the  stretching  weight, 
and  ;/  the  number  of  vibrations  per  second,  it  is  found  by  calculation  that 

n  =    '-  t,  /-4  ;  -  being  the  ratio  of  the  circumference  to  the  diameter,  <f 
2ri'\  Trd 

the  acceleration  of  gravity. 


242  On  Sound.  [267- 

The  above  formula  expresses  the  following  laws  : — 

I.  The  stretching  weight  or  tension  being  constant,  the  number  of  vibra- 
tions in  a  second  is  inversely  as  the  length. 

II.  The  number  of  vibrations  in  a  second  is  inversely  as  the  diameter  of 
the  string. 

III.  The  7iumber  of  vibrations  in  a  second  is  directly  as  the  square  root  of 
the  stretchiiig  weight  or  tensiott. 

IV.  The  7mmber  of  tnbrations  in  a  second  of  a  string  is  inversely  as  the 
square  root  of  its  de7isity. 

These  laws  are  applied  in  the  construction  of  stringed  instruments,  in 
which  the  length,  diameter,  tension,  and  material  of  the  strings  are  so 
chosen  that  given  notes  may  be  produced  from  them. 

268.  Experimental  verification  of  the  laws  of  the  transverse  vibra- 
tion of  string's. — Laiu  oj  the  lengths.  In  order  to  prove  this  law,  we  may  call 
to  mind  that  the  relative  numbers  of  vibrations  of  the  notes  of  the  gamut  are 
CDEFGABc 

T  9  5  4  3  5  1_5  ., 

If  now  the  entire  length  of  the  sonometer  be  made  to  vibrate,  and  then,  by 
means  of  the  bridge  B,  the  lengths  |,  |,  f,  |,  f,  ^,  |,  which  are  the  inverse  of 
the  above  numbers,  be  successively  made  to  vibrate,  all  the  notes  of  the 
gamut  are  successively  obtained,  which  proves  the  first  law. 

Law  of  the  diameters.  This  law  is  verified  by  stretching  upon  the  sono- 
meter two  cords  of  the  same  material,  the  diameters  of  which  are  as  3  to  2, 
for  instance.  When  these  are  made  to  vibrate,  the  second  cord  gives  the 
fifth  above  the  other  ;  which  shows  that  it  makes  three  vibrations  while  the 
first  makes  two. 

Latu  of  the  tensions.  Having  placed  on  the  sonometer  two  identical 
strings,  they  are  stretched  by  weights  which  are  as  4:9.  The  second  now 
gives  the  fifth  of  the  first,  from  which  it  is  concluded  that  the  numbers  of 
their  vibrations  are  as  2  :  3  ;  that  is,  as  the  square  roots  of  the  tensions.  If 
the  two  weights  are  as  16  to  25,  the  major  third  or  |  would  be  obtained. 

Law  of  the  densities.  Two  strings  of  the  same  radius,  but  different 
densities,  are  fixed  on  the  sonometer.  Having  been  subjected  to  the  same 
stretching  weight,  the  position  of  the  movable  bridge  on  the  denser  one  is 
altered  until  it  is  in  unison  with  the  other  string.  If  then  ^and  d'  are  the 
densities  of  the  two  strings,  and  /  and  /'  the  lengths  which  vibrate  in  unison, 

we  find  —=  ^'^— „.     But  as  we  know  from  the  first  law  that  -  =  '^  ,  we  ha\e 
/        s/d  V      n 

=  , ,  which  verifies  this  law.  Thus,  if  a  copper  wire,  whose  density  is  g 
n'       ^d  •'       ^' 

and  a  catgut  string  of  the  density  i,  are  of  equal  length  and  diameter,  and 

are  stretched  by  the  same  weight,  the  vibrations  of  the  copper  wire  will  be 

one-third  as  rapid  as  those  of  the  string. 

The  laws  of  vibrating  strings  presuppose  that  they  are  long,  flexible,  and 

tightly  stretched  ;  but  if  they  are  short,  stout,  and  iDut  little  stretched,  the 

rigidity  of  the  string  comes  into  play,  and  the  number  of  vibrations  they 

make  is  higher  than  the  theoretical  number  ;  the  effect  of  the  rigidity  is  the 

same  as  if  a  constant  weight  were  added  to  the  stretching  weight.      - 


-270] 


Wind  Instrnincnts. 


243 


269.  Nodes  and  loops. — Let  us  suppose  the  string  AD  (fig.  234)  to  begin 
vibrating,  the  ends  A  and  D  being  fixed,  and,  while  it  is  doing  so,  let  a  point 
B  be  brought  to  rest  by  a  stop,  and  let  us  suppose  DB  to  be  one-third  part 
of  AD.  The  part  DB  must  now  vibrate  about  B  and  D  as  fixed  points  in  the 
manner  indicated  by  the  continuous  and  dotted  lines  (fig.  235)  ;  now  all  parts 
of  the  same  string  tend  to  make  a  vibration  in  the  same  time  ;  accordingly,  the 
part  between  "A  and  B  will  not  perform  a  single  vibration,  but  will  divide  into 
two  at  the  point  C,  and  vibrate  in  the  manner  shown  in  the  figure.  If  BD 
were  one-fourth  part  of  AD  (fig.  236),  the  part  AB  would  be  subdivided  at 
C  and  C  into  three  vibrating  portions  each  equal  to  BD.  The  points  B,  C,  C 
are  called  nodes  or  nodal pohits  ;  the  middle  point  of  the  part  of  the  string 
between  any  two  consecutive  nodes  is  called  a  loop  or  ve7itral  segmetit.  It 
will  be  remarked  that  the  ratio  of  BD  :  BA  must  be  that  of  some  two  whole 
numbers,  for  example,  i  :  2,  i  :  3,  2  :  3,  &c.,  otherwise  the  nodes  cannot  be 
formed,  since  the  two  portions  of  the  string  cannot  then  be  made  to  vibrate 
at  the  same  time,  and  the  vibrations  will  interfere  with  and  soon  destroy  one 
another. 

If  now  we  refer  to  fig.  235,  the  existence  of  the  node  at  C  can  be  easily 
proved  by  bending  some  light  pieces  of  paper,  and  placing  them  as  riders 
on    the    string,  say 


three  pieces,  one 
at  C  and  the  others 
respectively  mid- 
way between  B  and 
C,  and  between  C 
and  A.  The  one  at 
C  experiences  only 
a  very  slight  motion, 
and  remains  in  its 
place,  thereby  prov- 
ing the  existence  of 
a  node  at  C  ;  the 
other  two  are  vio- 


Fig.  235. 


iiT 


Fig.  236. 


lently  shaken,  and  in  most  cases  thrown  off  the  string. 

When  a  musical  string  vibrates  between  fixed  points  A  and  B,  its  motion 
is  not  quite  so  simple  as  might  be  inferred  from  the  above  description.  In 
point  of  fact,  partial  vibrations  are  soon  produced,  and  superimposed  upon 
the  primary  vibrations.  The  partial  vibrations  correspond  to  the  half,  third, 
fourth,  &c.,  parts  of  the  string.  It  is  by  these  partial  vibrations  that  the 
harmonics  are  produced  which  accompany  the  fundamental  note  due  to  the 
primary  vibrations  ;  they  are  usually,  however,  so  feeble  as  to  be  impercep- 
tible to  ordinary  ears. 

270.  "Wind  instruments.- -In  the  cases  hitherto  considered,  the  sound 
results  from  the  vibrations  of  solid  bodies,  and  the  air  only  serves  as  a  vehicle 
for  transmitting  them.  In  wind  instruments,  on  the  contrary,  when  the  sides 
of  the  tube  are  of  adequate  thickness,  the  enclosed  column  of  air  is  the  sound- 
ing body.  In  fact,  the  substance  of  the  tubes  is  without  influence  on  the 
fundamental  note  ;  with  equal  dimensions,  it  is  the  same  whether  the  tubes 
are  of  glass,  of  wood,  or  of  metal.     These  different  materials  simply  do  no 

R  2 


Fig.  237. 


244  Oil  Sound.  [270- 

more  than  give  rise  to  different  harmonics,  and  thereby  impart  a  different 
quahty  to  the  compound  tone  produced. 

In  reference  to  the  manner  in  which  the  air  in  tubes  is  made  to  vibrate, 
wind  instruments  are  divided  into  iiwiith  instruments  and  reed  instruments. 

271.  iMCouth  instruments. — In  mouth  instruments  all  parts  of  the  mouth- 
piece are  fixed.     Fig.  238  represents  the  mouthpiece  of  an  organ  pipe,  and 

fig.  237  that  of  a  whistle,  or  of  a  flageolet.  In  both 
figures,  the  aperture  ib  is  called  the  mouth  ;  it  is 
here  that  air  enters  the  pipe  ;  b  and  o  are  the  lips., 
the  upper  one  of  which  is  bevelled.  The  mouth- 
piece is  fixed  at  one  end  of  a  tube,  the  other  end  of 
which  may  be  either  opened  or  closed.  In  fig.  238 
the  tube  can  be  fitted  on  a  wind-chest  by  means  of 
the  foot  P. 

When  a  rapid  current  of  air  enters  by  the  mouth, 
it  strikes  against  the  upper  lip,  and  a  shock  is  pro- 
duced which  causes  the  air  to  issue  from  bo  in  an 
intermittent  manner.  In  this  way,  pulsations  are 
produced  which,  transmitted  to  the  air  in  the  pipe, 
make  it  vibrate,  and  a  sound  is  the  result.  In 
order  that  a  pure  note  may  be  produced,  there  must 
be  a  certain  relation  between  the  form  of  the  lips 
and  the  magnitude  of  the  mouth  ;  the  tube  also 
ought  to  have  a  great  length  in  comparison  with  its  diameter.  The  number 
of  vibrations  depends  in  general  on  the  dimensions  of  the  pipe,  and  the 
velocity  of  the  current  of  air. 

272.  Xteed  instruments. — In  reed  instruments  a  simple  elastic  tongue 
sets  the  air  in  vibration.  The  tongue,  which  is  either  of  metal  or  of  wood,  is 
moved  by  a  current  of  air.  The  mouthpieces  of  the  oboe,  the  bassoon,  the 
clarionet,  the  child's  trumpet,  are  different  applications  of  the  reed,  which, 
it  may  be  remarked,  is  seen  in  its  simplest  form  in  the  Jew's  harp.  Some 
organ  pipes  are  reed  pipes,  others  are  mouth  pipes. 

Fig.  239  represents  a  model  of  a  reed  pipe  as  common!)'  shown  in 
lectures.  It  is  fixed  on  the  wind-chest  Q  of  a  bellows,  and  the  vibrations  of 
the  reed  can  be  seen  through  a  glass  plate,  E,  fitting  into  the  sides.  A 
wooden  horn,  H,  strengthens  the  sound. 

Fig.  240  shows  the  reed  out  of  the  pipe.  It  consists  of  four  pieces  :  ist, 
a  rectangular  wooden  tube  closed  below  and  open  abo\-e  at  o  ;  2nd,  a  copper 
plate  cc  forming  one  side  of  the  tube,  and  in  which  there  is  a  longitudinal 
aperture,  through  which  air  passes  from  the  tube  MN  to  the  orifice  0  ;  3rd, 
a  thin  elastic  plate,  z,  called  the  tongue,  which  is  fixed  at  its  upper  end,  and 
which  grazes  the  edge  of  the  longitudinal  aperture,  nearly  closing  it  ;  4th,  a 
curved  wire,  r,  which  presses  against  the  tongue,  and  can  be  moved  up  and 
down.  It  thus  regulates  the  length  of  the  tongue,  and  determines  the  pitch 
of  the  note.  It  is  by  this  wire  that  reed  pipes  are  tuned.  The  reed  being- 
replaced  in  the  pipe  MN,  when  a  current  of  air  enters  by  the  foot  P,  the 
tongue  is  compressed,  it  bends  inwards,  and  affords  a  passage  to  air,  \\hich 
escapes  by  the  orifice  o.  But,  being  elastic,  the  tongue  regains  its  original 
position,  and  performing  a  series  of  oscillations  successively  opens  and  closes 


-274]  On  the  Notes  produced  by  the  same  Pipe.  245 

the  orifice.     In  this  way  sonorous  waves  result  and  produce  a  note,  whose 
pitch  increases  with  the  velocity  of  the  current. 

In  this  reed  the  tongue  vibrates  alternately  before  and  behind  the  aper- 
tuie,  and  just  escapes  grazing  the  edges,  as  is  seen  in  the  harmonium,  con- 
certina, &c.  ;  such  a  reed  is  called  a  free  reed.  But  there  are  other  reeds 
called  beating  or  striking  reeds,  in  which  the  tongue,  which  is  larger  than 
the  orifice,  strikes  against  the  edges  at  each  oscillation,  closing  it  like  a  flap. 
The  reed  of  the  clarionet,  repre- 
sented in  fig.  241,  is  an  example 
of  this  ;  it  is  kept  in  its  place  by 
the  pressure  of  the  lips.  The 
reeds  of  the  oboe  and  bassoon 
are  also  of  this  kind. 

273  Of  the  notes  produced 
by  the  same  pipe. — Daniel 
Bernouilli  discovered  that  the 
same  organ  pipe  can  be  made 
to  yielr!  a  succession  of  notes  by 
properly  varying  the  force  of  the 
current  of  air.  The  results  he 
arrived  at  may  be  thus  stated  : — 

i.  If  the  pipe  is  open  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  fundamental 
note  by  i,  we  can,  by  gradually 
increasing  the  force  of  the  cur- 
rent of  air,  obtain  successively 
the  notes  2,  3,  4,  5,  &c.  ;  that  is 
to  say,  all  the  harmonics  of  the 
primary  note. 

ii.  If  the  pipe  is  closed  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  fundamental  note  by  i,  we  can,  by  gradually  increasing 
the  force  of  the  current  of  air,  obtain  successively  the  notes  3,  5,  7,  &c.  :  that 
is  to  say,  only  the  uneven  harmo7iics  of  the  primary  note. 

A  closed  and  an  open  pipe  yield  the  same  fundamental  note,  if  the  closed 
pipe  is  half  the  length  of  the  open  pipe,  and  if  in  other  respects  they  are  the 
same  ;  or,  what  is  an  ecjuivalent  statement,  with  a  closed  and  an  open  pipe 
of  the  same  length  the  former  gives  a  note  an  octave  higher  than  the  latter. 

In  any  case  it  is  impossible  to  produce  from  the  given  pipe  a  note  not 
included  in  the  above  series  respectively. 

Although  the  above  laws  are  enunciated  with  reference  to  an  organ  pipe, 
they  are  true  of  any  other  pipe  of  uniform  section. 

274.  On  the  nodes  and  loops  of  an  organ  pipe. — The  vibrations  of 
the  air  producing  a  musical  note  take  place  in  a  direction  parallel  to  the  axis 
of  the  pipe — not  transversely,  as  in  the  case  of  the  portions  of  a  vibrating 
strin*  In  the  former  case,  however,  as  well  as  in  the  latter,  the  phenomena 
of  nodes  and  loops  may  be  produced.  But  now  by  a  node  must  be  under- 
stood a  section  of  the  column  of  air  contained  in  the  pipe,  where  the  particles 


Fig.  240. 


246 


On  Sound. 


[274- 


remain  at  rest,  but  where  there  are  rapid  alternations  of  condensation  and 
rarefactioti.  By  a  loop  or  ventral  segment  must  be  understood  a  section  of 
the  column  of  air  contained  in  the  pipe  where  the  vibrations  of  the  particles 
of  air  have  the  greatest  amplitudes,  and  where  there  is  no  change  of  density. 
The  sections  of  the  column  of  air  are,  of  course,  made  at  right  angles  to  its 
axis.  When  the  column  of  air  is  divided  into  several  vibrating  portions,  it 
is  found  that  the  distance  between  any  two  consecutive  loops  is  constant, 
and  that  it  is  bisected  by  a  node.  We  can  now  consider  separately  the  cases 
of  the  open  and  closed  pipes. 

i.  In  the  case  of  a  stopped  pipe,  the  bottom  is  always  a  node,  for  the 
layer  of  air  in  contact  with  it  is  necessarily  at  rest,  and  only  undergoes 
variations  in  density.  At  the  mouthpiece,  on  the  contrary,  where  the  air  has 
a  constant  density  (that  of  the  atmosphere),  and  the  vibration  is  at  its  maxi- 
mum, there  is  always  a  loop.  In  any  stopped  pipe  there  is  at  least  one  node 
and  one  loop  (fig.  242)  ;  the  pipe  then  yields  its  fundamental  note,  and  the 


I 


Fig. 


¥ 


Fig.  243.         Fig.  244. 


Fig.  245. 


distance  VN  from  the  loop  to  the  node  is  equal  to  half  a  condensed  or 
rarefied  wave-length. 

If  the  current  of  air  be  forced,  the  mouthpiece  alwaj's  remains  a  loop, 
and  the  bottom  a  node,  the  column  divides  into  three  equal  parts  (fig.  243), 
and  an  intermediate  node  and  loop  are  formed.  The  sound  produced  is  the 
first  harmonic.  When  the  second  harmonic  (5)  is  produced,  there  are  two 
intermediate  nodes  and  two  loops,  and  the  tube  is  then  subdivided  into  five 
equal  parts  (fig.  244),  and  so  on. 

ii.  In  the  case  of  the  open  pipe,  whatever  note  it  produces,  there  must  be 
a  loop  at  each  end,  since  the  enclosed  column  of  air  is  in  contact  with  the 
external  air  at  those  points.  When  the  primary  note  is  produced,  there  will 
be  a  loop  at  each  end,  and  a  node  at  the  middlesectionof  the  pipe,  the  nodes 
and  loops  dividing  the  column  into  tzi'o  equal  parts  (fig.  245).  When  the 
first  harmonic  (2)  is  produced,  there  will  be  a  loop  at  each  end,  and  a  loop 


-274]         On  the  Nodes  and  Loops  of  an  Organ  Pipe.  247 

in  the  middle,  the  column  being  divided  into  four  equal  parts  by  the  alternate 
loops  and  nodes  (fig.  246).  When  the  second  harmonic  (3)  is  produced,  the 
column  of  air  will  be  divided  into  six  equal  parts  by  the  alternate  nodes  and 
loops,  and  so  on  (fig.  247).  It  will  be  remarked  that  the  successive  modes 
of  division  of  the  vibrating  column  are  the  only  ones  compatible  with  the 
alternate  recurrence  at  equal  intervals  of  nodes  and  loops,  and  with  the 
occurrence  of  a  loop  at  each  end  of  the  pipe. 

There  are  several  experiments  by  which  the  existence  of  nodes  and  loops 
can  be  shown. 

{a)  If  a  fine  membrane  is  stretched   over  a  pasteboard    ring,  and  has 


Fig.  24 


Fig.  249. 


Fig.  250. 


Fig.  251. 


sprinkled  on  it  some  fine  sand,  it  can  be  gradually  let  down  a  tube,  as  shown 
in  fig.  250.  Now,  suppose  the  tube  to  be  producing  a  musical  note.  As  the 
membrane  descends,  it  will  be  set  in  vibration  by  the  vibrating  air.  But 
when  it  reaches  a  node  it  will  cease  to  vibrate,  for  there  the  air  is  at  rest. 
Consequently,  the  grains  of  sand,  too,  will  be  at  rest,  and  their  quiescence 
will  indicate  the  position  of  the  node.  On  the  other  hand,  when  the  mem- 
brane reaches  a  loop — that  is,  a  point  where  the  ampUtude  of  the  vibrations 


248  On  Sound.  [274- 

of  the  air  attains  a  maximum — it  will  be  violently  agitated,  as  will  be  shown 
by  the  agitation  of  the  grains  of  sand.  And  thus  the  positions  of  the  loops 
can  be  rendered  manifest. 

(/;)  Again,  suppose  a  pipe  to  be  constructed  with  holes  bored  in  one  of 
its  sides,  and  these  covered  by  little  doors  which  can  be  opened  and  shut,  as 
shown  in  fig.  248.  Let  us  suppose  the  little  doors  to  be  shut  and  the  pipe  to 
be  caused  to  produce  such  a  note  that  the  nodes  are  at  N  and  N'  and  the 
loops  at  V,  V,  V".  At  the  latter  points  the  density  is  that  of  the  external 
air,  and  consecjuently  if  the  door  at  V  is  opened  no  change  is  produced  in 
the  note.  At  the  former  points,  N  and  N',  condensation  and  rarefaction  are 
alternately  taking  place.  Ifnow  the  door  at  N' is  opened,  this  alternation 
of  density  is  no  longer  possible,  for  the  density  at  this  open  point  must  be 
the  same  as  that  of  the  external  air,  and  consequently  N'  becomes  a  loop, 
and  the  note  yielded  by  the  tube  is  changed.  The  change  of  notes,  produced 
by  changing  the  fingering  of  the  flute,  is  one  form  of  this  experiment. 

{c)  Suppose  A,  in  fig.  249,  to  be  a  pipe  emitting  a  certain  note,  and  sup- 
pose P  to  be  a  plug,  fitting  the  tube,  fastened  to  the  end  of  a  long  rod  by 
which  it  can  be  forced  down  the  tube.  Now  when  the  plug  is  inserted, 
whatever  be  its  position,  there  will  be  a  node  in  contact  with  it.  Conse- 
quently, as  it  is  gradually  forced  down,  the  note  yielded  by  the  pipe  will 
keep  on  changing.  But  every  time  it  reaches  a  position  which  was  occupied 
by  a  node  before  its  insertion,  the  note  becomes  the  same  as  the  note 
originally  yielded.  For  now  the  column  of  air  vibrates  in  exactly  the  same 
manner  as  it  did  before  the  plug  was  put  in. 

{d)  Fig.  251  shows  another  mode  of  illustrating  the  same  point,  which  is 
identical  in  principle  with  Konig's  manometric  flames.  The  figure  repre- 
sents an  organ  pipe,  on  one  side  of  which  is  a  chest,  P,  filled  with  coal  gas, 
by  means  of  the  tube  S.  The  gas  from  the  chest  comes  out  in  three  jets.  A, 
B,  C,  and  is  then  ignited.  The  manner  in  which  the  gas  passes  from  the 
chest  to  the  point  of  ignition  is  shown  in  the  smaller  figure,  which  is  an 
enlarged  section  of  A.  A  circular  hole  is  bored  in  the  side  of  the  pipe  and 
covered  with  a  membrane  r.  A  piece  of  wood  is  fitted  into  the  hole  so  as 
to  leave  a  small  space  between  it  and  the  membrane.  The  gas  passes  from 
the  chest,  in  the  direction  indicated  by  the  arrow,  into  the  space  between 
the  membrane  and  the  piece  of  wood,  and  so  out  of  the  tube, ;;/,  at  the  mouth 
of  which  it  is  ignited.  Now  suppose  the  pipe  to  be  caused  to  yield  its 
primary  note,  then  as  it  is  an  open  pipe  there  ought  to  be  a  node  at  B, 
its  middle  point.  Consequently,  there  ought  to  be  rapid  changes  of  density 
at  B  ;  these  would  cause  the  membrane,  r,  to  vibrate,  and  thereby  blow  out 
the  flame,  ///,  and  this  is  what  actually  happens.  If  by  increasing  the  force 
of  the  wind  the  octave  to  the  primary  note  is  produced,  B  will  be  a  loop, 
and  A  and  C  nodes.  Consequently  the  flames  at  A  and  C  will  now  be  ex- 
tinguished, as  is,  in  point  of  fact,  the  case.  But  at  B,  there  being  no  change 
of  density,  the  membrane  is  unmoved,  and  the  flame  continues  to  burn 
steadily. 

By  each  and  all  of  these  experiments  it  is  shown  that  in  a  given  pipe, 
whether  open  or  closed,  there  are  always  a  certain  number  of  nodes,  and 
midway  between  any  two  consecutive  nodes  there  is  always  a  loop  ox  ventral 
seifinent. 


-276J     Existence  of  Nodes  and  Loops  in  a  Musical  Pipe.     249 

275.  Formulae  relative  to  the  number  of  vibrations  produced  by  a 

musical  pipe It  follows  from  what  has  been  said  that  the  column  of  air 

in  stopped  pipes  is  always  divided  by  the  nodes  and  loops  into  an  uneven 
number  of  parts  which  are  equal  to  each  other,  and  each  of  which  is  a  quarter 
of  a  complete  vibration  (figs.  242,  243,  and  244),  while  in  an  open  pipe  it  is 
divided  into  an  even  number  of  such  parts  (figs.  245,  246,  247).  If  L  be  the 
length  of  the  pipe,  /  the  wave-length  of  the  sound  which  it  emits,  and  p  any 

whole  number,  then  for  stopped  pipes  we  have  L  =  (2/  +  i)  -;  and  for 
open  pipes  L  =  2/-  =  ^  .  Replacing  in  each  of  these  formula;  /by  its  value 
-  (2^:;)  we  have  L  =  (2/)  +  i)  "''  and  L  =^''' ;  from  which  for  stopped  pipes 

1  {16    +    \]V  ,    r  M' 

we  ha\e  ;/  =  ^^i- — ^,  and  lor  open  ones  ii  =  -^. 

4L  2L 

The  laws  connecting  the  length  of  pipes  with  the  note  produced  only  hold 
for  narrow  pipes,  those,  for  instance,  whose  length  is  not  less  than  12  times 
their  diameter  ;  for  shorter  pipes  organ  builders  have  various  empirical  rules. 
AVithin  wide  limits  the  formula  holds,  L' =  L  - 1^,  where  L  is  the  theoretical 
length,  L'  the  length  sought,  while  ^is  the  diameter  of  the  round  pipe. 

If,  in  the  first  formula,  we  give  to/  the  successive  values  o,  i,  2,  3,4,  &c., 

we  have  n  =    "-'  ,    51-     ^'^''    that  is,  the  fundamental  sound  and  all  its  uneven 
4L'    4L     4L 

harmonics  ;  and  in  the  formula  for  the  open  pipe  we  get  similarly  ^    ,  "    ,A^-, 

&c.,  that  is,  the  fundamental  note  and  all  its  harmonics  even  and  uneven. 

276.  Sxplanation  of  the  existence  of  nodes  and  loops  in  a  musical 
pipe The  existence  of  nodes  and  loops  is  to  be  explained  by  the  co- 
existence in  the  same  pipe  of  two  equal  waves  tra\-elling  in  contrary 
directions. 

Let  A  (fig.  252)  be  a  point  from  which  a  series  of  waves  sets  out  towards 
B,  and  let  the  length  of  these  waves,  whether  of  condensation  or  rarefaction. 


Fig.  252. 

be  AC,  CD,  DB.  And  let  B  be  the  point  from  which  the  series  of  exactly 
equal  waves  sets  out  towards  A.  It  must  be  borne  in  mind  that  in  the  case 
of  a  wave  of  condensation  originating  at  A  the  particles  move  in  the  direc- 
tion A  to  B,  but  in  a  wave  of  condensation  originating  at  B  they  move  in  the 
direction  B  to  A.  Now  let  us  suppose  that  condensation  at  C,  caused  by  the 
wave  from  A,  begins  at  the  same  instant  that  condensation  caused  by  the 
wave  from  B  begins  at  D.  Consequently,  restricting  our  attention  to  the 
particles  in  the  hne  CD,  at  any  instant  the  velocities  of  the  particles  in  CD 
due  to  the  former  wave  will  be  represented  by  the  ordinates  of  the  curve 


2  50  On  Sound.  [276- 

SPRT,  while  those  due  to  the  wave  from  B  will  be  represented  by  the  co- 
ordinates of  the  curve  TQrS.  Then,  since  the  waves  travel  with  the  same 
velocity,  and  are  at  C  and  D  respectively  at  the  same  instant,  we  must  have, 
for  any  subsequent  instant,  CR  equal  to  Dr.  If,  therefore,  N  is  the  middle 
point  between  C  and  D,  we  must  have  rN  equal  to  RN,  and  consequently 
PN  equal  to  QN  ;  that  is  to  say,  if  the  particle  at  N  transmitted  only  one 
vibration,  its  motion  at  each  instant  would  be  in  the  opposite  phase  to  that 
of  its  motion  if  it  transmitted  only  the  other  vibration.  In  other  words,  the 
particle  N  will  at  every  instant  tend  to  be  moved  with  equal  velocity  in 
opposite  directions  by  the  two  waves,  and  therefore  will  be  permanently  at 
rest.  That  point  is  therefore  a  node.  In  like  manner  there  is  a  node  at  N' 
midway  between  A  and  C,  and  also  at  N"  midway  between  B  and  D.  In 
regard  to  the  motion  of  the  remaining  particles,  it  is  plain  that  their  respec- 
tive velocities  will  be  the  (algebraical)  sum  of  the  velocities  they  would  at 
each  instant  receive  from  the  waves  separately.  Hence,  at  the  instant  indi- 
cated by  the  diagram,  they  are  given  by  the  ordinates  of  the  curve  HNK. 
This  curve  will  change  from  instant  to  instant,  and  at  the  end  of  the  time 
occupied  by  the  passage  of  a  wave  of  condensation  (or  of  rarefaction)  from 
C  to  D  will  occupy  the  position  shown  by  the  dotted  line  Ji^k.  It  is  evident 
therefore  that  particles  near  N  have  but  small  changes  of  velocity,  whilst  those 
near  C  and  D  experience  large  changes  of  velocity. 

If  the  curve  HK  were  produced  both  ways,  it  would  always  pass  through 
N'  and  N'^ ;  the  part,  however,  between  N  and  W  would  sometimes  be  on 
one  side,  and  sometimes  on  the  other  side  of  AB.  Hence  all  the  particles 
between  N'  and  N  have  simultaneously,  first  a  motion  in  the  direction  A  to 
B,  and  then  a  motion  in  the  direction  B  to  A,  those  particles  near  C  having 
the  greatest  amplitude  of  vibrations.  Accordingly  near  N  and  N'  there  will 
be  alternately  the  greatest  condensation  and  rarefaction. 

This  explanation  applies  to  the  case  in  which  AB  is  the  axis  of  an  open 
organ-pipe,  A  being  the  end  where  the  mouthpiece  is  situated.  The  waves 
from  B  have  their  origin  in  the  reflections  of  the  series  of  waves  from  A.  In 
the  particular  case  considered,  the  note  yielded  by  the  pipe  is  that  indicated 
by  3  ;  that  is,  the  fifth  above  the  octave  to  the  primary  note.  A  similar  ex- 
planation can  obviously  be  applied  to  all  other  cases,  and  whether  the  end 
be  opened  or  closed.  But  in  the  latter  case  the  series  of  waves  from  the 
closed  end  must  commence  at  a  point  distant  from  the  mouthpiece  by  a 
space  equal  to  one  half,  or  three  halves,  or  five  halves,  &c.,  of  the  length  of 
a  wave  of  condensation  or  expansion. 

277.  Kundt's  determination  of  the  velocity  of  sound.^Kundt  has 
devised  a  method  of  determining  the  velocity  of  sound  in  solids  and  in 
gases  which  can  be  easily  performed  by  means  of  simple  apparatus,  and  is 
capable  of  great  accuracy.  A  glass  tube,  BB',  about  two  yards  long  (fig.  253) 
and  two  inches  in  internal  diameter,  is  closed  at  one  end  by  a  movable 
stopper,  b;  the  other  end  is  fitted  with  a  cork,  KK,  which  tightly  grasps  a 
glass  tube,  AA',  the  same  length,  but  of  smaller  diameter.  This  is  closed 
at  one  end  by  a  piston,  a,  which  moves  with  gentle  friction  in  the  outer 
tube,  BB'.  Then  by  rubbing  the  free  end  of  the  tube,  AA',  with  a  wet  cloth, 
it  produces  longitudinal  vibrations,  and  these  transmit  their  motion  to  the 
air  in  the  tube  ab.     If  the  tube  ab  contain  some  lycopodium  powder,  or,  still 


CJieviical  Harinonicon. 


251 


? 

m 

\ 


fii 


K 


-278] 

better,  powdered  cork,  this  is  set  in  active  vibration  and  then  arranges  itself 
in  small  patches  in  a  certain  definite  order,  as  represented  in  the  figure,  the 
nature  and  arrangement  of  which  depend  on  the  vibrating  part 
of  the  rod  and  the  tube. 

These  heaps  represent  the  nodes,  and  the  mean  distance  d 
between  them  can  be  measured  with  great  accuracy  ;  it  repre- 
sents the  distance  between  two  nodes,  or,  half  a  wave-length  ; 
that  is,  the  wave-length  of  the  sound  in  air  is  id.  If  the  rod 
has  the  length  s  and  is  grasped  in  the  middle  by  the  cork  KK, 
from  the  law  of  the  longitudinal  vibrations  of  rods  (281),  the 
wave-length  of  the  sound  it  then  emits  is  twice  its  length,  or  2^. 
That  is,  the  wave-length  of  the  vibrating  column  of  air  is  to 
that  in  the  rod  as  id :  is.  As  the  velocity  of  sound  in  any 
body  is  equal  to  the  wave-length  in  that  body  multiplied  by  the 
number  of  vibrations  in  a  second  ;  and  since  the  number  of 
vibrations  is  here  the  same  in  both  cases,  for  the  note  is  the 
same,  the  velocity  of  sound  in  the  glass  is  to  the 'velocity  of 
sound  in  air  as  isn  :  idn,  that  is,  as  ^  :  ^.  Thus  when  the  glass 
tube  was  clamped  in  the  middle  by  KK,  so  that  the  length  a^ 
was  equal  to  half  the  length  of  the  tube  AA',  the  number  of  the 
ventral  segments  was  found  to  be  eight.  This  corresponds  to 
a  ratio  of  wave-length  of  i  to  16  ;  in  other  words,  the  velocity 
of  sound  in  glass  is  16  times  that  in  air. 

The  method  is  capable  of  great  extension.  By  means  of 
the  stopcock  m,  different  gases  could  be  introduced  instead  of 
air,  and  corresponding  differences  found  for  the  length  of  the 
ventral  segments  ;  from  which,  by  a  simple  calculation,  the  cor- 
responding velocities  were  found.  Thus  the  velocities  of  sound 
in  carbonic  acid,  coal  gas,  and  hydrogen  were  found  to  be 
respectively  o'8,  r6,  and  3"56  that  of  air,  or  nearly  as  the  inverse 
squares  of  the  densities. 

So  also,  by  varying  the  material  of  the  rod  A  A',  different 
velocities  are  obtained.  Thus  the  velocity  in  steel  was  found  to 
be  I5'24,  and  that  in  brass  10-87  that  of  air. 

Kundfs  figures  may  also  be  obtained  by  providing  glass 
tubes  a  yard  or  two  in  length  with  lycopodium  powder,  as  in 
the  above  experiment,  and  hermetically  sealing  them  at  both 
ends.  The  tubes  are  then  put  into  longitudinal  vibrations  ; 
instead  of  air  they  may  be  filled  with  hydrogen  or  any  other  gas. 

Using  this  method,  with  iron  filings  instead  of  lycopodium,  Kundt  and 
Lehmann  determined  the  velocity  of  sound  in  water  contained  in  glass  tubes 
of  various  diameters  and  thicknesses  ;  the  thicker  the  tubes  and  the  smaller 
their  diameter,  the  more  nearly  do  the  results  agree  with  those  required  by 
theory  and  with  those  obtained  by  Colladon  and  Sturm  (234). 

278.  Chemical  barmonicon. — The  air  in  an  open  tube  may  be  made  to 
give  a  sound  by  means  of  a  luminous  jet  of  hydrogen,  coal  gas,  &c.  When 
a  glass  tube  about  12  inches  long  is  held  over  a  lighted  jet  of  hydrogen 
(fig.  254),  a  note  is  produced,  which,  if  the  tube  is  in  a  certain  position,  is  the 
fundamental  note  of  the  tube.     The  sounds  are  considered  to  arise  from  the 


r-K 


A 

Fig.  253. 


On  Sound. 


[278- 


successive,  exceedingly  rapid  explosions  produced  by  the  periodic  combina- 
tions of  the  atmospheric  oxygen  with  the  issuing  jet  of  hydrogen.  The 
apparatus  is  called  the  chemical  Jiarmonicon. 

Coal  gas  may  be  used  in  this  experiment  instead  of  hydrogen,  and 
indeed  from  its  brighter  flame  is  more  advantageous.  A  thin  metal  pipe 
about  8  inches  in  length  and  with  a  narrow  aperture  is  fitted  to  an  ordinary 
burner,  which  is  supplied  with  gas  through  a  caoutchouc  tube  connected  with 
a  reservoir  of  the  gas  which  is  under  rather  higher  pressure  than  usual. 

The  note  depends  on  the  size  of  the  flame  and  the  length  of  the  tube  : 
with  a  long  tube,  by  varying  the  position  of  the 
jet  in  the  tube,  the  series  of  notes,  in  the  ratio 
I  :  2  :  3  :  4  :  5,  is  obtained. 

If,  while  the  tube  emits  a  certain  sound,  the 
voice  or  the  syren  (242)  be  gradually  raised  to  the 
same  height,  as  soon  as  the  note  is  nearly  in 
unison  with  the  harmonicon,  the  flame  becomes 
agitated,  jumps  up  and  down,  and  is  finally  steady 
when  the  two  sounds  are  in  unison.  If  the  note 
of  the  syren  is  gradually  heightened  the  pulsations 
again  commence  ;  they  are  the  optical  expressions 
of  the  beats  (262)  which  occur  near  perfect  unison. 
If,  while  the  jet  burns  in  the  tube  and  produces 
a  note,  the  position  of  the  tube  is  slightly  altered, 
a  point  is  reached  at  which  no  sound  is  heard.  If 
now  the  voice,  or  the  syren.  Or  the  tuning-fork,  be 
pitched  at  the  note  produced  by  the  jet,  it  begins 
to  sing,  and  continues  to  sing  even  after  the  syren 
is  silent.  A  mere  noise,  or  shouting  at  an  incorrect 
pitch,  agitates  the  flame,  but  does  not  cause  it  to 
sing. 

These  effects  may  be  conveniently  studied  by 
p;,,  means  of  a  gas-burner,  over  which,  at  a  distance 

of  four  inches,  a  ring  covered  with  fine  wire  gauze 
is  fixed.  The  gas  is  lighted  above  the  gauze,  and  forms  a  very  sensitive 
flame,  especially  when  a  moderately  wide  tube  is  held  over  the  gauze.  If 
the  gauze  is  raised  with  the  tube,  the  flame  becomes  duller  and  smaller,  but 
begins  to  sound  with  a  uniform  loud  tone.  If  now  the  gauze  is  lowered  so 
that  the  flame  is  just  silent,  it  begins  at  once  when  a  sound  is  produced, 
but  ceases  with  the  sound. 

If  a  metal  tube  4  cm.  wide  and  15  to  20  cm.  high,  closed  at  the  bottom  by 
a  wire  gauze,  is  held  vertically  over  a  Bunsen's  jet,  an  acute  sound  is  heard, 
almost  as  loud  as  the  whistle  of  a  locomotive,  on  lighting  the  gas  inside  the 
tube. 

279.  String-ed  instruments. — Stringed  musical  instruments  depend  on 
the  production  of  transverse  vibrations.  In  some,  such  as  the  piano,  the 
sounds  are  constant,  and  each  note  requires  a  separate  string  ;  in  others, 
such  as  the  violin  and  guitar,  the  sounds  are  7'aried  by  the  fingering,  and 
can  be  produced  by  fewer  strings. 

In  the  piano  the  vibrations  of  the  strings  are  produced  by  the  stroke  of 


-279]  Stringed  Instruments.  253 

the  /uiiiiiucr,  which  is  moved  by  a  series  of  bent  levers  communicating  with 
the  ke\s.  The  sound  is  strengthened  by  the  vibrations  of  the  air  in  the 
sounchng  board  on  which  the  strings  are  stretched.  Whenever  a  key  is 
struck,  a  damper  is  raised  which  falls  when  the  finger  is  removed  from  the 
key,  and  stops  the  vibrations  of  the  corresponding  string.  By  means  of  a 
pedal  all  the  dampers  can  be  simultaneously  raised,  and  the  vibrations  then 
last  for  some  time. 

The  karp  is  a  sort  of  transition  from  the  instruments  with  constant  to 
those  with  variable  sounds.  Its  strings  correspond  to  the  natural  notes  of  the 
scale  ;  by  means  of  the  pedals  the  length  of  the  vibrating  parts  can  be 
changed,  so  as  to  produce  sharps  and  flats.  The  sound  is  strengthened  by 
the  sounding-box,  and  by  the  vibrations  of  all  the  strings  harmonic  with 
those  played. 

In  the  violin  and  guitar  each  string  can  give  a  great  number  of  sounds 
according  to  the  length  of  the  vibrating  part,  which  is  determined  by  the 
pressure  of  the  fingers  of  the  left  hand  while  the  right  hand  plays  the  bow, 
or  twitches  the  strings  themselves.  In  both  these  instruments  the  vibra- 
tions are  communicated  to  the  upper  face  or  belly  of  the  sounding-box  by 
means  of  the  bridge  over  which  the  strings  pass.  These  vibrations  are 
communicated  from  the  upper  to  the  lower  face  or  back  of  the  box  either  by 
the  sides  or  by  an  intermediate  piece  called  the  sound-post.  The  air  in  the 
interior  is  set  in  vibration  by  both  faces,  and  the  strengthening  of  the  sound 
is  produced  by  all  these  simultaneous  vibrations.  The  value  of  the  instru- 
ment consists  in  the  perfection  with  which  all  possible  sounds  are  intensified, 
which  depends  essentially  on  the  quality  of  the  wood,  the  mellowness  of 
which  increases  with  age,  and  on  the  relative  arrangement  of  the  parts. 

The  number  and  strength  of  the  harmonics  produced  in  a  twitched  or 
stroked  string  varies  with  the  manner  in  which  it  is  sounded  and  with  the 
nature  of  the  string.  The  sharper  the  edge  of  the  exciting  body  the  shorter 
and  broader  are  the  waves,  and  therefore  the  higher  and  stronger  are  the 
harmonics  and  the  shriller  the  clang  ;  if  the  strings  are  struck  with  a  metal 
rod  the  harmonics  are  so  predominant  that  the  fundamental  note  is  scarcely 
heard,  and  thus  what  is  called  a  hollow  sound  is  produced.  The  tone  is 
fullest  when  struck  with  the  finger,  and  somewhat  less  so  with  a  soft  hammer, 
as  in  the  piano.  The  deeper  harmonics  are  often  stronger  than  the  funda- 
mental note,  so  that  the  note  is  not  so  strong  but  is  richer  ;  all  the  har- 
monics, whose  nodes  are  in  the  place  struck,  are  wanting.  If  a  string  is  struck 
in  the  middle,  none  of  the  even  harmonics  are  produced,  and  therefore  all  the 
octaves  of  the  fundamental  note  are  wanting  ;  the  tone  is  nasal  and  hollow. 
This  is  the  characteristic  of  a  note  which  is  wanting  in  the  harmonics  nearer 
and  most  allied  to  the  fundamental  note.  If  the  string  is  struck  near  one  end, 
the  clang  has  a  jingling  character.  Instrument  makers,  led  by  practised 
ears,  have  long  found  it  advantageous  that  the  piano  be  struck  at  about 
one-seventh  of  the  length  of  the  string  ;  the  reason  for  this  advantage  lies  in 
the  fact  that  in  this  way  the  seventh  and  ninth  harmonics,  which  are  unhar- 
monic  with  each  other,  are  deadened,  while  the  deeper  harmonics — the 
octaves,  fifths,  thirds— preponderate,  and  the  clang  is  rich  and  harmonious- 

The  higher  harmonics  fade  away  in  gut-strings  more  rapidly  than  in 
metal  wires  ;  hence  the  guitar  and  the  harp  are  not  so  jingling  as  the  zither. 


2  54  On   Sound.  [280- 

280.  "Wind  instruments. — All  wind  instruments  may  be  referred  to  the 
different  types  of  sounding  tubes  which  have  been  described.  In  some,  such 
as  the  organ,  the  notes  ax&Jixed,  and  require  a  separate  pipe  for  each  note, 
in  others  the  notes  are  variable,  and  are  produced  by  only  one  tube  :  the 
flute,  horn,  &c.,  are  of  this  class. 

In  the  organ  the  pipes  are  of  various  kinds  ;  namely,  mouth  pipes,  open 
and  stopped,  and  reed  pipes  with  apertures  of  various  shapes.  By  means  of 
stops  the  organist  can  produce  any  note  by  both  kinds  of  pipe. 

In  the/iute,  the  mouthpiece  consists  of  a  simple  lateral  circular  aperture; 
the  current  of  air  is  directed  by  means  of  the  lips,  so  that  it  grazes  the  edge 
of  the  aperture.  The  holes  at  different  distances  are  closed  either  by  the 
fingers  or  by  keys  ;  when  one  of  the  holes  is  opened,  a  loop  is  produced  in 
the  corresponding  layer  of  air,  which  modifies  the  distribution  of  nodes  and 
loops  in  the  interior,  and  thus  alters  the  note.  The  whistling  of  a  key  is 
similarly  produced. 

The  pandccan  pipe  consists  of  stopped  pipes  of  different  lengths  corre- 
sponding to  the  different  notes  of  the  gamut. 

In  the  trumpet,  the  horn,  the  trombone,  cornet-a-piston,  and  ophicleide, 
the  lips  form  the  reed,  and  vibrate  in  the  mouthpiece.  In  the  //<7r«,  different 
notes  are  produced  by  altering  the  distance  of  the  lips.  In  the  trombone^ 
one  part  of  the  tube  slides  within  the  other,  and  the  performer  can  alter 
at  will  the  length  of  the  tube,  and  thus  produce  higher  or  lower  notes.  In 
the  cornet-a-piston,  the  tube  forms  several  convolutions  ;  pistons  placed  at 
different  distances  can,  when  closed,  cut  off  communication  with  other  parts 
of  the  tube,  and  thus  alter  the  length  of  the  vibrating  column  of  air. 


-281] 


Vibration  of  Rods. 


255 


CHAPTER   V. 

VIBRATION   OF    RODS,   PLATES,    AND    MEMBRANES. 

281.  Vibration  of  rods. — The  term  rods  is  applied  in  acoustics  to  solids 
whose  length  is  considerable  in  proportion  to  their  breadth  and  thickness  ; 
they  are  nevertheless  so  broad  and  thick  that,  while  they  have  not  the 
llexibility  of  strings,  they  have  yet  elasticity  enough  to  vibrate  without  being 
stretched  like  strings.  They  are  ordinarily  of  wood,  glass,  metal,  and  more 
particularly  of  tempered  steel.  Like  strings,  they  have  two  kinds  of  vibra- 
tions, lo7tgitudinal  and  transverse.  The  latter  are  produced  by  fixing  the 
rods  at  one  end,  and  passing  a  bow  across  the  free  part.  Longitudinal 
vibrations  are  produced  by  fixing  the  rod  at  any  part,  and  rubbing  it  length- 
wise with  a  piece  of  cloth  sprinkled 
with  resin.  But  in  the  latter  case 
the  sound  is  only  produced  when 
the  rod  has  been  fixed  at  some 
aliquot  part  of  its  length  from  the 
end,  as  a  half,  a  third,  or  a  quarter. 

It  is  shown  by  calculation  that 
tJie  number  of  transverse  vibratioiis 
made  in  a  given  time  by  rods  and 
thin  plates  of  the  same  material  is 
directly  as  their  thickness  and  ift- 
versely  as  the  square  of  their  length. 
The  width  of  the  plate  does  not 
affect  the  number  of  vibrations.  A 
wide  plate,  however,  requires  a 
greater  force  to  set  it  in  motion  than 
a  narrow  one.  It  is,  of  course,  pre- 
supposed that  one  end  of  the  vibrat- 
ing plate  is  clamped  or  is  otherwise 
held  firmly. 

The  laws  of  the  longitudinal  vi- 
brations of  strings  are  expressed  in 

the  formula  « *  ,  , 

2r/  V  -nd 
ti,  r,  /,  d,  and  g  have  all  the  same 
meaning  as  in  the  formula  for  the 
transverse  vibrations,  while  /x  is  the  F^s-  -55- 

modulus  of  elasticity  of  the  string, 

the  number  which  expresses  the  weight  by  which  it  must  be  stretched  in 
order  to  elongate  by  its  own  length  (88). 


—  A  /  eT,  in  which 

;r/  V  71 


2  56  On  Sound.  [281- 

Fig.  255  represents  an  instrument  invented  by  Marloye,  and  known  as 
Marloye's  Jim-p,  based  on  the  longitudinal  vibration  of  rods.  It  consists  of 
a  solid  wooden  pedestal,  in  which  are  fixed  twenty  thin  deal  rods,  some 
coloured  and  others  white.  They  are  of  such  a  length  that  the  white  rods 
give  the  diatonic  scale,  while  the  coloured  ones  give  the  semitones  and 
complete  the  chromatic  scale.  The  instrument  is  played  by  rubbing  the 
rods  in  the  direction  of  their  length  between  the  finger  and  thumb,  which 
have  been  previously  covered  with  powdered  resin.  The  notes  produced 
resemble  those  of  a  pandasan  pipe. 

The  tuning-fork.,  the  triangle.,  and  musical  boxes,  are  examples  of  the 
transverse  vibrations  of  rods.  In  musical  boxes,  small  plates  of  steel  of 
dititerent  dimensions  are  fixed  on  a  rod,  like  the  teeth  of  a  comb.  A  cylinder 
whose  axis  is  parallel  to  this  rod,  and  whose  surface  is  studded  with  steel 
teeth,  arranged  in  a  certain  order,  is  placed  near  the  plates.  By  means  of 
a  clockwork  motion,  the  cylinder  rotates,  and  the  teeth  striking  the  steel 
plates  set  them  in  vibration,  producing  a  tune,  which  depends  on  the  arrange- 
ment of  the  teeth  on  the  cyhnder. 

If  a  given  rod  be  clamped  either  in  the  middle,  or  at  both  ends,  the 
wave-length  of  the  note  produced  by  making  it  vibrate  longitudinally  is 
double  its  own  length  ;  and  if  it  be  clamped  at  one  end  only,  and  made  to 
vibrate  longitudinally,  the  wave-length  of  the  sound  is  four  times  its  own 
length.  Thus  the  former  case  is  analogous  to  an  open  pipe,  and  the  latter  to 
a  stopped  pipe,  in  respect  of  the  notes  produced. 

The  velocity  of  sound  in  any  solid  may  be  determined  experimentally  by 
clamping  it  at  one  end  and  putting  it  in  longitudinal  vibrations.  The  length 
of  a  stopped  pipe  is  next  ascertained  which  gives  the  same  note.  The 
velocity  of  sound  in  the  material  in  question  is  thus  to  its  velocity  in  air  in 
the  same  ratio  as  the  length  of  the  rod  to  the  length  of  the  stopped  pipe. 
Thus  a  rod  of  alder  a  metre  in  length  was  found  to  give  the  same  longitudinal 
note  as  a  stopped  pipe  7  cm.  in  length  ;  the  velocities  are  accordingly  as 
100  :  7,  or  the  velocity  of  sound  in  this  wood  is  14-3  times  that  in  air. 

Stefan  has  determined  the  velocity  of  sound  in  soft  bodies  by  attaching 
them,  in  the  form  of  rods,  to  long  glass  or  wooden  rods.  The  compound 
rod  was  made  to  vibrate  and  the  number  of  vibrations  of  the  note  was  de- 
termined. Knowmg  this,  and  also  the  velocity  of  sound  in  the  longer  rod, 
the  velocity  in  the  shorter  rod  was  at  once  obtained.  By  this  method  some 
of  the  numbers  in  the  table  in  article  235  were  obtained. 

Scratching  and  scraping  sounds  are  pi^oduced  by  moving  a  i^od  over  a 
smooth  surface  ;  the  rod  is  thereby  put  in  vibration,  which  vibrations  are 
regular  for  a  short  interval,  but  frequently  change  their  period  during  the 
motion. 

282.  Vibration  of  plates. — In  order  to  make  a  plate  vibrate,  it  is  fixed 
in  the  centre  (fig.  256),  and  a  bow  rapidly  drawn  across  one  of  the  edges  ; 
or  else  it  is  fixed  at  any  point  of  its  surface,  and  caused  to  vibrate  by 
rapidly  drawing  a  string  covered  with  resin  against  the  edges  of  a  central 
hole  (fig.  257). 

Vibrating  plates  contain  nodal  lines  (269),  which  vary  in  number  and 
position  according  to  the  form  of  the  plates,  their  elasticity,  the  mode  of 
excitation,  and  the  number  of  vibrations.     These  nodal  lines  may  be  made 


-282]  Vibrations  of  Plates.  257 

visible  by  covering  the  plate  with  fine  sand,  before  it  is  made  to  vibrate. 
As  soon  as  the  vibrations  commence,  the  sand  leaves  the  vibrating  parts, 
and  accumulates  on  the  nodal  lines,  as  seen  in  figs.  256  and  257. 

The  position  of  the  nodal  lines  may  be  determined  by  touching  the 
points  at  which  it  is  desired  to  produce  them.  Their  number  increases  with 
the  number  of  vibrations  ;  that  is,  as  the  note  given  by  the  plates  is  higher. 
The  nodal  lines  always  possess  great  symmetry  of  form,  and  the  same  form 


Fig.  256. 


Fig.  257. 


is  always  produced  on  the  same  plate  under  the  same  conditions.     They 
were  discovered  by  Chladni,  and  the  plates  are  known  as  Chladni's  plates. 

The  vibrations  of  plates  are  governed  by  the  following  law  : — In  plates 
of  the  same  kind  and  shape,  atid  giving  the  same  system  of  nodal  lines,  the 
number  of  vih'ations  i?i  a  second  is  directly  as  the  thickness  of  the  plates,  and 
inversely  as  their  area. 

Gongs  and  cymbals  are  examples  of  instruments  in  which  sounds  are 
produced  by  the  vibration  of  metal  plates.  The  glass  and  the  steel  harmo- 
nicon  depend  on  the  vibrations  of  glass  and  of  steel  plates  respectively. 

Bells,  which  are  to  be  regarded  as  curved  plates,  never  vibrate  as  a  whole 
but  when  they  give  their  fundamental  note  in  four  equal  parts  which  are 
separated  by  nodal  lines.  This  can  be  shown  by  suspending  pith  balls  by 
silk  threads  from  the  ends  of  glass  rods  arranged  crosswise,  so  that  the  pith 
balls  just  rest  against  the  rim  of  a  bell  jar  held  vertically  with  the  mouth 
upwards.  When  this  is  made  to  sound  by  drawing  a  bow  across  the  edge, 
the  balls  are  powerfully  repelled  from  the  ventral  segments,  but  with  far  less 
force  from  the  nodes. 

Bells  are  also  capable  of  vibrating  in  6,  8,  10,  or  12  parts,  producing  thus 
a  corresponding  series  of  over-tones.  The  note  of  a  bell  is  higher  in  pro- 
portion as  the  surface  is  smaller  and  the  substance  thicker. 

If  water  is  poured  into  a  bell  jar  which  is  made  to  vibrate  by  means  of  a 
violin  bow,  the  surface  of  the  water  forms  a  series  of  nodes  and  segments, 
and  water  is  projected  in  the  form  of  spray  from  the  ventral  segments.  If 
alcohol  or  ether  be  used  instead  of  water,  a  number  of  droplets  form  and 
group  themselves  into  beautiful  starlike  figures. 

S 


258 


On  Sound. 


[283- 


283.  Vibration  of  membranes. — In  consequence  of  their  flexibility, 
membranes  cannot  vibrate  unless  they  are  stretched,  like  the  skin  of  a  drum. 
The  sound  they  give  is  more  acute  in  proportion  as  they  are  smaller  and 
more  tightly  stretched.  To  obtain  vibrating  membranes,  Savart  fastened 
gold-beater's  skin  on  wooden  frames. 

In  the  drum.,  the  skins  are  stretched  on  the  ends  of  a  cylindrical  box. 
When  one  end  is  struck,  it  communicates  its  vibrations  to  the  internal 
column  of  air,  and  the  sound  is  thus  considerably  strengthened.  The  cords 
stretched  against  the  lower  skin  strike  against  it  when  it  vibrates,  and  pro- 
duce the  sound  characteristic  of  the  drum. 

Membranes  either  vibrate  by  direct  percussion,  as  in  the  drum,  or  they 
may  be  set  in  vibration  by  the  vibrations  of  the  air,  as  Savart  has  observed,, 


provided  these  vibrations  are  sufficiently  intense.  Fig.  258  shows  a  mem- 
brane vibrating  under  the  influence  of  the  vibrations  in  the  air  caused  by 
a  sounding  bell.  Fine  sand  strewn  on  the  membrane  shows  the  formation 
of  nodal  lines  just  as  upon  plates. 

Membranes  are  eminently  fitted  for  taking  up  the  vibrations  of  the  air, 
on  account  of  their  small  mass,  their  large  surface,  and  the  readiness  with 
which  they  subdivide.  With  a  pretty  strong  whistle,  nodal  lines  may  be 
produced  in  a  membrane  stretched  on  a  frame,  even  at  the  distant  end  of  a 
large  room. 

The  phenomenon  so  easily  produced  in  easily-moved  bodies  is  also  found 
in  larger  and  less  elastic  masses  ;  all  the  pillars  and  walls  of  a  church  vibrate 
more  or  less  while  the  bells  are  being  rung. 


284] 


Method  of  making    Vibrations  apparent. 


259 


CHAPTER   VI. 

GRAPHICAL   METHOD   OF   STUDYING   VIBRATORY   MOTIONS. 

284.  lissajous'inelhodof  making:  vibrations  apparent.— The  method 
of  Lissajous  exhibits  the  vibratory  motion  of  bodies  either  directly  or  by 
projection  on  a  screen.  It  has  also  the  great  advantage  that  the  vibratory 
motions  of  two  sounding  bodies  maybe  compared  without  the  aid  of  the  ear., 
so  as  to  obtain  the  exact  relation  between  them. 

This  method,  which  depends  on  the  persistence  of  visual  sensations  on 
the  retina  (625),  consists  in  fixing  a  small  mirror  on  the  vibrating  body,  so  as 
to  vibrate  with  it,  and  impart  to  a  luminous  ray  a  vibratory  motion  similar 
to  its  own. 

Lissajous  uses  tuning-forks,  and  fixes  to  one  of  the  prongs  a  small 
metal  mirror,  m  (fig.  259),  and   to   the   other  a  counterpoise,  ;?,  which  is 


^^XAAAi: 


Fig    259 

necessary  to  make  the  tuning-fork  vibrate  regularly  for  a  long  time.  At  a 
few  yards'  distance  from  the  mirror  there  is  a  lamp  surrounded  by  a  dark 
chimney,  in  which  is  a  small  hole  giving  a  single  luminous  point.  The 
tuning-fork  being  at  rest,  the  eye  is  placed  so  that  the  luminous  point  is  seen 
at  o.  The  tuning-fork  is  then  made  to  vibrate,  and  the  image  elongates  so 
as  to  form  a  persistent  image,  fz,  which  diminishes  in   proportion  as  the 


26o  On   Sound.  [284- 

amplitude  of  the  oscillation  decreases.  If,  during  the  oscillation  of  the 
mirror,  it  is  made  to  rotate  by  rotating  the  tuning-fork  on  its  axis,  a  sinuous 
line,  oix.,  is  produced  instead  of  the  straight  line  oi.  These  different  effects 
are  explained  by  the  successive  displacements  of  the  luminous  pencil,  and 
Ijy  the  duration  of  these  luminous  impressions  on  the  eye  after  the  cause 
has  ceased — a  phenomenon  to  which  we  shall  revert  in  treating  of 
vision. 

If,  instead  of  viewing  these    effects    directly,    they   are   projected  on  a 
screen,  the  experiment  is  arranged  as  shown  in  fig.  260  ;  the  pencil  reflected 


from  the  vibrating  mirror  is  reflected  a  second  time  from  the  fixed  mirror,  ;;/, 
which  sends  it  towards  an  achromatic  lens,  /,  placed  so  as  to  project  the 
images  on  the  screen. 

285.   Combination  of  two  vibratory  motions  intbe  same  direction. — 

Lissajous  resolved  the  problem  of  the  optical  combination  of  two  vibratory 
motions — vibrating  at  first  in  the  same  direction,  and  then  at  right  angles  to 
each  other. 

Fig.  261  represents  the  experiment  as  arranged  for  combining  two 
parallel  motions.  Two  tuning-forks  provided  with  mirrors  are  so  arranged 
that  the  light  reflected  from  one  of  them  reaches  the  other,  which  is  almost 
parallel  to  it,  and  is  then  sent  towards  a  screen  after  having  passed  through 
a  lens. 

If  now  the  first  tuning-fork  alone  vibrates,  the  image  on  the  screen  is 
the  same  as  in  figure  261  ;  but  if  they  both  vibrate,  supposing  they  are  in 
unison,  the  elongation  increases  or  diminishes  according  as  the  simultaneous 
motions  imparted  to  the  image  by  the  vibrations  of  the  mirrors  do  or  do  not 
coincide. 


optical  Combination  of  Tzvo    Vibratory  Motions.       261 

If  the  tuning-forks  pass  their  position  of  equihbrium  in  the  same  time 
and  in  the  same  direction,  the  image  attains  its  maximum  ;  and  the  image 
is  at  its  minimum  when  they  pass  at  the  same  time  but  in  opposite  direc- 
tions. Between  these  two  extreme  cases,  the  ampHtude  of  the  image  varies 
according  to  the  time  which  elapses  between  the  exact  instant  at  which  the 
tuning-forks  pass  through  their  position  of  rest  respectively.     The  ratio  of 


this  time  to  the  time  of  a  double  vibration  is  called  a  differeitce  of  phase  of 
the  vibration. 

If  the  tuning-forks  are  exactly  in  unison,  the  luminous  appearance  on  the 
screen  experiences  a  gradual  diminution  of  length  in  proportion  as  the  ampli- 
tude of  the  vibration  diminishes  ;  but  if  the  pitch  of  one  is  very  little  altered, 
the  magnitude  of  the  image  varies  periodically,  and,  while  the  beats  resulting 


g.  262. 


from  the  imperfect  harmony  are  distinctly  heard,  the  eye  sees  the  concomi- 
tant pulsations  of  the  image. 

286.  Optical  combination  of  two  vibratory  motions  at  rigrht  angles 
to  each  other. — The  optical  combination  of  two  rectangular  vibratory 
motions  is  effected  as  shown  in  figure  262  ;  that  is,  by  means  of  two  tuning- 
forks,  one  of  which  is  horizontal  and  the  other  vertical,  and  both  provided 


262  On  Sound.  [286- 

with  mirrors.  If  the  horizontal  fork  first  vibrates  alone,  a  horizontal  luminous 
outline  is  seen  on  the  screen,  while  the  vibration  of  the  other  produces  a 
vertical  image.  If  both  tuning-forks  vibrate  simultaneously,  the  two  motions 
combine,  and  the  reflected  pencil  describes  a  more  or  less  complex  cui-ve, 
the  form  of  which  depends  on  the  number  of  vibrations  of  the  two  tuning- 
forks  in  a  given  time.  This  curve  gives  a  valuable  means  of  comparing  the 
number  of  vibrations  of  two  sounding  bodies. 


Fig.  263. 

Fig.  263  shows  the  luminous  image  on  the  screen  when  the  tuning-forks 
are  in  unison  ;  that  is,  when  the  number  of  vibrations  is  equal. 

The  fractions  below  each  curve  indicate  the  differences  of  phase  between 
them.  The  initial  form  of  the  curve  is  determined  by  the  difference  of  phase. 
The  curve  retains  exactly  the  same  form  when  the  tuning-forks  are  in  unison, 
provided  that  the  amplitudes  of  the  two  rectangular  vibrations  decrease  in 
the  same  ratio. 


Fig.  264. 


If  the  tuning-forks  are  not  quite  in  unison,  the  initial  difference  of  phase 
is  not  preserved,  and  the  curve  passes  through  all  its  variations. 

Fig.  264  represents  the  different  appearances  of  the  luminous  image 
when  the  difference  between  the  tuning-forks  is  an  octave  :  that  is,  when  the 


-287] 


Leon  Scott's  PJionautograph. 


263 


numbers  of  their  vibrations  are  as  1:2;  and  fig.  265  gives  the  series  of 
curves  when  the  numbers  of  the  vibrations  are  as  3  :  4. 

It  will  be  seen  that  the  curves  are  more  complex  when  the  ratios  of  the 


Fig.  265. 

numbers  of  vibrations  are  less  simple.     Lissajous  examined  these  curves 
theoretically,  and  has  calculated  their  general  equations. 

When  these  experiments  are  made  with  the  electric  light,  instead  of  an 
ordinary  lamp,  the  phenomena  are  remarkably  brilliant. 


287.  Iieon  Scott's  Phonautograpta. — This  apparatus  registers  not  only 
the  vibrations  produced  by  solid  bodies,  but  also  those  produced  by  wind  in- 
struments, by  the  voice  in  singing,  and  even  by  any  noise  whatsoever  ;  for 


264 


On  Sound. 


[287- 


instance,  that  of  thunder,  or  the  report  of  a  cannon.  It  consists  of  an  elhp- 
soidal  barrel,  AB,  about  a  foot  and  a  half  long  and  a  foot  in  its  greatest  dia- 
meter, made  of  plaster  of  Paris.  The  end  A  is  open,  but  the  end  B  is 
closed  by  a  solid  bottom,  to  the  middle  of  which  is  fixed  a  brass  tube  a,  bent 
at  an  elbow  and  terminated  by  a  ring,  on  which  is  fixed  a  flexible  membrane 
which,  by  means  of  a  second  ring,  can  be  stretched  to  the  required  extent. 
Near  the  centre  of  the  membrane,  fixed  by  sealing-wax,  is  a  hog's  bristle, 
which  acts  as  a  style,  and,  of  course,  shares  the  movements  of  the  membrane. 
In  order  that  the  style  shall  not  be  at  a  node^  the  stretching  ring  is  fitted 
with  a  movable  piece,  z,  or  subdivider,  which,  being  made  to  touch  the  mem- 
brane first  at  one  point  and  then  at  another,  enables  the  experimenter  to 
alter  the  arrangements  of  the  nodal  lines  at  will.  By  means  of  the  sub- 
divider,  the  point  is  made  to  coincide  with  a  loop  ;  that  is,  a  point  where  the 
vibrations  of  the  membrane  are  at  a  maximum. 

When  a  sound  is  produced  near  the  apparatus,  the  air  in  the  ellipsoid, 
the  membrane,  and  the  style  will  vibrate  in  unison  with  it,  and  it  only  remains 
to  trace  on  a  sensitive  surface  the  vibrations  of  the  style,  and  to  fix  them. 
For  this  purpose  there  is  placed  in  front  of  the  membrane  a  brass  cylinder, 
C,  turning  round  a  horizontal  axis  by  means  of  a  handle,  ;;/.     On  the  pro- 


Fig.  267. 


P  ig.  268. 


longed  axis  of  the  cylinder  a  screw  is  cut  which  works  in  a  nut ;  conse- 
quently, when  the  handle  is  turned,  the  cylinder  gradually  advances  in  the 
direction  of  its  axis.  Round  the  cylinder  is  wrapped  a  sheet  of  paper 
covered  with  a  thin  layer  of  lampblack. 

The  apparatus  is  used  by  bringing  the  prepared  paper  into  contact  with 
the  point  of  the  style,  and  then  setting  the  cylinder  in  motion  round  its  axis. 
So  long  as  no  sound  is  heard,  the  style  remains  at  rest,  and  merely  removes 
the  lampblack  along  a  line  which  is  a  helix  on  the  cylinder,  but  which  be- 
comes straight  when  the  paper  is  unwrapped.  But  when  a  sound  is  heard, 
the  membrane  and  the  style  vibrate  in  unison,  and  the  line  traced  out  is  no 
longer  straight,  but  undulates,  each  undulation  corresponding  to  a  double 


-288] 


Koniz's  Mano metric  Flames. 


>6s 


vibi-ation  of  the  style.  Consequently,  the  figures  thus  obtained  faithfully 
denote  the  number,  amphtude,  and  isochronism  of  the  vibrations. 

Fig.  267  shows  the  trace  produced  when  a  simple  note  is  sung,  and 
strengthened  by  means  of  an  upper  octave.  The  latter  note  is  represented 
by  the  curve  of  lesser  amplitude.  Fig.  268  represents  the  sound  produced 
jointly  by  two  pipes  whose  notes  ditfer  by  an  octave.  The  lower  line  ot 
fig.  269  represents  the  rolling  sound  of  the  letter  R  when  pronounced  with 
a  ring. 

The  upper  line  of  fig.  269  represents  the  perfectly  isochronous  vibrations 
of  a  tuning-fork  placed  near  the  ellipsoid.  This  line  was  traced  by  a  fine 
point  on  one  branch  of  the  fork,  which  was  thus  found  to  make  exactly  500 
vibrations  per  second.  Hence,  each  undulation  of  the  upper  line  corresponds 
to  the  5^^  part  of  a  second  ;  and  thus  these  lines  become  very  exact  means 
of  measuring  short  intervals  of  time.  For  example,  in  fig.  269  each  of  the 
separate  shocks  producing  the  rolling  sound  of  the  letter  R  corresponds  to 
about  18  double  vibrations  of  the  tuning-fork,  and  consequently  lasts  about 
i*-  or  about  J^  of  a  second. 

288.  Konigr's  manometric  flames. — Konig's  method  consists  in  trans- 
mitting the  motion  of  the  waves  which  form  a  sound  to  gas  flames,  which, 
by  their  pulsations,  indicate  the  nature  of  the  sounds.     For  this  purpose  a 


^:T 


^--kk- 


.^jaJ 


Fig.  270. 


metal  capsule,  represented  in  section  at  A,  fig.  270,  is  divided  into  two  com- 
partments by  a  thin  membrane  ot  caoutchouc  ;  on  the  right  of  the  figure 
is  a  gas  jet,  and  below  it  a  tube  conveying  coal  gas  ;  on  the  left  is  a  tubu- 
lure,  to  which  may  be  attached  a  caoutchouc  tube.     The  other  end  of  this 


266  On  Sound.  [288- 

may  be  placed  at  the  node  of  an  organ-pipe  (274),  or  it  terminates  in  a 
mouthpiece  in  front  of  which  a  given  note  may  be  sung  ;  this  is  the  arrange- 
ment represented  in  fig.  270. 

Fig.  271. 


Fig.  272. 

When  the  sound-waves  enter  the  capsule  by  the  mouthpiece  and  the 
tube,  the  membrane  yielding  to  the  condensation  and  rarefaction  of  the 
waves,  the  coal  gas  in  the  compartment  on  the  right  is  alternately  contracted 
and  expanded,  and  hence  are  produced   alternations  in  the  length  of  the 

Fig.  273. 


flame,  which  are,  however,  scarcely  perceptible  when  the  flame  is  observed 
directly.  But  to  render  them  distinct  they  are  received  on  a  mirror  with 
four  faces,  M,  which  may  be  turned  by  two  cog-wheels  and  a  handle.     As 


-289] 


Dcterini)iation  of  the  Intensity  of  Sotuids. 


267 


long  as  the  flame  burns  steadily,  there  appears  in  the  mirror,  when  turned,  a 
continuous  band  of  light.  But,  if  the  capsule  is  connected  with  a  sounding 
tube  yielding  the  fundamental  note,  the  image  of  the  flame  takes  the  form 
represented  in  fig.  271,  and  that  of  the  figure  272  if  the  sound  yields  the 
octave.  If  the  two  sounds  reach  the  capsule  simultaneously,  the  flame  has 
the  appearance  of  fig.  273  ;  in  that  case,  however,  the  tube  leading  to  the 
capsule  must  be  connected  by  a  T-pipe  with  two  sounding-tubes,  one  giving 
the  fundamental  note,  and  the  other  the  octave.  If  one  gives  the  funda- 
mental note  and  the  other  the  third,  the  flame  has  the  appearance  of  figure  274. 
If  the  vowel  E  be  sung  in  front  of  the  mouthpiece  first  upon  f,  and  then 


K,g.  .70. 


upon  c' ,  the  rotating  mirror  gives  the  flames  represented  in  figs.  275  and 
276. 

289.  Determination  of  the  intensity  ot  sounds. — Meyer  has  devised 
a  plan  by  which  the  intensities  of  two  sounds  of  the  same  pitch  may  be 
directly  compared.  The  two  sounds  are  separated  from  each  other  by  a 
medium  impervious  to  sound,  and  in  front  of  each  of  them  is  a  resonance 
globe  (255)  accurately  tuned  to  the  sound.  Each  of  these  resonance  globes 
is  attached  by  means  of  caoutchouc  tubes  of  equal  length  to  the  two  ends  of 
a  U-tube,  in  the  middle  of  the  bend  of  which  is  a  third  tube  provided  with  a 
manometric  capsule. 

If  the  resonance  globes  are  each  at  the  same  distance  from  the  sounding 
bodies,  and  if  the  note  of  only  one  of  them  is  produced,  the  flame  vibrates. 
If  both  sounds  are  produced,  and  they  are  of  the  same  intensity,  and  in  the 
same  phase,  they  interfere  completely  in  the  tube,  so  that  the  flame  of  the 
manometric  capsule  is  quite  stationary',  and  appears  in  the  turning  mirror  as 
a  straight  luminous  band. 

If,  however,  the  sounds  are  not  of  the  same  intensity,  the  interference 
will  be  incomplete,  and  the  luminous  band  will  be  jagged  at  the  edge.  The 
distance  of  one  of  the  sounds  from  the  resonance  globes  is  altered  until  the 


268 


On   Sound. 


[289- 


flame  is  stationary.     The  intensities  of  the  two  sounds  are  thus  directly  as 
the  squares  of  their  distances  from  the  resonators. 

290.  Acoustic  attraction  and  repulsion. — It  was  observed  by  Guyot, 
and  afterwards  independently  by  Guthrie  and  by  Schellbach,  that  a  sound- 
ing body,  one  in  a  state  of  vibration  therefore,  exercises  an  action  on  a 
body  in  its  neighbourhood  which  is  sometimes  one  of  attraction  and  some- 
times of  repulsion.  The  vibrations  of  an  elastic  medium  attract  bodies 
which  are  specifically  heavier  than  itself,  and  repel  those  which  are  specifi- 
cally lighter.  Thus  a  balloon  of  goldbeater's  skin  filled  with  carbonic  acid 
is  attracted  towards  the  opening  of  a  resonance-box  on  which  is  a  vibrating 
tuning-fork  ;  while  a  similar  balloon  filled  with  hydrogen  and  tied  down  by 
a  thread  is  repelled.  This  result  always  follows,  even  when  the  hydrogen 
balloon  is  made  heavier  than  air  by  loading  it  with  wax. 

A  light  piece  of  cardboard  suspended  and  held  near  a  tuning-fork  moves 
towards  it  when  the  fork  is  made  to  vibrate.  If  the  tuning-fork  is  suspended 
and  is  then  made  to  vibrate,  it  moves  towards  the  card  if  the  latter  is  fixed. 
Two  suspended  tuning-forks  in  a  state  of  vibration  move  towards  each 
other.  The  flame  of  a  candle  placed  near  the  end  of  a  sounding  tuning- 
fork  was  repelled  if  held  near  it  ;  if  held  underneath  it  was  flattened  out  to  a 
disc.  A  gas  flame  near  the  end  of  the  tuning-fork  was  divided  into  two  arms. 
Guthrie  found  that,  when  one  prong  of  a  tuning-fork  is  enclosed  in  a  tube 
provided  with  a  capillary  tube  dipping  into  a  liquid,  and  is  set  in  vibration 
by  bowing  the  free  prong,  the  air  around  the  en- 
closed prong  is  expanded,  and  he  thence  con- 
cluded that  the  approach,  above  described,  of  a' 
suspended  body  to  the  sounding-fork  is  due  to 
the  diminution  of  the  pressure  of  the  air  between 
the  fork  and  the  body  below  that  on  the  other 
side  of  the  body. 

A  cylindrical  resonator  of  stiff  drawing-paper 
is  fastened  to  a  strip  of  wood,  which  is  provided 
with  a  glass  cap  and  counterpoise,  and  thus  can 
be  made  to  turn  on  a  needle  point.  If  the  open 
end  of  the  sounding-box  of  a  tuning-fork  vibrating 
in  unison  with  the  resonator  is  brought  near  this, 
it  is  repelled  even  at  a  distance  of  some  inches. 
When  a  small  mill  with  four  arms  (fig.  277),  each 
provided  with  a  small  resonator,  is  placed  near 
the  open  end  of  the  sounding-box,  the  repulsion 
is  so  strong  as  to  produce  a  uniform  rotation. 
These  phenomena  do  not  seem  to  be  due  to  the  aspirating  action  of  cur- 
rents of  air,  nor  are  they  caused  by  any  heating  effect  ;  and  it  must  be  con- 
fessed that  the  phenomena  require  further  elucidation  ;  they  are  of  special 
interest  as  furnishing  a  possible  clue  to  the  solution  of  the  problem  of  attrac- 
tion in  general. 

291.  Phonograph.  Craphophone — In  the  year  1877  Edison  devised  the 
apparatus  known  as  the ///cW(^_o"r<:7//^  for  recording  and  reproducing  sound, 
which  is  equally  remarkable  for  the  simplicity  of  its  construction  and  for  the 
striking  character  of  the  results  which  it  produces. 


Fig.  277. 


-291] 


Edison's  Phonograph. 


269 


This  instrument  is  illustrated  in  fig.  278,  and  it  consists  generally  of  a 
cylinder  C,  mounted  on  a  horizontal  axis  AA',  which  can  be  rotated  beneath 
a  mouthpiece  E,  by  means  of  a  winch-handle  M,  the  speed  of  rotation  being 
controlled  by  a  fly-wheel  attached  to  one  end  of  the  spindle  AA',  and  the 
whole  is  supported  by  a  base-board  L.  Upon  the  cylindric  surface  of  C  is 
cut  a  helical  groove,  and  one  end  of  the  spindle  A'  is  formed  into  a  screw  the 
pitch  of  which  is  equal  to  that  of  the  groove  upon  the  cylinder.  This  screw 
works  in  a  correspondingly  screwed  bearing,  so  that  on  turning  the  handle  the 
cylinder  not  only  rotates  upon  its  axis  but  also  travels  from  end  to  end  in  a 
direction  parallel  to  its  axis. 


Fig.  279. 


The  mouthpiece  is  closed  with  a  diaphragm  or  membrane  P,  to  the 
centre  of  which  is  attached,  by  means  of  a  caoutchouc  tube,  a  small  style  S 
directed  towards  the  cylinder,  and  which  is  caused 
to  vibrate  longitudinally  by  the  vibratoiy  action  of  the 
diaphragm  P,  and  the  position  of  the  mouthpiece  is  so 
adjusted  that  the  point  of  the  style  is  always  directed 
to  the  centre  of  the  helical  groove  in  the  cylinder.  On 
this  grooved  cylinder  is  stretched  a  sheet  of  tinfoil 
which  bridges  over  the  grooves,  being  supported  by 
the  ridges  and  the  position  of  the  mouthpiece,  and  its 
distance  from  the  cylinder  is  adjusted  by  the  handle  ;«, 
which  can  be  fixed  in  its  place  by  the  set  screw  v. 
Their  position  and  distance  are  so  adjusted  that 
when  the  apparatus  is  at  rest  the  point  of  the  style 
is  within  the  groove  and  a  little  lower  than  the  top  of  the  ridge. 

If,  while  the  cylinder  is  being  rotated,  sounds  or  words  be  uttered  into 
the  mouthpiece,  the  diaphragm  attached  thereto  will  be  set  into  vibration 
and  will  cause  the  style  to  indent  on  the  foil  a  groove  of  varying  depth,  the 
bottom  of  which  is  a  mechanical  record  of  the  vibration  of  the  diaphragm, 
and  therefore  of  the  sounds  by  which  those  vibrations  were  set  up,  and  as 
the  tinfoil  is  a  very  imperfectly  elastic  material  it  is  able  to  retain  the  record 
so  made. 

If  now  this  record  be  passed  again  beneath  the  style  the  varying  indenta- 
tions on  the  foil  will  cause  the  style  to  vibrate  as  it  did  when  it  produced  the 
indentations,  and  the  diaphragm  will  be  similarly  set  into  vibration,  and  will 
reproduce  the  sound  by  which  it  was  in  the  first  instance  set  into  vibi'ation. 

In  this  way  sound  may  be  reproduced  so  as  to  be  audible  to  a  large 
audience  ;  the  articulation  is  distinct  though  feeble  ;  it  reproduces  the 
voice  of  a  person  who  speaks  into  it,  but  with  a  nasal  intonation.     Speech 


270  On  Sound  [291- 

may  thus  be  stored  up  on  a  sheet  of  tinfoil  and  kept  for  an  indefinite  period, 
and  the  sound  may  be  reproduced  more  than  once  from  the  same  record, 
but  after  a  second  reproduction  the  clearness  is  greatly  diminished. 

If  the  velocity  of  rotation  be  greater  than  before,  the  pitch  of  the  sound 
is  raised;  and  if  it  be  not  uniform,  then,  m  the  case  of  a  song,  the  reproduc- 
tion is  incorrect.  In  order  to  produce  a  uniform  velocity  the  instrument  may 
with  advantage  be  driven  by  clockwork. 

There  is  great  difference  in  the  distinctness  with  which  the  various  con- 
sonants and  vowels  are  reproduced,  the  most  distinct  are  words  containing 
the  vowels  A,  O,  and  U,  and  the  consonants  /,  k,  and  r ;  the  s  and  similar 
consonants,  on  the  contrary,  are  seldom  distinct.  If  the  phonograph  be 
rotated  in  the  reverse  direction,  the  sounds  of  which  the  words  are  made 
up  retain  their  character,  but  are  produced  in  the  reverse  order. 

If  the  instrument  be  reset  to  the  starting-point  of  the  phonographic 
record  of  a  song,  and  be  again  sung  into,  it  will  reproduce  both  series  of 
sounds,  as  if  two  persons  were  singing  at  the  same  time  ;  and,  by  repeating 
the  same  process,  a  third  or  fourth  succession  of  sounds  may  be  added, 
and  the  whole  will  be  heard  together  and  without  the  one  record  destroying 
the  other. 

The  impressions  on  the  tinfoil  appear  at  first  sight  as  a  series  of  successive 
points  or  dots,  but  when  examined  under  a  microscope  they  are  seen  to  have 
a  distinct  form  of  their  own.  When  a  cast  is  taken  by  means  of  fusible 
metal  and  a  longitudinal  section  made,  the  outline  closely  resembles  the 
jagged  edge  of  a  Konig's  flame.  Mr.  Edison  states  that  as  many  as  40,000 
words  can  be  registered  on  a  space  not  exceeding  10  square  inches. 

The  phonograph  has  been  used  with  great  advantage  by  Jenkins  and 
King  for  the  analysis  of  vocal  sounds,  for  which  purpose  it  is  better  suited 
than  Konig's  flames. 

The  graphophone,  invented  by  Mr.  Sumner  Tainter,  in  conjunction  with 
Professor  Graham  Bell  and  Dr.  Chichester  Bell,  consists  essentially  of  three 
parts  :  the  recorder,  the  cylinder  on  which  the  record  is  made,  and  the 
reproducer. 

The  cylinder  is  a  hollow  cone  of  cardboard  coated  with  a  composition  of 
wax  and  paraffin  ;  it  is  mounted  horizontally  and  is  rotated  by  means  of  a 
treadle  underneath  the  table,  which  supports  the  whole  apparatus.  Between 
the  treadle  and  the  cylinder  is  interposed  a  very  ingenious  governor  by  which 
the  speed  of  rotation  of  the  cylinder  may  be  regulated  to  perfect  uniformity, 
the  force  required  for  this  rotation  being  very  small. 

On  a  bar  parallel  to  and  in  front  of  the  cylinder  is  clamped  the  recorder, 
which  consists  of  an  exceedingly  minute  cutting  point,  or  rather  chisel,  fixed  to 
a  mica  diaphragm.  This  diaphragm  is  at  the  end  of  a  flexible  tube  provided 
with  a  mouthpiece.  If  this  be  spoken  into,  the  diaphragm  vibrates  with  a 
to  and  fro  motion,  and  if  at  the  same  time  the  cylinder  rotates  at  a  uniform 
speed  the  style  cuts  or  carves  out  a  groove  in  the  surface  of  the  wax,  forming 
a  very  irregular  outline  which  is  the  exact  reproduction  of  the  sound  wave. 
Therein  lies  the  difference  between  the  graphophone  and  the  phonograph, 
for  in  the  latter  the  record  is  produced  by  a  process  of  indentation,  while  in 
the  former  the  record  of  the  sound  waves  is  engraved  in  a  waxy  material. 
The  grooves  are  so  excessively  minute  that  their  variations  in  depth  cannot 


-291]  GraphopJione.  27 1 

be  recognised  by  the  naked  eye  ;  they  are  not  more  than  the  ^h^  of  a"  inch  in 
diameter,  and  there  are  160  to  the  inch. 

The  reproducer  consists  of  a  hght  ebonite  tube,  at  one  end  of  which  is  the 
enlargement  containing  the  diaphragm,  which,  hke  that  of  the  recorder,  is  of 
mica,  but  is  somewhat  smaller.  The  diaphragm  is  connected  by  means  of  a 
fine  waxed  silk  thread  with  a  fine  steel  point  or  hook  which  rocks  on  a  pivot 
at  the  end  of  the  tube.  There  is  an  arrangement  by  which  this  reproducer 
can  be  clamped  in  front  of  the  recorder,  so  that  when  the  cylinder  is  rotated 
the  reproducer  travels  at  a  proportionate  speed,  allowing  the  small  point  to 
rest  in  the  groove  forming  the  sound  record,  and  along  which  it  rides  and 
vibrates  ;  and  these  vibrations  are  transmitted  to  the  mica  diaphragm,  and, 
being  communicated  to  the  ear,  faithfully  reproduce  the  sound. 

Notwithstanding  what  appears  the  very  yielding  character  of  the  wax, 
the  sounds,  and  even  elaborate  pieces  of  music,  are  reproduced  with  great 
fidelity,  and  it  is  stated  that  the  same  record  will  reproduce  the  original 
sound  some  thousand  times. 


272 


071  Heat.  [292- 


BOOK   VI. 

ON    HEAT. 


CHAPTER    I. 

PRELIMINARY    IDEAS.      THERMOMETERS. 

292.  Heat.  Hypotheses  as  to  its  nature. — In  ordinary  language  the 
term  Jieat  is  used  not  only  to  express  a  particular  sensation,  but  also  to  de- 
scribe that  particular  state  or  condition  of  matter  which  produces  this  sensa- 
tion. Besides  producing  this  sensation,  heat  acts  variously  upon  bodies  ;  it 
melts  ice,  boils  water,  makes  metals  red-hot,  produces  electrical  currents, 
decomposes  compound  bodies,  and  so  forth. 

Two  theories  as  to  the  cause  of  heat  have  been  propounded  :  these  are, 
the  theory  of  emission.,  and  the  theo7y  of  undulation. 

On  the  first  theory,  heat  is  caused  by  a  subtle  imponderable  fluid,  which 
surrounds  the  molecules  of  bodies,  and  which  can  pass  from  one  body  to 
another.  These  heat  atjnospheres.,  which  thus  surround  the  molecules,  exert 
a  repelling  influence  on  each  other,  in  consequence  of  which  heat  acts  in 
opposition  to  the  force  of  cohesion.  The  entrance  of  this  substance  into  our 
bodies  produces  the  sensation  of  warmth,  its  egress  the  sensation  of  cold. 

On  the  second  hypothesis  the  heat  of  a  body  is  caused  by  an  extremely 
rapid  oscillating  or  vibratory  motion  of  its  molecules  ;  and  the  hottest  bodies 
are  those  in  which  the  vibrations  have  the  greatest  velocity  and  the  greatest 
amplitude.  At  any  given  time  the  whole  of  the  molecules  of  a  body  possess 
a  sum  of  vis  viva,  which  is  the  heat  they  contain.  To  increase  their  tempera- 
ture is  to  increase  their  ins  viva  ;  to  lower  their  temperature  is  to  decrease 
their  vis  viva.  Hence,  on  this  view,  heat  is  not  a  substance  but  a  condition 
of  matter.,  and  a  condition  which  can  be  transferred  from  one  body  to  another. 
When  a  heated  body  is  placed  in  contact  with  a  cooler  one,  the  former  cedes 
more  molecular  motion  than  it  recei\es  ;  but  the  loss  of  the  former  is  the 
equivalent  of  the  gain  of  the  latter. 

It  is  also  assumed  that  there  is  an  imponderable  elastic  ether,  which  per- 
vades all  matter  and  infinite  space.  A  hot  body  sets  this  in  rapid  vibration, 
and  the  vibrations  of  this  ether  being  communicated  to  material  objects  set 
them  in  more  rapid  vibration  ;  that  is,  increase  their  temperature.  Here  we 
have  an  analogy  with  sound ;  a  sounding  body  is  in  a  state  of  vibration,  and 


292]  Heat.     Hypotheses  as  to  its  Nature.  273 

its  vibrations  are  transmitted  by  atmospheric  air  to  the  auditoiy  apparatus 
in  which  is  produced  the  sensation  of  sound. 

This  hypothesis  as  to  the  nature  of  heat  is  now  admitted  by  the  most 
distinguished  physicists.  It  affords  a  better  explanation  of  all  the  phenomena 
of  heat  than  any  other  theory,  and  it  reveals  an  intimate  connection  between 
heat  and  light.  It  will  be  subsequently  seen  that  by  the  friction  of  bodies 
against  each  other  an  indefinite  quantity  of  heat  is  produced.  Experiment 
has  shown  that  there  is  an  exact  equivalence  between  the  motion  thus  de- 
stroyed and  the  heat  produced.  These  and  many  other  facts  are  utterly 
inexplicable  on  the  assumption  that  heat  is  a  substance,  and  not  a  form  of 
motion. 

In  what  follows,  however,  the  phenomena  of  heat  will  be  considered,  as 
far  as  possible,  independently  of  either  hypothesis  ;  but  we  shall  subsequently 
return  to  the  reason  for  the  adoption  of  the  latter  hypothesis. 

Assuming  that  the  heat  of  bodies  is  due  to  the  motion  of  their  particles, 
we  may  admit  the  following  explanation  as  to  the  nature  of  this  motion  in 
the  various  forms  of  matter  : — 

In  solids  the  molecules  have  a  kind  of  vibratory  motion  about  certain 
fixed  positions.  This  motion  is  probably  veiy  complex  ;  the  constituents  of 
the  molecule  may  oscillate  about  each  other,  besides  the  oscillation  of  the 
molecule  as  a  whole  ;  and  this  latter  again  may  be  a  to-and-fro  motion,  or  it 
may  be  a  rotatoiy  motion  about  the  centre.  In  cases  in  which  external 
forces,  such  as  violent  shocks,  act  upon  the  body,  the  molecules  may  per- 
manently acquire  fresh  positions. 

In  the  liquid  state  the  molecules  have  no  fixed  positions.  They  can 
rotate  about  their  centres  of  gravity,  and  the  centre  of  gravity  itself  may 
move.  But  the  repellent  action  of  the  motion,  compared  with  the  mutual 
attraction  of  the  molecules,  is  not  sufficient  to  separate  the  molecules  from 
each  other.  A  molecule  no  longer  adheres  to  particular  adjacent  ones  ;  but 
it  does  not  spontaneously  leave  them  except  to  come  into  the  same  relation 
to  fresh  ones  as  to  its  previous  adjacent  ones.  Thus  in  a  liquid  there  is  a 
vibratory,  rotatory,  and  progressive  motion. 

In  Xh^  gaseous  state  the  molecules  are  entirely  without  the  sphere  of  their 
mutual  attraction.  They  fly  forward  in  straight  lines  according  to  the  ordi- 
nary laws  of  motion,  until  they  impinge  against  other  molecules  or  against 
a  fixed  envelope  which  they  cannot  penetrate,  and  then  return  in  an  opposite 
direction,  with,  in  the  main,  their  original  velocity.  If  the  molecules  were  in 
space,  where  no  external  force  could  act  upon  them,  they  would  fly  apart,  and 
disappear  in  infinity.  But  if  contained  in  any  vessel,  the  molecules  con- 
tinually impinge  in  all  directions  against  the  sides,  and  thus  arises  the  pres- 
sure which  a  gas  exerts  on  its  vessel. 

The  perfection  of  the  gaseous  state  implies  that  the  space  actually 
occupied  by  the  molecules  of  the  gas  be  infinitely  small  compared  with  the 
entire  volume  of  the  gas  ;  that  the  time  occupied  by  the  impact  of  a  mole- 
cule either  against  another  molecule,  or  against  the  sides  of  the  vessel,  be 
infinitely  small  in  comparison  with  the  inter\-al  between  any  two  impacts  ; 
and  that  the  influence  of  molecular  attraction  be  infinitely  small.  .  When 
these  conditions  are  not  fulfilled  the  gas  partakes  more  or  less  of  the  nature 
of  a  liquid,  and  exhibits  certain  deviations  from  Boyle's  law  (180).    This  is  the 

T 


274  On  Heat.  [292- 

case  with  all  gases  ;  to  a  very  slight  extent  with  the  less  easily  condensable 
gases,  but  to  a  far  greater  extent  with  vapours  and  the  more  condensable 
gases,  especially  near  their  points  of  liquefaction. 

293.  Dynamical  theory  of  g-ases. — We  have  seen  that  in  the  gaseous 
condition  the  particles  are  assumed  to  fly  about  in  right  lines  in  all  possible 
directions.  A  rough  illustration  of  this  condition  of  matter  is  afforded  by 
imagining  the  case  of  a  number  of  bees  enclosed  in  a  box. 

Let  us  suppose  a  cubical  vessel  to  be  filled  with  air  under  standard  con- 
ditions of  temperature  and  pressure.  Let  the  length  of  the  sides  be  a.  We 
will  for  the  present  suppose  that  each  particle  moves  freely  in  the  space 
without  striking  against  another  particle.  All  possible  motions  may  be  con- 
ceived to  be  resolved  into  motions  in  three  directions  which  are  parallel  to 
the  faces  of  the  cube.  Conceive  any  single  particle,  of  mass  in  ;  it  will  strike 
against  one  face  with  such  a  velocity,  //,  as  not  only  to  annul  its  own  motion, 
but  to  cause  it  to  rebound  in  the  opposite  direction  with  the  same  velocity  ; 
hence  the  measure  of  the  momentum  with  which  it  strikes  against  the  side 
will  be  imu.  Now,  by  their  rapid  succession  and  their  uniform  distribution, 
the  total  action  of  these  separate  impacts  is  to  produce  a  pressure  against 
the  sides  of  the  vessel  which  is  the  elastic  force  of  the  gas  ;  and,  to  measure 
the  pressure  on  the  side,  we  must  multiply  the  momentum  of  each  individual 
impact  by  the  total  number  of  such  impacts. 

Since  the  length  of  the  side  is  a,  if  there  are  n  molecules  in  the  unit 

of  space,  there  will  be  ncv'  in  the  volume  of  the  cube,  of  which    will    be 

3 
moving  in  a  direction  parallel  to  each  one  of  the  sides.     To  get  the  number 
of  impacts  on  one  face,  we  must  remember  that  they  succeed  each  other,, 
after  the  interval  of  time  recjuired  for  a  particle  to  fly  to  the  opposite  side 
and  back  again.     Hence,  u  being  the  velocity,  the  number  of  impacts  which 

each  particle  makes  in  the  unit  of  time,  a  second,  will  be  -^'  ,and  the  number 

7.  a 

of  all  such  which  strike  against  one  side  will  be  ^nd^^-  -  pta'-u. 

Now,  since  each  one  exerts  a  pressure  represented  by  2mu,  we  shall  have 
for  the  total  pressure  p  on  the  surface  n~ 

pd^  =  \a-nmir., 

and  therefore  the  pressure  on  the  unit  of  surface  will  be 

p  =  ^ntnu^. 

Now,  if  N  is  the  number  of  molecules  in  the  volume  7/,  N  =  nv,  ancll 
therefore 

p  =  ^  —  mtr  ;  that  is,  pv  =  ^Nmu'~. 

V. 

But,  for  any  given  mass  of  gas,  N,  w,  and  z/  are  constant  quantities,  and  the 
product /2/  must  therefore  also  be  constant  ;  this,  however,  is  only  one  form 
of  expressing  Boyle's  law  (180). 

294.  Molecular  velocity. — In  the  formula  p  =  ^n;/nr,  nnt  represents  the 
mass  in  unit  volume  which  we  may  designate  as  the  density  p,  of  the  gas. 


-294]  Molecular   Velocity  of  Gases.  275 

referred  to  that  of  water,  and  which  can  be  directly  measured  ;  and,  since  the 
pressure^  is  also  capable  of  direct  measurement,  we  can  calculate  the  third 
magnitude  u  in  absolute  measure. 

The  pressure  jZ^  on  a  gas  is  equal  to  the  action  of  gravity  on  a  column  of 
mercury  of  given  height  h  ;  so  that,  if  S  is  the  density  of  mercury  =  I3'596, 
and_^  the  acceleration  of  gravity,^  =  bgh  and 

u-  =  ^-^-. 

•Now,  if  a  be  the  specific  gravity  of  the  gas  as  compared  with  air,  which  is 

lighter  than  water,  p  x  773"3  =  o-,  or  p  =  — - — , 

773'3  773'3 

^■2  ^  3  X   13-596  X  076  X  9'8i[5  X  yyy^ 
<r 

which  gives  u  =      ''-  ;  that  is,  that  for  atmospheric  air  the  mean  velocity  of 

the  particles  is  485  metres  in  a  second.  For  other  gases  we  have,  expressed 
in  the  same  units, 

O  -  461 

N  =  492 
H  =  1844 

In  a  gas  the  velocities  of  the  particles  are  unequal ;  since,  even  supposing 
that  they  were  all  originally  the  same,  it  is  not  difficult  to  see  that  they  would 
soon  alter.  For  imagine  a  particle  to  be  moving  parallel  to  one  side,  and  to 
be  struck  centrically  by  another  moving  at  right  angles  to  the  direction  of 
its  motion,  the  particle  struck  would  proceed  on  its  new  path  with  increased 
velocity,  while  the  striking  particle  would  rebound  in  a  different  direction 
with  a  smaller  velocity. 

Notwithstanding  the  accidental  character  of  the  velocity  of  any  individual 
particle  in  such  a  mass  of  gas  as  we  have  been  considering,  there  will,  at  any 
one  given  time,  be  a  certain  average  distribution  of  velocities.  Now,  from 
considerations  based  on  the  theory  of  probabilities,  it  follows  that  some 
velocities  will  be  more  probable  than  others — that  there  will,  indeed,  be  one 
velocity  which  is  more  probable  than  any  other.  This  is  called  the  most 
probable  velocity.  The  mean  velocity  oi  ^ho.  particle,  as  found  above,  is 
not  this,  nor  is  it  the  same  as  the  arithmetical  mean  of  all  the  velocities  ;  it 
may  be  defined  to  be  that  velocity  which,  if  all  the  molecules  possessed  it, 
would  give  rise  to  the  same  mean  energy  of  the  molecular  impacts  against 
the  side  as  that  which  actually  exists.  This  mean  velocity  is  about  j^-  greater 
than  the  arithmetical  mean  velocity,  and  is  \\  that  of  the  most  probable 
single  velocity. 

Theoretical  as  well  as  experimental  observations  render  it  possible  to 
determine  with  great  probability  not  only  the  average  length  of  the  path 
which  a  molecule  traverses  before  it  encounters  another,  but  also  the  number 
of  impacts  in  a  given  time.  Thus,  in  air,  measured  under  standard  con- 
ditions, the  length  of  the  mean  path  of  a  molecule  is  calculated  to  be  0-000095 
mm.,  and  the  number  of  impacts  in  a  second  4,700  millions.  For  hydrogen 
these  numbers  are  0-0001855  mm.  for  the  length  of  path,  and  9,480  millions 


2/6  On  Heat.  [294- 

for  the  number  of  impacts.  Hence  it  is  that,  notwithstanding  these  enormous 
velocities,  gases  diffuse  but  slowly,  as  is  observed  in  the  case  of  those  with 
strong  odours. 

It  follows  from  the  above  equation  that 

u  :  u^  =  ^/'oT  :  ^-^ 

that  is,  that  the  molecular  velocities  are  inversely  as  the  square  roots  of  the 
densities  or  the  molecular  weights.  This  is  confirmed  by  experiments  on 
diffusion  (190). 

The  magnitudes  of  the  molecules  themselves  have  been  calculated  by 
several  observers  from  different  methods  based  on  various  physical  pheno- 
mena. Loschmidt  found,  for  instance,  that  the  diameter  of  the  molecule  of 
hydrogen  was  41,  oxygen  7,  and  nitrogen  8  hundred  millionths  of  a  centi- 
metre.    The  results  of  other  calculations  agree  remarkably  with  these. 

295.  General  effects  of  heat. — The  general  effects  of  heat  upon  bodies 
may  be  classed  under  three  heads.  One  portion  is  expended  in  raising  the 
temperature  of  the  body  ;  that  is,  in  increasing  the  vis  viva  of  its  molecules. 
In  the  second  place,  the  molecules  of  bodies  have  a  certain  attraction  for 
each  other,  to  which  is  due  their  relative  position  ;  hence  a  second  portion 
of  heat  is  consumed  in  augmenting  the  amplitude  of  the  oscillations,  by 
which  an  increase  of  volume  is  produced,  or  in  completely  altering  the 
relative  positions  of  the  molecules,  by  which  a  change  of  state  is  effected. 
These  two  effects  are  classed  as  internal  work.  Thirdly,  since  bodies  are 
surrounded  by  atmospheric  air  which  exerts  a  certain  pressure  on  their  sur- 
face, this  has  to  be  overcome  or  lifted  through  a  certain  distance.  The  heat 
or  work  required  for  this  is  called  the  exterftal  work. 

If  Q  units  of  heat  are  imparted  to  a  body,  and  if  A  be  the  quantity  of 

heat  which  is  equivalent  to  the  unit  of  work  ;  then  if  W  is  the  amount  of 

heat  which  serves  to  increase  the  temperature,  I  that  required  to  alter  the 

position  of  the  molecules,  and  if  L  be  that  expended  in  external  work,  then 

Q  =  A  (W  +  I  -t-  L). 

296.  Expansion. — All  bodies  expand  by  the  action  of  heat.  As  a  general 
rule,  gases  are  the  most  expansible,  then  liquids,  and  lastly  solids. 


Fig.  280. 

In  solids  which  have  definite  figures,  we  can  either  consider  the  expan- 
sion in  one  dimension,  or  the  linear  expansion  ;  in  two  dimensions,  the 
superficial  expansion  ;  or  in  three  dimensions,  the  cubical  expansion  or  the 


-296] 


Expansion. 


V7 


expansion  of  volume,  although  one  of  these  never  takes  place  without  the 
other.  As  liquids  and  gases  have  no  definite  figures,  the  expansions  of 
volume  have  in  them  alone  to  be  considered. 

To  show  the  linear  expansion  of  solids,  the  apparatus  represented  in  fig. 
280  may  be  used.  A  metal  rod.  A,  is  fixed  at  one  end  by  a  screw,  B,  while 
the  other  end  presses  against  the  short  arm  of  an  index,  K,  which  moves  on 
a  scale.  Below  the  rod  there  is  a  sort  of  cylindrical  lamp  in  which  alcohol 
is  burned.  The  needle  K  is  at  first  at  the  zero  point,  but  as  the  rod  becomes 
heated  it  expands,  and  moves  the  needle  along  the  scale. 

The  cubical  expansion  of  solids  is  shown  by  a  Graiiesande' s  ring.  This 
consists  of  a  brass  ball  a  (fig.  281),  which  at  the  ordinary  temperature  passes 


% 


Fig.  28 


Fig.  282.  Fig.  2S3. 


freely  through  a  ring,  111,  almost  of  the  same  diameter.  But  when  the  ball 
has  been  heated,  it  expands  and  no  longer  passes  through  the  ring. 

In  order  to  show  the  expansion  of  liquids,  a  large  glass  bulb  provided 
with  a  capillary  stem  is  used  (fig.  282).  If  the  bulb  and  a  part  of  the  stem 
contain  some  coloured  liquid,  the  liquid  rapidly  rises  in  the  stem  when  heat 
is  applied,  and  the  expansion  thus  observed  is  far  greater  than  in  the  case 
of  solids. 

The  same  apparatus  may  be  used  for  showing  the  expansion  of  gases. 
Being-  filled  with  air,  a  small  thread  of  mercury  is  introduced  into  the  capillary 
tube  to  serve  as  index  (fig.  283).  When  the  globe  is  heated  in  the  slightest 
degree,  even  by  approaching  the  hand,  the  expansion  is  so  great  that  the 
index  is  driven  to  the  end  of  the  tube,  and  is  finally  expelled.  Hence,  even 
for  a  very  small  degree  of  heat,  gases  are  highly  expansible. 

In  these  different  experiments  the  bodies  contract  on  cooling,  and  when 
they  have  attained  their  former  temperature  they  resume  their  original 
volume.  Certain  metals,  however,  especially  zinc,  form  an  exception  to  this 
rule,  and  it  appears  also  to  be  the  case  with  some  kinds  of  glass. 


2/8  On  Heat.  [297- 


MEASUREMENT   OF    TEMPERATURE.      THERMOMETRY. 

297.  Temperature. — The  temperature  or  hotness  of  a  Ijody,  indepen- 
dently of  any  hypothesis  as  to  the  nature  of  heat,  may  be  defined  as  being 
the  greater  or  less  extent  to  which  it  tends  to  impart  sensible  heat  to  other 
bodies.  The  temperature  of  a  body  must  not  be  confounded  with  the  quati- 
tity  of  heat  it  possesses  :  a  body  may  have  a  high  temperature  and  yet 
have  a  very  small  quantity  of  heat,  and,  conversely,  a  low  temperature  and  yet 
possess  a  large  amount  of  heat.  If  a  cup  of  water  be  taken  from  a  bucketful, 
both  will  indicate  the  same  temperature,  yet  the  quantities  they  possess  will 
be  diffei-ent.  This  subject  of  the  quantity  of  heat  will  be  afterwards  more 
fully  explained  in  the  chapter  on  Specific  Heat. 

298.  T\xeTm.ometeTS.— Thermometers  are  instruments  for  measuring 
temperatures.  Owing  to  the  imperfections  of  our  senses  we  are  unable  to 
measure  temperatures  by  the  sensation  of  heat  or  cold  which  they  produce 
in  us,  and  for  this  purpose  recourse  must  be  had  to  the  physical  actions  of 
heat  on  bodies.  These  actions  are  of  various  kinds,  but  the  expansion  of 
bodies  has  been  selected  as  the  easiest  to  observe.  But  heat  also  produces 
electrical  phenomena  in  bodies  ;  and  on  these  the  most  delicate  methods 
of  observing  temperatures  have  been  based,  as  we  shall  see  in  a  subsequent 
chapter. 

Liquids  are  best  suited  for  the  construction  of  thermometers^the  ex- 
pansion of  solids  being  too  small,  and  that  of  gases  too  great.  Mercury  and 
alcohol  are  the  only  licjuids  used — the  former  because  it  only  boils  at  a  very 
high  temperature,  and  the  latter  because  it  does  not  solidify  at  the  greatest 
known  cold. 

The  mercurial  thermometer  is  the  most  extensively  used.  It  consists  of 
a  capillary  glass  tube,  at  the  end  of  which  is  blown  the  bulb,  a  cylindrical 
or  spherical  reservoir.  Both  the  bulb  and  a  part  of  the  stem  are  filled  with 
mercury,  and  the  expansion  is  measured  by  a  scale  graduated  either  on  the 
stem  itself,  or  on  a  frame  to  which  it  is  attached. 

Besides  the  manufacture  of  the  bulb,  the  construction  of  the  thermometer 
comprises  three  opeiations  :  the  calibration  of  the  tube,  or  its  division  into 
parts  of  equal  capacity  ;  the  introduction  of  the  mercury  into  the  reservoir  ; 
and  the  graduation. 

299.  Division  of  the  tube  into  parts  of  equal  capacity.  Calibration. 
As  the  indications  of  the  thermometer  are  only  correct  when  the  divisions 
of  the  scale  correspond  to  equal  expansions  of  the  mercury  in  the  reservoir, 
the  scale  must  be  graduated,  so  as  to  indicate  parts  of  equal  capacity  in  the 
tube.  If  the  tube  were  quite  cylindrical,  and  of  the  same  diameter  through- 
out, it  would  only  be  necessaiy  to  divide  it  into  equal  lengths.  But  as  the 
diameter  of  glass  tubes  is  usually  greater  at  one  end  than  another,  parts  of 
equal  capacity  in  the  tube  are  represented  by  unequal  lengths  of  the  scale. 

In  order,  therefore,  to  select  a  tube  of  uniform  bore,  it  is  calibrated;  for 
this  purpose,  a  thread  of  mercury  about  an  inch  long  is  introduced  into  the 
capillary  tube,  and  moved  in  different  positions  in  the  tube,  care  being  taken 
to  keep  it  at  the  same  temperature.  If  the  thread  is  of  the  same  length  in 
every  part  of  the  tube,  it  shows  that  the  capacity  is  everywhere  the  same  ; 


Determmation  of  the  Fixed  Points  of  a  Thermometer.    279 

but  if  the  thread  occupies  different  lengths  the  tube  is  rejected,  and  another 
one  sought. 

300.  Filling-  the  thermometer. — In  order  to  fill  the  thermometer  with 
mercury,  a  small  funnel,  C  (fig.  284),  is  blown  on  at  the  top,  and  is  filled 
with  mercury  ;  the  tube  is  then  slightly  inclined,  and  the  air  in  the  bulb 
expanded  by  heating  it  with  a  spirit  lamp.  The  expanded  air  partially 
escapes  by  the  funnel,  and,  on  cooling,  the  air  which  remains  contracts,  and 
a  portion  of  the  mercury  passes  into  the  bulb  D.  The  bulb  is  then  again 
warmed,  and  allowed  to  cool,  a  fresh  quantity  of  mercury  enters,  and  so  on, 
until    the   bulb   and  part  of  the  tube  are  full  of 

mercury.  The  mercury  is  then  heated  to  boiling  ; 
the  mercurial  vapours  in  escaping  carry  with  them 
the  air  and  moisture  which  remain  in  the  tube. 
The  tube,  being  full  of  the  expanded  mercury  and 
of  mercurial  vapour,  is  hermetically  sealed  at  one 
end.  When  the  thermometer  is  cold,  the  mercury 
ought  to  fill  the  bulb  and  a  portion  of  the  stem. 

301.  Graduation  of  the  thermometer. — The 
thermometer  being  filled,  it  requires  to  be  gradu- 
ated ;  that  is,  to  be  provided  with  a  scale  to  which 
variations  of  temperature  can  be  referred.  And, 
first  of  all,  two  points  must  be  fixed  which  repre- 
sent identical  temperatures,  and  which  can  always 
be  easily  reproduced. 

Experiment  has  shown  that  ice  constantly  melts 
at  the  same  temperature,  whatever  be  the  degree  of 
heat,  and  that  distilled  water  under  the  same  pres- 
sure and  in  a  vessel  of  the  same  kind  always  boils 
at  the  same  temperature.  Consequently,  for  the 
first  fixed  point,  or  zero,  the  temperature  of  melting 
ice  has  been  taken :  and  for  a  second  fixed  point, 
the  temperature  of  boiling  water  in  a  metal  vessel 
under  the  normal  atmospheric  pressure  of  760 
millimetres. 

This  interval  of  temperature — that  is,  the  range 
from  zero  to  the  boiling  point — is  taken  as  the  unit  for  comparing  tempera- 
tures ;  just  as  a  certain  length,  a  foot  or  a  metre  for  instance,  is  used  as  a 
basis  for  comparing  lengths. 

302.  Determination  of  the  fixed  points. — To  obtain  zero,  snow  or 
pounded  ice  is  placed  in  a  vessel  in  the  bottom  of  which  is  an  aperture  by 
which  water  escapes  (fig.  285).  The  bulb  and  a  part  of  the  stem  of  the 
thermometer  are  immersed  in  this  for  about  a  quarter  of  an  hour,  and  a 
mark  made  at  the  level  of  the  mercury,  which  represents  zero. 

According  to  Bunsen  it  is  doubtful  whether  a  very  accurate  determination 
is  obtained  by  placing  a  thermometer  in  melting  ice,  for  some  slight  admix- 
tures lower  the  freezing  point  considerably.  The  best  plan  is  to  let  water,  in 
which  is  the  thermometer,  be  over-cooled  (345)  and  then  made  to  freeze  by 
shaking  ;  the  point  to  which  the  mercury  rises  is  the  true  melting  point. 

The  second  fixed  point  is  determined  by  means  of  the  apparatus  repre- 


Fig   284. 


2  So 


On  Heat. 


[302- 


sented  in  the  figures  286  and  287,  of  which  fig.  287  represents  a  vertical  sec- 
tion. In  both,  the  same  letters  designate  the  same  parts.  The  whole  of  the 
apparatus  is  of  metal.  A  central  tube,  A,  open  at  both  ends,  is  fixed  on  a 
cylindrical  vessel  containing  water  ;  a  second  tube, 
B,  concentric  with  the  first,  and  surrounding  it, 
is  fixed  on  the  same  vessel,  M.  In  this  second 
cylinder,  which  is  closed  at  both  ends,  there  are 
three  tubulures,  a,  E,  D.  A  cork,  in  which  is  the 
thermometer  /,  fits  in  a.  To  E,  a  glass  tube,  con- 
taining mercury,  is  attached,  which  serves  as  a 
manometer  for  measuring  the  pressure  of  the  vapour 
in  the  apparatus.  D  is  an  escape  tube  for  the 
vapour  and  condensed  water. 

The  apparatus  is  placed  on  a  furnace  and  heated 
till  the  water  boils  ;  the  vapour  produced  in  M  rises 
in  the  tube  A,  and,  passing  through  the  two  tubes 
in  the  direction  of  the  arrows,  escapes  by  the  tubu- 
lure  D.  The  thermometer  /  being  thus  surrounded 
with  vapour,  the  mercury  expands,  and,  when  it 
has  become  stationary',  the  point  at  which  it  stops 
is  marked.  This  is  the  point  sought  for.  The 
object  of  the  second  case,  B,  is  to  avoid  the  cooling 
of  the  central  tubulure  by  its  contact  with  the  air. 
The  determination  of  the  point  100  (see  next  Article)  would  seem  to 
require  that  the  height  of  the    barometer  during  the  experiment  should  be 


Fig.  285. 


Fig.  2S6. 


Fig.  287. 


760  millimetres,  for,  when  the  barometric  height  is  greater  or  less  than  this 
quantity,  water  boils  either  above  or  below  100  degrees.     But  the  point  100 


-303] 


Construction  of  the  Scale  of  a  Thermometer. 


t 


may  always  be  exactly  obtained,  by  making  a  suitable  correction.  For 
every  27  millimetres  difference  in  height  of  the  barometer  there  is  a  differ- 
ence in  the  boiling  point  of  i  degree.  If,  for  example,  the  height  of  the 
barometer  is  778— that  is,  iS  millimetres,  or  two-thirds  of  27,  above  7.60 — 
water  would  boil  at  100  degrees  and  two-thirds.  Consequently  ioo§  would 
ha\e  to  be  marked  at  the  point  at  which  the  mercury  stops. 

Gay-Lussac  observed  that  water  boils  at  a  somewhat  higher  temperature 
in  a  glass  than  in  a  metal  vessel  ;  and  as  the  boiling  point  is  raised  by  any 
salts  which  are  dissolved,  it  has  been  assumed  that  it  was  necessary  to  use 
a  metal  vessel  and  distilled  water  in  fixing  the  boiling  point.  Rudberg 
showed,  however,  that  these  latter  precautions  are  superfluous.  The  nature 
of  the  vessel  "and  salts  dissolved  in  ordinary  water  influence  the  tempei'ature 
of  boiling  water,  but  not  that  of  the  vapour  which  is  formed.  That  is  to 
say,  that  if  the  temperature  of  boiling  water  from  any  of  the  above  causes 
is  higher  than  100  degrees,  the  temperature  of  the  vapour  does 
not  exceed  100,  provided  the  pressure  is  not  more  than  760 
millimetres.  Consequently,  the  higher  point  may  be  determined 
in  a  vessel  of  any  material,  provided  the  thermometer  is  quite 
surrounded  by  vapour,  and  does  not  dip  in  the  water. 

Even  with  distilled  water,  the  bulb  of  the  thermometer  must 
not  dip  in  the  liquid,  for,  strictly  speaking,  it  is  only  the  upper 
layer  that  really  has  the  temperature  of  100  degrees,  since  the 
temperature  increases  from  layer  to  layer  towards  the  bottom,  in 
consequence  of  the  increased  pressure. 

303.  Construction  of  the  scale. — Just  as  the  foot-rule 
which  is  adopted  as  the  unit  of  comparison  for  length,  is  divided 
into  a  number  of  equal  divisions  called  inches  for  the  purpose  of 
having  a  smaller  unit  of  comparison,  so  likewise  the  unit  of  com- 
parison of  temperatures,  the  range  from  zero  to  the  boiling  point, 
must  be  divided  into  a  number  of  parts  of  equal  capacity  called 
degrees.  On  the  Continent,  and  more  especially  in  France,  this 
space  is  divided  into  100  parts,  and  this  division  is  called  the 
Centigrade  or  Celsius  scale  ;  the  latter  being  the  name  of  the 
inventor.  The  Centigrade  thermometer  is  almost  exclusively 
adopted  in  foreign  scientific  works,  and,  as  its  use  is  gradually 
extending  in  this  country,  it  has  been  and  will  be  adopted  in 
this  book. 

The  degrees  are  designated  by  a  small  cypher  placed  a  little 
above  on  the  right  of  the  number  which  marks  the  temperature, 
and  to  indicate  temperatures  below  zero  the  minus  sign  is  placed 
before  them.     Thus,  —  15°  signifies  15  degrees  below  zero. 

In  accurate  thermometers  the  scale  is  marked  on  the  stem 
itself  (fig.  288).  It  cannot  be  displaced,  and  its  length  remains 
fixed,  as  glass  has  very  little  expansibility.  The  graduation  is 
effected  by  covering  the  stem  with  a  thin  layer  of  wax,  and 
then  marking  the  divisions  of  the  scale,  as  well  as  the  corre-  Fig.  i>ss. 
spending  numbers,  with  a  steel  point.  The  thermometer  is 
then  exposed  for  about  ten  minutes  to  the  vapours  of  hydrofluoric  acid, 
which    attacks    the  glass    where   the    wax   has   been    removed.      The   rest 


282  On  Heat.  [303- 

of  the  wax  is  then  removed,  and  the  stem  is  found  to  be  permanently 
etched. 

Besides  the  Centigrade  scale  two  others  are  frequently  used — FaJii'enheif  s 
scale  and  Reaumur'' s  scale. 

In  Reaumur's  scale  the  fixed  points  are  the  same  as  on  the  Centigrade 
scale,  but  the  distance  between  them  is  divided  into  80  degrees,  instead  of 
into  100.  That  is  to  say,  80  degrees  Reaumur  are  equal  to  100  degrees 
Centigrade  ;  one  degree  Reaumur  is  equal  to  ^~°  or  |  of  a  degree  Centigrade, 
and  one  degree  Centigrade  equals  ^^-^  or  |  degrees  Reaumur.  Consequently, 
to  convert  any  number  of  Reaumui-'s  degrees  into  Centigrade  degrees  (20,  for 
example),  it  is  merely  necessary  to  multiply  them  by  |  (which  gives  25). 
Similarly,  Centigrade  degrees  are  converted  into  Reaumur  by  multiplying 
them  by  |. 

The  thermometric  scale  invented  by  Fahrenheit  in  17 14  is  still  much 
used  in  England,  and  also  in  Holland  and  North  America.  The  higher  fixed 
point  is,  like  that  of  the  other  scales,  the  temperature  of  boiling  water  ;  but 
the  null  point  of  zero  is  the  temperature  obtained  by  mixing  equal  weights 
of  sal-ammoniac  and  snow,  and  the  interval  between  the  two  points  is 
divided  into  212  degrees.  The  zero  was  selected  because  the  temperature 
was  the  lowest  then  known,  and  was  thought  to  represent  absolute  cold. 
When  Fahrenheit's  thermometer  is  placed  in  melting  ice  it  stands  at  32  de- 
grees, and  therefore  100  degrees  on  the  Centigrade  scale  are  equal  to  180 
degrees  on  the  Fahrenheit  scale,  and  thus  i  degree  Centigrade  is  equal  to  f 
of  a  degree  Fahrenheit,  and,  inversely,  i  degree  Fahrenheit  is  equal  to  |  of  a 
degree  Centigrade. 

If  it  be  required  to  convert  a  certain  number  of  Fahrenheit  degrees  (95, 
for  example)  into  Centigrade  degrees,  the  number  32  must  first  be  subtracted 
in  order  that  the  degrees  may  count  from  the  same  part  of  the  scale.  The 
remainder  in  the  example  is  thus  63,  and,  as  i  degree  Fahrenheit  is  equal 
to  I  of  a  degree  Centigrade,  63  degrees  are  equal  to  63  x  §  or  35  degrees 
Centigrade. 

If  F  be  the  given  temperature  in  Fahrenheit  degrees  and  C  the  corre- 
sponding temperature  in  Centigrade  degrees,  the  former  may  be  converted 
into  the  latter  by  means  of  the  formula 

(F-32)|  =  C, 

and,  conversely,  Centigrade  degrees  may  be  converted  into  Fahrenheit  by 
means  of  the  formula 

f  C  +  32  =  F. 

The  formuke  are  applicable  to  all  temperatures  of  the  two  scales,  pro- 
vided the  signs  are  taken  into  account.  Thus,  to  convert  the  temperature 
of  5  degrees  Fahrenheit  into  Centigrade  degrees,  we  have 

(5-32)1==^^= -15  C. 

In  like  manner  we  ha\'e,  for  converting  Reaumur  into  Fahrenheit  degrees, 
the  formula 

f  R  +  32  =  F, 


-307j        Conditions  of  the  Delicacy  of  a   Thermometer.  283 

and,  conversely,  for  changing  Fahrenheit  into  Reaumur  degrees,  the  formula 

(F-32)|  =  R. 

304.  Displacement  of  zero.- — Thermometers,  even  when  constructed 
with  the  greatest  care,  are  subject  to  a  source  of  error  which  must  be  taken 
into  account ;  that  is,  that  in  course  of  time  the  zero  tends  to  rise,  the  dis- 
placement sometimes  extending  to  as  much  as  two  degrees  ;  so  that  when 
the  thermometer  is  immersed  in  melting  ice  it  no  longer  sinks  to  zero. 

This  is  generally  attributed  to  a  diminution  of  the  volume  of  the  bulb  and 
also  of  the  stem,  occasioned  by  the  pressure  of  the  atmosphere.  It  is  usual 
with  very  accurate  thermometers  to  fill  them  two  or  three  years  before  they 
are  graduated.  Joule  once  observed  that  even  after  twenty-five  years  a  deli- 
cate thermometer  indicated  a  displacement  of  zero. 

Besides  this  slow  displacement,  there  are  often  variations  in  the  position 
of  the  zero,  when  the  thermometer  has  been  exposed  to  temperatures  above 
60°,  caused  by  the  fact  that  the  bulb  and  stem  do  not  contract  on  cooling  to 
their  original  volume  (294)  ;  these  differences  are  greater  the  thicker  the  glass 
sides,  and  hence  it  is  necessary  from  time  to  time  to  verify  the  position  of 
zero  when  a  thermometer  is  used  for  delicate  determinations. 

Regnault  noticed  that  some  mercurial  thermometers,  which  agree  at  0° 
and  at  100°,  differ  between  these  points,  and  that  these  differences  frequently 
amount  to  several  degrees.  Regnault  ascribed  this  to  the  unequal  expansion 
of  different  kinds  of  glass. 

305.  Iiimits  to  the  employment  of  mercurial  thermometers.- — Of  all 
thermometers  in  which  liquids  are  used,  the  one  with  mercury  is  the  most 
useful,  because  this  liquid  expands  most  regularly,  and  is  easily  obtained 
pure,  and  because  its  expansion  between  -36°  and  100°  is  regular ;  that  is, 
proportional  to  the  degree  of  heat.  It  also  has  the  advantage  of  having  a 
very  low  specific  heat.  But  for  temperatures  below  —  36°  C.  the  alcohol 
thermometer  must  be  used,  since  mercury  solidifies  at  —  40°  C.  Above  100 
degrees  the  coefficient  of  expansion  mcreases,  and  the  indications  of  the 
mercurial  thermometer  are  only  approximate,  the  error  rising  sometimes  to 
several  degrees.  Mercury  thermometers  also  cannot  be  used  for  temperatures 
above  350°,  for  this  is  the  boiling  point  of  mercuiy. 

306.  Alcohol  thermometer. — The  alcohol  thermoineter  differs  from  the 
mercury  thermometer  in  being  filled  with  coloured  alcohol.  But  as  the 
expansion  of  liquids  is  less  regular  in  proportion  as  they  are  near  the  boiling 
point,  alcohol,  which  boils  at  78°  C.,  expands  y&xy  irregularly.  Hence, 
alcohol  thermometers  are  usually  graduated  by  placing  them  in  baths  at 
different  temperatures  together  with  a  standard  mercurial  thermometer,  and 
marking  on  the  alcohol  thermometer  the  temperature  indicated  by  the 
mercury  thermometer.  In  this  manner  the  alcohol  thermometer  is  compar- 
able with  the  mercury  one  ;  that  is  to  say,  it  indicates  the  same  temperatures 
under  the  same  conditions.  The  alcohol  thermometer  is  especially  used  for 
low  temperatures,  for  it  does  not  solidify  at  the  greatest  known  cold. 

307.  Conditions  of  the  delicacy  of  a  thermometer. — A  thermometer 
may  be  delicate<.in  two  ways  : — 1.  When  it  indicates  very  small  changes  of 
temperature.  2.  When  it  quickly  assumes  the  temperature  of  the  surround- 
ing medium. 


284 


On  Heat. 


[307- 


The  first  object  is  attained  by  having  a  very  narrow  capillary  tube  and  a 
very  large  bulb  ;  the  expansion  of  the  mercury  on  the  stem  is  then  limited 
to  a  small  number  of  degrees,  from  lo  to  20  or  20  to  30  for  instance,  so  that 
each  degree  occupies  a  great  length  on  the  stem,  and  can  be  subdivided  into 
very  small  fractions.  The  second  kind  of  delicacy  is  obtained  by  making 
the  bulb  very  small,  for  then  it  rapidly  assumes  the  temperature  of  the  liquid 
in  which  it  is  placed. 

A  good  mercury  thermometer  should  answer  to  the  following  tests  : — 
When  its  bulb  and  stem,  to  the  top  of  the  column  of  mercury,  are  immersed 
in  melting  ice,  the  top  of  the  mercury  should  exactly  indicate  0°  C.  ;  and 
when  suspended  with  its  bulb  and  scale  immersed  in  the  steam  of  water 
boiling  in  a  metal  vessel  (as  in  fig.  286)  the  barometer  standing  at  760  mm., 
the  mercury  should  be  stationary  at  100°  C.  When  the  instrument  is 
inverted,  the  mercury  should  fill  the  tube,  and  fall  with  a  metallic  click,  thus 
showing  the  complete  exclusion  of  air.  The  value  of  the  degrees  should  be 
uniform  ;  to  ascertain  this  a  little  cylinder  of  mercury  may  be  detached  from 
the  column  by  a  slight  jerk,  and  on  inclining  the  tube  it  may  be  made  to 
pass  from  one  portion  of  the  bore  to  another.  If  the  scale  be  properly 
graduated,  the  column  will  occupy  an  equal  number  of  degrees  in  all  parts 
of  the  tube. 

308.  3>ifferential  thermometer. — Sir  John  Leslie  constructed  a  ther- 
mometer for  showing  the  difference  of  temperature  of  two  neighbouring 


Fig.  290. 

places,  from  which  it  has  received  the  name  of  the  differe7itial  ihcrinoiiicter. 
A  modified  form  of  it  is  that  devised  by  Matthiessen  (fig.  289),  which  has 
the  advantage  of  being  available  for  indicating  the  temperature  of  liquids. 
It  consists  of  a  bent  glass  tube,  each  end  of  which  is  bent  twice,  and 
terminates  in  a  bulb  ;  the  bulbs  being  pendent  can  be  readily  immersed  in 


-310]  RutJierford's  Maximum  and  Minimum  Thermometers.  285 

a  liquid.  The  bend  contains  some  coloured  liquid,  and  in  a  tube  which 
connects  the  two  limbs  is  a  stopcock,  by  which  the  liquid  in  each  limb  is 
easily  brought  to  the  same  level.     The  whole  is  supported  by  a  frame. 

When  one  of  the  bulbs  is  at  a  higher  temperature  than  the  other,  the 
liquid  in  the  stem  is  depressed  and  rises  in  the  other  stem.  The  instru- 
ment is  now  only  used  as  a  thennoscope  ;  that  is,  to  indicate  a  difference 
of  temperature  between  the  two  builds,  and  not  to  measure  its  amount. 

309.  Breg'uet's  metallic  thermometer. — Breguet  invented  a  ther- 
mometer of  considerable  delicacy,  which  depends  on  the  unequal  expansion 
of  metals.  It  consists  of  three  strips  of  platinum,  gold,  and  silver,  which  are 
passed  through  a  rolling  mill  so  as  to  form  a  very  thin  metallic  ribbon.  This 
is  then  coiled  in  a  spiral  form,  as  seen  in  fig.  290,  and,  one  end  being  fixed  to 
a  support,  a  light  needle  is  fixed  to  the  other,  which  is  free  to  move  round  a 
graduated  scale. 

Silver,  which  is  the  most  expansible  of  the  metals,  forms  the  inner  face 
of  the  spiral,  and  platinum  the  outer.  When  the  temperature  rises,  the 
silver  expands  more  than  the  gold  or  platinum,  the  spiral  unwinds  itself,  and 
the  needle  moves  from  left  to  right  of  the  above  figure.  The  contrary  effect 
is  produced  when  the  temperature  sinks.  The  gold  is  placed  between  the 
other  two  metals  because  its  expansibility  is  intermediate  between  that  of 
the  silver  and  the  platinum.  Were  these  two  metals  employed  alone,  their 
rapid  unequal  expansion  might  cause  a  fracture.  Breguet's  thermometer  is 
empirically  graduated  in  Centigrade  degrees,  by  comparing  its  indications 
with  those  of  a  standard  mercury  thermometer. 

On  this  principle  depend  several  forms  of  pocket  thermometers,  and  it  is 
also  applied  in  some  registering  thermometers. 

310.  Xtutberford's  maximum  and  minimum  thermometers. — It  is 
necessary,  in  meteorological  observations,  to  know  the  highest  temperature 


Fig.  291. 

of  the  day  and  the  lowest  temperature  of  the  night.  Ordinary  thermometers 
could  only  give  these  indications  by  a  continuous  observation,  which  would 
be  impracticable.  Several  instruments  have  accordingly  been  invented  for 
this  purpose,  the  simplest  of  which  is  Rutherford's.  On  a  rectangular  piece 
of  plate-glass  (fig.  291)  two  thermometers  are  fixed,  whose  stems  are  bent 
horizontally.  The  one.  A,  is  a  mercury,  and  the  other,  B,  an  alcohol 
thermometer.  In  A  there  is  a  minute  piece  of  iron  wire.  A,  moving  freely  in 
the  tube,  which  serves  as  an  index.     The  thermometer  being  placed  hori- 


286  On  Heat.  [310- 

zontally,  when  the  temperature  rises  the  mercury  pushes  the  index  before  it. 
But  as  soon  as  the  mercury  contracts,  the  index  remains  in  that  part  of  the 
tube  to  which  it  has  been  moved,  for  there  is  no  adhesion  between  the  iron 
and  the  mercury.  In  this  way  the  index  registers  the  highest  temperature 
which  has  been  attained  ;  in  the  figure  this  is  32°.  In  the  minimum  ther- 
mometer there  is  a  small  hollow  glass  tube  which  serves  as  index.  When  it 
is  at  the  end  of  the  column  of  liquid,  and  the  temperature  falls,  the  column 
contracts,  and  carries  the  index  with  it,  in  consequence  of  adhesion,  until  it 
has  reached  the  greatest  contraction.  When  the  temperature  rises  the  alcohol 
expands,  and,  passing  between  the  sides  of  the  tube  and  the  index,  does  not 
displace  B.  The  position  of  the  index  gives  therefore  the  lowest  temperature 
which  has  been  reached  ;  in  the  figure  this  is  8-5  degrees  below  zero. 

311.  Pyrometers. — The  name  pyrometers  is  given  to  instruments  for 
measuring  temperatures  so  high  that  mercurial  thermometers  could  not  be 
used.  The  older  contrivances  for  this  purpose — Wedgwood's,  Daniell's 
(which  in  principle  resembled  the  apparatus  in  fig.  280),  Brongniart's,  &c. — 
have  gone  entirely  out  of  use.  None  of  them  give  an  exact  measure  of  tem- 
perature. The  arrangements  now  used  for  the  purpose  are  either  based  on 
the  expansion  of  gases  and  vapours,  on  the  specific  heat  of  solids,  or  on  the 
electrical  properties  of  bodies,  and  will  be  subsequently  described. 

312.  Different  remarkable  temperatures. — The  following  table  gives 
some  of  the  most  remarkable  points  of  temperature.  It  may  be  observed 
that  it  is  easier  to  produce  very  high  temperatures  than  very  low  degrees  of 
cold. 

Greatest  artificial  cold  produced  by  a  bath  of  bisulphide 

of  carbon  and  liquid  nitrous  acid          ....  -  140°  C. 

Greatest  cold  produced  by  ether  and  liquid  carbonic  acid  .  -no 

Greatest  natural  cold  recorded  in  Arctic  expeditions           .  -    587 

Mercury  freezes —    39'4 

Mixture  of  snow  and  salt     .         .         .         .         .         .         .  -    20 

Ice  melts      .......•••  o 

Greatest  density  of  water +4 

Mean  temperature  of  London 9'9 

Blood  heat 36"6 

Water  boils 100 

Mercury  boils 35° 

Sulphur  boils 44° 

Red  heat  (just  visible)         .       (Daniell)     ....  526 

Silver  melts         ...              „             ....  1000 

Zinc  boils    ....              „             ....  1040 

Cast  iron  melts   ...              „             ....  1530 

Highest  heat  of  wind  furnace          „             ....  1800 

Platinum  melts 2000 

Iridium        „ 2700 


-314]  Expansion  of  Solids,  287- 


CHAPTER   II. 

EXPANSION   OF   SOLIDS. 

313.  Iiinear  expansion  and  cubical  expansion.  Coefficients  of 
expansion. — It  has  been  already  explained  that  in  solid  bodies  the  expansion 
may  be  according  to  three  dimensions — linear,  superficial,  and  cubical. 

The  coefficient  of  Ihiear  expansiojt  is  the  elongation  of  the  unit  of  length 
of  a  body  when  its  temperature  rises  from  zero  to  i  degree  ;  the  coefficiefit  of 
superficial  expa?ision  is  the  increase  of  the  surface  in  being  heated  from  zero 
to  I  degree,  and  the  coefficient  of  cubical  expansion  is  the  increase  of  the 
unit  of  volume  under  the  same  circumstances. 

These  coefficients  vary  with  different  bodies,  but  for  the  same  body  the 
coefficient  of  cubical  expansion  is  three  times  that  of  the  linear  expansiofi,  as 
is  seen  from  the  following  considerations  : — Suppoae  a  cube,  the  length  of 
whose  side  is  i  at  zero.  Let  k  be  the  elongation  of  this  side  in  passing  from 
zero  to  I  degree,  its  length  at  i  degree  will  be  i  +  k,  and  the  volume  of  the 
cube,  which  was  i  at  zero,  will  be  {i  +  kf,  or  i  +  3/^  +  3^'- +  z^''.  But  as  the 
elongation  k  is  always  a  very  small  fraction  (see  table.  Art.  316),  its  square, 
k',  and  still  more  its  cube,  P,  are  so  small  that  they  may  be  neglected,  and 
the  value  at  i  degree  becomes  very  nearly  i  +  3/^.  Consequently,  the  increase 
of  volume  is  2)k,  or  thrice  the  coefficient  of  linear  expansion. 

In  the  same  manner  it  may  be  shown  that  the  coefficient  of  superficial 
expansion  is  double  the  coefficient  of  linear  expansion. 

314.  Measurement  of  the  coefficient  of  linear  expansion.  Xiavoisier 
and  Dbaplace's  metbod. — The  apparatus  used  by  Lavoisier  and  Laplace  for 
determining  the  coefficients  of  linear  expansion  (fig.  292),  consists  of  a  brass 


'lliiiliii(liiiiiiii(iiiiiimnlnl(inilinnnil!ii1iriniminiiltii[ 

■liiiiiii 


Fig.  292. 


trough,  placed  on  a  furnace  between  four  stone  supports.  On  the  two  sup- 
ports on  the  right  hand  there  is  a  horizontal  axis,  at  the  end  of  which  is  a 
telescope  ;  on  the  middle  of  this  axis,  and  at  right  angles  to  it,  is  fixed  a 
glass  rod,  turning  with  it,  as  does  also  the  telescope.    The  other  two  supports 


288  On  Heat.  [314- 

are  joined  by  a  cross-piece  of  iron,  to  which  another  glass  rod  is  fixed,  also 
at  right  angles.  The  trough,  which  contains  oil  or  water,  is  heated  by  a  fur- 
nace not  represented  in  the  figure,  and  the  bar  whose  expansion  is  to  be 
determined  is  placed  in  it. 

Fig.  293  represents  a  section  of  the  apparatus  ;  G  is  the  telescope,  KH 
the  bar,  whose  ends  press  against  the  two  glass  rods  F  and  D.     As  the  rod 


A. 

r 

- l:^ 

i- 

=.■«: 

cJ 

=> 

1 

F      

\ 

i 

I 

3) 

K                                                                     H 

J 

i 

Fig.  293. 

F  is  fixed,  the  bar  can  only  expand  in  the  direction  KH,  and  in  order  to 
eliminate  the  effects  of  friction  it  rests  on  two  glass  rollers.  Lastly,  the 
telescope  has  a  cross-wire  in  the  eyepiece,  which,  when  the  telescope  moves, 
indicates  the  depression  by  the  corresponding  number  of  divisions  on  a 
vertical  scale,  AB,  at  a  distance  of  220  yards. 

The  trough  is  first  filled  with  ice,  and  the  bar  being  at  zero,  the  division 
on  the  scale  AB,  corresponding  to  the  wire  of  the  telescope,  is  read  ofif.  The 
ice  having  been  removed,  the  trough  is  filled  with  oil  or  water,  which  is 
heated  to  a  given  temperature.  The  bar  then  expands,  and  when  its  tempe- 
rature has  become  stationaiy,  which  is  determined  by  means  of  thermometers, 
the  division  of  the  scale,  seen  through  the  telescope,  is  read  ofif. 

From  these  data  the  elongation  of  the  bar  is  determined  ;  for  since  it  has 
become  longer  by  a  quantity,  CH,  and  the  optical  axis  of  the  telescope  has 
become  inclined  in  the  direction  GB,  the  two  triangles,  GHC  and  ABG, 
are  similar,  for  they  have  the  sides  at  right  angles  each  to  each,  so  that 
FTG  G  FT 
AT?  ="ar'     ^^  ^^  same  way,  if  HC'  were  another  elongation,  and  AB'  a 

corresponding  deviation,  there  would  still  be     .-„>=  r^\    from    which    it. 

follows  that  the  ratio  between  the  elongation  of  the  bar  and  the  deflection 

G  FT 

of  the  telescope  is  constant,  for  it  is  always  equal  to         .      A  preliminary 

AG 

FTG 

measurement  has  shown  that  this  ratio  was  ^\-^.     Consequently,     -—  =  =:ij, 

AB 
whence    HC  =    —  ;  that  is,  the  total  elongation  of  the  bar  is  obtained  by 

744 
dividing  the  length  on  the  scale  traversed  by  the  cross-wire  by  744.     Divid- 
ing this  elongation  by  the  length  of  the  bar,  and  then  by  the  temperature  of 
the  bath,  the  quotient  is  the  dilatation  for  the  unit  of  length  and  for  a  single 
degree — in  other  words,  the  coefificient  of  linear  dilatation. 

315.  Roy  and  Ramsden's  method. — Lavoisier  and  Laplace's  method  is 
founded  on  an  artifice  which  is  frequently  adopted  in  physical  determinations, 
and  which  consists  in  amplifying  by  a  known  amount  dimensions  which,  in 
themselves,  are  too  small  to  be  easily  measured.    Unfortunately,  this  plan  is 


315] 


Roy  mid  Raiiisdcifs  Method. 


289 


often  more  fallacious  than  profitable,  for  it  is  first  necessary  to  determine 
the  ratio  of  the  motion  measured  to  that  on  which  it  depends.  In  the  pre- 
sent case,  it  is  necessary  to  know  the  lengths  of  the  arms  of  the  lever  in  the 
apparatus.  But  this  preliminary  operation  may  introduce  errors  of  such 
importance  as  partially  to  counterbalance  the  advantage  of  great  delicacy. 
The  following  method,  used  by  General  Roy  in  1787,  and  which  was  devised 
by  Ramsden,  depends  on  another  principle.  It  measures  the  elongations 
directly,  and  without  amplifying  them  ;  but  it  measures  them  by  means  of  a 
micrometric  telescope,  which  indicates  very  small  displacements. 

The  apparatus  (fig.  294)  consists  of  three  parallel  metal  troughs  about  6 
feet  long.     In  the  middle  one  there  is  a  bar  of  the  body  whose  expansion  is 


j«J*|I95iJiqi||iu|^V;;jj^^  ^l^  ^ri»l«OUM!*JJI 


nv^Eiiiii      I 


Fig.  294. 

to  be  determined,  and  in  the  two  others  are  cast-iron  bars  of  exactly  the 
same  length  as  this  bar.  Rods  are  fixed  vertically  on  both  ends  of  these 
three  bars.  On  the  rods  in  the  troughs  A  and  B  there  are  rings  with  cross- 
wires  like  those  of  a  telescope.  On  the  rods  in  the  trough  C  are  small  tele- 
scopes, also  provided  with  cross-wires. 

The  troughs  being  filled  with  ice,  and  all  three  bars  at  zero,  the  points  of 
intersection  of  the  wires  in  the  disc,  and  of  the  wires  in  the  telescope,  are 
all  in  a  line  at  each  end  of  the  bar.  The  temperature  in  the  middle  trough 
is  then  raised  to  100°  C.  by  means  of  spirit  lamps  placed  beneath  the  trough; 
the  bar  expands,  but  as  it  is  in  contact  with  the  end  of  the  screw,  a,  fixed  on 
the  side,  all  the  elongation  takes  place  in  the  direction  jim,  and,  as  the  cross- 
wire  n  remains  in  position,  the  cross-wire  m  is  moved  towards  B  by  a  quan- 
tity equal  to  the  elongation.  But  since  the  screw  a  is  attached  to  the  bar, 
by  turning  it  slowly  from  right  to  left,  the  bar  is  moved  in  the  direction  mn, 
and  the  cross-wire  fn  regains  its  original  position.     To  effect  this,  the  screw 

U 


290  On  Heat.  [315- 

has  been  turned  by  a  quantity  exactly  equal  to  the  elongation  of  the  bar, 
and,  as  this  advance  of  the  screw  is  readily  deduced  from  the  number  of 
turns  of  its  thread  (ii),  the  total  expansion  of  the  bar  is  obtained,  which, 
divided  by  the  temperature  of  the  bath,  and  this  quotient  by  the  length  of 
the  bar  at  zero,  gives  the  coefficient  of  linear  expansion. 

316.   Coefficients  of  linear  expansion. — By  one  or  the   other  method 
the  following-  results  have  been  obtained  : — 


Coefficients  of , 

linear  expansioii 

I  for  1°  between  0° 

and  100^  C. 

Diamond     . 

o-oooooii8o 

Bronze     . 

0-000018167 

Pine     . 

0-000006080 

Brass 

0-000018782 

Graphite 

0-000007860 

Silver 

0-000019097 

Marble 

0-000008490 

Tin  . 

0-00002 1 730 

White  glass 

0-000008613 

Aluminium 

0-000023130 

Platinum     . 

0-000008842 

Lead 

0-000028575 

Untempered  steel 

0-000010788 

Zinc 

0-000029417 

Cast  iron     . 

0-000011250 

Sodium  chloride 

0-000040390 

Sandstone  . 

0-0000 1 1740 

Ice  . 

0-000052000 

Wrought  iron 

0-000012204 

Sulphur'  . 

0-000064130 

Tempered  steel  . 

0-000012395 

Ebonite  (17°  to  3 

5°)  0-000080600 

Gold    . 

0-000014660 

Paraffin    . 

0-000278540 

Copper 

0-000017182 

Guttapercha     . 

0-000598000 

From  what  has  been  said  about  the  Hnear  expansion  (313),  the  coefficients 
of  cubical  expansion  of  solids  are  obtained  by  multiplying  those  of  hnear 
expansion  by  3. 

The  coefficients  of  the  expansion  of  the  metals  vary  with  their  physical 
condition,  being  different  for  the  same  metal  according  as  it  has  been  cast 
or  hammered  and  rolled,  hardened  or  annealed.  As  a  general  rule,  opera- 
tions which  increase  the  density  increase  also  the  rate  of  expansion.  But 
even  for  substances  in  apparently  the  same  condition,  different  observers 
have  found  very  unequal  amounts  of  expansion  ;  this  may  arise  in  the  case 
of  compound  substances,  such  as  glass,  brass,  or  steel,  from  a  want  of  uni- 
formity in  chemical  composition,  and  in  simple  bodies  from  slight  differences 
of  physical  state. 

The  expansion  of  amorphous  solids,  and  of  those  which  crystallise  in  the 
regular  system,  is  the  same  for  all  dimensions,  unless  they  are  subject  to  a 
strain  in  some  particular  direction.  A  fragment  of  such  a  substance  varies 
in  bulk,  but  retains  the  same  shape.  Crystals  not  belonging  to  the  regular 
system  when  heated,  exhibit  an  unequal  expansion  in  the  direction  of  their 
different  axes,  in  consequence  of  which  the  magnitude  of  their  angles,  and 
therefore  their  form,  is  altered.  In  the  dimetric  system  the  expansion  is  the 
same  in  the  direction  of  the  two  equal  axes,  but  different  in  the  third.  In 
crystals  belonging  to  the  hexagonal  system  the  expansion  is  the  same  in  the 
direction  of  the  three  secondary  axes,  but  different  from  that  according  to 
the  principal  one.    In  the  trimetric  system  it  is  different  in  all  three  directions. 

To  the  general  law  that  all  bodies  expand  by  heat  there  is  an  important 
exception  in  the  case  of  iodide  of  silver,  which  contracts  somewhat  when 


-318]        FornmlcB  relative  to  the  Expansion  of  Solids.  291 

heated.     Between  -60°  and  +  142°  C.  it  has  a  negative  coefficient  of  expan- 
sion, the  vahie  of  which  is  0*000001 39  for  1°  C. 

Fizeau  determined  the  expansion  of  a  great  number  of  ciystaUised  bodies 
by  an  optical  method.  He  placed  thin  plates  of  the  substance  on  a  glass 
plate  and  let  yellow  light  pass  through  them.  He  thus  obtained  alternately 
yellow  and  dark  Newton's  rings  {q.ii.).  On  heating,  the  plate  of  the  substance 
expanded,  the  thin  layer  of  air  became  thinner,  and  the  position  of  the  rings 
was  altered.  From  the  alteration  in  their  position  the  amount  of  the  expan- 
sion could  be  deduced.  Among  the  results  he  has  obtained  is  the  curious 
one  that  certain  crystallised  bodies,  such  as  diamond,  emerald,  and  cuprous 
oxide,  contract  on  being  cooled  to  a  certain  temperature,  but  as  the  cooling 
is  continued  below  this  temperature  they  expand.  They  have  thus  a  tem- 
perature of  maximum  density,  as  is  the  case  with  water  (329).  In  the  case 
of  emerald  and  cuprous  oxide  this  temperature  is  at  —  4-2°,  in  the  case  of 
diamond  at  —42-3°. 

317.  The  coefficients  of  expansion  increase  with  the  temperature. — 
According  to  Matthiessen,  who  determined  the  expansion  of  some  metals  and 
alloys  by  weighing  them  in  water  at  different  temperatures,  the  coefficients 
of  expansion  are  not  quite  regular  between  o^  and  100°.  He  found  the  fol- 
lowing values  for  the  linear  expansion  between  0°  and  100°  : — 

Zinc       .  .  .  L^=  Lq  ( I -1-0-00002741 /  + 0-0000000235 /-) 

Lead     .  .  .  Lj=  L^  (i  -1- 0-00002716  / -1- 0*0000000074  ^') 

Silver    .  .  Lj=  L(t -f  0-00001809 /-i- 0-0000000135 /-) 

Copper.  .  .  Lj=  Ly  ( I  -1-0-00001408 /-I- 0-0000000264 /-) 

Gold      .  .  .  Lj=  L^  (i -I- 0-00001358 /-1-0-0000000112 /-) 

Matthiessen  further  found  that  the  coefficients  of  expansion  of  an  alloy  are 
very  nearly  equal  to  the  mean  of  the  coefficients  of  expansion  of  the  volumes 
of  the  metals  composing  it. 

3 1 8.  Formulae  relative  to  the  expansion  of  solids, — Let  /  be  the  length 
of  a  bar  at  zero,  /'  its  length  at  the  temperature  f  C,  and  a  its  coefficient  of 
linear  expansion.  The  tables  usually  give  the  expansion  for  1°  between  0° 
and  100°  as  in  Art.  316,  or  for  100°;  in  this  latter  case  a  is  obtained  by 
dividing  the  number  by  100. 

The  elongation  corresponding  to  /  is  /  times  a  or  at  for  a  single  unit  of 
length,  or  atl  for  /  units.  The  length  of  the  bar  which  is  /  at  zero  is  I  +  afl 
at  i,  consequently, 

r  =  l  +  atl=l{\\at). 

This  formula  gives  the  length  of  a  body  /'  at  /'',  knowing  its  length  /  at 
zero,  and  the  coefficient  of  expansion  a  ;  and  by  simple  algebraical  transforma- 
tions we  can  obtain  from  it  formulae  for  the  length  at  zero,  knowing  the 
length  /'  at  /°,  and  also  for  finding  a,  the  coefficient  of  linear  expansion, 
knowing  the  lengths  /'  and  /  at  t°  and  zero  respectively. 

The  formulas  for  cubical  expansion  are  entirely  analogous  to  the  preceding. 

The  following  are  examples  of  the  application  of  these  formulae  : — 

(i.)  A  metal  bar  has  a  length  /'  at  t'°  ;  what  will  be  its  length  /  at  /°  ? 

From  the  above  formula  we  first  get  the  length  of  the  given  bar  at  zero, 

u  2 


292  On  Heat.  [318- 

which  is ;  by  means  of  the  same  formula  we  pass  from  zero  to  /'"  in 

multiplying  by  i  +  at.,  which  gives  for  the  desired  length  the  formula 
lJ\^^(it) 
I  +  at' 
(ii.)  The  density  of  a  body  being  ^at  zero,  required  its  density  d'  at  t°. 
If  I  be  the  volume  of  the  body  at  zero,  and  D  its  coefficient  of  cubical 
expansion,  the  volume  at  t  will  be  i  +  D/ ;  and  as  the  density  of  a  body  is  in 
inverse  ratio  of  the  volume  which  the  body  assumes  in  expanding,  we  get 
the  inverse  proportion, 

d' :  d=\     :     i  +  D/ 

d'         I  ,,        d 

or  d  ■ 


d      i+Dt  i+Dt 

Consequently,  when  a  body  is  heated  from  o  to  /^,  its  density,  and  therefore 
its  weight  for  an  equal  volume,  is  inversely  as  the  expression,  i  +  Dt. 

319.  A.ppIications  of  the  expansion  of  solids. — In  the  arts  we  meet 
with  numerous  examples  of  the  influence  of  expansion,  (i.)  The  bars  of 
furnaces  must  not  be  fitted  tightly  at  their  extremities,  but  must,  at  least, 
be  free  at  one  end,  otherwise  in  expanding  they  would  split  the  masonry. 
(ii.)  In  making  railways  a  small  space  is  left  between  the  successive  rails,  for, 
if  they  touched,  the  force  of  expansion  would  cause  them  to  curve  or  would 
break  the  chairs,  (iii.)  Water-pipes  are  fitted  to  one  another  by  means  of 
telescope  joints,  which  allow  room  for  expansion,  (iv.)  If  a  glass  vessel  is 
heated  or  cooled  too  rapidly,  it  cracks,  especially  if  it  be  thick  ;  this  arises 
from  the  fact  that,  since  glass  is  a  bad  conductor  of  heat,  the  sides  become  un- 
equally heated,  and  consequently  unequally  expanded,  which  causes  a  fracture. 
(v.)  The  cracking  off  of  a  portion  of  a  glass  tube  by  red-hot  charcoal  is  due 
to  the  expansion  of  the  heated  parts,  which  detach  themselves  from  the  rest. 

When  bodies  have  been  heated  to  a  high  temperature,  the  force  pro- 
duced by  their  contraction  on  cooling  is  very  considerable  ;  it  is  equal  to 
the  force  which  is  needed  to  compress  or  expand  the  material  to  the  same 
extent  by  mechanical  means.  According  to  Barlow,  a  bar  of  malleable  iron 
a  square  inch  in  section  is  stretched  xooUo^^"^  ^^  '^^  length  by  a  weight  of  a 
ton  ;  the  same  increase  is  experienced  by  about  9'^  C.  A  difference  of  45° 
C.  between  the  cold  of  winter  and  the  heat  of  summer  is  not  unfrequently 
experienced  in  this  country.  In  that  range,  a  wrought-iron  bar  ten  inches 
long  will  vary  in  length  by  ^^^^^  '^^  ^'^  inch,  and  will  exert  a  strain,  if  its  ends 
are  securely  fastened,  of  fifty  tons.  It  has  been  calculated  from  Joule's  data 
that  the  work  done  by  heat  in  expanding  a  pound  of  iron  between  0°  and  100°, 
during  which  it  increases  about  ^so  of  i*^s  bulk,  is  equal  to  16,000  foot- 
pounds ;  that  is,  it  could  raise  a  weight  of  over  7  tons  through  a  height  of  one 
foot. 

(i.)  An  application  of  this  contractile  force  is  seen  in  the  mode  of  secur- 
ing tires  on  wheels.  The  tire  being  made  red-hot,  and  thus  considerably 
expanded,  is  placed  on  the  circumference  of  the  wheel  and  then  cooled. 
The  tire,  when  cold,  embraces  the  wheel  with  such  force  as  not  only  to 
secure  itself  on  the  rim  but  also  to  press  home  the  joints  of  the  spokes  into 
the  felloes  and  nave,     (ii.)  Another  interesting  application  was  made  in  the 


-320]  Compensation  Penduhini.  293 

case  of  a  gallery  at  the  Conservatoire  des  Arts  at  Metiers  in  Paris,  the  walls 
of  which  had  begun  to  bulge  outwards.  Iron  bars  were  passed  across  the 
building  and  screwed  into  plates  on  the  outside  of  the  walls.  Each  alternate 
bar  was  then  heated  by  means  of  lamps,  and  when  the  bar  had  expanded 
it  was  screwed  up.  The  bars  being  then  allowed  to  cool  contracted,  and  in 
so  doing  drew  the  walls  together.  The  same  operation  was  performed  on 
the  other  bars. 

320.  Compensation  pendulum. — An  important  application  of  the  ex- 
pansion of  metals  has  been  made  in  the  compensation  pcnduliun.  This  is 
a  pendulum  in  which  the  elongation,  when  the 
temperature  rises,  is  so  compensated  that  the 
distance  between  the  centre  of  suspension  and 
the  centre  of  oscillation  (80)  remains  constant, 
which,  from  the  laws  of  the  pendulum  (81),  is 
necessary  for  isochronous  oscillations,  and  in 
order  that  the  pendulum  may  be  used  as  a 
regulator  of  clocks. 

In  fig.  295,  which  represents  the  gridiron 
pendulum,  one  of  the  commonest  forms  of  com- 
pensation pendulum,  the  ball,  L,  instead  of 
being  supported  by  a  single  rod,  is  supported 
by  a  framework,  consisting  of  alternate  rods  of 
steel  and  brass.  In  the  figure,  the  shaded  rods 
represent  steel  ;  including  a  small  steel  rod,  b, 
which  supports  the  whole  of  the  apparatus, 
there  are  six  of  them.  The  rest  of  the  rods, 
four  in  number,  are  of  brass.  The  rod  /,  which 
supports  the  ball,  is  fixed  at  its  upper  end  to  a 
horizontal  cross-piece  ;  at  its  lower  end  it  is 
free,  and  passes  through  the  two  circular  holes 
in  the  lower  horizontal  cross-pieces. 

Now  it  is  easy  to  see  from  the  manner  in 
which  the  vertical  rods  are  fixed  to  the  cross- 
pieces,  that  the  elongation  of  the  steel  rods  can 
only  take  place  downward,  and  that  of  the 
brass  rods  upward.  Consequently,  in  order 
that  the  pendulum  may  remain  of  the  same : 
length,  it  is  necessary  that  the  elongation  of 
the  brass  rods  shall  tend  to  make  the  ball 
rise,   by   exactly   the   same   quantity   that    the  '^'  ^^^' 

elongation  of  the  steel  rod  tends  to  lower  it ;  a  result  which  is  attained 
when  the  sum  of  the  lengths  of  the  steel  rods  A  is  to  the  sum  of  the  lengths 
of  the  brass  rods  B  in  the  inverse  ratio  of  the  coefficients  of  expansion  of 
steel  and  brass,  a  and  b  ;  that  is,  in  the  proportion  \:^  =  b:a. 

The  elongation  of  the  rod  may  also  be  compensated  for  by  means  of 
compensating  strips.  These  consist  of  two  blades  of  copper  and  iron 
soldered  together  and  fixed  to  the  pendulum  rod,  as  represented  in  fig.  296. 
The  copper  blade,  which  is  more  expansible,  is  below  the  iron.  When  the 
temperature  sinks,  the  pendulum  rod  loecomes  shorter,  and  the  ball  rises.     But 


294 


On  Heat. 


[320 


at  the  same  time  the  compensating  strips  become  curved,  as  seen  in  fig.  297, 
in  consequence  of  the  copper  contracting  more  than  the  iron,  and  two 
metal  balls  at  their  extremities  become  lower.     If  they  have  the  proper  size 


Fig.  296. 

in  reference  to  the  pendulum  ball,  the  parts  which  tend  to  approach  the 
centre  of  suspension  compensate  those  which  tend  to  remove  from  it,  and  the 
centre  of  oscillation  is  not  displaced.  If  the  temperature  rises,  the  pendu- 
lum ball  descends;  but  at  the  same  time  the  small  balls  ascend,  as  shown  in 
fig.  298,  so  that  there  is  always  compensation. 

One  of  the  most  simple  compensating  pendulums  is  the  mercury  pendii- 
luni,  invented  by  an  English  watchmaker,  Graham.  The  ball  of  the  pendu- 
lum, instead  of  being  solid,  consists  of  a  glass  cylinder,  containing  pure 
mercury,  which  is  placed  in  a  sort  of  stirrup,  supported  by  a  steel  rod. 
When  the  temperature  rises  the  rod  and  stirrup  become  longer,  and  thus 
lower  the  centre  of  gravity;  but  at  the  same  time  the  mercury  expands,  and, 
rising  in  the  cylinder,  produces  an  inverse  effect,  and  as  mercury  is  much 
more  expansible  than  steel,  a  compensation  may  be  effected  without  making 
the  mercurial  vessel  of  undue  dimensions. 

The  same  principle  is  applied  in  the  coinpc?tsati?ig balattces  of  chronometers 
(fig.  299).  The  motion  here  is  regulated  by  a  balance  or  wheel,  furnished  with 
a  spiral  spring  not  represented  in  the  figure,  and  the  time 
of  the  chronometer  depends  on  the  force  of  the  spring,  the 
mass  of  the  balance,  and  on  its  circumference.  Now 
when  the  temperature  rises  the  circumference  increases, 
and  the  chronometer  goes  slower  ;  and  to  prevent  this 
part  of  the  mass  must  be  brought  nearer  the  axis.  The 
circumference  of  the  balance  consists  of  compensating 
strips  BC,  of  which  the  more  expansible  metal  is  on  the 
outside,  and  towards  the  end  of  these  are  small  masses 
of  metal  D,  which  p'ay  the  same  part  as  the  balls  in  the  above  case.  When 
the  radius  is  expanded  by  heat,  the  small  masses  are  brought  nearer  the 
centre  in  consequence  of  the  curvature  of  the  strips  ;  and  as  they  can  be 
fixed  in  any  position,  they  are  easily  arranged  so  as  to  compensate  for  the 
expansion  of  the  balance.  It  may,  however,  here  be  observed  that  the  chief 
action  of  heat  on  chronometers  is  to  expand  and  soften  the  spring,  and 
thereby  lessen  its  elasticity;  this  action  produces  five  times  the  effect  on  the 
rate  that  the  expansion  of  the  balance-wheel  does. 


Fig.  299. 


-321] 


Apparent  and  Real  Expansion. 


'-9S 


CHAPTER    III. 

EXPANSION    OF    LIQUIDS. 

321.  Apparent  and  real  expansion. — A  hollow  space  enclosed  by  a 
solid  expands  as  if  it  were  wholly  occupied  by  the  solid  ;  for  consider  a 
section  of  a  glass  tube ;  we  may  regard  this 
as  made  up  of  a  series  of  innumerable  con- 
centric circles  ;  when  the  tube  is  heated  each 
of  these  glass  circles  becomes  longer,  and  in 
doing  so  must  press  outwards,  and  these 
expansions  and  elongations  are  the  same 
whether  there  is  another  circle  within  it  or 
not ;  the  hollow  space  will  become  larger 
just  as  if  it  were  a  solid  glass  rod.  This  may 
be  illustrated  by  the  following  experiment. 
If  a  flask  of  thin  glass,  provided  with  a  nar- 
row stem,  the  flask  and  part  of  the  stem 
being  filled  with  some  coloured  liquid,  be 
immersed  in  hot  water  (fig.  300),  the  column 
of  liquid  in  the  stem  at  first  sinks  from  3  to 
a,  but  then  immediately  after  rises,  and  con- 
tinues to  do  so  until  the  liquid  inside  has  the 
same  temperature  as  the  hot  water.  The 
first  sinking  of  the  liquid  is  not  due  to  its  '^'  ^°°' 

contraction  ;  it  arises  from  the  expansion  of  the  glass,  which  becomes  heated 
before  the  heat  can  reach  the  liquid  ;  but  the  expansion  of  the  liquid  soon 
exceeds  that  of  the  glass,  and  the  liquid  then  ascends. 

Hence  in  the  case  of  liquids  we  must  distinguish  between  the  apparent 
and  the  real  or  absolute  expansion.  The  apparent  expansion  is  that  which 
•is  actually  observed  when  liquids  contained  in  vessels  are  heated  ;  the  abso- 
lute expansion  is  that  which  would  be  observed  if  the  vessel  did  not  expand  ; 
or,  as  this  is  never  the  case,  it  is  the  apparent  expansion  corrected  for  the 
simultaneous  expansion  of  the  containing  vessel. 

As  has  been  already  stated,  the  cubical  expansion  of  liquids  is  alone  con- 
sidered ;  and  as  in  the  case  of  solids,  the  coeffidettt  of  expansion  of  a  liquid 
is  the  mcrease  of  the  unit  of  volume  for  a  single  degree  ;  but  a  distinction 
is  here  made  between  the  coefficient  of  absolute  expa?ision  and  the  coefficient 
of  apparefit  expansion.  Of  the  many  methods  which  have  been  employed 
for  determining  these  two  coefficients,  we  shall  describe  that  of  Dulong  and 
Petit. 


296 


On  Heat. 


[322- 


322.  Coefficient  of  the  absolute  expansion  of  mercury. — In  order  to 
determine  the  coefificient  of  the  absolute  expansion  of  mercury,  the  influence 
of  the  envelope  must  be  eliminated.  Dulong  and  Petit's  method  depends  on 
the  hydrostatical  principle  that  in  two  communicating  vessels,  the  heights 
of  two  columns  of  liquid  in  equilibrium  are  inversely  as  their  densities  (108), 
a  principle  independent  of  the  diameters  of  the  vessels,  and  therefore  of 
their  expansions. 

The  apparatus  consists  of  two  glass  tubes,  A  and  B  (fig.  301),  joined  by 
a  capillary  tube  and  kept  vertical  on  an  iron  support,  KM,  the  horizontality 
of  which  is  adjusted  by  means  of  two  levelling  screws  and  two  spirit  levels, 
;//  and  7i.     Each  of  the  tubes  is  surrounded  by  a  metal  case,  of  which  the 


Fig.  30X. 

smaller,  D,  is  filled  with  ice  ;  the  other,  E,  containing  oil,  can  be  heated  by 
the  furnace,  which  is  represented  in  section  so  as  to  show  the  case.  Mercuiy 
is  poured  into  the  tubes  A  and  B  ;  it  remains  at  the  same  level  in  both,  as 
long  as  they  are  at  the  same  temperature,  but  rises  in  B  in  proportion  as  it 
is  heated,  and  expands. 

Let  h  and  d  be  the  height  and  density  of  the  mercury  in  the  leg  A,  at 
the  temperature  zero,  and  h'  and  d'  the  same  quantities  in  the  leg  B.  From 
the  hydrostatical  principle  previously  cited  we  have  hd  =  h'd'.     Now  from 


the  problem  in  Art.   318,  d' ■■ 


. ,  D  being  the  coefficient  of  absolute 


expansion  of  mercury  ;    substituting  this   value  of  d'  in  the  equation,  we 

have  — ^--,  =hd.  {xom  which  we  get  D  = —-"— , 
I  +  D/  '  *"  ht 

The  coefficient  of  absolute  expansion  of  mercury  is  obtained  from  this 

formula,  knowing  the  heights  h'  and  /;,  and  the  temperature  /  of  the  bath  in 

which  the  tube  B  is  immersed.     In  Dulong  and  Petit's  experiment  this  tem- 


-324]  Weight  Thermometer.  297 

perature  was  measured  by  a  weight  thermometer,  P  (323),  the  mercury  of 
which  overflowed  into  the  basin,  C,  and  by  means  of  an  air  thermometer,  T 
(334) ;  the  heights  //  and  h  were  measured  by  a  cathetometer,  K  (88). 

Dulong  and  Petit  found  by  this  method  that  the  coefficient  of  absohite 
expansion  of  mercury  between  0°  and  100°  C.  is  ■~^,  But  they  found  that 
the  coefficient  increased  with  the  temperature.  Between  100°  and  200° 
it  is  ^Jj5,'and  between  200°  and  300°  it  is  ^3.  The  same  observation 
has  been  made  in  reference  to  other  hquids,  showing  that  their  expansion 
is  not  regular.  It  has  been  found  that  this  expansion  is  less  regular  in 
proportion  as  liquids  are  near  a  change  in  their  state  of  aggregation  ;  that 
is,  approach  their  freezing  or  boiling  points.  Dulong  and  Petit  found  that 
the  expansion  of  mercury  between  —  36°  and  100°  is  practically  quite  uniform. 

Regnault,  who  determined  this  important  physical  constant,  found  that 
the  mean  coefficient  between  0°  and  100°  is  5555,  between  100°  and  200°, 
^^Vj,  and  between  200°  and  300°,  j-^-^. 

323.  Coefficient  of  the  apparent  expansion  of  mercury. — The  co- 
efficient of  apparent  expansion  of  a  liquid  varies  with  the  nature  of  the 
envelope.    That  of  mercury  in  glass 

was  determined  by  means  of  the 
apparatus  represented  in  fig.  302. 
It  consists  of  a  glass  cylinder  to 
which  is  joined  a  bent  capillary 
glass  tube,  open  at  the  end.  3^ 

The  apparatus  is  weighed  first 
empty,  and  then  when  filled  with  F,^  ^o„ 

mercury    at    zero  :    the   difference 

gives  the  weight  of  the  mercury,  P.  It  is  then  raised  to  a  known  tempera- 
ture, /;  the  mercury  expands,  a  certain  quantity  passes  out,  which  is  received 
in  the  capsule  and  weighed.  If  the  weight  of  this  mercury  be/,  that  of  the 
mercury  remaining  in  the  apparatus  will  be  P  -p. 

When  the  temperature  is  again  zero,  the  mercury  in  cooling  produces  an 
empty  space  in  the  vessel,  which  represents  the  contraction  of  the  weight  ot 
mercury  P  — /,  from  t°  to  zero,  or,  what  is  the  same  thing,  the  expansion 
of  the  same  weight  from  o  to  /f°  ;  that  is,  the  weight  p  represents  the  ex- 
pansion of  the  weight  P-/,  for  f.     If  this  weight  expands  in  glass  by  a 

quantity  p  for  f,  a  single  unit  of  weight  would  expand  -—^ — -   for  /°,  and 

^ —  for  a  single  degree  ;    consquently,  for  D',  the  coefficient  of  ap- 

{V-p)t 

parent  expansion   of  mercury  in  glass,  we  have  D' =  — — 2^ Dulong 

and  Petit  found  the  coefficient  of  apparent  expansion  of  mercuiy  in  glass  to 
be  -i- 

'-"-    6480- 

324.  'Weight  thermometer. — The  apparatus  represented  in  fig.  302  is 
called  the  lueight  thermometer,  because  the  temperature  can  be  deduced 
from  the  weight  of  mercury  which  overflows. 

The  above  experiments  have  placed  the  coefficient  of  apparent  e.xpansion 

at  ,  1--  ;  we  have  therefore  the  equation  -    ^        =  j:^\;-,  from   which  we  get 


298  On  Heat.  [324- 

t  =  -^ — ^,  a  formula  which  gives  the  temperature  /when  the  weights  P  and 
F-p 

p  are  known. 

325.  Coefficient  of  the  expansion  of  g^lass. — As  the  absolute  expansion 
of  a  liquid  is  the  apparent  expansion, //«^.y  the  expansion  due  to  the  envelope, 
the  coefficient  of  the  cubical  expansion  of  glass  is  obtained  by  taking  the 
difference  between  the  coefficient  of  absolute  expansion  of  mercury  in  glass 
and  that  of  its  apparent  expansion.  That  is,  the  coefficient  of  cubical  expan- 
sion of  glass  is 

55'oS  -  6i08  =  38f  00  =  0-00002  584. 

Regnault  found  that  the  coefficient  of  expansion  varies  with  different 
kinds  of  glass,  and  further  with  the  shape  of  the  vessel.  For  ordinary 
chemical  glass  tubes,  the  coefficient  is  0-0000254. 

326.  Coefficients  of  expansion  of  various  liquids. — The  coefficient  of 
apparent  expansion  of  liquids  may  be  determined  by  means  of  an  application 
of  the  principle  of  the  weight  thermometer,  and  the  absolute  expansion  is 
obtained  by  adding  to  this  coefficient  the  expansion  of  the  glass. 

Mean  coefficieiifs  of  absolute  expansioji  of  liquids  for  1°  C. 


Mercury    . 

.  o-oooiS 

Fixed  oils    . 

.  o-ooo8o 

Water  saturated  with 

Nitric  acid  . 

.  o-ooiio 

salt 

.  0-00050 

Alcohol 

.  0-00104 

Sulphuric  acid  . 

.  0-00063 

Bisulphide  of  carbon 

.  0-00114 

Oil  of  turpentine 

.  0-00090 

Chloroform  . 

.  o-ooiii 

Ether 

.  0-00015 

Bromine 

.  0-00104 

The  numbers  here  given  only  hold  for  moderate  temperatures.  The  co- 
efficient of  expansion  of  almost  all  liquids  increases  gradually  from  zero,  and 
can  only  be  expressed  with  accuracy  by  a  somewhat  comphcated  formula 

in  which  /  is  the  temperature,  and  o,  /3,  and  7  are  constants  specially  deter- 
mined for  each  liquid.  The  expansion  of  mercury  is  practically  Constant 
between  —36°  and  100°  C,  while  water  contracts  from  zero  to  4°,  and  then 
expands. 

For  many  physical  experiments  a  knowledge  of  the  exact  expansion  of 
water  is  of  great  importance.  This  physical  constant  was  determined  with 
great  care  by  Matthiessen,  who  found  that  between  4"  and  30°  it  may  be 
expressed  by  the'formula 

V/=  I -0-00000253  (/- 4)    -1- 0-0000008389  (^'- 4)-    +0-00000007173(^-4)^; 

and  between  30  and  100  by  V/  =  0-999695  +  0-0000054724/-  -t-  o-oooooooi  126/^ 
Many  liquids,  with  low  boiling  points,  especially  condensed  gases,  have  very 
high  coefficients  of  expansion.  Thilorier  found  that  liquid  carbonic  acid 
expands  four  times  as  much  as  air.  Drion  confirmed  this  observation  and 
has  obtained  analogous  results  with  chloride  of  ethyle,  liquid  sulphurous 
acid,  and  liquid  hyponitrous  acid. 


-329]  Maximum  Density  of  Water.  299 

327.  Correction  of  the  barometric  Iieigrbt. — It  has  been  already  ex- 
plained under  the  barometer  (164),  that,  in  order  to  make  the  indications  of 
this  instrument  comparable  in  different  places  and  at  different  times,  they 
must  be  reduced  to  a  uniform  temperature,  which  is  that  of  melting  ice.  The 
correction  is  made  in  the  following  manner  : — 

Let  H  be  the  barometric  height  at  /f°,  and  h  its  height  at  zero,  d  the 
density  of  mercury  at  zero,  and  d'  its  density  at  t°.     The  heights  H  and  h 

are  inversely  as  the  densities  rfand  d'  ;  that  is,  -  =  -.      If  we  call  one  the 

H      d 

volume  of  mercury  at  zero,  its  volume  at  t°  will  be    i  +  D/,  D  being  the  co- 
efficient of  absolute  expansion  of  mercury.    But  these  volumes,  i  -f-  D/  and  i, 

are  inversely  as  the  densities  d  and  d' ;  that  is      =    —p.  ,•  Consequently, 

A  I  ,  ,  H 

--  = =:^,  whence  h  = . 

H      I  +  D/'  I  +  D/ 

/       5508  +  / 
■-5558 

In  this  calculation,  the  coefficient  of  absolute  expansion  of  mercury  is 
taken,  and  not  that  of  apparent  expansion  ;  for  the  value  H  is  the  same  as 
if  the  glass  did  not  expand,  the  barometric  height  being  independent  of  the 
diameter  of  the  tube,  and  therefore  of  its  expansion. 

328.  Correction  of  tbermometric  readiD§rs. — If  the  whole  column  of 
mercury  of  a  thermometer  is  not  immersed  in  the  space  whose  temperature 
is  to  be  determined,  it  is  necessary  to  make  a  correction,  which  in  the 
accurate  determination  of  jDoiling  points,  for  instance,  is  of  great  import- 
ance, in  order  to  arrive  at  the  true  temperature  which  the  thermometer 
should  show.  That  part  of  the  stem  which  projects  will  have  a  tempera- 
ture which  must  be  estimated,  and  which  may  roughly  be  taken  as  some- 
thing over  that  of  the  surrounding  air. 

Supposing,  for  instance,  the  actual  reading  is  160°  and  that  the  whole  of 
the  part  over  80°  is  outside  the  vessel,  while  the  temperature  of  the  surround- 
ing air  IS  1 5°.  We  will  assume  that  the  mean  temperature  of  the  stem  is  25°, 
and  that  a  length  of  160° -80°  is  to  be  heated  through  160-25  =  135°  ;  this 

gives  80  X  -i^    =   1-66   (taking   the  coefficient    of  apparent    expansion    of 

6480 
mercury)  ;  so  that  the  true  reading  is  161 -66. 

329.  Force  exerted  by  liquids  in  expanding:. — The  force  which  liquids 
exert  in  expanding  is  very  great,  and  equal  to  that  which  would  be  required 
in  order  to  bring  the  expanded  liquid  back  to  its  original  volume.  Now  we 
know  what  an  enormous  force  is  required  to  compress  a  liquid  to  even  a 
veiy  small  extent  (97).  Thus  between  0°  and  10°,  mercury  expands  by 
0-0015790  of  its  volume  at  0°  ;  its  compressibility  is  0-00000295  of  its  volume 
for  one  atmosphere  ;  hence  a  pressure  of  more  than  600  atmospheres  would 
be  requisite  to  prevent  mercury  expanding  when  it  is  heated  from  0°  to  10°. 
In  like  manner  a  pressure  of  140  atmospheres  would  be  required  to  prevent 
water  from  expanding  when  its  temperature  was  raised  from  4°  to  14°. 


300  On  Heat.  [330- 

330.  Maximum  density  of  water. — Water  presents  the  remarkable 
phenomenon  that  when  its  temperature  sinks  it  contracts  up  to  4°  ;  but 
from  that  point,  although  the  cooling  continues,  it  expands  up  to  the  freezing 
point,  so  that  4°  represent  the  point  of  greatest  contraction  of  water. 

Many  methods  have  been  used  to  determine  the  maximum  density  of 
water.  Hope  made  the  following  experiment  : — He  took  a  deep  vessel 
with  two  apertures  in  the  sides,  in  which  he  fixed  thermometers,  and 
having  filled  the  vessel  with  water  at  0°,  he  placed  it  in  a  room  at  a  tem- 
perature of  15°.  As  the  layers  of  liquid  at  the  sides  of  the  vessel  became 
heated  they  sank  to  the  bottom,  and  the  lower  thermometer  marked  4°  while 
the  upper  one  was  still  at  zero.  Hope  then  made  the  inverse  experiment ; 
having  filled  the  vessel  with  water  at  15°,  he  placed  it  in  a  room  at  zero. 
The  lower  thermometer  having  sunk  to  4°  remained  stationary  for  some 
time,  while  the  upper  one  cooled  down  until  it  reached  zero.  Both  these 
experiments  prove  that  water  is  heavier  at  4°  than  at  0°,  for  in  both  cases  it 
sinks  to  the  lower  part  of  the  vessel. 

This  last  experiment  may  be  adapted  for  lecture  illustration  by  using  a 
cylinder  containing  water  at  15°  C,  partially  surrounded  by  a  jacket  contain- 
ing bruised  ice  (fig.  303). 

Hallstrom  made  a  determination  of  the  maximum  density  of  water  in  the 
following  manner  : — He  took  a  glass  bulb,  loaded  with  sand,  and  weighed  it 

in  water  of  different  temperatures.  Allow- 
ing for  the  expansion  of  glass,  he  found 
that  4-1°  was  the  temperature  at  which  it 
lost  most  weight,  and  consequently  this 
was  the  temperature  of  the  maximum 
density  of  water. 

Despretz  arrived  at  the  temperature 
4°  by  another  method.  He  took  a  water 
thermometer — that  is  to  say,  a  bulbed 
tube  containing  water — and,  placing  it  in 
a  bath,  the  temperature  of  which  was  in- 
dicated by  an  ordinary  mercury  thermo- 
meter, found  that  the  water  contracted  to 
the  greatest  extent  at  4°,  and  that  this 
therefore  is  the  point  of  greatest  density. 
This  phenomenon  is  of  great  import- 
ance in  the  economy  of  nature.  In  winter 
the  temperature  of  lakes  and  rivers  falls, 
from  being  in  contact  with  the  cold  air 
i.;.^.  30,.  and  from  other  causes,  such  as  radiation. 

The  cold  water  sinks  to  the  bottom,  and 
a  continual  series  of  currents  goes  on  until  the  whole  has  a  temperature  of 
4°.  The  cooling  on  the  surface  still  continues,  but  the  cooled  layers  being 
lighter  remain  on  the  surface,  and  ultimately  freeze.  The  ice  formed  thus 
protects  the  water  below,  which  remains  at  a  temperature  of  4°,  even  in  the 
most  severe  winters,  a  temperature  at  which  fish  and  other  inhabitants  of 
the  water  are  not  destroyed. 

Salt  dissolved  in  water  lowers  the  temperature  of  the  maximum  density, 


-330] 


Maxiinuin  Density  of  Water. 


301 

this 


so  that  sea  water  exhibits  such    a  maximum.     According   to  Rosetti, 
temperature  is  between  3°-2  and  3°-9  in  the  Adriatic. 

The  following  table  of  the  density  of  pure  water  at  various  temperatures 
is  based  on  several  sets  of  observations  : — 

Density  of  water  between  0°  and  30°. 


Tempe- 

Densities 

Tempe- 

Densities 

Tempe- 

Densities 

ratures 

ratures 

ratures 

0 

0-99988 

12 

0-99955 

24 

0-99738 

I 

0-99993 

13 

0-99943 

25 

0-99704 

2 

0-99997 

14 

0-99930 

26 

0-99689 

3 

0-99999 

15 

0-99915 

27 

0-99662 

4 

I  -00000 

16 

0-99900 

28 

0-99635 

5 

0-99999 

17 

0-99884 

29 

0-99607 

6 

0-99997 

1       18 

0-99800 

30 

0-99579 

7 

0-99994 

i       19 

0-99847 

40 

0-99226 

8 

0-99988 

;    20 

0-99807 

50 

0-98320 

9 

0-99982 

21 

0-99806 

60 

0-98232 

10 

0-99974 

22 

0-99785 

70 

0-97796 

II 

0-99965 

23 

0-99762 

80 

0-97191 

?02 


On  Heat. 


[331- 


CHAPTER    IV. 

EXPANSION   AND   DENSITY   OF   GASES. 

331.  Gay-Xussac's  method. — Gases  are  the  most  expansible  of  all 
bodies,  and  at  the  same  time  the  most  regular  in  their  expansion.  The  co- 
efficients of  expansion,  too,  of  the  several  gases  differ  only  by  very  small 
quantities.     The  cubical  expansion  of  gases  need  alone  be  considered. 

Gay-Lussac  first  determined  the  coefficient  of  the  expansion  of  gases  by 
means  of  the  apparatus  represented  in  fig.  304. 

In  a  rectangular  metal  bath,  about  16  inches  long,  was  fitted  an  air 
thermometer,  which  consisted  of  a  capillary  tube,  AB  with  a  bulb,  A,  at  one 

end.      The    tube 
'^  was  divided  into 

parts  of  equal 
capacity,  and  the 
contents  of  the 
bulb  ascertained 
ni  terms  of  these 
parts.  This  was 
effected  by  weigh- 
ing the  bulb  and 
tube  full  of  mer- 
cury at  zero, 
and  then  heating 
slightly  to  expel 
a  small   quantity 


Fig.  304. 


of  mercury,  which  was  weighed.  The  apparatus  being  again  cooled  down 
to  zero,  the  vacant  space  in  the  tube  corresponded  to  the  weight  of  mercury 
which  had  overflowed  ;  the  volume  of  mercury  remaining  in  the  apparatus, 
and  consequently  the  volume  of  the  bulb,  was  determined  by  calculations 
analogous  to  those  made  for  the  piezometer  (98). 

In  order  to  fill  the  thermometer  with  dry  air  it  was  first  filled  with 
mercury,  which  was  boiled  in  the  bulb  itself  A  tube,  C,  filled  with  chloride 
of  calcium,  was  then  fixed  on  to  its  end  by  means  of  a  cork.  A  fine  platinum 
wire  having  then  been  introduced  into  the  stem  AB,  through  the  tube  C,  and 
the  apparatus  being  slightly  inclined  and  agitated  from  time  to  time,  air 
entered,  having  been  previously  well  dried  by  passing  through  the  chloride 
of  calcium  tube.  The  whole  of  the  mercury  was  displaced,  with  the  excep- 
tion of  a  small  thread,  which  remained  in  the  tube  AB  as  an  index. 

The  air  thermometer  was  then  placed  in  the  box  filled  with  melting  ice, 
the  index  moved  towards  A,  and  the  point  was  noted  at  which  it  became 


-332]  Problems  on  the  Expansion  of  Gases.  303 

stationary.  This  gave  the  volume  of  air  at  zero  ;  for  the  capacity  of  the 
bulb  was  known.  Water  or  oil  was  then  substituted  for  the  ice,  and  the 
bath  successively  heated  to  different  temperatures.  The  air  expanded  and 
moved  the  index  from  A  towards  B.  The  position  of  the  index  in  each  case 
was  noted,  and  the  corresponding  temperature  was  indicated  by  means  of 
the  thermometers  D  and  E. 

Assuming  that  the  atmospheric  pressure  did  not  vary  during  the  experi- 
ment, and  neglecting  the  expansion  of  the  glass  as  being  small  in  comparison 
with  that  of  the  air,  the  total  expansion  of  the  air  is  obtained  by  subtracting 
from  its  volume  at  a  given  temperature  its  volume  at  zero.  Dividing  this  by  a 
given  temperature,  and  then  by  the  number  of  units  contained  in  the  volume 
at  zero,  the  quotient  is  the  coefficient  of  expansion  for  a  single  unit  of  volume 
and  a  single  degree  ;  that  is,  the  coefficiejit  of  expansion.  It  will  be  seen, 
further  on,  how  corrections  for  pressure  and  temperature  may  be  intro- 
duced. 

By  this  method  Gay-Lussac  found  that  the  coefficient  of  expansion  of  air 
was  0-00375 ;  the  two  following  laws  hold  in  reference  to  the  expansion  of 
gases : — 

I.  All  gases  have  the  same  cofficient  of  expaiision  as  air. 

II.  This  coefficient  is  the  same  whatever  be  the  pressure  sipported  by 
the  gas. 

These  simple  laws  are  not,  however,  rigorously  exact  (333)  ;  they  only 
express  the  expansion  of  gases  in  an  approximate  manner.  These  laws  were 
discovered  independently  by  Dalton  and  by  Gay-Lussac,  and  are  usually 
ascribed  to  them.  The  first  discoverer  of  the  former  law  was,  however, 
Charles. 

332.  Problems  on  the  expansion  of  gases. — Many  of  the  problems 
relative  to  the  expansion  of  gases  are  similar  to  those  on  the  expansion  of 
liquids.  With  obvious  modifications,  they  are  solved  in  a  similar  manner. 
In  most  cases  the  pressure  of  the  atmosphere  must  be  taken  into  account 
in  considering  the  expansion  of  gases.  The  following  is  an  example  of  the 
manner  in  which  this  correction  is  made  : — 

i.  The  volume  of  a  gas  at  t°,  and  under  the  pressure  H,  is  V;  what  will 
be  the  volume  V  of  the  same  gas  at  zero,  and  under  the  normal  pressure 
760  millimetres  ? 

Here  there  are  two  corrections  to  be  made  ;  one  relative  to  the  tempera- 
ture, and  the  other  to  the  pressure.  It  is  quite  immaterial  which  is  taken 
first.  If  a  be  the  coefficient  of  cubical  expansion  for  a  single  degree,  by 
reasoning  similar  to  that  in  the  case  of  linear  expansion  (318),  the  volume  of 

the  gas  at  zero,  but  still  under  the  pressure  H,  will  be .    This  pressure 

is  reduced  to  the  pressure  760  in  accordance  with  Boyle's  law  (180),  by 

putting  V  X  760  = X  H  :  whence  V  =  — — j . 

"^  I+a/  '  760  (I -t- a/) 

ii,  A  volume  of  gas  weighs  P'  at  t° ;  what  will  be  its  weight  at  zero? 

Let  P'  be  the  desired  weight,  a  the  coefficient  of  expansion  of  the  gas, 

d'  its  density  at  /°,  and  d  its  density  at  zero.     As  the  weights  of  equal 

volumes  are  proportional  to  the  densities,  we  have  —  =  — .     If  i  be  the 


304 


On  Heat. 


[332- 


volume  of  a  gas  at 

are  inversely  as  the  volumes 


\t :  but  as  the  densities 


and  therefore 


From  this  equation  we  get 


hence  P  =P'(i  +  at). 

which  gives  the  weight  at  t,  know- 


zero,  its  \'olume  at  /  will  be  i 

'^'=      '^ 
d~  \  +  at' 
I 
+  at 

P  _ 
I   +  at 

ing  the  weight  at  zero,  and  which  further  shows  that  the  weight  P'  is  inversely 
as  the  binomial  of  expansion  i  +  at. 

333.  Reg-nault's  method.— Regnault  used  successfully  four  different 
methods  for  determining  the  expansion  of  gases.  In  some  of  them  the 
pressure  was  constant  and  the  volume  variable,  as  in  Gay-Lussac's  method  ; 
in  others  the  volume  remained  the  same  while  the  pressure  varied.  The 
first  method  will  be  described.  It  is  the  same  as  that  used  by  Rudberg  and 
Dulong,  but  is  distinguished  by  the  care  with  which  all  sources  of  error  are 
avoided. 

The  apparatus  consisted  of  a  pretty  large  cylindrical  reservoir,  B  (fig. 
305),  terminating  in  a  bent  capillary  tube.     In  order  to  fill  the  reservoir  with 


Fig.  305- 

dry  air,  it  was  placed  in  a  hot-water  bath,  and  the  capillary  tube  connected 
by  a  caoutchouc  tube  with  a  series  of  drying  tubes.  These  tubes  were 
joined  to  a  small  air-pump,  P,  by  which  a  vacuum  could  be  produced  in  the 
reservoir  while  at  a  temperature  of  100°.  The  reservoir  was  first  exhausted, 
and  air  afterwards  admitted  slowly  ;  this  operation  was  repeated  a  great 
many  times,  so  that  the  air  in  the  reservoir  became  quite  dry,  for  the  mois- 
ture adhering  to  the  sides  passed  off  in  vapour  at  100°,  and  the  air  which 
entered  became  dry  in  its  passage  through  the  U  tubes. 

The  reservoir  was  then  kept  for  half  an  hour  at  the  temperature  of  boil- 
ing water  ;  the  air-pump  having  been  detached,  the  diying  tubes  were  then 
disconnected,  and  the  end  of  the  tube  hermetically  sealed,  the  height  H  of 
the  barometer  being  noted.     When  the  reservoir  B  was  cool,  it  was  placed 


-333] 


Regnaiilfs  MetJiod. 


305 


in  the  apparatus  represented  in  fig.  306.  It  was  there  quite  surrounded 
with  ice,  and  the  end  of  the  tube  dipped  in  the  mercury  bath,  C.  After  the 
air  in  the  reservoir  B  had  sunk  to  zero,  the 
point  b  was  broken  off  by  means  of  a  forceps  ; 
the  air  in  the  interior  became  condensed  by 
atmospheric  pressure,  the  mercury  rising  to  a 
height  cG.  In  order  to  measure  the  height  of 
this  column,  Gf,  which  will  be  called  h^  a  mov- 
able rod,  go,  was  lowered  until  its  point,  <?,  was 
flush  with  the  surface  of  the  mercury  in  the 
bath  ;  the  distance  between  the  point  0  and  the 
level  of  the  mercury  G  was  measured  by  means 
of  the  cathetometer.  The  point  b  was  finally 
closed  with  wax  by  means  of  the  spoon  «,  and 
the  barometric  pressure  noted  at  this  moment. 
If  this  pressure  be  H',  the  pressure  in  the  reser- 
voir is  W  -h. 

The  reservoir  was  now  weighed  to  ascertain 
P,  the  weight  of  the  mercury  which  it  con- 
tained. It  was  then  completely  filled  with  mer- 
cury at  zero,  in  order  to  have  the  weight  P'  of  __ 

the  mercury  in  the  reservoir  and  in  the  tube.  ^      ,. 

If  S  be  the  coefficient  of  the  cubical  expan- 
sion of  glass,  and  D  the  density  of  mercury  at  zero,  the  coefficient  a  of 
the  cubical    expansion   of  air  is  determined    in  the   following  manner:  — 

P' 
The  volume  of  the  reservoir  and  of  the  tube  at  zero  is       ,  from  the  formula 

P  =  VD  (126)  ;  consequently,  this  volume  is 

P' 

D 

at  the  temperature  /°,  assuming,  as  is  the  case,  that  the  reservoir  and  tube 
expand  as  if  they  were  soUd  glass  (321).  But  from  the  formula  P  =  VD,  the 
volume  of  air  in  the  reservoir  at  zero,  and  under   the   pressure  H'  — //,  is 

D     ■ 

P^-P 
D 


(i+S/) (I) 


At  the  same  pressure,  but  at  /°,  its  volume  would  be 

(l+n/) 


and  by  Boyle's  law  (180),  at  the  pressure  H,  at  which  the  tube  was  sealed, 
this  volume  must  have  been 


(P' 


DH 


(2) 


Now  the  volumes  represented  by  these  formulte,  (i)  and  (2),  are  each 
equal  to  the  volume  of  the  leservoir  and  the  tube  at  t°  ;  they  are  therefore 
equal.     Removing  the  denominators,  w^e  have 

P'(i+5/)H  =  (P'-P)(i+«/)(H'-/2) (3) 

from  which  the  value  of  a  is  deduced. 

X 


3o6  On  Heat.  [333- 

The  means  of  a  great  number  of  experiments  between  zero  and  ioo°  and 
for  pressure  between  300  millimetres  and  500  millimetres,  gave  the  following 
numbers  for  the  coefficients  of  expansion  for  a  single  degree  : — 


Air     . 

.     0-003667 

Carbonic  acid . 

.     0-003710 

Hydrogen . 

.     0-003661 

Nitrous  oxide  . 

.     0-003719 

Nitrogen  . 

.     0-003661 

Cyanogen 

.     0-003877 

Carbonic  oxide . 

.     0-003667 

Sulphurous  acid 

.     0-003903 

These  numbers,  with  which  the  results  obtained  by  Magnus  closely  agree, 
show  that  the  coefficients  of  expansion  of  the  permanent  gases  differ  very 
little  ;  but  that  they  are  somewhat  greater  in  the  case  of  the  more  easily 
condensable  gases,  such  as  carbonic  and  sulphurous  acids.  Regnault  has 
further  found  that,  at  the  same  temperature,  the  coefficient  of  expansion  of 
any  gas  increases  with  the  pressure  which  it  supports.  Thus,  while  the 
coefficient  of  expansion  of  air  under  a  pressure  of  i  lo-mm.  is  0-003648,  under 
a  pressure  of  3655  mm.,  or  nearly  five  atmospheres,  it  is  0-003709. 

The  number  found  by  Regnault  for  the  coefficient  of  the  expansion  of 
air,  0-003667,  is  equal  to  :^^  =  ^ig  nearly  ;  and  if  we  take  the  coefficient  of  ex- 
pansion at  0-0036666  ...  it  may  be  represented  by  the  fraction  jii^, 
which  is  convenient  for  purposes  of  calculation. 

The  small  differences  in  the  expansibility  of  various  gases  may  be  ascribed 
to  the  circumstance  that  when  a  gas  is  heated  the  relative  positions  of  the 
atoms  in  the  molecules  are  thereby  altered  ;  and  a  certain  amount  of  internal 
work  is  required  for  this,  which  is  different  for  different  gases. 

334.  Air  thermometer. — The  air  thermometer  is  based  on  the  expan- 
sion of  air.  When  it  is  used  to  measure  small  differences  of  temperature,  it 
has  the  same  form  as  the  tube  used  by  Gay-Lussac  in  determining  the  ex- 
pansion of  air  (fig.  304),  that  is,  a  capillary  tube  with  a  bulb  at  the  end.  The 
reservoir  being  filled  with  dry  air,  an  index  of  coloured  sulphuric  acid  is 
passed  into  the  tube  ;  the  apparatus  is  then  graduated  in  Centigrade  degrees 
by  comparing  the  positions  of  the  index  with  the  indications  of  a  mercurial 
thermometer.  Of  course  the  end  of  the  tube  must  remain  open  ;  otherwise, 
the  air  above  the  index  condensing  or  expanding  at  the  same  time  as  that  in 
the  bulb,  the  index  would  remain  stationary.  A  correction  must  be  made 
at  each  observation  for  the  atmospheric  pressure. 

When  considerable  variations  of  temperature  are  to  be  measured,  the 
tube  has  a  form  hke  that  used  in  Regnault's  experiments  (figs.  305  and  306). 
By  experiments  made  as  described  in  Art.  333,  P,  P',  H,  H',  and  h  may 
be  found,  and  the  coefficients  a  and  S  being  known,  the  temperature  t  to 
which  the  tube  has  been  raised  is  readily  reduced  from  the  equation  (3). 

Regnault  found  that  the  air  and  the  mercurial  thermometer  agree  up  to 
260°,  but  above  that  point  mercury  expands  relatively  more  than  air.  In 
cases  where  very  high  temperatures  are  to  be  measured,  the  reservoir  is 
made  of  platinum.  The  use  of  an  air  thermometer  is  seen  in  Dulong  and 
Petit's  experiment  (322)  ;  it  was  by  such  an  apparatus  that  Pouillet  measured 
the  temperature  corresponding  to  the  colours  which  metals  take  when  heated 
in  a  fire,  and  found  them  to  be  as  follows  : — 


335J 


Incipient  red 
Dull  red 
Cherry  red   . 


Density  of  Gases. 

525°  C.     Dark  orange  , 
.     700  White     . 

.     900  Dazzling  white 


307 


1100°  C 


1500 


In  the  measurement  of  high  temperatures  Deville  and  Trpost  used  with 
advantage  the  vapour  of  iodine  instead  of  air,  and,  as  platinum  has  been 
found  to  be  permeable  to  gases  at  high  temperatures,  they  employed  porce- 
lain instead  of  that  metal. 

The  expansion  of  gases  has  been  determined  by  Jolly  by  means  of  a 
form  of  apparatus  which  is  also  a  convenient  form  of  air  thermometer  (fig, 
^yO'j).  A  quadrangular  post  rests  on  a  tripod  ;  on  one  side 
of  this  post  is  a  graduated  glass  scale,  while  in  the  two 
others  are  grooves  in  which  screw-blocks  A  and  A'  can  be 
slid  up  and  down  and  adjusted  at  any  height. 

A  glass  bulb  a  is  prolonged  in  a  tube  bent  twice,  the 
end  of  which  is  provided  with  a  stopcock,  not  shown  in 
the  figure,  and  in  which  can  be  fitted  a  glass  tube  R  sup- 
ported by  the  block  A.  This  again  is  fitted  to  a  flexible 
india-rubber  tube,  at  the  other  end  of  which  is  an  open 
glass  tube  R'  fixed  to  the  block  A'.  This  tube  contains 
mercury. 

The  bulb  a  having  been  filled  with  dry  air,  the  stopcock 
is  closed,  the  tube  R  fixed,  and  the  stopcock  opened. 
The  bulb  a  is  then  immersed  to  the  stem  in  melting  ice, 
and  when  it  is  supposed  that  the  temperature  is  stationary, 
the  tube  R'  is  moved  up  and  down  until  the  mercury  in 
the  other  limb  is  at  a  mark  S.  The  difference  betv/een 
the  levels  of  the  mercury  at  S  and  at  R'  is  noted.  If  the 
latter  is  higher  the  difference  is  added  to,  and  if  lower 
subtracted  from,  the  barometric  height  at  the  time,  to  give 
the  pressure  h  in  the  vessel  a. 

The  bulb  a  is  then  placed  in  a  space  at  any  constant 
temperature,  and  the  same  operation  repeated  to  get  the 
pressure  /;,  From  the  ratio  of  the  total  pressures  in  the  two  cases  we  get 
the  coefficient  of  expansion  a  from  the  formula  h  :  h^  =  i  +ai  :  i  +  ai\  By 
means  of  this  apparatus  Jolly  found  0-00366957  for  the  value  of  a. 

335.  Density  of  g-ases. — The  relative  density  of  a  gas,  or  its  specific 
gravity,  is  the  ratio  of  the  weight  of  a  certain  volume  of  the  gas  to  that  of 
the  same  volume  of  air  ;  both  the  gas  and  the  air  being  at  zero  and  under  a 
pressure  of  760  millimetres. 

In  order,  therefore,  to  find  the  specific  gravity  of  a  gas,  it  is  necessary  to 
determine  the  weight  of  a  certain  volume  of  this  gas  at  a  pressure  of  760 
millimetres,  and  a  temperature  of  zero,  and  then  the  weight  of  the  same 
volume  of  air  under  the  same  conditions.  For  this  purpose  a  large  globe  of 
about  two  gallons'  capacity  is  used,  the  neck  of  which  is  provided  with  a 
stopcock,  which  can  be  screwed  to  the  air-pump.  The  globe  is  first  weighed 
empty,  and  then  full  of  air,  and  afterwards  full  of  the  gas  in  question.  The 
weights  of  the  gas  and  of  the  air  are  obtained  by  subtracting  the  weight  of 
the  exhausted  globe  from  the  weight  of  the  globes  filled,  respectively,  with 

X  2 


Fig.  307, 


3o8  On  Heat.  [335- 

air  and  gas.  The  quotient,  obtained  by  dividing  the  latter  by  the  former, 
gives  the  specific  gravity  of  the  gas.  It  is  difficult  to  make  these  determina- 
tions at  the  same  temperature  and  pressure,  and  therefore  all  the  weights 
are  reduced  to  zero  and  the  normal  pressure  of  760  millimetres. 

The  gases  are  dried  by  causing  them  to  pass  through  drying  tubes  before 
they  enter  the  globe,  and  air  must  also  be  passed  over  potash  to  free  it  from 
carlDonic  acid.  And  as  even  the  best  air-pumps  never  produce  a  perfect 
vacuum,  it  is  necessary  to  exhaust  the  globe  until  the  manometer  in  each 
case  marks  the  same  pressure. 

The  globe  having  been  exhausted,  dried  air  is  allowed  to  enter,  and  the 
process  is  repeated  several  times  until  the  globe  is  perfectly  dried.  It  is  then 
finally  exhausted  until  the  residual  pressure  in  millimetres  is  e.  The  weight 
of  the  exhausted  globe  is/.  Air,  which  has  been  dried  and  purified  by  passing 
through  potash  and  chloride  of  calcium  tubes,  is  then  allowed  to  enter 
slowly.  The  weight  of  the  globe  full  of  air  is  P.  If  H  is  the  barometric 
height  in  millimetres,  and  f  the  temperature  at  the  time  of  weighing,  P  -p  is 
the  weight  of  the  air  in  the  globe  at  the  temperature  /,  and  the  pressure  H  -  ^. 

To  reduce  this  weight  to  the  pressure  760  millimetres  and  the  tempera- 
ture zero,  let  a  be  the  coefficient  of  the  expansion  of  air,  and  8  the  coefficient 
of  the  cubical  expansion  of  glass.     From  Boyle's  law  the  weight,  which  is 

P  -p  at  f  and  a  pressure  of  H  -  ^,  would  be  ^  —~'flj^^  under  the  pressure 

H  — ^ 

760  millimetres  and  at  the  same  temperature  f.     If  the  temperature  is  0°, 

the  capacity  of  the  globe  will  diminish  in  the  ratio  i  +  S/  to   i,  while  the 

weight  of  the  gas  increases  in  the  ratio  1:1+  «/,  as  follows  from  the  problems 

in  Art.  332.     Consequently,  the  weight  of  the  air  in  the  globe  ato"^  and  at  the 

pressure  760  millimetres  will  be 

76o(i^«0 

^       ^^(H  ~c){i+bt)  ^  ' 

Further,  let  a'  be  the  coefficient  of  expansion  of  the  gas  in  question  ;  let 
P'  be  the  weight  of  the  globe  full  of  gas  at  the  temperature  /'  and  the  pres- 
sure H',  and  let/'  be  the  weight  of  the  globe  when  it  is  exhausted  to  the 
pressure  e  ;  the  weight  of  the  gas  in  the  globe  at  the  pressure  760  and  the 
temperature  zero  will  be 

iV'-p')     76oii+aY)^         ....         (2) 

Dividing  the  latter  formula  by  the  former  we  obtain  the  density 

n-(P^-/')(H-^)(i+ar)(i+a/) 

(F-p)  (H'-e)  (i+o/)(n  SO 
If  the  temperature  and  the  pressure  do  not  vary  during  the  experiment, 

H  =  H'  and  /  =  /' ;  whence  D  =  (-^-:i^lil±«_'^_),  and  if  n  =  a',  D  =  ^'~J'. 
(P-/)(i+a/j'  P-p 

336.    Reg-nault's    xnetbod   of   deterxniningr    the    density    of   gases. — 

Regnault  so  modified  the  above  method  that  many  of  the  corrections  may 
be  dispensed  with.     The  globe  in  which  the  gas  is  weighed  is  suspended 


336] 


Density  of  Gases. 


309 


from  one  pan  of  a  balance,  and  is  counterpoised  by  means  of  a  second  globe 
of  the  same  dimensions,  and  hermetically  sealed,  suspended  from  the  other. 
These  two  globes,  expanding  at  the  same  time,  always  displace  the  same 
cjuantity  of  air,  and  consec^uently  variations  in  the  temperature  and  pressure 
of  the  atmosphere  do  not  influence  the  weighing.  The  globe  too,  is  filled 
with  the  air  or  with  the  gas,  at  the  temperature  of  zero.  This  is  effected  by 
placing  it  in  a  vessel  full  of  ice,  as  shown  in  fig.  308.  It  is  then  connected 
with  a  three-way  cock,  A,  by  which  it  may  be  connected  either  with  an  air- 
pump,  or  with  the  tubes  M  and  N,  which  are  connected  with  the  reservoir 
of  gas.  The  tubes  M  and  N  contain  substances  which  by  their  action  on 
the  gas  dry  and  also  purify  it. 

The  stopcock  A  being  so  turned  that  the  globe  is  only  connected  with 
the  air-pump,  a  vacuum  is  produced  ;  by  means  of  the  same  cock,  the  con- 
nection with  the  pump  being  cut  off,  but  established  with  M  and  N,  the 


Fig.  308. 

gas  soon  fills  the  globe.  But,  as  the  exhaustion  could  not  have  been  com- 
plete, and  some  air  must  have  been  left,  the  globe  is  again  exhausted  and 
the  gas  allowed  to  enter,  and  the  process  is  repeated  until  it  is  thought  all 
air  is  removed.  The  vacuum  being  once  more  produced,  a  differential 
barometer  (fig.  152),  connected  with  the  apparatus  by  the  tube  E,  indicates 
the  pressure  of  the  residual  rarefied  gas  e.  Closing  the  cock  B  and  de- 
taching A,  the  globe  is  removed  from  the  ice,  and  after  being  cleaned  is 
weighed. 

This  gives  the  weight  of  the  empty  globe/  ;  it  is  again  replaced  m  the 
ice,  the  stopcock  A  adjusted,  and  the  gas  allowed  to  enter,  care  being  taken 
to  leave  the  stopcocks  open  long  enough  to  allow  the  gas  in  the  globe  to  ac- 
quire the  pressure  of  the  atmosphere,  H,  which  is  marked  by  the  barometer. 
The  stopcock  A  is  then  closed,  A  removed,  and  the  globe  weighed  with  the 
same  precautions  as  before.     This  gives  the  weight  P'  of  the  gas. 


310 


On  Heat. 


[336- 


D 


The  same  operations  are  then  repeated  on  this  globe  with  air,  and  two 
corresponding  weights  j^J  and  P  are  obtained.  The  only  correction  necessary 
is  to  reduce  the  weights  in  the  two  cases  to  the  standard  pressure  by  the 
method  described  in  the  preceding  paragraph.  The  correction  for  temperature 
is  not  needed,  as  the  gas  is  at  the  temperature  of  melting  ice.  The  ratio  of 
the  weight  of  the  gas  to  that  of  the  air  is  thus  obtained  by  the  formula 

v-p- 

337.  Density  of  grases  which  attack  metals. — For  gases  which  attack 
the  ordinary  metals,  such  as  chlorine,  a  metal  stopcock  cannot  be  used,  and 
vessels  with  ground-glass  stoppers  are  substituted.  The  gas  is  introduced 
by  a  bent  glass  tube,  the  vessel  being  held  either  upright  or  inverted,  accord- 
ing as  the  gas  is  heavier  or  lighter  than  air  ;  when  the  vessel  is  supposed  to 
be  full,  the  tube  is  withdrawn,  the  stopper  inserted,  and  the  weight  taken. 
This  gives  the  weight  of  the  vessel  and  gas.  If  the  capacity  of  the  vessel 
be  measured  by  means  of  water,  the  weight  of  the  air  which  it  contains  is 
deduced,  for  the  density  of  air  at  0°  C.  and  760  millimetres  pressure  is  ^i^ 
that  of  distilled  water  under  the  same  circumstances.  The  weight  of  the 
vessel  full  of  air,  less  the  weight  of  the  contained  air,  gives  the  weight  of  the 
vessel  itself.  From  these  three  data — the  weight  of  the  vessel  full  of  the  gas, 
the  weight  of  the  air  which  it  contains,  and  the  weight  of  the  vessel  alone — 
the  specific  gravity  of  the  gas  is  readily  deduced,  the  necessary  corrections 
being  made  for  temperature  and  pressure. 


Density  of  gases  at  zero  and  at  a  pressure  of -bo  niillimetres,  that  of 
air  being  taken  as  ttnity . 


Air       . 

I  -oooo 

Sulphuretted  hydrogen 

1-1912 

Hydrogen    . 

0-0693 

Hydrochloric  acid 

1-2540 

Ammoniacal  gas  . 

0-5367 

Protoxide  of  nitrogen  . 

1-5270 

Marsh  gas   . 

0-5590 

Carbonic  acid 

1-5291 

Carbonic  oxide    . 

0-9670 

Cyanogen     . 

I -8600 

Nitrogen      . 

0-9714 

Sulphurous  acid  . 

2-2474 

Binoxide  of  nitrogen 

I  -0360 

Chlorine 

3-4400 

Oxygen 

I-I057 

Hydriodic  acid     . 

4-4430 

Regnault  made  the  following  determinations  of  the  weight  of  a  litre  of 
the  most  important  gases  at  0°  C.  and  760  mm. : — 

Air.         .         .     1-293187  grms.         Nitrogen  .     1-256157  grms. 

Oxygen  .         .     1-429802      ,,  Carbonic  acid     1-977414      „ 

Hydrogen        .     0-089578      „ 


-338] 


Fusion.     Its  Laivs. 


311 


CHAPTER   V. 

CHANGES   OF   CONDITION.      VAPOUR. 


338.  Fusion.  Its  laws. — The  only  phenomena  of  heat  with  which  we 
have  hitherto  been  engaged  have  been  those  of  expansion.  In  the  case  of 
solids  it  is  easy  to  see  that  this  expansion  is  limited.  For  in  proportion  as 
a  body  absorbs  a  larger  quantity  of  heat,  the  vis  viva  of  the  molecules  is 
increased,  and  ultimately  a  point  is  reached  at  which  the  molecular  attraction 
is  not  sufificient  to  retain  the  body  in  the  solid  state.  A  new  phenomenon  is 
then  produced;  melting  ox  fusion  takes  place;  that  is,  the  body  passes  from 
the  solid  into  the  liquid  state. 

Some  substances,  however,  such  as  paper,  wood,  wool,  and  certain  salts, 
do  not  fuse  at  a  high  temperature,  but  are  decomposed.  Many  bodies  have 
long  been  considered  refractory — that  is,  incapable  of  fusion  ;  but,  in  pro- 
portion as  it  has  been  possible  to  produce  higher  temperatures,  their  number 
has  diminished.  Gaudin  succeeded  in  fusing  rock  crystal  by  means  of  a 
lamp  fed  by  a  jet  of  oxygen  ;  and  Despretz,  by  combining  the  effects  of  the 
sun,  the  voltaic  battery,  and  the  oxy-hydrogen  blowpipe,  melted  alumina 
and  magnesia,  and  softened  carbon  so  as  to  be  flexible,  which  is  a  condition 
near  that  of  fusion. 

It  has  been  found  experimentally  that  the  fusion  of  bodies  is  governed 
by  the  two  following  laws  : — 

I.  E'i'e7y  substa?tce  begins  to  fuse  at  a  certain  temperature,  which  is 
invai'iable  for  each  substance,  if  the  pressure  be  coftstant. 

II.  Whatever  be  the  intensity  of  the  source  of  heat,  from  the  moment 
fusion  begins,  the  temperature  of  the  body  ceases  to  rise,  and  remains  constant 
tin  til  the  fusioji  is  complete. 

Melting  points  of  certain  substances. 


Mercury     . 

-38-8° 

Potassium 

55' 

Oil  of  turpentine 

-27 

Margaric  acid  . 

57 

Bromine     . 

-  12 

Stearine    . 

60 

Ice     . 

0 

White  wax 

65 

Nitrobenzene 

+  3-0 

Wood's  fusible  metal 

68 

Formic  acid 

8-5 

Stearic  acid      . 

70 

Acetic  acid 

17 

Sodium     . 

90 

Butter 

T:) 

Rose's  fusible  metal . 

94 

Rubidium  . 

39 

Sulphur    . 

114 

Phosphorus 

44 

Benzoic  acid      . 

120 

Spermaceti 

49 

Indium     . 

176 

On 

Heat. 

Tin 

228° 

Aluminium 

Bismuth    . 

246 

Silver 

Cadmium  . 

321 

Gold 

Lead 

335 

Copper     . 

Zinc  .... 

422 

Iron. 

Antimony 

450 

Platinum . 

Arsenic 

.     500 

Iridium    . 

Magnesium 

•     750 

[338- 


850° 
954 
1035 
1054 
1500 

1775 
1950 


Some  substances  pass  from  the  solid  to  the  liquid  state  without  showing 
any  definite  melting  point  ;  for  example,  glass  and  iron  become  gradually 
softer  and  softer  when  heated,  and  pass  by  imperceptible  stages  from  the 
solid  to  the  liquid  condition.  This  inter- 
mediate condition  is  spoken  of  as  the  state 
oi  vitreous  fusion.  Such  substances  may  be 
said  to  melt  at  the  lowest  temperature  at 
which  perceptible  softening  occurs,  and  to  be 
fully  melted  when  the  further  elevation  of 
temperature  does  not  make  them  more  fluid  ; 
but  no  precise  temperature  can  be  given  as 
their  melting  points. 

The  determination  of  the  melting  point 
of  a  body  is  a  matter  of  considerable  im- 
portance in  fixing  the  identity  of  many  che- 
mical compounds,  and  is  moreover  a  point 
of  frequent  practical  application  in  deter- 
mining the  commercial  value  of  tallow  and 
other  fats. 

It  is  done  as  follows  : — A  portion  of  the 
substance  is  melted  in  a  watch-glass,  and  a 
small  quantity  of  it  sucked  into  a  fine  capil- 
laiy  tube,  which  is  then  placed   in  a  bath 
T       of  clear  water  (fig.  309)  attached  to  a  ther- 

==^- ^^^^^Z=^       mometer,  and  the  temperature  of  the  bath 

Fig  30Q  is   gradually   raised    until    the    substance  is 

completely  melted,  which  from  its  small  mass 
is  very  easily  observed.  The  bath  is  then  allowed  to  cool,  and  the  solidi- 
fying point  noted  ;  and  the  mean  of  the  two  is  taken  as  the  true  melting 
point. 

339.  Influence  of  pressure  on  the  melting-  point. — Thomson  and 
Clausius  have  deduced  from  the  principles  of  the  mechanical  theory  of  heat 
that,  with  an  increase  of  pressure,  the  melting  point  of  a  body  must  be  raised. 
All  bodies  which  expand  on  passing  from  the  solid  to  the  liquid  state  have 
to  perform  external  work — namely,  tc  raise  the  pressure  of  the  atmosphere 
by  the  amount  of  this  expansion.  Under  ordinary  circumstances,  the 
amount  of  external  work  which  solids  and  liquids  thus  perfoi"m  is  so  small 
that  it  may  be  neglected.  But,  if  the  external  pressure  be  increased,  the 
power  of  overcoming  it  can  only  be  obtained  by  an  increase  of  vis  viva  of 
the  molecules.     The  increase  can  do  more  work  ;  the  temperature  of  fusion 


-339]         lufiiiciicc  of  Pressjire  on  the  Melting  Point.  3 1 3 

and  the  heat  of  fusion  are  both  increased.  Bunsen  examined  the  influence 
of  pressure  on  the  melting  point  by  means  of  the  apparatus  represented  in 
fig.  310,  in  which  act  is  a  thick  tube  about  the  thickness  of  a  straw  in  the 
clear,  in  the  parts  ca  and  the  bent  part  b.  The  whole  tube  having  been  filled 
with  mercury,  it  was  sealed  at  «,  and  then  a  small  quantity  was  driven  out 
at  b  and  some  of  the  substance  introduced  ;  the  end  b  was  then  w 

sealed  and  a  opened,  and  the  whole  tube  gently  warmed  so  as 
to  expel  some  mercury,  upon  which  a  was  again  hermetically 
sealed. 

When  the  tube  was  placed  in  a  bath  of  warm  water  a  little 
above  the  melting  point  of  the  body,  the  mercury  expanded  and 
a  pressure  resulted  which  could  be  accurately  measured  from 
the  diminution  in  volume  of  the  air  in  ca.,  which  was  carefully 
calibrated  for  this  purpose.  By  carefully  raising  or  lowering 
the  instrument  in  the  water,  the  pressure  could  be  increased 
or  diminished  at  will.  It  only  then  remained  to  observe  the 
temperature  at  which  the  substance  solidified,  and  the  corre- 
sponding pressure  at  that  moment.  In  this  way  Bunsen  found 
that  spermaceti,  which  melts  at  48°  under  a  pressure  of  i  atmo- 
sphere, melts  at  51"  under  a  pressure  of  156  atmospheres. 
Hopkins  found  that  spermaceti  melted  at  60° under  a  pressure 
of  519  atmospheres,  and  at  80°  under  792  atmospheres;  the 
meltmg  point  of  sulphur  under  these  pressures  was  respectively 
135°  and  141°. 

But  with  regard  to  those  bodies  which  contract  on  passing 
from  the  solid  to  the  liquid  state,  and  of  which  water  is  the  best 
example,  the  reverse  is  the  case.  Melting  ice  has  no  external  p.^  ^^^ 
work  to  perform,  since  it  has  no  external  pressure  to  raise  ;  on 
the  contrary,  in  melting,  it  absorbs  external  w^ork,  which,  transformed  into 
heat,  renders  a  smaller  quantity  of  heat  necessary  ;  the  external  work  acts  in 
the  same  direction  as  the  internal  heat — namely,  in  breaking  up  the  crystal- 
line aggregates.  Yet  these  differences  of  temperature  must  be  but  small,  for 
the  molecular  forces  in  solids  preponderate  far  over  the  external  pressure  ; 
the  internal  work  is  far  greater  than  the  external. 

Sir  W.  Thomson  found  that  increase  of  pressure  lowered  the  melting- 
point  of  ice.  The  apparatus  consisted  of  a  piezometer  (fig.  311)  ;  a  thick 
leaden  ring  divided  the  vessel  into  two  compartments,  the  upper  one  of  which 
contained  water  and  the  lower  one  crushed  ice,  which  was  thus  prevented 
from  rising,  This  also  served  to  support  a  thermometer  enclosed  in  a  very 
stout  tube,  and  a  manometer  with  compressed  air.  The  pressures  were 
exerted  by  means  of  a  screw  piston  V. 

Sir  W.  Thomson  thus  found  that  pressures  of  St  and  16 "8  atmospheres 
lowered  the  melting  point  of  ice  by  0-059'^  and  0-126°  respectively.  These 
results  justify  the  theoretical  previsions  of  Prof.  J.  Thomson,  according  to 
which  an  increase  of  pressure  of  n  atmospheres  lowers  the  melting  point  of 
ice  by  0-0074;;°  C.,  so  that  a  pressure  of  135  atmospheres,  or  about  2,000 
pounds  to  the  square  inch,  would  lower  the  melting  point  1°  C. 

This  lowering  of  the  melting  point  is  also  shown  by  the  experiment  of 
Mousson  (fig.  312).     The  apparatus  consists  of  a  stout  steel  tube  closed 


314  On  Heat.  [339- 

at  one  end  by  a  screw  and  with  a  screw  piston  at  the  other  (fig.  312).  The 
tube  is  filled  with  water  and  a  metal  bullet  introduced.  When  the  apparatus 
is  closed  it  is  inverted  so  that  the  bullet  rests  on  the  piston,  and  placed  thus 

in  a  freezing  mixture  ; 
the  water  freezes  and 
presses  the  ball  against 
the  piston.  This  is  then 
turned  again,  and  pressure 
is  gradually  applied  by 
turning  the  handle  of  the 
screw.  When  the  lower 
screw  is  opened  the 
copper  ball  falls  out,  and 
is  followed  by  a  thick 
cylinder  of  ice  which  must 


Fig.  311.  Fig.  312. 

have  been  formed  at  the  moment  of  opening.     Hence  the  ice  must,  by  a 
pressure  estimated  at  13,000  atmospheres,  have  been  converted  into  water 

at  about  -18°  C. 

This  influence  is  likewise  readily 
demonstrated  by  an  experiment  of 
Von  Helmholtz  (fig.  313).  Water 
is  boiled  in  a  flask  until  all  air  is 
expelled,  and  it  is  then  closed.  It 
is  afterwards  placed  in  a  freezing 
mixture  so  that  some  ice  forms 
inside.  This  is  then  allowed  to 
melt  again  in  great  part,  and  the 
flask  is  placed  in  a  vessel  of  water 
containing  lumps  of  ice.  It  is  then 
found  that  the  still  unfrozen  water 
inside  the  flask  freezes  while  that 
of  the  outside  is  melting. 

340.  Alloys.     Fluxes. — Alloys 

are    generally    more    fusible    than 

any  of  the  metals    of  which   they 

'°'  ^^■''  are   composed  ;    for    instance,    an 

alloy   of  5  parts   of  tin  and    i   of  lead  fuses  at   194°.     The  alloy  known  as 

Rose's  fusible  inctal^  which  consists  of  4  parts  of  bismuth,  i   part  of  lead. 


-342] 


Solution.  3 1  5 


and  I  of  tin,  melts  at  94°,  and  an  alloy  of  i  or  2  parts  of  cadmium  with  2 
parts  of  tin,  4  parts  of  lead,  and  7  or  8  parts  of  bismuth,  known  as  Wood's 
fusible  Jlieial,  melts  between  66°  and  71°  C.  An  alloy  of  potassium  and 
sodium  in  equivalent  proportions  is  liquid  at  the  ordinary  temperature. 
F'usible  alloys  are  of  extended  use  in  soldering  and  in  taking  casts.  Steel 
melts  at  a  lower  temperature  than  iron,  though  it  contains  carbon,  which 
is  almost  completely  infusible. 

Mixtures  of  the  fatty  acids  melt  at  lower  temperatures  than  the  pure  acids. 
A  mixture  of  the  chlorides  of  potassium  and  of  sodium  fuses  at  a  lower  tem- 
perature than  either  of  its  constituents  ;  the  same  is  the  case  with  a  mixture 
of  the  carbonates  of  potassium  and  sodium,  especially  when  they  are  mixed 
in  the  proportion  of  their  chemical  equivalents. 

An  application  of  this  property  is  met  with  in  the  case  o{ fluxes,  which  are 
much  used  in  metallurgical  operations.  They  consist  of  substances  which, 
when  added  to  an  ore,  partly  by  their  chemical  action,  help  the  reduction  of 
the  substance  to  the  metallic  state,  and,  partly,  by  presenting  a  readily 
fusible  medium,  promote  the  agglomeration  of  the  individual  particles  with 
the  formation  of  a  mass  of  metal  or  regulus. 

341.  Xiatent  heat. — Since,  during  the  passage  of  a  body  from  the  solid 
to  the  liquid  state,  the  temperature  remains  constant  until  the  fusion  is  com- 
plete, whatever  be  the  intensity  of  the  source  of  heat,  it  must  be  concluded 
that,  in  changing  their  condition,  bodies  absorb  a  considerable  amount  of 
heat,  the  only  effect  of  which  is  to  maintain  them  in  the  liquid  state.  This 
heat,  which  is  not  indicated  by  the  thermometer,  is  called  latent  heat  or 
latent  heat  of  fusion,  an  expression  which,  though  not  in  strict  accordance 
with  modern  ideas,  is  convenient  from  the  fact  of  its  universal  recognition 
and  employment  (461). 

An  idea  of  what  is  meant  by  latent  heat  maybe  obtained  from  the  follow- 
ing experiment  :— If  a  pound  of  water  at  80°  is  mixed  with  a  pound  of  water 
at  zero,  the  temperature  of  the  mixture  is  40°.  But  if  a  pound  of  pounded  ice 
at  zero  is  mixed  with  a  pound  of  water  at  80°,  the  ice  melts  and  two  pounds 
of  water  at  zero  are  obtained.  Consequently  the  mere  change  of  a  pound  of 
ice  to  a  pound  of  water  at  the  same  temperature  requires  as  m.uch  heat  as 
will  raise  a  pound  of  water  through  80°.  This  quantity  of  heat  represents 
the  latent  heat  of  the  fusion  of  ice,  or  the  latent  heat  of  water. 

Every  liquid  has  its  own  latent  heat,  and  in  the  chapter  on  Calorimetiy 
we  shall  show  how  this  is  determined. 

342.  Solution. — A  body  is  said  to  dissolve  when  it  becomes  liquid  in  con- 
sequence of  an  attraction  between  its  molecules  and  those  of  a  liquid.  Gum 
arabic,  sugar,  and  most  salts  dissolve  in  water.  The  weight  dissolved  gene- 
rally increases  with  the  temperature.  When  a  Hquid  has  dissolved  as  much 
as  it  can  at  a  particular  temperature,  it  is  said  to  be  saturated. 

During  solution,  as  well  as  during  fusion,  a  certain  quantity  of  heat  always 
becomes  latent,  and  hence  it  is  that  the  solution  of  a  substance  usually 
produces  a  diminution  of  temperature.  In  certain  cases  however,  instead 
of  the  temperature  being  lowered,  it  actually  rises,  as  when  caustic  potash  is 
dissolved  in  water.  This  depends  upon  the  fact  that  two  simultaneous 
and  contrar)'  phenomena  are  produced.  The  first  is  the  passage  from  the 
solid  to  the  liquid  condition,  which  always  lowers  the  temperature.     The 


3i6  On  Heat.  [342- 

second  is  the  chemical  combination  of  the  body  dissolved  with  the  hquid, 
and  which,  as  in  the  case  of  all  chemical  combinations,  produces  an  increase 
of  temperature.  Consequently,  as  the  one  or  the  other  of  these  effects  pre- 
dominates, or  as  they  are  equal,  the  temperature  either  rises  or  sinks,  or 
remains  constant. 

343.  Solidification — Solidification  or  congelation  is  the  passage  of  a 
body  from  the  liquid  to  the  solid  state.  This  phenomenon  is  regulated  by 
the  two  following  laws  : — 

I.  Every  body,  under  the  same  pressure,  solidifies  at  a  fixed  temperature, 
which  is  the  same  as  that  of  ficsio7i. 

II.  Frojn  the  commencement  to  the  end  of  the  solidification,  the  tempera- 
ture of  a  liquid  remains  constant. 

Certain  bodies,  more  especially  some  of  the  fats,  present  an  exception  to 
the  first  law,  in  so  far  that  by  repeated  fusions  they  seem  to  undergo  a 
molecular  change  which  alters  their  melting  point. 

The  second  law  is  the  consequence  of  the  fact  that  the  latent  heat  ab- 
sorbed during  fusion  becomes  free  at  the  moment  of  solidification. 

The  application  of  the  very  low  temperature  which  can  now  be  so  readily 
procured  has  lessened  the  number  of  those  liquids  which  it  was  formerly 
thought  could  not  be  solidified.  By  allowing  liquid  ethylene  (382)  to  boil  in 
a  vacuum,  Wroblewski  and  Olszewski  obtained  a  temperature  of  —  136°. 
They  observed  that  carbon  disulphide  solidified  at  -  116°  and  fused  again  at 
about  —110°.  Absolute  alcohol  became  viscid  at  —  129°  and  solidified  at 
—  130-5°.     Pure  ether  solidifies  at  129°. 

Water  containing  a  salt  dissolved  always  solidifies  below  zero;  the  de- 
pression of  the  freezing  point  is  proportional  to  the  weight  of  salt  dissolved, 
at  any  rate  for  weak  solutions.     This  is  known  as  Blagden^s  law. 

If  several  salts  which  have  no  chemical  action  on  each  other  be  dis- 
solved in  a  given  weight  of  water  the  loweinng  of  the  freezing  point  is  the 
sum  of  the  depressions  which  each  of  them,  would  produce  separately  if  dis- 
solved in  the  same  quantity  of  water. 

When  the  numbers  observed  in  any  experiment  of  this  kind  do  not  agree 
with  those  calculated,  this  points  to  the  occurrence  of  some  chemical  action 
between  the  substances  dissolved,  and  the  observation  of  such  deviations 
has  been  of  use  in  questions  of  chemical  statics. 

The  elaborate  researches  of  Raoult  on  the  temperature  of  solidification 
of  solutions  of  bodies  in  water  and  other  solvents  have  led  to  important  con- 
clusions. The  temperature  at  which  a  solution  solidifies,  or  its  freezing  point, 
is  always  lov/er  than  that  of  the  pure  solvent.  If  P  be  the  weight  in  grammes 
of  any  substance  dissolved  in  100  grammes  of  a  solvent,  and  C  be  the  depres- 

C         ■ 

sion  in  the  freezing  point  observed,  then      =  A  is  the  depression  which  would 

be  produced  by  dissolving  07ie  gramme  of  the  substance  in  100  grammes, 
and  is  known  as  the  coefficient  of  depression. 

A  comparison  of  the  values  for  A  for  various  substances  and  the  same 
solvent  shows  that  they  differ  considerably  ;  this  is  not  so  if  we  compare  the 
depressions  produced  by  molecular  weights  of  the  substances.  That  is,  if  we 
multiply  the  value  of  A  in  the  above  equation  by  M,  the  molecular  weight  of 
the  substance  dissolved,  we  obtain  the  depression  which  would  be  produced 


-345]  Retardation  of  the  Point  of  Solidification.  317 

by  dissolving  one  molecule  of  a  body  in  100  grammes  of  the  solvent,  or  the 
coefficient  of  inotecular  dep7'ession  ;  this  is  called  T,  and  we  have  T  =  -5—. 

Now  it  is  found  that  in  a  very  large  number  of  cases  the  value  of  T,  for 
one  and  the  same  solvent,  is  a  constant  number  ;  it  has  the  value  19  for 
water,  39  for  glacial  acetic  acid,  and  49  for  benzene. 

This  relation  makes  it  possible  to  calculate  the  molecular  weight  of  a 
solid  in  solution  by  means  of  a  simple  determina- 
tion of  the  freezing  point  of  a  solution,  which  is 
effected  by  means  of  the  apparatus  represented  in 
fig.  314,  due  to  Prof  Ramsay.  A  wide  test-tube  is 
closed  by  an  indiarubber  stopper  A  perforated  with 
two  holes.  In  one  of  these  is  a  sensitive  thermo- 
meter D,  specially  graduated,  and  by  which  the 
looth  of  a  degree  may  be  read  off.  In  the  other  is 
a  piece  of  wide  glass  tubing  B,  through  which  a 
stirrer  C  moves  freely  up  and  down.  The  beaker 
E  contains  hot  or  cold  water,  as  required,  in  order 
to  raise  the  temperature  above,  or  depress  it  below, 
the  melting  point  of  the  solvent. 

Since  C  and  P  are  known,  M   is   determined 
from  the  formula 

^  { 

where  T  is  the  constant  for  the  particular  solvent 
employed,  which  is  ordinary  glacial  acetic  acid  in 
the  majority  of  cases. 

344.  Crystallisation,  —  Generally    speaking.  Fig  31^ 
bodies  which  pass   slowly  from  the  liquid  to  the 

solid  state  assume  regular  geometrical  forms,  such  as  the  cube  prisms, 
rhombohedra,  &c.  ;  these  are  called  crystals.  If  the  crystals  are  formed 
from  a  body  in  fusion,  such  as  sulphur  or  bismuth,  the  crystallisation  is 
said  to  take  place  by  the  dry  way.  The  crystallisation  is  said  to  be  by  the 
moist  way  when  it  takes  place  owing  to  the  slow  evaporation  of  a  solution  of 
a  salt,  or  when  a  solution  saturated  at  a  higher  temperature  is  allowed  to 
cool  slowly.     Snow,  ice,  and  many  salts  present  examples  of  crystallisation. 

345.  Retardation  of  the  point  of  solidification. — The  freezing  point  of 
pure  water  can  be  diminished  by  several  degrees,  if  the  water  be  previously 
freed  from  air  by  boiling  and  be  then  kept  in  a  perfectly  still  place.  In 
fact,  it  may  be  cooled  to  —  15°  C,  and  even  lower,  without  freezing.  But 
when  it  is  slightly  agitated,  the  liquid  at  once  solidifies.  This  may  be  con- 
veniently shown  by  means  of  the  apparatus  represented  in  fig.  315,  which 
consists  of  a  delicate  thermometer,  round  the  bulb  of  which  is  a  wider  one 
containing  some  water.  Before  sealing  at  a  the  whole  outside  bulb  was 
filled  with  water,  which  was  then  boiled  out  and  sealed  so  that  over  the 
water  the  space  is  quite  empty.  This  is  clamped  in  a  retort  stand,  and 
ether  is  dropped  on  it,  that  which  has  dropped  off,  and  become  colder, 
being  used  over  and  over  again.     In  this  way  the  temperature  may  soon 


3i8 


On  Heat. 


[345- 


be  reduced  to  —  6°,  and  if  then  the  bulb  be  shaken  part  of  the  water  freezes 
and  the  temperature  rises  to  zero.  The  smaller  the  quantity  of  liquid,  the 
lower  is  the  temperature  to  which  it  can  be  cooled,  and  the  greater  the 
mechanical  disturbance  it  supports  without  fi-eezing.  Fournet  has  observed 
the  frequent  occurrence  of  mists  formed  of  particles  of  liquid 
matter  suspended  in  an  atmosphere  whose  temperature  was  io° 
or  even  15°  below  zero. 

A  very  rapid  agitation  also  prevents  the  formation  of  ice. 
The  same  is  the  case  with  all  actions  which,  hindering  the 
molecules  in  their  movements,  do  not  permit  them  to  arrange 
themselves  in  the  conditions  necessary  for  the  solid  state. 
Despretz  was  able  to  lower  the  temperature  of  water  contained  in 
ly  fine  capillary  tubes  to  —  20°  without  their  solidifying.  This 
experiment  shows  how  it  is  that  plants  in  many  cases  do  not 
become  frozen  even  during  severe  cold,  as  the  sap  is  contained 
in  very  fine  capillary  vessels. 

If  water  contains  salts,  or  other  foreign  bodies,  its  freezing  point 
is  lowered.  Sea  water  freezes  at  -2'5°to  —  3°C.  ;  the  ice  which 
forms  is  quite  pure,  and  a  saturated  solution  remains.  In  Finland 
advantage  is  taken  of  this  property  to  concentrate  sea-water  for 
the  purpose  of  extracting  salt  from  it.  If  water  contains  alcohol, 
precisely  analogous  phenomena  are  observed  ;  the  ice  formed  is 
pure,  and  practically  all  the  alcohol  is  contained  in  the  residue. 

Dufour  has  observed  some  very  curious  cases  of  liquids  cooled 
out  of  contact  with  solid  bodies.  His  mode  of  experimenting  was 
to  place  the  liquid  in  another  of  the  same  specific  gravity  but  of 
lower  melting  point,  and  in  which  it  is  insoluble.  Drops  of  water, 
for  instance,  suspended  in  a  mixture  of  chloroform  and  oil,  usually 
solidified  between  -  4°  and  -  12°,  while  still  smaller  globules  cooled 
down  to  —18°  or  -20°.  Contact  with  a  fragment  of  ice  immedi- 
ately set  up  congelation.  Globules  of  sulphur  (which  solidifies 
p;„  at    115°)    remained  liquid   at    40°;    and   globules    of   phosphorus 

(solidifying  point  42°)  at  20°. 
The  superfusion  of  phosphorus  may  be  illustrated  by  the  experiment  repre- 
sented by  fig.  316.  A  long  test  tube  containing  phosphorus,  A,  and  covered 
with  a  layer  of  water,  is  fixed  along  with  a  thermometer  T  in  a  large  flask  con- 
taining water.  This  flask  is  raised  to  a  temperature  of  about  44°  at  which  the 
phosphorus  fuses,  and  is  then  withdrawn  from  the  source  of  heat  ;  as  its  mass 
is  considerable,  it  cools  very  slowly  and  the  phosphorus  remains  liquid  even  at 
ordinary  temperature.  A  glass  rod  may  even  be  dipped  into  it  without  change  ; 
but  if  the  rod  be  rubbed  along  solid  phosphorus  so  as  to  detach  a  small  par- 
ticle, it  at  once  brings  about  solidification  if  dipped  in  the  melted  mass. 

When  a  liquid  solidifies  after  being  cooled  below  its  normal  freezing  pointy 
the  solidification  takes  place  very  rapidly,  and  is  accompanied  by  a  disen- 
gagement of  heat,  which  is  sufficient  to  raise  its  temperature  from  the  point 
at  which  solidification  begins  up  to  its  ordinary  freezing  point.  This  is 
well  seen  in  the  case  of  hyposulphite  of  sodium,  which  melts  in  its  own 
water  of  crystallisation  at  45°,  and  when  carefully  cooled  will  remain  liquid 
at  the  ordinary  temperature  of  the    atmosphere.     If  it  then  be  made  to 


m 


-346]  Change  of  Volume  on  Solidification.  319 

solidify  by  agitation,  or  by  adding  a  small  fragment  of  the  solid  salt,  the 
rise  of  temperature  is  distinctly  felt  by  the  hand.  In  this  case  the  heat, 
which  had  become  latent  in  the  process  of  liquefaction,  again  l^ecomes  free,, 
and  a  portion  of  the  sub- 
stance remains  melted  ;  for 
it  is  kept  liquid  by  the  heat 
of  solidification  of  that  which 
has  solidified. 

346.  Change  of  volume 
on  solidification  and  lique- 
faction.— The  rate  of  ex- 
pansion of  bodies  generally 
increases  as  they  approach 
their  melting  points,  and  is 
in  most  cases  followed  by  a 
further  expansion  at  the 
moment  of  liquefaction,  so 
that  the  liquid  occupies  a 
greater  volume  than  the  solid 
from  which  it  is  formed.  The 
apparatus  represented  in  fig. 
317  is  well  adapted  for  ex- 
hibiting this  phenomenon. 
It  consists  of  a  glass  tube, 
ab,  containing  water  or  some 
other  suitable  liquid,  to  which 
is  carefully  fitted  a  cork  with 

a  graduated  glass  tube  c.  This  forms,  in  fact,  a  thermometer,  and  the 
values  of  the  degrees  on  the  tube  c  are  determined  in  terms  of  the 
capacity  of  the  whole  apparatus.  A  known  volume  of  the  substance  is. 
placed  in  the  tube  aa  and  the  cork  inserted  ;  the  apparatus  is  then 
placed  in  a  space  at  a  temperature  very  little  below  the  melting  point 
of  the  body  in  question,  until  it  has  acquired  its  temperature,  and  the 
position  of  the  liquid  in  c  is  noted.  The  temperature  is  then  allowed 
to  rise  slowly,  and  the  position  noted  when  the  melting  is  complete. 
Knowing  then  the  difference  in  the  two  readings  and  the  volume  of  the 
substance  under  experiment,  and  making  a  correction  for  the  expansion  of 
the  liquid  and  of  the  glass,  it  is  easy  to  deduce  the  increase  due  to  the 
melting  alone.  Phosphorus,  for  instance,  increases  about  3-4  per  cent,  on 
liquefaction  ;  that  is,  100  volumes  of  solid  phosphorus  at  44°  (the  melting 
point)  become  103-4  at  the  same  temperature  when  melted.  Sulphur  expands 
about  5  per  cent,  on  liquefying,  and  stearic  acid  about  1 1  per  cent. 

Water  presents  a  remarkable  exception ;  it  expands  at  the  moment  of 
solidifying,  or  contracts  on  melting,  by  about  10  per  cent.  One  volume  of 
ice  at  0°  gives  0-9 178  of  water  at  0°,  or  i  volume  of  water  at  0°  gives  i'io2 
of  ice  at  the  same  temperature.  In  consequence  of  this  expansion,  ice  floats 
on  the  surface  of  water.  According  to  Dufour,  the  specific  gravity  of  ice  is 
0-9178  ;  Bunsen  found  for  ice  which  had  been  freed  from  water  by  boiling 
the  somewhat  smaller  number  0-91674. 


Fig. 


Fig.  317. 


320  On  Heat.  [346- 

The  iiicrease  of  volume  in  the  formation  of  ice  is  accompanied  by  an 
expansive  force  whicii  sometimes  produces  powerful  mechanical  effects,  of 
which  the  bursting  of  water-pipes  and  the  breaking  of  jugs  containing  water 
are  familiar  examples.  The  splitting  of  stones,  rocks,  and  the  swelling  up 
of  moist  ground  during  frost,  are  caused  by  the  fact  that  water  penetrates 
into  the  pores  and  there  becomes  frozen ;  in  short,  the  great  expansion  of 
water  on  freezing  is  the  most  active  and  powerful  agent  of  disintegration  on 
the  earth's  surface. 

The  expansive  force  of  ice  was  strikingly  shown  by  some  experiments  of 
Major  Williams,  in  Canada.  Having  cjuite  filled  a  13-inch  iron  bomb-shell 
with  water,  he  firmly  closed  the  touch-hole  with  an  iron  plug  weighing  three 
pounds  and  exposed  it  in  this  state  to  the  frost.  After  some  time  the  iron 
plug  was  forced  out  with  a  loud  explosion,  and  thrown  to  a  distance  of  415 
feet,  and  a  cylinder  of  ice  8  inches  long  issued  from  the  opening  (fig.  318). 
In  another  case  the  shell  burst  before  the  plug  was  driven  out,  and  in  this 
case  a  sheet  of  ice  spread  out  all  round  the  crack.  It  is  probable  that  under 
the  great  pressure  some  of  the  water  still  remained  licjuid  up  to  the  time 
at  which  the  resistance  was  overcome  ;  that  it  then  issued  from  the  shell  in 
a  liquid  state,  but  at  a  temperature  below  0°,  and  therefore  instantly  began 
to  solidify  when  the  pressure  was  removed,  and  thus  retained  the  shape  of 
the  orifice  whence  it  issued. 

Cast-iron,  bismuth,  and  antuBony  expand  on  solidifying,  like  water,  and 
can   thus  be  used  for  casting  ;  but  gold,  silver,  and  copper  contract,  and 
hence  coins  of  these  metals  cannot  be  cast,  but  must  be  stamped  with  a  die. 
This  increase  of  volume  when  liquids  solidify,  and  the  correlated  decrease 
on  melting  again,  in  the  case  of  water  and  some  other 
crystalline  substances  such  as  bismuth,  are  probably  due  to 
the  fact  that  such  bodies  are  aggregates  of  small  crys- 
talline masses,  which   are  grouped  in  such  a  way  that 
small   interstices    are    formed.      When  the  liquid  melts 
these  interstices  fill  up  owing  to  the  mobility  of  the  mole- 
Fig.  31S.  cules,  and,  notwithstanding  the  greater  space  which  each 
individual  group  takes  up,  owing  to  expansion,  there  is  a  decrease  of  volume. 
347.  rreezing-  mixtures. — The  absorption  of  heat  in   the  passage   of 
bodies  from  the  solid  to  the  liquid  state  has  been  used  to  produce  artificial 
cold.     This  is  effected  by  mixing  together  bodies  which  have  an  affinity  for 
each  other,  and  of  which  one  at  least  is  solid,  such  as  water  and  a  salt,  ice 
and  a  salt,  or  an  acid  and  a  salt.     Chemical  affinity  accelerates  the  fusion  : 
the  portion  which  melts  robs  the  rest  of  the  mixture  of  a  large  quantity  of 
sensible  heat,  which  thus  becomes  latent.     In  many  cases  a  very  consider- 
able diminution  of  temperature  is  produced. 

The  following  table  gives  the  names  of  the  substances  mixed,  their  pro- 
portions, and  the  corresponding  diminutions  of  temperature  : — 

Parts  Reduction  of 

Substances  by  weight  temperature 

Sulphate  of  sodium  .         .         .         8 )  o  0 

Hydrochloric  acid  .         .         .         .         5,  +10  to -17 

Pounded  ice  or  snow       .         .         .         21 


Common  salt 


-I-  lo^to-ii 


+ lo'to- 


-348]  Guth'ie's  Researches.  321 

.    Parts  Reduction  of 

Substances  by  weight  temperature 

Sulphate  of  sodium .  .  .  .  3)               +10°  to -19° 

Dilute  nitric  acid     .  .  .  .  2 ) 

Sulphate  of  sodium .  .  .  .  6  j 

Nitrate  of  ammonium  .  .  .  5-               +10°  to -26° 

Dilute  nitric  acid     .  .  .  .  4' 

Phosphate  of  sodium  .  .  .  9 ) 

Dilute  nitric  acid     .  .  .  .  4  j 

If  the  substances  taken  be  themselves  previously  cooled  down,  a  still 
more  considerable  diminution  of  temperature  is  occasioned. 

Freezing  mixtures  are  frequently  used  in  chemistry,  in  physics,  and  in 
domestic  economy.  One  form  of  the  portable  ice-making  machines  which 
have  come  into  use  during  the  last  few  years  consists  of  a  cylindrical 
metallic  vessel  divided  into  four  concentric  compartments.  In  the  central 
one  is  placed  the  water  to  be  frozen  ;  in  the  next  there  is  the  freezing 
mixture,  which  usually  consists  of  sulphate  of  sodium  and  hydrochloric  acid  ; 
6  pounds  of  the  former  and  5  of  the  latter  will  make  5  to  6  pounds  of  ice  in 
an  hour.  The  third  compartment  also  contains  water,  and  the  outside  one 
contains  some  badly  conducting  substance,  such  as  cotton,  to  cut  off  the 
influence  of  the  external  temperature.  The  best  effect  is  obtained  when 
pretty  large  quantities  (2  or  3  pounds)  of  the  mixture  are  used,  and  when 
the  ingredients  are  intimately  mixed.  It  is  also  advantageous  to  use  the 
machines  for  a  succession  of  operations. 

348.  Guthrie'.s  researclies.— It  appears  from  the  experiments  of  the  late 
Dr.  Guthrie  that  what  are  called  freezing  mixtures  may  be  divided  into  two 
classes,  namely  those  in  which  one  of  the  constituents  is  liquid  and  those 
in  which  both  are  soHd.  The  temperature  indicated  by  the  thermometer 
placed  in  a  freezing  mixture  is,  of  course,  due  to  the  loss  of  heat  by  the 
thermometer  to  the  liquefying  freezing  mixture,  and  is  measured  by  the  rate 
of  such  loss.  The  quantity  of  heat  absorbed  by  the  freezing  mixture  is 
obviously  the  heat  required  to  melt  the  constituents,  together  with  (  ±  )  the 
heat  of  combination  of  the  constituents.  When  one  constituent  is  Hquid, 
as  when  hydrochloric  acid  is  added  to  ice,  then  a  lower  temperature  is  got 
by  previously  cooling  the  hydrochloric  acid.  There  is  no  advantage  in 
cooling  the  ice.  But  when  both  constituents  are  solid,  as  in  the  case  of  the 
ice-salt  freezing  mixture,  there  is  no  advantage  to  be  gained  by  cooling  one 
or  both  constituents.  Within  very  wide  limits  it  is  also  in  the  latter  case  a 
matter  of  indifference  as  to  the  ratio  between  the  constituents.  Nor  does  it 
matter  whether  the  ice  is  finely  powdered  as  snow  or  in  pieces  as  large  as  a  pea. 

The  different  powers  of  various  salts  when  used  in  conjunction  with  ice 
as  freezing  mixtures  appear  to  have  remained  unexplained  until  Guthrie 
showed  that,  with  each  salt,  there  is  always  a  minimum  temperature  below 
which  it  is  impossible  for  an  aqueous  solution  of  any  strength  of  that  salt  to 
exist  in  the  liquid  form  ;  that  there  is  a  certain  strength  of  solution  for  each 
salt  which  resists  solidification  the  longest,  that  is,  to  the  lowest  temperature. 
Weaker  solutions  give  up  ice  on  being  cooled,  stronger  solutions  give  up  the 
salt  either  in  the  anhydrous  state  or  in  combination  with  water.  That 
particular  strength   of  a  particular  salt,  which  resists  solidification  to  the 

Y 


322  On  Heat.  [348- 

lowest  temperature,  is  called  by  Guthrie  a  cryohydrate.  It  is  of  such  a 
strength  that  when  cooled  below  o°  C.  it  solidifies  as  a  whole  ;  that  is,  the 
ice  and  the  salt  solidify  together  and  form  crystals  of  constant  composition 
and  constant  melting  and  the  same  solidifying  temperatures.  The  liquid 
portion  of  a  freezing  mixture,  as  long  as  the  temperature  is  at  its  lowest,  is, 
indeed,  a  melted  cryohydrate.  The  slightest  depression  of  temperature  below 
this  causes  solidification  of  the  cryohydrate,  and  hence  the  temperature  can 
never  sink  below  the  solidifying  temperature  of  the  cryohydrate. 

Guthrie  has  also  shown  that  colloid  bodies,  such  as  gum  and  gelatine, 
neither  raise  the  boiling  point  of  water  nor  depress  the  solidifying  point,  nor 
can  they  act  as  elements  in  freezing  mixtures. 

VAPOURS.      MEASUREMENT   OF   THEIR   TENSION. 

349.  Vapours. — We  have  already  seen  (146)  that  vapours  are  the  aeriform 
fluids  into  which  volatile  substances,  such  as  ether,  alcohol,  water,  and 
mercury,  are  changed  by  the  absorption  of  heat.  Volatile  liquids  are  those 
which  thus  possess  the  property  of  passing  into  the  aeriform  state,  and  fixed 
liquids  are  those  which  do  not  form  vapour  at  any  temperature  without 
undergoing  chemical  decomposition,  such  as  the  fatty  oils.  Ice  and  snow 
volatilise  in  closed  spaces,  forming  crystals  on  the  cooled  parts.  The  forma- 
tion of  vapour  is  thus  not  restricted  to  the  liquid  state,  and  in  some  bodies^ 
such  as  arsenic,  the  boiling  point  is  below  the  freezing  point.  As  the  boiling 
point  is  raised  by  pressure  it  is  possible  to  liquefy  such  bodies  also,  by  apply- 
ing sufficient  pressure. 

Iodine  melts  at  104°  and  boils  at  175°  under  ordinary  pressure.  It  there- 
fore evaporates  after  melting  ;  but  at  a  pressure  of  250  mm.  its  boiling  point 
is  below  its  melting  point,  and  it  then  evaporates  without  melting.  Even  at 
ordinary  temperatures  a  considerable  quantity  volatilises  without  melting. 

Vapours  are  transparent,  like  gases,  and  generally  colourless  ;  there  are 
only  a  few  coloured  liquids 'which  also  give  coloured  vapours. 

350.  Vaporisation  — The  passage  of  a  liquid  into  the  gaseous  state  is 
designated  by  the  general  term  vaporisation  ;  the  term  evaporation  espe- 
cially refers  to  the  slow  production  of  vapour  at  the  free  surface  of  a  liquid,, 
and  boiling  to  its  rapid  production  in  the  mass  of  the  liquid  itself  We  shall 
presently  see  (356)  that  at  the  ordinary  atmospheric  pressure,  ebullition, 
like  fusion,  takes  place  at  a  definite  temperature.  This  is  not  the  case 
with  evaporation,  which  occurs  even  with  the  same  liquid  at  very  different 
temperatures,  although  the  formation  of  a  vapour  seems  to  cease  below  a 
certain  point.  Mercury,  for  example,  gives  no  vapour  below  -  10°,  nor  sul- 
phuric acid  below  30°. 

351.  Elastic  force  of  vapour. — Like  gases,  vapours  have  a  certain 
elastic  force,  in  virtue  of  which  they  exert  pressures  on  the  sides  of  vessels  in 
which  they  are  contained.  The  elastic  force  of  vapour  may  be  demonstrated 
by  the  following  experiment  :— A  quantity  of  mercury  is  placed  in  a  bent 
glass  tube  (fig.  319),  the  shorter  leg  of  which  is  closed  ;  a  few  drops  of  ether 
are  then  passed  into  the  closed  leg  and  the  tube  is  immersed  in  a  water  bath 
at  a  temperature  of  about  45°.  The  mercury  then  sinks  slowly  in  the  short 
branch,  and  the  space  ab  is  filled  with  a  gas  which  has  all  the  appearance  of 


-352J 


Formation  of  Vapour  in  a    Vacuum. 


323 


air,  and  whose  elastic  force  counterbalances  the  pressure  of  the  coknnn  of 
mercury  cd.,  and  the  atmospheric  pressure  on  d.  This  gas  is  the  vapour  of 
ether.  If  the  water  be  cooled,  or  if  the  tube  be  removed  from  the  bath,  the 
vapour  which  fills  the  space  ab  disappears,  and  the  drop  of  ether  is  reproduced. 
If,  on  the  contraiy, 
the  bath  be  heated  still 
higher,  the  level  of  the 
mercury  descends  be- 
low b,  indicating  an 
increase  in  the  elastic 
force  of  the  vapour. 

352.  rormation  of 
vapour  In  a  vacuum. 
— In  the  previous  ex- 
periment the  liquid 
changed  very  slowly 
into  the  vaporous  con- 
dition ;  this  occurs 
also  when  a  liquid  is 
freely  exposed  to  the 
air.  In  both  cases  the 
atmosphere  is  an  ob- 
stacle to  the  vapori- 
sation. In  a  vacuum 
there  is  no  resistance, 
and  the  formation  of 
vapour  is  instanta- 
neous, as  is  seen  in 
the  following  experi- 
ment : —  Four  baro- 
meter tubes,  filled  with 

mercury,  are  immersed  in  the  same  trough,  fig.  320.  One  of  them.  A, 
serves  as  a  barometer,  and  a  few  drops  of  water,  alcohol,  and  ether  are  re- 
spectively introduced  into  the  tubes  B,  C,  D.  When  the  liquids  reach  the 
vacuum,  a  depression  of  the  mercury  is  at  once  produced.  And  as  this 
depression  cannot  be  caused  by  the  weight  of  the  liquid,  which  is  an  ex- 
tremely small  fraction  of  the  weight  of  the  displaced  mercury,  it  must  be 
due  to  the  formation  of  some  vapour  whose  elastic  force  has  depressed  the 
column  of  mercury. 

The  experiment  also  shows  that  the  depression  is  not  the  same  in  all  the 
tubes  ;  it  is  greater  in  the  case  of  alcohol  than  of  water,  and  greater  with 
ether  than  wfth  alcohol.  We  consequently  obtain  the  two  following  laws  of 
the  formation  of  vapours  : — 

I.  In  a  vacuum  all  volatile  liquids  qrc  instantaneously  co  freer  ted  into 
vapour. 

II.  At  the  same  temperature  the  vapours  of  different  liquids  have  different 
elastic  forces. 

For  example,  at  20°  the  tension  of  ether  vapour  is  25  times  as  great  as 
that  of  aqueous  vapour. 

Y   2 


F.g. 


Fig.  320. 


324  On  Heat.  [353- 

353.  Saturated  vapour.  Maximum  of  tension. — When  a  very  small 
quantity  of  a  volatile  liquid,  such  as  ether,  is  introduced  into  a  barometer 
tube,  it  is  at  once  completely  vaporised,  and  the  mercurial  column  is  not 
depressed  to  its  full  extent ;  for  if  some  more  ether  be  introduced  the 
depression  increases.  By  continuing  the  addition  of  ether,  it  finally  ceases 
to  vaporise,  and  remains  in  the  liquid  state.     There  is,  therefore,  for  a  cer- 

tam  temperature,  a  limit  to  the  quantity  of  vapour 
which  can  be  formed  in  a  given  space.  This  space 
is  accordingly  said  to  be  saturated.  Further,  when 
the  vaporisation  of  the  ether  ceases,  the  depression 
of  the  mercurial  column  stops.  And  hence  there 
is  a  limit  to  the  tension  of  the  vapour,  a  limit 
which,  as  we  shall  presently  see  (354),  varies  with 
the  temperature. 

To  show  that,  in  a  closed  space,  saturated  with 
vapour  and  containing  liquid  ///  excess^  the  tempera- 
ture remaining  constant,  there  is  a  maximian  of 
teiision  which  the  vapour  cannot  exceed,  a  baro- 
metric tube  is  used  which  dips  in  a  deep  bath 
(fig.  321).  This  tube  is  filled  with  mercury,  and 
then  so  much  ether  is  added  as  to  be  in  excess 
after  the  Torricellian  vacuum  is  saturated.  The 
height  of  the  mercurial  column  is  next  noted  by 
means  of  the  scale  graduated  on  the  tube  itself 
Now,  whether  the  tube  be  depressed,  which  tends 
to  compress  the  vapour,  or  whether  it  be  raised, 
which  tends  to  expand  it,  the  height  of  the  mercurial 
column  is  constant.  The  tension  of  the  vapour 
remains  constant  in  the  two  cases,  for  the  depres- 
sion neither  increases  nor  diminishes  it.  Hence  it 
is  concluded  that  when  the  saturated  vapour  is 
compressed,  a  portion  returns  to  the  liquid  state  ; 
that  when,  on  the  other  hand,  the  pressure  is 
diminishedj  a  portion  of  the  excess  of  liquid  vapor- 
ises, and  the  space  occupied  by  the  vapour  is  again 
saturated  ;  but  in  both  cases  the  tension  and  the 
density  of  the  vapour  remain  constant. 

354.  Unsaturated  vapours. — From  what  has  been  said,  vapours  pre- 
sent two  vei-y  different  states,  according  as  they  are  saturated  or  not.  In 
the  first  case,  where  they  are  saturated  and  in  contact  with  the  liquid,  they 
differ  completely  from  gases,  since  for  a  given  temperature  they  can  neither 
be  compressed  nor  expanded  ;  their  elastic  force  and  their  density  remain 
constant. 

In  the  second  case,  on  the  contrary,  where  they  are  not  saturated,  they 
exactly  resemble  gases.  For  if  the'  experiments  (fig.  321)  be  repeated,  only  a 
small  quantity  of  ether  being  introduced,  so  that  the  vapour  is  not  saturated, 
and  if  the  tube  be  then  slightly  raised,  the  level  of  the  mercury  is  seen  to  rise, 
which  shows  that  the  elastic  force  of  the  vapour  has  diminished.  Similarly, 
by  immersing  the  tube  still  more,  the  level  of  the  mercury  sinks.    The  vapour 


Fig.  321 


-356 J  Tension  of  Aqueous    Vapour  beloiv  Zero.  325 

consequently  behaves  just  as  a  gas  would  do,  its  tension  diminishes  when  the 
volume  increases,  and  vice  7'ef-sd  ;  and  as  in  both  cases  the  volume  of  the 
vapour  is  inversely  as  the  pressure,  it  is  concluded  that  icnsaturated  vapours 
obey  Boyle's  law. 

When  an  unsaturated  vapour  is  heated,  its  volume  increases  like  that  of 
a  gas  ;  and  the  number  0"oo366,  which  is  the  coefficient  of  the  expansion  of 
air,  may  be  taken  for  that  of  vapours. 

Hence  we  see  that  the  physical  properties  of  unsaturated  vapours  are 
comparable  with  those  of  gases,  and  that  the  formulae  for  the  compressibility 
and  expansibility  of  gases  (182  and  332)  also  apply  to  unsaturated  vapours. 

355.  Tension  of  aqueous  vapour  belowr  zero. — In  order  to  measure 
the  elastic  force  of  aqueous  vapour  below  zero,  Gay-Lussac  used  two  baro- 
meter tubes  filled  with  mercury,  and  placed  in 
the  same  bath  (fig.  322).  The  straight  tube,  A, 
serves  as  a  barometer  ;  the  other,  C,  is  bent,  so 
that  part  of  the  Torricellian  vacuum  can  be  sur- 
rounded by  a  freezing  mixture,  B  (347).  When 
a  little  water  is  admitted  into  the  bent  tube,  the 
level  of  the  mercury  sinks  below  that  in  the 
tube  A,  to  an  extent  which  varies  with  the  tem- 
perature of  the  freezing  mixture. 

At       o*^  the  depression  is  .  4'54  millimetres 

„  -    1°      ,, 
„  -   3°      „ 


•  4-25 
■  3-63 

•  3-II 
.  2-67 
.  2 -08 
.  0-84 

•  0-36 


These  depressions,  which  must  be  due  to 
the  pressure  of  aqueous  vapour  in  the  space  BC, 
show  that  even  at  very  low  temperatures  there 
is  always  some  aciueous  vapour  in  the  atmo- 
sphere. 

Although  in  the  above  experiment  the  part  B 
and  the  part  C  are  not  both  immersed  in  the 
freezing  mixture,  we  shall  presently  see  that 
when  two  communicating  vessels  are  at  different 
temperatures,  the  tension  of  the  vapour  is  the 
same  in  both,  and  always  corresponds  to  that  of  the  lower  temperature. 

That  water  evaporates  even  below  zero  follows  from  the  fact  that  wet  linen 
exposed  to  the  air  during  frost  becomes  first  stiff  and  then  dry,  showing  that  the 
particles  of  water  evaporate  even  after  the  latter  has  been  converted  into  ice. 

356.  Tension  of  aqueous  vapour  between  zero  and  one  hundred 
degrees. — i.  Daltoiis  method.  Dalton  measured  the  elastic  force  of  aqueous 
\apour  between  0°  and  100°  by  means  of  the  apparatus  represented  in 
fig.  323.  Two  barometer  tubes,  A  and  B,  are  filled  with  mercur}',  and  inverted 
in  an  iron  bath  full  of  mercury,  which  is  placed  on  a  furnace.     The  tube  A 


Fig.  322. 


326 


On  Heat. 


[356- 


contains  a  small  quantity  of  water.  The  tubes  are  supported  in  a  cylindrical 
vessel  full  of  water,  the  temperature  of  which  is  indicated  by  the  thermometer. 
The  bath  being  gradually  heated,  the  water  in  the  cylinder  becomes  heated 
too  ;  the  water  which  is  in  the  tube  A  vaporises,  and  in  proportion  as  the 
tension  of  its  vapour  increases,  the  mercury  sinks.  The  depressions  of  the 
mercury  corresponding  to  each  degree  of  the  thermometer  are  indicated  on 
the  scale  E,  and  in  this  manner  a  table  of  the  elastic  forces  between  zero  and 
1 00°  has  been  constructed. 

ii.  Regnaidfs  method.—  Dalton's  method  is  wanting  in  precision,  for  the 
liquid  in  the  cylinder  has  not  everywhere  the  same  temperature,  and  con- 


Fig.  323.  r  1       -4 

sequently  the  exact  temperature  of  the  aqueous  vapour  is  not  shown. 
Regnault's  apparatus  is  a  modification  of  that  of  Dalton.  The  cylindrical 
vessel  is  replaced  by  a  large  cylindrical  zinc  drum,  MN  (fig.  324),  in  the 
bottom  of  which  are  two  tubulures.  The  .tubes  A  and  B  pass  through  these 
tubulures,  and  are  fixed  by  caoutchouc  collars.  The  tube  containing  vapour, 
B,  is  connected  with  a  flask,  a.,  by  means  of  a  brass  three-way  tube,  O.  The 
third  limb  of  this  tube  is  connected  with  a  drying  tube,  D,  containing 
pumice  charged  with  sulphuric  acid,  which  is  connected  with  the  air-pump. 


-357]      Tension  of  Aqueous    Vapour  above   lOO  degrees.         327 

When  the  flask  a  contains  some  water,  a  small  portion  is  distilled  into  B 
by  gently  heating  the  flask.  Exhausting,  then,  by  means  of  the  air-pump, 
the  water  distils  continuously  from  the  flask  and  from  the  barometric  tube 
towards  D,  which  condenses  the  vapour.  After  having  vaporised  some 
quantity  of  water,  and  when  it  is  thought  that  the  air  in  the  tube  is  with- 
drawn, the  capillary  tube  which  connects  B  with  the  three-way  tube  is  sealed. 
The  tube  B  being  thus  closed,  it  is  experimented  with  as  in  Dalton's  method. 

The  drum,  MN,  being  filled  with  water,  is  gently  heated  by  a  spirit  lamp, 
which  is  screened  from  the  tubes  by  a  wooden  board.  By  means  of  a 
stirrer,  K,  all  parts  of  the  liquid  are  kept  at  the  same  temperature.  In  the 
side  of  the  drum  is  a  glass  window,  through  which  the  height  of  the  mercury 
in  the  tubes  can  be  read  off  by  means  of  a  cathetometer  ;  from  the  difference 
in  these  heights,  reduced  to  zero,  the  tension  of  vapour  is  deduced.  By 
means  of  this  apparatus,  the  elastic  force  of  vapour  between  0°  and  50°  has 
been  determined  with  accuracy. 


F.s    S25 


357.   Tension  of  aqueous  vapour  above  one  hundred  degrees. — Two 

methods  have  been  employed  for  determining  the  tension  of  aqueous  vapour 
at  temperatures  above  100°;  the  one  by  Dulong  and  Arago,  in  1830,  and  the 
other  by  Regnault,  in  1844. 

Fig.  325  represents  a  vertical  section  of  the  apparatus  used  by  Dulong 
and  Arago.  It  consisted  of  a  copper  boiler,  k,  with  very  thick  sides,  and  of 
about  20  gallons'  capacity.  Two  gun-barrels,  a,  of  which  only  one  is  seen  in 
the  drawing,  were  firmly  fixed  in  the  sides  of  the  boiler,  and  plunged  in  the 
water.  The  gun-barrels  were  closed  below,  and  contained  mercury,  in  which 
were  placed  thermometers,  /,  indicating  the  temperature  of  the  water  and  of 
the  vapour.  The  tension  of  the  vapour  was  measured  by  means  of  a  mano- 
meter with  compressed  air,  ;//,  previously  graduated  (184)  and  fitted  into 
an  iron  vessel,  d^  filled  with  mercury.     In  order  to  see  the  height  of  the 


328 


On  Heat. 


[357- 


mercury  in  the  vessel,  it  was  connected  above  and  below  with  a  glass  tube,  ;?, 
in  which  the  level  was  always  the  same  as  in  the  bath.  A  copper  tube,  i, 
connected  the  upper  part  of  the  vessel,  d,  with  a  vertical  tube,  c,  fitted  in  the 
boiler.  The  tube  /  and  the  upper  part  of  the  bath  d  were  filled  with  water, 
which  was  kept  cool  by  means  of  a  current  of  cold  water  flowing  from  a 
reservoir,  and  circulating  through  the  tube  b. 

The  vapour  which  was  disengaged  from  the  tube  c  e.xerted  a  pressure 
on  the  water  of  the  tube  /  ;  this  pressure  was  transmitted  to  the  water  and 
to  the  mercury  in  the  bath  d^  and  the  mercury  rose  in  the  manometer.  By 
noting  on  the  manometer  the  pressures  corresponding  to  each  degree  of  the 
thermometer,  Dulong  and  Arago  were  able  to  make  a  direct  measurement 
of  the  tension  up  to  24  atmospheres,  and  the  tension  from  this  pressure  to 
50  atmospheres  was  determined  by  calculation. 

358.  Tension  of  vapour  below  and  above  one  hundred  degrees. — 
Regnault  devised  a  method  by  which  the  tension  of  vapour  may  be  measured 


Fig.  326. 

at  temperatures  either  below  or  above  100°.  It  depends  on  the  principle 
that  when  a  liquid  boils,  the  tension  of  the  vapour  is  equal  to  the  pressure 
it  supports  (363).  If,  therefore,  the  temperature  and  the  correspondmg 
pressure  are  known,  the  question  is  solved,  and  the  method  merely  consists 
in  causing  water  to  boil  in  a  vessel  under  a  given  pressure,  and  measuring 
the  corresponding  temperature. 

The  apparatus  consists  of  a  copper  retort,  C  (fig.  326),  hermetically  sealed 
and  about  two-thirds  full  of  water.    In  the  cover  there  are  four  thermometers, 


358] 


Table  of  Tensions  of  Aqueous    Vapour. 


two  of  which  just  dip  into  the  water,  and  two  descend  ahiiost  to  the  bottom. 
By  means  of  a  tube,  AB,  the  retort  C  is  connected  with  a  glass  globe,  M,  of 
about  6  gallons'  capacity,  and  full  of  air.  The  tube  AB  passes  through  a 
metal  cylinder,  D,  through  which  a,  current  of  cold  water  is  constantly 
tlowing  from  the  reservoir  E.  To  the  upper  part  of  the  globe  a  tube  with 
two  branches  is  attached,  one  of  which  is  connected  with  a  manometer,  O  ; 
the  other  tube,  HH',  which  is  of  lead,  can  be  attached  either  to  an  exhaust- 
ing or  a  condensing  air-pump,  according  as  the  air  in  the  globe  is  to  be  rare- 
fied or  condensed.  The  reservoir  K,  in  which  is  the  globe,  contains  water 
at  the  temperature  of  the  surrounding  air. 

If  the  elastic  force  of  aqueous  vapour  below  ioo°  is  to  be  measured,  the 
end  H'  of  the  lead  pipe  is  connected  with  the  plate  of  the  air-pump,  and 
the  air  in  the  globe  M,  and  consequently  that  in  the  retort  C,  is  rarefied. 
The  retort  being  gently  heated,  the  water  begins  to  boil  at  a  temperature 
below  ioo°,  in  consequence  of  the  diminished  pressure.  And  since  the  vapour 
is  condensed  in  the  tube  AB,  which  is  always  cool,  the  pressure  originally 
indicated  by  the  manometer  does  not  increase,  and  therefore  the  tension  of 
the  vapour  during  ebullition  remains  equal  to  the  pressure  on  the  liquid. 

A  little  air  is  then  allowed  to  enter  ;  this  alters  the  pressure,  and  the 
liquid  boils  at  a  new  temperature  ;  both  these  are  read  off,  and  the  experi- 
ment repeated  as  often  as  desired  up  to  ioo°. 

In  order  to  measure  the  tension  above  ioo°,  the  tube  H'  is  connected 
with  a  condensing  pump,  by  means  of  which  the  air  in  the  globe  M  and  that 
in  the  vessel  C  are  exposed  to  successive  pressures,  higher  than  the  atmo- 
sphere. The  ebullition  is  retarded  (367),  and  it  is  only  necessary  to  observe 
the  difference  in  the  height  of  the  mercury  in  the  two  tubes  of  the  mano- 
meter O,  and  the  corresponding  temperature,  in  order  to  obtain  the  tension 
for  a  given  temperature.  The  following  tables  by  Regnault  give  the  tension 
of  acjueous  vapour  from  —  10°  to  104°  : — 


Tensiojis  of  aqueous  vapour  from 

-  10°  to  104°  C. 

Tempe- 

Tensions in 

Tempe- 

Tensions in 

Tempe- 

Tensions in 

Tempe- 

Tensions in 

ratures 

millimetres 

ratures 

millimetres 

ratures 

millimetres 

ratures 

millimetres 

-10° 

2-078 

1       12° 

10-457 

29° 

29-782 

90° 

525-45 

8 

2-456 

13 

1 1  -062 

30 

31-548       I 

91 

545-78 

6 

2-890 

14 

1 1  -906 

31 

33-405       1 

92 

566-76 

4 

3-387 

i       15 

12-699 

32 

35-359 

93 

588-41 

2 

3'955 

16 

13-635 

33 

37-410 

94 

610-74 

0 

4-600 

i       17 

14-421 

34 

39-565 

95 

633-78 

H-     I 

4-940 

1       ^8 

15-357 

35 

41-827 

96 

657-54 

2 

5-302 

1       19 

16-346 

40 

54-906 

97 

682-03 

3 

5-687 

j       20 

17-391 

45 

71-391 

98 

707-26 

4 

6-097 

..    21 

18-495 

50 

91-982 

98-5 

720-15 

5 

6-534 

22 

19-659 

55 

117-479 

99-0 

733-91 

6 

6-998 

-3 

20-888 

60 

148-791 

99-5 

746-50 

7 

7-492 

;        -4 

22-184 

65 

186-945 

loo-o 

760-00 

8 

S-ot7 

25 

23-550 

70 

233-093 

100-5 

773-71 

9 

8-574 

'        26 

24-998 

75 

288-517 

loi-o 

787-63 

10 

9-165 

I,       27 

26-505 

80 

354-643 

I02-0 

816-17 

II 

9-792 

:     28 

28-101 

85 

433-41 

104-0 

875-69 

330 


On  Heat. 


[358- 


Tensions  in  atmospheres  from  loo 

'  to  230-9°. 

1 

Number 

Number 

Number 

Number 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

spheres 

spheres 

spheres 

spheres 

ioo-o° 

I 

170-8° 

8 

198-8° 

.5 

217-9° 

22 

I  12-2 

i         '-' 

175-8 

9 

201-9 

16 

220-3 

23 

I20-6 

2 

180-3 

10 

204-9 

17 

222-5 

24 

133-9 

3 

184-5 

II 

207-7 

18 

224-7 

25 

I44-0 

4 

188-4 

12 

210-4 

19 

226-8 

26 

152-2 

5 

192-1 

13 

213-0 

20 

228-9 

27 

156-2 

1      6 

195-5 

14 

215-5 

21 

230-9 

28 

165-3 

7 

In  the  second  table  the  numbers  were  obtained  by  direct  observation 
up  to  24  atmospheres  ;  the  others  were  calculated  by  the  aid  of  a  formula  of 
interpolation. 

This  table  and  the  one  next  following  show  that  the  elastic  force  increases 
much  more  rapidly  than  the  temperature.  It  has  been  attempted  to  express 
the  relation  between  them  by  formukt,  but  none  of  the  formula;  seems  to  have 
the  simplicity  which  characterises  a  true  law. 

359.  Tension  of  the  vapours  of  different  liquids. — Regnault  deter- 
mined the  elastic  force,  at  various  temperatures,  of  a  certain  number  of 
liquids  which  are  given  in  the  following  table  : — 


Liquids 

Tempe- 
ratures 

Tensions  in 
millimetres 

Liquids 

Tempe- 
ratures 

millimetres 

( 

0° 

0-02 

f 

-20° 

68 

Mercury     . 

50 

o-ii 

Ether 

1 

0 

182 

( 

100 

0-74 

I 

60 

1728 

0 

13 

100 

4950 

Alcohol.     . 

50 

100 

-20 

220 

1695 

43 

Sulphurous 
acid 

1 

-20 

0 

60 

479 
1165 
8124 

Bisulphide       ] 

0 

132 

{ 

-30 

876 

of  carbon       1 

60 

1 164 

Ammonia . 

0 

3163 

100 

3329 

^ 

30 

8832 

360.  Tension  of  the  vapours  of  mixed  liquids. — Regnault's  experiments 
on  the  tension  of  the  vapour  of  mixed  liquids  prove  that  (i.)  when  two  liquids 
exert  no  solvent  action  on  each  other — such  as  water  and  bisulphide  of  carbon, 
or  water  and  benzole — the  tension  of  the  vapour  which  rises  from  them  is 
nearly  equal  to  the  sum  of  the  tensions  of  the  two  separate  'liquids  at  the 
same  temperature  ;  (ii.)  with  water  and  ether.,  which  partially  dissolve  each 
other,  the  tension  of  the  mixture  is  much  less  than  the  sum  of  the  tensions 
of  the  separate  liquids,  being  scarcely  equal  to  that  of  the  ether  alone  ; 
(iii.)  when  two  liquids  dissolve  in  all  proportions,  as  ether  and  bisulphide  of 
carbon,  or  water  and  alcohol,  the  tension  of  the  vapour  of  the  mixed  liquids 
is  intermediate  between  the  tensions  of  the  separate  liquids. 


362J 


Evaporation.      Causes  luliich  Accelerate  it. 


331 


Wiillner  has  shown  that  for  weak  sokitions  the  tension  of  aqueous  vapour 
emitted  from  a  sahne  solution,  as  compared  with  that  of  pure  water,  is 
diminished  by  an  amount  proportional  to  the  quantity  of  anhydrous  salt  dis- 
solved, when  the  salt  crystallises  without  water  or  yields  efflorescent  crystals  : 
when  the  salt  is  deliquescent,  or  has  a  powerful  attraction  for  water,  the  re- 
duction of  tension  is  proportional  to  the  quantity  of  crystallised  salt. 

361.  Tension  in  two  communicatingr  vessels  at  different  tempera- 
tures.— When  two  vessels  containing  the  same  liquid,  but  at  different  tem- 
peratures, are 
connected  with 
each  other,  the 
elastic  force  is 
not  that  corre- 
sponding to  the 
mean  of  the  two 
temperatures,  as 
would  naturally 
be  supposed. 
Thus,  if  there 
are  two  globes 
(fig.  327),  one,  A, 
containing  water 
kept  at  zero  by 
means  of  melting 
ice,  the  other,  B, 

containing  water  at  100°,  the  tension,  as  long  as  the  globes  are  not  con- 
nected, is  4  to  6  millimetres  in  the  first,  and  760  millimetres  in  the  second. 
But  when  they  are  connected  by  opening  the  stopcock  C,  the  vapour  in  the 
globe  B,  from  its  greater  tension,  passes  into  the  other  globe,  and  is  there 
condensed,  so  that  the  vapour  in  B  can  never  reach  a  higher  pressure  than 
that  in  the  globe  A.  The  liquid  simply  distils  from  B  towards  A  without 
any  increase  of  tension. 

From  this  experiment  the  general  principle  may  be  deduced  that  luhen 
two  vessels  containing  the  same  liquid,  but  at  different  temperatures,  are  con- 
nected, tlie  pressure  is  identical  in  both  vessels,  atzd  is  the  same  as  that  corre- 
sponding to  the  lower  temperature.  An  application  of  this  principle  has  been 
made  by  Watt  in  the  condenser  of  the  steam-engine. 

362.  evaporation.  Causes  which  accelerate  it. — Evaporation,  as  has 
been  already  stated  (349),  is  the  slow  production  of  vapour  at  the  surface  of 
a  liquid.  It  is  in  consequence  of  this  evaporation  that  wet  clothes  dry  when 
exposed  to  the  air,  and  that  open  vessels  containing  water  become  empty. 
The  vapours  which,  rising  in  the  atmosphere,  condense,  and,  becoming  clouds, 
fall  as  rain,  are  due  to  the  evaporation  from  seas,  lakes,  rivers,  and  the  earth. 

Four  causes  influence  the  rapidity  of  the  evaporation  of  a  liquid  :  i.  the 
temperature  ;  ii.  the  quantity  of  the  same  vapour  in  the  surrounding  atmo- 
sphere ;  iii.  the  renewal  of  this  atmosphere  ;  iv.  the  extent  of  the  surface  of 
evaporation. 

Increase  of  temperature  accelerates  the  evaporation  by  increasing  the 
elastic  force  of  the  vapours. 


33: 


On  Heat. 


[362- 


In  order  to  understand  the  intluence  of  the  second  cause,  it  is  to  be  ob- 
served that  no  evaporation  could  take  place  in  a  space  already  saturated 
with  vapour  of  the  same  licpid,  and  that  it  would  reach  its  maximum  in 
air  completely  freed  from  this  vapour.  It  therefore  follows  that  between 
these  two  extremes,  the  rapidity  of  evaporation  varies  according  as  the 
surrounding  atmosphere  is  already  more  or  less  charged  with  the  same 
vapour. 

The  effect  of  the  renewal  of  this  atmosphere  is  similarly  explained  ;  for 
if  the  air  or  gas,  which  surrounds  the  liquid,  is  not  renewed,  it  soon  becomes 
saturated,  and  evaporation  ceases.  Dalton  found  that  the  ratios  of  the 
evaporation  in  a  feeble,  medium,  and  strong  draught  were  respectively  as 
270  :  347  :  424.  He  also  observed  that  the  quantity  evaporated  in  perfectly 
dry,  almost  still  air,  at  a  temperature  of  20°,  was  equivalent  to  o-i  of  a  gramme 
on  a  square  decimetre  of  surface  in  a  minute. 
The  effect  of  the  fourth  cause  is  self-evident. 

Vegetation  exercises  a  great  influence  on  evaporation.  Schiibler  found 
that  the  evaporation  from  a  space  covered  with  meadow  grass,  in  the  most 
vigorous  stage  of  its  growth,  was  thrice  as  rapid  as  that  from  an  adjacent 
surface  of  water.     As  the  plants  ripened  the  evaporation  diminished. 

363.  Xiaws  of  ebullition — Ebullition., 
or  boiling,  is  the  rapid  production  of 
elastic  bubbles  of  vapour  in  the  mass  of  a 
liquid  itself. 

When  a  liquid,  water  for  example,  is 
heated  at  the  lower  part  of  a  vessel,  the 
first  bubbles  are  due  to  the  disengagement 
of  air  which  had  previously  been  absorbed. 
Small  bubbles  of  vapour  then  begin  to 
rise  from  the  heated  parts  of  the  sides, 
but  as  they  pass  through  the  upper  layers, 
the  temperature  of  which  is  lower,  they 
condense  before  reaching  the  surface.  The 
formation  and  successive  condensation  of 
these  first  bubbles  occasion  the  singitig 
noticed  in  liquids  before  they  begin  to 
boil.  Lastly,  large  bubbles  rise  and  burst 
on  the  surface,  and  this  constitutes  the 
phenomenon  of  ebullition  (fig.  328). 

The  laws  of  ebullition  have  been 
determined  experimentally,  and  are  as 
follows  : — 

I.  Tlic  tcmpe7'atiire  of  ebullition  or  the  boiling  point  increases  with  the 
pressure. 

II.  For  a  given  pressure  ebullition  begins  at  a  certain  te7nperature,  which 
varies  in  differ e7tt  liquids.,  but  which,  for  equal  pressures,  is  always  the  same 
in  the  same  liquid. 

III.  Whatever  be  the  intensity  of  the  source  of  heat,  as  soon  as  ebullition 
begins  the  temperature  of  the  liquid  remains  statiottary. 


Fig  328 


*J  1  UeorcticaL  HxpU 
Boiling  points 

ination  c 
aide?-  the 

]/  iLvaporation  and  h mil 
pressure  ofj6o  niillinietres. 

Lition. 

Nitrous  oxide 

■     -93° 

Butyric  acid 

156° 

Carbonic  acid 

.      -80 

Turpentine 

157 

Ammonia 

•     -39 

Aniline 

182 

Chloride  of  methyle 

•      -23 

Iodine 

200 

Cyanogen 

-20 

Naphthaline 

217 

Sulphurous  acid    . 

-  10 

Benzoic  acid     . 

261 

Chloride  of  ethyle 

.     +  ir 

Phosphorus 

290 

Aldehyde 

21 

Diphenylamine 

310 

Ether     . 

21 

Strong  sulphuric  acid 

318 

Bisulphide  of  carbon 

47 

Phenanthrene   . 

340 

Acetone 

•         56 

Mercury    . 

-358 

Bromine 

■         58 

Phosphate  of  phenyl 

407 

Methylic  alcohol  . 

66 

Arsenic 

437 

Alcohol 

•         78 

Sulphur     . 

448 

Benzole 

80 

Phosphorus  pentasulphide 

530 

Distilled  water 

100 

Selenium  . 

665 

Acetic  acid    . 

117 

Cadmium  . 

746 

Amylic  alcohol 

131 

Zinc  .... 

940 

Propionic  acid 

•       137 

Kopp  has  pointed  out  that  in  homologous  chemical  compounds  the  same 
difference  in  chemical  composition  frequently  involves  the  same  difference 
of  boiling  points  ;  and  he  has  shown  that  in  a  very  extensive  series  of  com- 
pounds, the  fatty  acids  for  instance,  the  difference  of  CH'-  is  attended  by 
a  difference  of  19°  C.  in  the  boiling  poini.  In  other  series  of  homologous 
compounds,  the  corresponding  difference  in  the  boiling  point  is  30°,  and  in 
others  again  24°. 

364.  Theoretical  explanation  of  evaporation  and  ebullition. — From 
what  has  been  said  about  the  nature  of  the  motion  of  the  molecules  in  liquids 
(292),  it  may  readily  be  conceived  that  in  the  great  variety  of  these  motions, 
the  case  occurs  in  which,  by  a  fortuitous  concurrence  of  the  progressive, 
vibratory,  and  rotatory  motions,  a  molecule  is  projected  from  the  surface  of 
the  liquid  with  such  force  that  it  overleaps  the  sphere  of  the  action  of  its  cir- 
cumjacent molecules,  before,  by  their  attraction,  it  has  lost  its  initial  velocity  ; 
and  that  it  then  flies  into  the  space  above  the  liquid. 

Let  us  first  suppose  this  place  limited  and  originally  vacuous ;  it  gradu- 
ally fills  with  the  propelled  molecules,  which  act  like  a  gas  and  in  their 
motion  are  driven  against  the  sides  of  the  envelope.  One  of  these  sides, 
however,  is  the  surface  of  the  liquid  itself,  and  a  molecule  when  it  strikes 
against  this  surface  will  not  in  general  be  repelled,  but  will  be  retained  by  the 
attraction  which  the  adjacent  ones  exert.  Equilibrium  will  be  established 
when  as  many  molecules  are  dispersed  in  the  surrounding  space  as,  on  the 
average,  impinge  against  the  surface  and  are  retained  by  it  in  the  unit  of 
time.  This  state  of  equilibrium  is  not,  however,  one  of  rest,  in  which  eva- 
poration has  ceased,  but  a  condition  in  which  evaporation  and  condensation, 
which  are  equally  strong,  continually  compensate  each  other. 

The  density  of  a  vapour  depends  on  the  number  of  molecules  which  are 


334  On  Heat.  [364- 

repelled  in  a  given  time,  and  this  manifestly  depends  on  the  motion  of  the 
molecules  in  the  liquid,  and  therefore  on  the  temperature. 

What  has  been  said  respecting  the  surface  of  the  liquid  clearly  applies  to 
the  other  sides  of  the  vessel  within  which  the  vapour  is  formed  :  some  vapour 
is  condensed,  this  is  subject  to  evaporation,  and  a  condition  ultimately  occurs 
in  which  evaporation  and  condensation  are  equal.  The  quantity  of  vapour 
necessary  for  this  depends  on  the  density  of  vapour  in  the  closed  space,  on 
the  temperature  of  the  vapour  and  of  the  sides  of  the  vessel,  and  on  the  force 
with  which  this  attracts  the  molecules.  The  maximum  will  be  reached  \\'hen 
the  sides  are  covered  v^nth  a  layer  of  liquid,  which  then  acts  like  the  free 
surface  of  a  liquid. 

In  the  interior  of  a  liquid  it  may  happen  that  the  molecules  repel  each 
other  with  such  force  as  to  momentarily  destroy  the  coherence  of  the  mass. 
The  small  vacuous  space  which  is  thereby  formed  is  entirely  surrounded  by 
a  medium  which  does  not  allow  of  the  passage  of  the  repelled  molecules. 
Hence  it  cannot  increase  and  maintain  itself  as  a  bubble  of  vapour,  unless  so 
many  molecules  are  projected  from  the  inner  sides  that  the  internal  pressure 
which  thereby  results  can  balance  the  external  pressure  which  tends  to 
condense  the  bubble.  The  expansive  force  of  the  enclosed  vapour  must 
therefore  be  so  much  the  greater,  the  higher  the  external  pressure  on  the 
liquid,  and  thus  we  see  the  influence  of  pressure  on  the  temperature  of 
boiling. 

365.  Influence  of  substances  in  solution  on  the  boiling  point. — The 
ebullition  of  a  liquid  is  the  more  retarded  the  greater  the  quantity  of  any 
substance  it  may  contain  in  solution,  provided  that  the  substance  be  not 
volatile,  or,  at  all  events,  be  less  volatile  than  the  liquid  itself  Water,  which 
boils  at  100°  when  pure,  boils  at  the  following  temperatures  when  saturated 
with  different  salts  : — 

Water  saturated  with  common  salt  .         .         boils  at  102° 

„  ,,  nitrate  of  potassium  .,       116 

„  „  carbonate  of  potassium  „       135 

„  „  chloride  of  calcium  „       179 

Acids  in  solution  present  analogous  results  ;  but  substances  merely 
mechanically  suspended,  such  as  earthy  matters,  bran,  wooden  shavings,  &c., 
do  not  affect  the  boiling  point. 

Absorbed  air  exerts  a  very  marked  influence  on  the  boiling  point  of 
water.  Deluc  first  observed  that  water  freed  from  air  by  ebullition,  and 
placed  in  a  flask  with  a  long  neck,  could  be  raised  to  112°  without  boiling. 
M.  Donny  examined  this  phenomenon  by  means  of  the  apparatus  depicted  in 


figure  329.     It  consists  of  a  glass  tube  CAB,  bent  at  one  end  and  closed  at 
C,  while  the  other  is  blown  into  a  pear-shaped  bulb,  B,  drawn  out  to  a 


-366]  Influence  of  Nature  of  Vessel  on  the  Boiling  Point.     335 

point.  The  tube  contains  water  which  is  boiled  until  all  air  is  expelled,  and 
the  open  end  is  hermetically  sealed.  By  inclining  the  tube  the  water  passes 
into  the  bent  end  CA  ;  this  end  being  placed  in  a  bath  of  chloride  of  calcium, 
the  temperature  maybe  raised  to  130°  without  any  signs  of  boiling.  At  138° 
the  liquid  is  suddenly  converted  into  steam  and  the  water  is  thrown  over 
into  the  bulb,  which  is  smashed  if  not  sufficiently  strong. 

Boiled-out  water,  covered  with  a  layer  of  oil,  may  be  raised  to  120°  with- 
out boiling,  but  above  this  temperature  it  suddenly  begins  to  boil,  and  with 
almost  explosive  violence. 

When  a  liquid  is  suspended  in  another  of  the  same  specific  gravity,  but 
of  higher  boiling  point,  with  which  it  does  not  mix,  it  may  be  raised  far  be- 
yond its  boiling  point  without  the  formation  of  a  trace  of  vapour.  Dufour 
has  made  a  number  of  valuable  experiments  on  this  subject  ;  he  used  in  the 
case  of  water  a  mixture  of  oil  of  cloves  and  linseed  oil,  and  placed  in  it 
globules  of  water,  and  then  gradually  heated  the  oil  ;  in  this  way  ebullition 
rarely  set  in  below  110°  or  115°  ;  very  commonly  globules  of  10  millimetres' 
diameter  reached  a  temperature  of  120°  or  130°,  while  very  small  globules  of 
I  to  3  millimetres  reach  the  temperature  of  175°,  a  temperature  at  which 
the  tension  of  vapour  on  a  free  surface  is  8  or  9  atmospheres. 

At  these  high  temperatures  the  contact  of  a  solid  body,  or  the  production 
of  gas  bubbles  in  the  liquid,  occasioned  a  sudden  vaporisation  of  the  globule, 
accompanied  by  a  sound  like  the  hissing  of  a  hot  iron  in  water. 

Saturated  aqueous  solutions  of  sulphate  of  copper,  chloride  of  sodium,, 
&c.,  remain  liquid  at  a  temperature  far  beyond  their  boiling  point,  when 
immersed  in  melted  stearic  acid.  In  like  manner,  globules  of  chloroform 
(which  boils  at  61°),  suspended  in  a  solution  of  chloride  of  zinc,  could  be 
heated  to  97°  or  98°  without  boiling. 

It  is  a  disputed  question  as  to  what  is  the  temperature  of  the  vapour 
from  boiling  saturated  saline  solutions.  It  has  been  stated  by  Rudberg  to 
be  that  of  pure  water  boiling  under  the  same  pressure.  The  most  recent 
experiments  of  Magnus  seem  to  show,  however,  that  this  is  not  the  case,  but 
that  the  vapour  of  boiling  solutions  is  hotter  than  that  of  pure  water  ;  and 
that  the  temperature  rises  as  the  solutions  become  more  concentrated,  and 
therefore  boil  at  higher  temperatures.  Nevertheless,  the  vapour  was  always 
found  somewhat  cooler  than  the  mass  of  the  boiling  solution,  and  the  differ- 
ence was  greater  at  high  than  at  low  temperatures. 

The  boiling  point  of  a  liquid  is  usually  lowered  when  it  is  mixed  with  a 
more  volatile  liquid  than  itself,  but  raised  when  it  contains  one  which  is  less 
volatile.  Thus  a  mixture  of  two  parts  alcohol  and  one  of  water  boils  at  83°, 
a  mixture  of  two  parts  of  bisulphide  of  carbon  and  one  part  of  ether  boils 
at  38°.  In  some  cases  the  boiling  point  of  a  mixture  is  lower  than  that  of 
either  of  its  constituents.  A  mixture  of  water  and  bisulphide  boils  at  43°, 
the  boiling  point  of  the  latter  being  46°.  On  this  depends  the  following 
curious  experiment.  If  water  and  bisulphide  of  carbon,  both  at  the  tempe- 
rature 45°,  are  mixed  together,  the  mixture  at  once  begins  to  boil  briskly. 

366.  Influence  of  the  nature  of  the  vessel  on  the  boiling'  point.— 
Gay-Lussac  observed  that  water  in  a  glass  vessel  required  a  higher  tempera- 
ture for  ebullition  than  in  a  metal  one.  Taking  the  temperature  of  boiling 
water  in  a  copper  vessel  at    100°,  its  boiling  point  in  a  glass  vessel  was. 


^^6  On  Heat,  [366- 

found  to  be  loi'^  ;  and  if  the  glass  vessel  had  been  previously  cleaned  by 
means  of  sulphuric  acid  and  of  potass,  the  temperature  would  rise  to  105°, 

or  even  to  106°,  before  ebullition  com- 
menced. A  piece  of  metal  placed  in 
the  bottom  of  the  vessel  was  always 
sufficient  to  lower  the  temperature  to 
100°,  and  at  the  same  time  to  prevent 
the  violent  concussions  which  accom- 
pany the  ebullition  of  saline  or  acid 
solutions  in  glass  vessels.  Whatever 
be  the  boiling  point  of  water,  the  tem- 
perature of  its  vapour  is  uninfluenced 
by  the  substance  of  the  vessels. 

367.  Influence  of  pressure  en 
the  boiling-  point. — We  see  from  the 
table  of  tensions  (35S)  that  at  100^, 
the  temperature  at  which  water  boils 
under  a  pressure  of  760  millimetres, 
which  is  that  of  the  atmosphere,  aque- 
ous vapour  has  a  tension  exactly  equal 
to  this  pressure.  This  principle  is 
general,  and  may  be  thus  enunciated  : 
A  liquid  boils  zvhen  the  tensio?!  of  its 
vapour  is  equal  to  tJie  pressure  it  sup- 
ports. Consequently,  as  the  pressure 
increases  or  diminishes,  the  tension  of  the  vapour,  and  therefore  the  tempe- 
rature necessary  for  ebullition,  must  increase  or  diminish.  Hence  a  liquid 
has,  strictly  speaking,  an  indefinite  number  of  boiling  points. 

In  order  to  show  that  the  boiling  point  is  lower  under  diminished  pres- 
sure, a  small  dish  containing  water  at  30°  is  placed  under  the  receiver  of  an 
air-pump,  which  is  then  exhausted.  The  liquid  soon  begins  to  boil,  the 
vapour  formed  being  pumped  out  as  rapidly  as  it  is  generated. 

A  paradoxical  but  very  simple  experiment  also  well  illustrates  the  de- 
pendence of  the  boiling  point  on  the  pressure.  In  a  glass  flask,  water  is 
boiled  for  some  time,  and  when  all  air  has  been  expelled  by  the  steam,  the 
flask  is  closed  by  a  cork  and  inverted,  as  shown  in  fig.  330.  If  the  bottom 
is  then  cooled  by  a  stream  of  cold  water  from  a  sponge,  the  water  begins  to 
boil  again.  This  arises  from  the  condensation  of  the  steam  above  the  sur- 
face of  the  water,  by  which  a  partial  vacuum  is  produced. 

It  is  in  consequence  of  this  diminution  of  pressure  that  liquids  boil  on 
high  mountains  at  lower  temperatures.  On  Mont  Blanc,  for  example,  water 
boils  at  84°,  and  at  Quito  at  90°. 

On  the  more  rapid  evaporation  of  water  under  feeble  pressures  is  based 
the  use  of  the  air-pump  in  concentrating  those  solutions  which  either  cannot 
bear  a  high  degree  of  heat,  or  which  can  be  more  cheaply  evaporated  in  an 
exhausted  space.  Howard  made  a  most  important  and  useful  application  of 
this  principle  in  the  manufacture  of  sugar.  The  syrup,  in  his  method,  is 
enclosed  in  an  air-tight  vessel,  which  is  exhausted  by  a  steam-engine.  The 
evaporation  consequently  goes  on  at  a  lower  temperature,  which  secures  the 


Fig.  330. 


Fig.  3^ 


-369]     Measurement  of  Heights  by  the  Boiling  Point.  337 

syrup  from  injury.     The  same  plan  is  adopted  in  evaporating  the  juice  of 
certain  plants  used  in  preparing  medicinal  extracts. 

On  the  other  hand,  boiling  is  retarded  by  increasing  the  pressure  : 
under  the  pressure  of  two  atmospheres,  for  example,  water  only  boils  at  1 20°-6. 

368.  Franklin's  experiment. — The  influence  of  pressure  on  boiling  may 
further  be  illustrated  by  means  of  an  experiment  originally  made  by  Frank- 
lin. The  apparatus  consists  of  a  bulb,  cc,  and  a  tube,  (5,  joined  by  a  tube  of 
smaller  dimensions  (fig.  331).     The 

tube  b  is  drawn  out,  and  the  appa- 
ratus filled  with  water,  which  is 
then  in  part  boiled  away  by  means 
of  a  spirit  lamp.  When  it  has 
been  boiled  sufficiently  long  to 
expel  all  the  air,  the  tube  b  is  sealed. 
There  is  then  a  vacuum  in  the 
apparatus,  or  rather  there  is  a  pres- 
sure due  to  the  tension  of  acjueous 
vapour,  which  at  ordinary  tempe- 
ratures is  very  small.  Consequently,  if  the  bulb,  a,  be  placed  in  the  hand,  the 
heat  is  sufficient  to  produce  a  pressure  which  drives  the  water  into  the  tube, 
b,  and  causes  a  brisk  ebullition. 

369.  measurement  of  heights  by  the  boil-  ^  -.  ' 
Ingr  point.— From  the  connection  between  the 
boiling  point  of  water  and  the  pressure,  the 
heights  of  mountains  may  be  measured  by  the 
thermometer  instead  of  by  the  barometer.  Sup- 
pose, for  example,  it  is  found  that  water  boils 
on  the  summit  of  a  mountain  at  90°,  and  at  its 
base  at  98°;  at  these  temperatures  the  elastic 
force  or  tension  of  the  vapour  is  equal  to  that  of 
the  pressure  on  the  liquid  ;  that  is,  to  the  pres- 
sure of  the  atmosphere  at  the  two  places  re- 
spectively. Now,  the  tensions  of  aqueous  vapour 
for  various  temperatures  have  been  determined, 
and  accordingly  the  tensions  corresponding  to 
the  above  temperatures  are  sought  in  the  tables. 
These  numbers  represent  the  atmospheric  pres- 
sures at  the  two  places  ;  in  other  words,  they 
give  the  barometric  heights,  and  from  these  the 
height  of  the  mountain  may  be  calculated  by 
the  method  already  given  (178).  An  ascent  of 
about  1,080  feet  produces  a  diminution  of  1°  C. 
in  the  boilmg  point. 

The  instruments  used  for  this  purpose  are 
called  thermo-barometers  or  hypsometers,  and 
were  first  applied  by  Wollaston.  They  consist  es- 
sentially of  a  small  metallic  vessel  for  boiling  water 
(fig.  332),  fitted  with  very  delicate  thermometers, 
which  are  only  graduated  from  80°  to  100^  ;  so  that,  as  each  degree  occupies 

z 


33^ 


On  Heat. 


[369- 


a  considerable  space  on  the  scale,  the  loths,  and  even  the  looths,  of  a 
degree  may  be  estimated,  and  thus  it  is  possible  to  determine  the  height  of 
a  place  by  means  of  the  boiling  point  to  within  about  lo  feet. 

370.  Formation  of  vapour  in  closed  tubes. — We  have  hitherto  con- 
sidered vapours  as  being  produced  in  an  indefinite  space,  or  where  they 
could  expand  freely,  and  it  is  only  under  this  condition  that  boiling  can 
take  place.  In  a  closed  vessel  the  vapours  produced  finding  no  issue,  their 
tension  and  their  density  increase  with  the  temperature,  but  that  rapid  disen- 
gagement of  vapour  which  constitutes  boiling  is  impossible.  Hence,  while 
the  temperature  of  a  liquid  in  an  open  vessel  can  never  exceed  that  of  boil- 
ing, in  a  closed  vessel  it  may  be  much  higher.  The  liquid  state  has, 
nevertheless,  a  limit  ;  for,  according  to  experiments  by  Cagniard- 
Latour,  if  either  water,  alcohol,  or  ether  be  placed  in  strong  glass 
tubes,  which  are  hermetically  sealed  after  the  air  has  been  ex- 
pelled by  boiling,  and  if  then  these  tubes  are  exposed  to  a 
sufficient  degree  of  heat,  a  moment  is  reached  at  which  the 
liquid  suddenly  disappears,  and  is  converted  into  vapour  at 
200°,  occupying  a  space  less  than  double  its  volume  in  the  liquid 
state,  its  tension  being  then  38  atmospheres. 

Alcohol  which  half  fills  a  tube  is  converted  into  vapour  at 
207°  C.  If  a  glass  tube  about  half  filled  with  water,  in  which 
some  carbonate  of  soda  has  been  dissolved,  to  diminish  the 
action  of  the  water  on  the  glass,  be  heated,  it  is  completely 
vaporised  at  about  the  temperature  of  melting  zinc. 

When  chloride  of  ethyle  is  heated  in  a  very  stout    sealed 

tube,  the  upper  surface  ceases  to  be  distinct  at  170°,  and  is 

replaced  by  an  ill-defined  nebulous  zone.     As  the  temperature 

rises  this  zone  increases  in  width  in  both  directions,  becoming 

m  at  the  same  time  more  transparent  ;  after  a  time  the  liquid  is 

^  I  completely  vaporised,  and  the  tube  becomes    transparent  and 

H  seemingly  empty.     On  cooling,  the  phenomena  are  reproduced  in 

opposite  order.     Similar  appearances  are  observed  on  heating 

ether  in  a  sealed  tube  at  190°. 

Andrews  made  a  series  of  observations  on  the  behaviour 
of  condensed  gases  at  different  temperatures,  by  means  of  an 
apparatus,  the  principal  features  of  which  are    represented  in 

fig-  333- 

The  pure  and  dry  gas  is  contained  in  a  tube  g,  which  is 
sealed  at  one  end,  and  the  gas  is  shut  in  by  a  thread  of  mer- 
cury.    The  tube  is  inserted  in  a  brass  end-piece,  E,  which  is 
firmly  screwed  on  a  strong  copper  tube,  R.     At  the  other  end  is 
a  similar  piece,  in  which  a  steel  screw  works,  perfect  tightness 
Fig.  333.         being  ensured  by  good  packing.     The  tube  is  full  of  water,  so 
that   by  turning  this  screw  the  pressure  on  the   enclosed  gas 
can   be  increased  up  to  500  atmospheres.      In  some  cases  the  projecting 
capillary  tube    is  bent  downwards,  so  that  it  can  be  placed  in  a  freezing 
mixture. 

Andrews  found  on  raising  liquid  carbonic  acid  in  such  a  tube  to  a  tempe- 
rature of  31°  C.  that  the  surface  of  demarcation  between  the  liquid  and  the 


-370] 


Formation  of  Vapour  in  Closed  Tubes. 


339 

gas  became  fainter,  lost  its  curvature,  and  gradually  disappeared.  The 
space  was  then  occupied  by  a  homogeneous  fluid,  which,  when  the  pressure 
was  suddenly  diminished,  or  the  temperature  slightly  lowered, 
exhibited  a  peculiar  appearance  of  moving  or  flickering  stride 
throughout  its  whole  mass.  Above  30°  no  apparent  liquefac- 
tion of  carbonic  anhydride,  or  separation  into  two  distinct 
forms  of  matter,  could  be  effected,  not  even  when  the  pressure 
of  400  atmospheres  was  applied. 

From  similar  observations  made  with  other  substances  it 
seems  that  there  exists  for  eveiy  liquid  a  temperature,  the 
critical  poittt  or  critical  temperature.  While  below  this  critical 
point  a  sudden  transition  from  gas  to  liquid  is  accompanied 
by  a  sudden  diminution  of  volume,  and  liquid  and  gas  are 
separated  by  a  sharp  line  of  demarcation,  above  this  critical 
point  the  change  is  connected  with  a  gradual  diminution  of 
volume,  and  is  quite  imperceptible.  The  condensation  can, 
indeed,  only  be  recognised  by  a  sudden  ebullition  when  the 
pressure  is  lessened.  Hence,  ordinary  condensation  is  only 
possible  at  a  temperature  below  the  critical  point,  and  it  is  not 
surprising,  therefore,  that  mere  pressure,  however  great,  should 
have  failed  to  liquefy  many  of  the  gases. 

The  phenomenon  of  the  critical  temperature  may  also  be 
conveniently  illustrated  by  the  following  arrangement  (fig.  334), 
which  is  also  well  adapted  for  projection  on  a  screen  by 
means  of  a  magic-lantern  for  lecture  purposes.  A  stout  glass  "^llilSili^ 
tube  about  2-5"""  wide  and  40*"'"  long,  contains  liquid  sulphurous  pig.  334. 
acid,  and  is  supported,  with  the  drawn-out  end  downwards,  in 
a  test-tube  by  means  of  a  wire  frame.  Pure  melted  paraffin  is  added  to 
about  lo''™  above  the  inner  tube.  The  whole  arrangement  is  suspended  in 
a  retort-holder,  and  heat  applied  with  a  spirit  lamp.  With  careful  manipula- 
tion there  is  no  danger,  and  the  course  of  the  phenomenon  is  readily  seen 
through  the  clear  paraffin. 

The  boiling  point  of  a  body  may  be  defined  as  the  temperature  above 
which  a  body  passes  into  the  state  of  gas,  not  only  on  the  surface  but  in  the 
body  of  the  liquid  ;  this  temperature  is  therefore  different  for  different 
pressures,  and  is  accordingl}'-  a  relative  magnitude.  The  absolute  boilino- 
point  is  the  temperature  at  which  a  body  is  converted  into  gas,  whatever 
be  the  pressure  ;  it  is  identical  with  the  critical  temperature.  Mendelejeff 
found  that  a  relation  existed  between  the  absolute  temperature  and  the 
capillarity  of  liquids.  Increase  of  temperature  diminishes  the  cohesion,  and 
therefore  the  capillarity  of  liquids.  The  capillarity  ultimately  vanishes 
and  the  temperature  at  which  this  takes  place  is  the  absolute  boiling 
point.     Some  of  them  are  very  low  ;  that  of  air,  for  instance,  is  -  158^. 

The  critical  pressure  is  that  at  which  condensation  takes  place  at  the 
critical  temperature,  and  the  volume  of  the  saturated  vapour  at  the  critical 
temperature,  and  under  the  critical  pressure,  is  called  the  critical  volume. 

A  vapour  may  be  defined  as  being  a  gas  at  any  temperature  below  its 
critical  point.  Hence  a  vapour  can  be  converted  into  a  liquid  by  pressure 
alone,  and  can  therefore  exist  in  the  pressure  of  its  own  liquid,  while  a  o-as 


340 


On  Heat. 


[370- 


requires  cooling  as  well  as  pressure  to  convert  it  into  a  liquid  ;  that  is,  to  alter 
its  arrangement  in  such  a  manner  that  a  liquid  can  be  seen  to  be  separated 
from  a  gas  by  a  distinctly  bounded  surface. 

371.  Papin's  dig-ester. — Papin  appears  to  have  been  the  first  to  investi- 
gate the  effects  of  the  production  of  vapour  in  closed  vessels.  The  apparatus 
which  bears  his  name  consists  of  a  cylin- 
drical iron  vessel  (fig.  335),  provided  with 
a  cover,  which  is  firmly  fastened  down 
by  the  screw  B.  In  order  to  close  the 
vessel  hermetically,  sheet  lead  is  placed 
between  the  edges  of  the  cover  and  the 
vessel.  At  the  bottom  of  a  cylindrical 
cavity,  which  traverses  the  cylinder  S, 
and  the  tubulure  ^,  the  cover  is  perforated 
by  a  small  orifice  in  which  there  is  a  rod 
71.  This  rod  presses  against  a  lever  A, 
movable  at  a.,  and  the  pressure  may  be 
regulated  by  means  of  a  weight  movable 
on  this  lever.  The  lever  is  so  weighted 
that  when  the  pressure  in  the  interior  is 
equal  to  six  atmospheres,  for  example,  the 
valve  rises  and  the  vapour  escapes.  The 
destruction  of  the  apparatus  is  thus 
avoided,  and  this  mechanism  has  hence 
received  the  name  of  safety-valve.  The 
digester  is  filled  about  two-thirds  with 
water,  and  is  heated  on  a  furnace.  The 
water  may  thus  be  raised  to  a  temperature 
far  .above  100°,  and  the  pressure  of  the  vapour  increased  to  several  atmo- 
spheres, according  to  the  weight  on  the  lever. 

We  have  seen  that  water  boils  at  much  lower  temperatures  on  high 
mountains  (367) ;  the  temperature  of  water  boiling  in  open  vessels  in  such 
localities  is  not  sufficient  to  soften  animal  fibre  completely  and  extract 
the  nutriment,  and  hence  Papin's  digester  is  used  in  the  preparation  of 
food. 

Papin's  digester  is  used  in  extracting  gelatine.  When  bones  are  digested 
in  this  apparatus  they  are  softened,  so  that  the  gelatine  which  they  contain 
is  dissolved  :  the  part  through  which  the  screw  B  passes  is  made  of  such 
elasticity  that  it  yields,  and  the  lid  opens  when  the  pressure  of  the  vapour 
becomes  dangerous. 

372.  Iiatent  lieat  of  vapour. — As  the  temperature  of  a  liquid  remains 
constant  during  boiling,  whatever  be  the  source  of  heat  (363),  it  follows 
that  a  considerable  quantity  of  heat  becomes  absorbed  in  boiling,  the  only 
effect  of  which  is  to  transform  the  body  from  the  liquid  to  the  gaseous  con- 
dition. And,  conversely,  when  a  saturated  vapour  passes  into  the  state  of 
liquid,  it  gives  out  a  definite  amount  of  heat. 

These  phenomena  were  first  observed  by  Black,  and  he  described  them 
by  saying  that  during  vaporisation  a  quantity  of  sensible  heat  became  latent, 
and  that  the  latent  heat  again  became  free  during  condensation.    The  quan- 


Fig.  335- 


-372]  Latent  Heat  of  Evaporation.  341 

tity  of  heat  which  a  liquid  must  absorb  in  passing  from  the  liquid  to  the 
gaseous  state,  and  which  it  gives  out  in  passing  from  the  state  of  vapour  to 
that  of  liquid,  is  spoken  of  as  the  latent  heat  of  evaporation. 

The  analogy  of  these  phenomena  to  those  of  fusion  will  be  at  once  seen  ; 
the  modes  of  determining  them  will  be  described  in  the  chapter  on  Calori- 
metry  ;  but  the  following  results,  which  have  been  obtained  for  the  latent 
heats  of  evaporation  at  0°,  may  be  here  given  : — 


Water       . 

.     607 

Bisulphide  of  carbon  . 

.     90 

Alcohol    . 

.         .     236 

Turpentine 

•     74 

Acetic  acid 

.     102 

Bromine 

■     49 

Ether       . 

•       94 

Iodine 

.     24 

The  meaning  of  these  numbers  is,  in  the  case  of  water,  for  instance,  that 
it  requires  as  much  heat  to  convert  a  pound  of  water  from  the  state  of  liquid 
at  boiling  point,  to  that  of  vapour  at  the  same  temperature,  as  would  raise 
a  pound  of  water  through  607  degrees,  or  607  pounds  of  water  through  one 
degree  ;  or  that  the  conversion  of  one  pound  of  vapour  of  alcohol  at  0° 
into  liquid  alcohol  of  the  same  temperature  would  heat  208  pounds  of  water 
through  one  degree. 

Watt,  who  investigated  the  subject,  held  that  the  whole  quantity  of  heat 
necessary  to  raise  a  given  weight  of  water  from  zero  to  any  temperature, 
and  then  to  evaporate  it  entirely,  or  what  is  called  the  heat  of  evaporation., 
is  a  constant  quantity.  His  experiments  showed  that  this  quantity  is  640. 
Hence  the  lower  the  temperature  the  greater  the  latent  heat,  and,  on  the  other 
hand,  the  higher  the  temperature  the  less  the  latent  heat.  The  latent  heat  of 
the  vapour  of  water  evaporated  at  100°  would  be  540,  while  at  50  degrees  it 
would  be  590.  At  higher  temperatures  the  latent  heat  of  aqueous  vapour 
would  go  on  diminishing.  Water  evaporated  under  a  pressure  of  1 5  atmo- 
spheres at  a  temperature  of  200°  would  have  a  latent  heat  of  440,  and  if  it 
could  be  evaporated  at  640°  it  would  have  no  latent  heat  at  all. 

Regnault,  who  examined  this  question  with  great  care,  found  that  the 
total  quantity  of  heat  necessary  for  the  evaporation  of  water  increases  with 
the  temperature,  and  is  not  constant,  as  Watt  had  supposed.  It  is  repre- 
sented by  the  formula 

Q  =  606-5  +o'3o5^) 

in  which  Q  is  the  total  quantity  of  heat,  and  /  the  temperature  of  the  water 
during  evaporation,  while  the  numbers  are  constant  quantities.  The  total 
quantity  of  heat  necessary  to  evaporate  water  at  100°  is  606-5  -t-  (0-305  ■•<  100) 
=  637  ;  at  120°  it  is  643  ;  at  150°  it  is  651  ;  and  at  180°  it  is  661. 

Thus  the  heat  required  to  raise  a  pound  of  water  from  zero  and  convert 
it  into  steam  at  100°  represents  a  mechanical  work  of  885430  units,  which 
would  be  sufficient  to  raise  a  ton  weight  through  a  height  of  nearly  400  feet. 

The  total  heat  of  the  evaporation  of  ether  is  expressed  by  a  formula 
similar  to  that  of  water,  namely,  Q  =  64 +  0-045/;  and  that  for  chloroform 
Q  =  67 +  0-1375/. 

The  heat  which  is  expended  simply  in  evaporating  a  liquid,  and  which  is 
spoken  of  as  the  latent  heat,  produces  no  rise  of  temperature,  and  only 
appears  as  doing  the  work  of  a  change  of  state.     One  portion  of  this  work 


342  On  Heat.  [372- 

is  expended  in  overcoming  the  cohesion  of  the  particles  in  the  liquid  state, 
and  enabling  them  to  assume  the  gaseous  form — this  is  the  internal  work., 
and  is  by  much  the  greater ;  the  other,  the  external  work,  is  expended  in 
overcoming  the  external  pressure  on  the  vapour  formed,  and  which  is  much 
larger  than  in  the  original  liquid  state,  for  the  volume  is  greatly  increased. 

Knowing  the  increase  of  volume,  and  the  pressure,  the  external  work  may 
readily  be  calculated  ;  for  if  the  volumes  of  unit  weight  of  the  substance  in  the 
state  of  lic]uid  and  of  vapour  are  respectively  s  and  cr,  and  the  pressure  for 
unit  surface  is^,  then  the  external  work  is  \p  {(t  —  s),  A  being  the  mechanical 
equivalent  of  heat.     So  that,  if  r  is  tjie  total  heat  of  evaporation, 

r  =  p  +  Kp  {(T-s) 
in  which  p  is  the  internal  work.     From  the  values  of  r  and  of  A/  {^~^)i  it  is 
easy  to  deduce  that  of  p,  and  it  is  found  that  this  value  decreases  as  the  tem- 
perature increases. 

Thus  for  the  temperatures  o,  50,  100,  and  150°  the  values  are  576,  536, 
496,  and  457°  respectively  ;  that  is,  that  when  water  at  0°  is  converted  into 
vapour,  a  greater  internal  work  is  required  to  overcome  the  cohesion,  than 
at  100°  for  instance. 

373.  Cold  due  to  evaporation.  Mercury  frozen. — Whatever  be  the 
temperature  at  which  a  vapour  is  produced,  an  absorption  of  heat  always 
takes  place.  If,  therefore,  a  liquid  evaporates,  and  does  not  receive  from 
without  a  quantity  of  heat  equal  to  that  which  is  expended  in  producing  the 
vapour,  its  temperature  sinks,  and  the  cooling  is  greater  in  proportion  as  the 
evaporation  is  more  rapid. 

Leslie  succeeded  in  freezing  water  by  means  of  rapid  evaporation.  Under 
the  receiver  of  the  air-pump  is  placed  a  vessel  containing  strong  sulphuric 
acid,  and  above  it  a  thin  metal  capsule,  A  (fig.  336),  containing  a  small 

quantity  of  water.  By 
exhausting  the  receiver 
the  water  begins  to 
boil  (360),  and  since 
the  vapour  is  absorbed 
by  the  sulphuric  acid 
as  fast  as  it  is  formed, 
a  rapid  evaporation 
is  produced,  which 
quickly  effects  the 
freezing  of  the  water. 

This  experiment  is 
best  performed  by 
using,  instead  of  a  thin 
metal  dish,  a  watch- 
glass  coated  with  lamp- 
black and  resting  on  a  cork.  The  advantage  of  this  is  twofold  :  firstly,  the 
lampblack  is  a  very  bad  conductor ;  and,  secondly,  it  is  not  moistened  by  the 
liquid,  which  remains  in  the  form  of  a  globule  not  in  contact  with  the  glass. 
A  small  porous  dish  may  also  advantageously  be  used.    ' 

The  same  result  is  obtained  by  means  of  Wollaston's  cryophorus  (fig. 
'iyj),  which  consists  of  a  bent  glass  tube  provided  with  a  bulb  at  each  end. 


-373]  Cold  due  to  Evaporation.  343 

The  apparatus  is  prepared  by  infroducing  a  small  quantity  of  water,  which 
is  then  boiled  so  as  to  expel  all  air.  It  is  then  hermetically  sealed,  so  that 
on  cooling  it  contains  only  water  and  the  vapour  of  water.  The  water  being 
introduced  into  the  bulb  A,  the  other  bulb  is  immersed  in  a  freezing 
mixture.  The  vapour  in  the  tube  is  thus  condensed  ;  the  water  in  A  rapidly 
yields  more.  But  this  rapid  production  of  vapour  requires  a  large  amount 
of  heat,  which  is  abstracted  from  the  water  in  A,  and  its  temperature  is  so 
much  reduced  that  it  freezes. 

By  using  liquids  more  volatile  than  water,  more  particularly  liquid  sul- 
phurous acid,  which  boils  at  -  10°,  or  still  better,  chloride  of  methyle,  which 
is  now  prepared  industrially  in  large  quantities,  a  degree  of  cold  is  obtained 
sufficiently  low  to  freeze  mercury.  This  experiment  may  be  made  on  a 
small  scale  by  covering  the  bulb  of  a  thermometer  with  cotton  wool,  and, 
after  having  moistened  it  with  the  liquid  in  question,  placing  it  under  the 
receiver  of  the  air-pump.  When  a  vacuum  is  produced  the  mercury  is 
quickly  frozen. 

By  passing  a  current  of  air,  previously  cooled,  through  liquid  chloride  of 
methyle,  temperatures  of  from  —23°  to  —70°  C.  may  be  maintained  with 
great  constancy  for  several  hours.  Thilorier,  by  directing  a  jet  of  liquid 
carbonic  acid  on  the  bulb  of  an  alcohol  thermometer,  obtained  a  tempera- 
ture of  — 100°  without  freezing  the  alcohol  (343). 

By  means  of  the  evaporation  of  bisulphide  of  carbon  the  formation  of  ice 
may  be  illustrated  without  the  aid  of  an  air-pump.  A  little  water  is  dropped 
on  a  board,  and  a  capsule  of  thin  copper  foil,  containing  bisulphide  of  carbon, 
is  placed  on  the  water.  The  evaporation  of  the  bisulphide  is  accelerated  by 
means  of  a  pair  of  bellows,  and  after  a  i&w  minutes  the  water  freezes  round 
the  capsule  so  that  the  latter  adheres  to  the  wood. 

In  like  manner,  if  some  water  be  placed  in  a  test-tube,  which  is  then 
dipped  in  a  glass  containing  some  ether,  and  a  current  of  air  be  blown 
through  the  ether  by  means  of  a  glass  tube  fitted  to  the  nozzle  of  a  pair  of 
bellows,  the  rapid  evaporation  of  the  ether  very  soon  freezes  the  water  in 
the  tube.  Richardson's  apparatus  for  producing  local  aneesthesia  also  de- 
pends on  the  cold  produced  by  the  evaporation  of  ether. 

The  cold  produced  by  evaporation  is  used  in  hot  climates  to  cool  water 
by  means  of  alcarrazas.  These  are  porous  earthen  vessels,  through  which 
water  percolates,  so  that  on  the  outside  there  is  a  continual  evaporation, 
which  is  accelerated  when  the  vessels  are  placed  in  a  current  of  air.  For 
the  same  reason  wine  is  cooled  by  wrapping  the  bottles  in  wet  cloths  and 
placing  them  in  a  draught. 

In  Harrison's  method  of  making  ice  artificially,  a  steam-engine  is  used 
to  work  an  air-pump  which  produces  a  rapid  evaporation  of  some  ether,  in 
which  is  immersed  the  vessel  containing  the  water  to  be  frozen.  The  apparatus 
is  so  constructed  that  the  vaporised  ether  can  be  condensed  and  used  again. 

The  cooling  effect  produced  by  a  wind  or  draught  does  not  necessarily 
arise  from  the  wind  being  cooler,  for  it  may,  as  shown  by  the  thermometer, 
be  actually  warmer,  but  arises  from  the  rapid  evaporation  it  causes  from  the 
surface  of  the  skin.  We  have  the  feeling  of  oppression  even  at  moderate 
temperatures,  when  we  are  in  an  atmosphere  saturated  by  moisture,  in  which 
no  evaporation  takes  place. 


344 


On  Heat. 


[374- 


374.  Carre's  apparatus  for  freezing-  water.- — We  have  already  seen 
that  when  any  Hquid  is  converted  into  vapour  it  absorbs  a  considerable 
quantity  of  sensible  heat  ;  this  furnishes  a  source  of  cold  which  is  more 
abundant  the  more  volatile  the  liquid,  and  the  greater  its  heat  of  vaporisation. 

This  property  of  liquids  has  been  utilised  by  M.  Carre,  in  freezing  water 
by  the  distillation  of  ammonia.  The  apparatus  consists  of  a  cylindrical 
boiler  C  (figs.  338,  339),  and  of  a  slightly  conical  vessel  A,  which  is  the 
freezer.  These  two  vessels  are  connected  by  a  tube,  in,  and  a  brace,  «,  binds 
them  firmly.  They  are  made  of  strong  galvanised  iron  plate,  and  can  resist 
a  pressure  of  seven  atmospheres. 

The  boiler  C,  which  holds  about  two  gallons,  is  three  parts  filled  with  a 
strong  solution  of  ammonia.  In  a  tubulure  in  the  upper  part  of  the  boiler 
some  oil  is  placed,  and  in  this  a  thermometer  t.  The  freezer  A  consists  of 
two  concentric  envelopes,  in  such  a  manner  that,  its  centre  being  hollow,  a 


1.^ 


F 'g-  33S. 


Fiy;.  330. 


metal  vessel,  G,  containing  the  water  to  be  frozen,  can  be  placed  in  this  space. 
Hence  only  the  annular  space  between  the  sides  of  the  freezer  is  in  commu- 
nication with  the  boiler  by  means  of  the  tube  m.  In  the  upper  part  of  the 
freezer  there  is  a  small  tubulure,  which  can  be  closed  by  a  metal  stopper,  and 
by  which  the  solution  of  ammonia  is  introduced. 

The  formation  of  ice  comprises  two  distinct  operations.  In  the  first, 
the  boiler  is  placed  in  a  furnace  F,  and  the  freezer  in  a  bath  of  cold  water  of 
about  12°.  The  boiler  being  heated  to  130°,  the  ammoniacal  gas  dissolved 
in  the  water  of  the  boiler  is  disengaged,  and,  in  virtue  of  its  own  pressure,  is 
liquefied  in  the  freezer  A,  along  with  about  a  tenth  of  its  weight  of  water.  This 
distillation  of  C  towards  A  lasts  about  an  hour  and  a  quarter,  and  when  it  is 
finished  the  second  operation  commences  ;  this  consists  in  placing  the  boiler 
in  the  cold-water  bath  (fig.  339),  and  the  freezer  A  outside,  care  being  taken 
to  surround  it  with  dry  flannel.     The  vessel  G,  about  three-quarters  full  of 


-374]  Carre's  Apparatus  for  Freezing   Water.  345 

water,  is  placed  in  the  freezer.  As  the  boiler  cools,  the  ammoniacal  gas  with 
which  it  is  filled  is  again  dissolved  ;  the  pressure  thus  being  diminished,  the 
ammonia  which  has  been  liquefied  in  the  freezer  is  converted  into  the  gaseous 
form,  and  now  distils  from  A  towards  C,  to  redissolve  in  the  water  which 
has  remained  in  the  boiler.  During  this  distillation  the  ammonia  which  is 
gasified  absorbs  a  great  quantity  of  heat,  which  is  withdrawn  from  the  vessel 
G  and  the  water  it  contains.  Hence  it  is  that  this  water  freezes.  In  order 
to  have  better  contact  between  the  sides  of  the  vessel  G  and  the  freezer, 
alcohol  is  poured  between  them.  In  about  an  hour  and  a  quarter  a  perfectly 
compact  cylindrical  block  of  ice  can  be  taken  from  the  vessel  G. 

This  apparatus  gives  about  four  pounds  of  ice  in  an  hour,  at  a  price  of 
about  a  farthing  per  pound  ;  large  continuously  working  apparatus  have,  how- 
ever, been  constructed,  which  produce  as  much  as  800  pounds  of  ice  in  an  hour. 
Carre  has  constructed  an  ice-making  machine  which  is  an  industrial 
application  of  Leslie's  experiment  {yri)^  and  by  which  considerable  quantities 
of  water  may  be  frozen  in  a  short  time.  It  consists  of  a  cylinder  R,  about  15 
niches  long  by  4  in  diameter,  made  of  an  alloy  of  lead  and  antimony 
(fig.  340).  At  one  end  is  a  funnel  E,  by  which  strong  sulphuric  acid  can  be 
introduced  ;  at  the  other  is  a  tubulure  w,  to  which  is  screwed  a  dome  d  that 
supports  a  series  of  obstacles  intended  to  prevent  any  sulphuric  acid  from 
spirting  into  m  and  b.  There  are,  moreover,  on  the  receiver  a  wide  tube  u, 
closed  by  a  thick  glass  disc  O,  and  a  long  tube  /^,  to  the  top  of  which  is  fitted 
the  bottle  C  con- 
taining water  to  be 
frozen.  The  dome 
c/,  the  disc  O,  and 
the  stopper  i  of  the 
funnel  E  are  all 
sealed  with  wax. 

On  the  side  of 
the  receiver  is  an 
air-pump  P,  con- 
nected with  it  by  a 
tube  <^,  and  worked 
by  a  handle  M.  To 
this  handle  is  at- 
tached a  rod  /, 
which,  by  the 
mechanism  repre- 
sented on  the  left 
of  the  figure,  works 
a  stirrer  A  in  the 
sulphuric  acid.  A 
lever  x  connected 
with  a  horizontal 
axis  which  tra- 
verses a  small  stuff"-  Fig.  340. 
ing-box  n,  trans- 
mits its  backward  and  forward  motion  to  the  rod  e  and  to  the  stirrer.     This 


346 


071  Heat. 


[374- 


and    the    stuffing-box  ;/  are  fitted  in  a  tubulure  on  the  side  of  the  tubu- 
kire  VI. 

The  smallest  size  which  Carre  makes  contains  2-5  kilogrammes  of  sul- 
phuric acid,  and  the  water-bottle  about  400  grammes,  when  it  is  one-third  full. 
After  about  70  strokes  of  the  piston  the  water  begins  to  boil  ;  the  acid  being 
in  continued  agitation,  the  vapour  is  rapidly  absorbed  by  it,  and  the  pump  is 
worked  until  freezing  begins.  For  this  purpose  it  is  merely  necessary  to 
give  a  few  strokes  every  five  minutes.  The  rate  of  freezing  depends  on  the 
strength  of  the  acid  ;  when  this  gets  very  dilute  it  requires  renewal  ;  but  12 
water-bottles  can  be  frozen  with  the  same  quantity  of  acid. 

LIQUEFACTION   OF   VAPOUR   AND   GASES. 

375.  lilquefaetion  of  vapours. — The  liquefactioji  or  condensatiotj  of 
vapours  is  their  passage  from  the  aeriform  to  the  liquid  state.  Condensa- 
tion may  be  due  to  three  causes — cooling,  compression,  or  chemical  action. 
For  the  first  two  causes  the  vapours  must  be  saturated  (353),  while  the 
latter  produces  the  liquefaction  of  the  most  rarefied  vapours.  Thus,  a  large 
number  of  salts  absorb  and  condense  the  aqueous  vapour  in  the  atmosphere, 
however  small  its  quantity. 

When  vapours  are  condensed,  their  latent  heat  becomes  free  ;  that  is,  it 
affects  the  thermometer.  This  is  readily  seen  when  a  current  of  steam  at 
100°  is  passed  into  a  vessel  of  water  at  the  ordinary  temperature.  The  liquid 
becomes  rapidly  heated,  and  soon  reaches  100°.  The  quantity  of  heat  given 
up  in  liciuefaction  is  equal  to  the  quantity  absorbed  in  producing  the  vapour. 

376.  aistillation.       Stills. — Distillation  is  an    operation    by   which  a 


Fig.  341- 

volatile  liquid  may  be  separated  from  substances  which  it  holds  in  solution 
or  by  which    two  licpids  of  different  volatilities  may  be  separated.      The 


-377j 


Liebi^'s  Condenser, 


347 


operation  depends  on  the  transformation  of  liquids  into  vapour  by  the  action 
of  heat,  and  on  the  condensation  of  this  vapour  by  cooHng. 

The  apparatus  used  in  distillation  is  called  a  still.  Its  form  may  vary 
greatly,  but  it  consists  essentially  of  three  parts  ;  ist,  the  body  A  (fig.  341), 
a  copper  vessel  containing  the  liquid,  the  lower  part  of  which  fits  in  the 
furnace  ;  2nd,  the  /lead,  B,  which  fits  on  the  body,  and  from  which  a  lateral 
tube,  C,  leads  to  ;  3rd,  the  worm,  S,  a  long  spiral  tin  or  copper  tube  placed 
in  a  cistern  kept  constantly  full  of  cold  water.  The  object  of  the  worm  is  to 
condense  the  vapour  by  exposing  a  greater  extent  of  cold  surface. 

To  free  ordinary  water  from  the  many  impurities  which  it  contains,  it  is 
placed  in  a  still  and  heated.  The  vapours  disengaged  are  condensed  in  the 
worm,  and  the  distilled  water  arising  from  the  condensation  is  collected  in 
the  receiver  D.  The  vapours  in  condensing  rapidly  heat  the  water  in  the 
cistern,  which  must,  therefore,  be  constantly  renewed.  For  this  purpose  a 
continual  supply  of  cold  water  passes  into  the  bottom  of  the  cistern,  while 
the  lighter  heated  water  rises  to  the  surface  and  escapes  by  a  tube  in  the  top 
of  the  cistern. 

■yj'].  Iilebig-'s  Condenser. — In  distilling  small  quantities  of  liquids,  or  in 
taking  the  boiling  point  of  a  liquid,  so  as  not  to  lose  any  of  it,  the  apparatus 
known  as  Liebig's  Condenser  is  extremely  useful.  It  consists  of  a  glass 
tube,  //  (fig.  342),  about  thirty  inches  long,  fitted  in  a  copper  or  tin  tube 
by  means  of  perforated  corks.  A  constant  supply  of  cold  water  from  the 
vessel  a  passes  into  the  space  between  the  two  tubes,  being  conveyed  to  the 


Fig.  342- 


lower  part  of  the  condenser  by  a  funnel  and  tube  g,  flowing  out  from  the 
upper  part  of  the  tube/  The  liquid  to  be  distilled  is  contained  in  a  retort, 
the  neck  of  which  is  placed  in  the  tube  ;  the  condensed  liquid  drops  quite 
cold  into  a  vessel  placed  to  receive  it  at  the  other  extremity  of  the  con- 
densing tube. 


348 


On  Heat. 


[378- 


Fig.  343. 

glass   is  filled  with  the  -wine  up  to  a 


378.  j^pparatus  for  determining^  the  alcoholic  value  of  wines. — One 

of  the  forms  of  this  apparatus  consists  of  a  glass  flask  resting  on  a  tripod, 
and  heated   by  a  spirit  lamp  (fig.  343).     By  means  of  a  caoutchouc  tube 

this  is  connected 

^Bii»' '^1   "     „|,  with     a      worm 

^''*  placed  in  a  cop- 

per vessel  filled 
with  cold  water, 
and  below  which 
is  a  test  glass 
for  collecting  the 
distillate.  On 
this  are  three 
divisions,  one  a, 
which  measures 
the  quantity  of 
wine  taken  ;  the 
two  others  indi- 
J^  eating  one-half 
l^^gflsiigHE=^  and  one-third  of 

"  this  volume. 

The  test- 
this  is  then  poured  into  the  flask, 
which  having  been  connected  with  the  worm,  the  distillation  is  commenced. 
The  liquid  which  distils  over  is  a  mixture  of  alcohol  and  water  ;  for  ordinary 
wines,  such  as  clarets  and  hocks,  about  one-third  is  distilled  over,  and 
for  wines  richer  in  spirit,  such  as  sherries  and  ports,  one-half  must  be 
distilled  ;  experiment  has  shown  that  under  these  circumstances  practically  all 
the  alcohol  passes  over  in  the  distillate.  The  measure  is  then  filled  up  with 
distilled  water  to  a  ;  this  gives  the  mixture  of  alcohol  and  water  of  the  same 
volume  as  the  wine  taken,  free  from  all  solid  matters,  such  as  sugar,  colour- 
ing matter,  and  acid,  but  containing  all  the  alcohol.  The  specific  gravity 
of  this  distillate  is  then  taken  by  means  of  an  alcoholometer  (128),  and  the 
number  thus  obtained  corresponds  to  a  certain  strength  of  alcohol  as  indi- 
cated by  the  tables. 

379.  Safety-tube. — In  preparing  gases  and  collecting  them  over  mercury 
or  water,  it    occasionally  happens    that   these   liquids  rush  back  into  the 

generating  vessel,  and  destroy  the  operation. 
This  arises  from  an  excess  of  atmospheric  pressure 
over  the  elastic  force  in  the  vessel.  If  a  gas — 
sulphurous  acid  for  example — be  generated  in  the 
^^1  -^-^5— -  J^.         flask  in  (fig.  344),  and  be  passed  into  water  in  the 

|l|  t^  %^^^^^'  vessel  A,  as  long  as  the  gas  is  given  off  freely, 
its  elastic  force  exceeds  the  atmospheric  pressure, 
and  the  weight  of  the  column  of  water,  o;i,  so  that 
the  water  in  the  vessel  cannot  rise  in  the  tube, 
and  absorption  is  impossible.  But  if  the  tension 
decreases,  either  through  the  flask  becoming 
disengaged  too  slowly,  the  external  pressure  pre- 


cooled  or  the  gas  beinc 


-380] 


Liquefaction  of  Gases. 


349 


vails,  and  when  it  exceeds  the  internal  tension  by  more  than  the  weight  of 
the  cokimn  of  water  £•<?,  the  water  rises  into  the  flask,  and  the  operation  is 
spoiled.     This  accident  is  prevented  by  means  of  safety-tubes. 

These  are  tubes  which  prevent  absorption  by  allowing  the  air  to  enter  in 
proportion  as  the  internal  tension  decreases.  The  simplest  is  a  tube  C 
(fig.  345),  passing  through  the  cork  which 
closes  the  flask  M,  in  which  the  gas  is 
generated,  and  dipping  in  the  liquid. 
When  the  tension  of  the  gas  diminishes  in 
M,  the  atmospheric  pressure  on  the  water 
in  the  bath  E  causes  it  to  rise  to  a  certain 
height  in  the  tube  DA ;  but  this  pressure, 
acting  also  on  the  liquid  in  the  tube  C, 
depresses  it  to  the  same  depth,  assuming 
that  the  liquid  has  the  same  density  as 
the  water  in  E.  Now,  as  this  depth  is 
less  than  the  height  DH,  air  enters  by  the 
aperture,  before  the  water  in  the  bath  can 
inse  to  A,  and  no  absorption  takes  place. 

■},%o.  I.iquefaction  of  gases. — We  have  already  seen  that  a  saturated 
vapour,  the  temperature  of  which  is  constant,  is  liquefied  by  increasing  the 
pressure,  and  that,  the  pressure  remaining  constant,  it  is  brought  into  the 
liquid  state  by  diminishing  the  temperature. 

Unsaturated  vapours  behave  in  all  respects  like  gases.  For  the  gaseous 
form  is  accidental,  and  is  not  inherent  in  the  nature  of  the  substance.  At 
ordinary  temperatures  sulphurous  anhydride  is  a  gas,  while  in  countries  near 
the  poles  it  is  a  liquid  ;  in  temperate  climates  ether  is  a  liquid,  at  a  tropical 
heat  it  is  a  gas.  And  just  as  unsaturated  vapours  may  be  brought  to  the 
state  of  saturation,  and  then  liquefied,  by  suitably  diminishing  the  tempe- 
rature or  increasing  the  pressure,  so  by  the  same  means  gases  may  be 
liquefied.  But  as  they  are  mostly  very  far  removed  from  this  state  of  satura- 
tion, great  cold  and  pressure  are  i^equired.  Some  of  them  may  indeed  be 
liquefied  either  by  cold  or  by  pressure  ;  for  the  majority,  however,  both 
agencies  must  be  simultaneously  employed.  The 
recent  researches  of  Cailletet  and  of  Pictet  (382) 
have  shown  that  the  distinction  permanent  gas 
no  longer  exists,  now  that  all  are  liquefied. 

We  have  seen  that  there  is  for  each  gas  a 
critical  temperature  (370),  so  that  no  pressure 
however  great  can  liquefy  a  gas  which  is  above  this 
temperature.  If  a  gas  is  below  this  point,  then 
the  nearer  it  is  to  it  the  greater  is  the  pressure 
required  ;  conversely,  if  the  temperature  is  very 
low,  the  pressure  required  to  liquefy  it  may  be 
low  too. 

Faraday  was  the  first  to  liquefy  some  of  the  gases.  His  method  con- 
sists in  enclosing  in  a  bent  glass  tube  (fig.  346)  substances  by  whose 
chemical  action  the  gas  to  be  liquefied  is  produced,  and  then  sealing  the 
shorter  leg.     In  proportion  as  the  gas  is  disengaged  its  pressure  increases, 


Fig.  346. 


350  On  Heat.  [380- 

and  it  ultimately  liquefies  and  collects  in  the  shorter  leg,  more  especially  if  its 
condensation  is  assisted  by  placing  the  shorter  leg  in  a  freezing  mixture.  A 
small  manometer  may  be  placed  in  the  apparatus  to  indicate  the  pressure. 

Cyanogen  gas  is  readily  liquefied  by  heating  cyanide  of  mercury  in  a  bent 
tube  of  this  description  ;  other  gases  have  been  condensed  by  taking  advan- 
tage of  special  reactions,  the  consideration  of  which  belongs  rather  to 
chemistry  than  to  physics.  For  example,  chloride  of  silver  absorbs  about 
200  times  its  volume  of  ammoniacal  gas  ;  when  the  compound  thus  formed 
is  placed  in  the  long  leg  of  a  bent  tube  and  gently  heated,  while  the  shorter 
leg  is  immersed  in  a  freezing  mixture,  a  quantity  of  liquid  ammoniacal 
gas  speedily  collects  in  the  shorter  leg. 

381.  Apparatus  to  liquefy  and  solidify  gases. — Thilorier  first  con- 
structed an  apparatus  by  which  considerable  quantities  of  carbonic  acid 
could  be  liquefied.  Its  principle  is  the  same  as  that  used  by  Faraday  in 
working  with  glass  tubes  ;  the  gas  is  generated-  in  an  iron  cylinder,  and 
passes  through  a  metal  tube  into  another  similar  cylinder,  where  it  con- 
denses. The  use  of  this  apparatus  is  not  free  from  danger;  many  accidents 
have  already  happened  with  it,  and  it  has  been  superseded  by  an  apparatus 
constructed  by  Natterer,  of  Vienna,  which  is  both  convenient  and  safe. 

A  perspective  view  of  the  apparatus,  as  modified  by  Bianchi,  is  repre- 
sented in  fig.  348,  and  a  section  on  a  larger  scale  in  fig.  347.  It  consists  of 
a  wrought-iron  reservoir  A,  of  something  less  than  a  quart  capacity,  which 
can  resist  a  pressure  of  more  than  600  atmospheres.  A  small  force-pump  is 
screwed  on  the  lower  part  of  this  reservoir.  The  piston  rod  /  is  mo\'ed  by 
the  crank-rod  E,  which  is  worked  by  the  handle  M.  As  the  compression  of 
the  gas  and  the  friction  of  the  piston  produce  a  considerable  disengagement 
of  heat,  the  reservoir  A  is  surrounded  by  a  copper  vessel,  in  which  ice  or  a 
freezing  mixture  is  placed.  The  water  arising  from  the  melting  of  the  ice 
passes  by  a  tube  m  into  a  cylindrical  copper  case  C,  which  surrounds  the 
force-pump,  from  whence  it  escapes  through  the  tube  n  and  the  stopcock  o. 
The  whole  arrangement  rests  on  an  iron  frame,  PQ. 

The  gas  to  be  liquefied  is  previously  collected  in  airtight  bags  R,  from 
whence  it  passes  into  a  bottle  V,  containing  some  suitable  drying  substance  ; 
it  then  passes  into  the  condensing  pump  through  the  vulcanised  india-rubber 
tube  H.  After  the  apparatus  has  been  worked  for  some  time  the  reservoir 
A  can  be  unscrewed  from  the  pump  without  any  escape  of  the  liquid,  for  it  is 
closed  below  by  a  valve  S  (fig.  347).  In  order  to  collect  some  of  the  liquid 
gas,  the  reservoir  is  inverted,  and  on  turning  the  stopcock  r  the  liquid  escapes 
by  a  small  tubulure  x. 

When  carbonic  acid  has  been  liquefied  and  is  allowed  to  escape  into  the 
air,  a  portion  only  of  the  liquid  volatilises  ;  in  consequence  of  the  heat  ab- 
sorbed by  this  evaporation,  the  rest  is  so  much  cooled  as  to  solidify  in  white 
flakes  like  snow  or  anhydrous  phosphoric  acid.  This  may  be  collected  by  plac- 
ing a  stout  woollen  bag  like  a  tobacco  pouch  over  a  pipe  attached  to  the  tube  x: ; 
if  the  porous  mass  is  compressed  or  hammered  in  stout  wooden  cj^linders, 
sticks  of  solid  carbonic  acid  are  obtained,  very  like  chalk  in  appearance. 

Solid  carbonic  acid  evaporates  very  slowly.  By  means  of  an  alcohol 
thermometer  its  temperature  has  been  found  to  be  about  —90°.  A  small 
quantity  placed  on  the  hand  does  not  produce  the  sensation  of  such  great 


-381] 


Apparatus  to  Liquefy  and  Solidify  Gases. 


351 


cold  as  might  be  expected.  This  arises  from  the  imperfect  contact.  But  if 
the  soHd  be  mixed  with  ether  the  cold  produced  is  so  intense  that  when  a 
little  is  placed  on  the  skin  all  the  effects  of  a  severe  burn  are  produced.  A 
mixture  of  these  two  substances  solidifies  four  times  its  weight  of  mercury 
in  a  few  minutes.  When  a  tube  containing  liquid  carbonic  acid  is  placed  in 
thismixture,  the  liquid  becomes  solid  and  looksjike  a  transparent  piece  of  ice. 


Fig.  34S. 

The  most  remarkable  liquefaction  obtained  by  this  apparatus  is  that  of 
nitrous  oxide.  The  gas  once  liquefied  only  evaporates  slowly,  and  produces 
a  temperature  of  88°  below  zero.  Mercury  placed  in  it  in  small  quantities 
instantly  solidifies.  The  same  is  the  case  with  water  ;  it  must  be  added 
drop  by  drop,  otherwise,  its  latent  heat  being  much  greater  than  that  ot 
mercury,  the  heat  given  up  by  the  water  in  solidifying'would  be  sufficient  to 
cause  an  explosion  of  the  nitrous  oxide. 

Nitrous  oxide  is  readily  decomposed  by  heat,  and  has  the  property  of 
supporting  the  combustion  of  bodies  with    almost  as  much  brilliancy  as 


352  On  Heat.  [381- 

oxygen  ;  and  even  at  low  temperatures  it  preserves  this  property.  When  a 
piece  of  incandescent  charcoal  is  thrown  on  liquid  nitrous  oxide,  it  continues 
to  burn  with  a  brilliant  light. 

The  cold  produced  by  the  evaporation  of  ether  (373)  has  been  used  by 
Loir  and  Drion  in  the  liquefaction  of  gases.  By  passing  a  current  of  air 
from  a  blowpipe  bellows  through  several  tubes  into  a  few  ounces  of  ether,  a 
temperature  of  —  34°  C.  can  be  reached  in  five  or  six  minutes,  and  may  be 
kept  up  for  fifteen  or  twenty  minutes.  By  evaporating  liquid  sulphurous 
acid  in  the  same  manner  a  great  degree  of  cold,  —50°  C,  is  obtained.  At 
this  temperature  ammoniacal  gas  may  be  liquefied.  By  rapidly  evaporating 
liquid  ammonia  under  the  air-pump,  in  the  presence  of  sulphuric  acid,  a 
temperature  of  —87°  is  attained,  which  is  found  sufficient  to  liquefy  carbonic 
acid  under  the  ordinary  pressure  of  the  atmosphere. 

2,^1..  Cailletet's  and  Pictet's  researches. — Cailletet  and  Pictet,  working 
independently,  but  simultaneously,  have  effaced  the  old  distinction  between 
permanent  and  non-permanent  gases,  by  effecting 
the  liquefaction  of  oxygen  and  hydrogen,  and  other 
gases  which  it  was  supposed  could  not  be  condensed. 
This  has  been  accomplished  by  means  of  powerful 
material  appliances  directed  with  great  skill  and 
ingenuity.  The  critical  temperature  of  these  gases 
is  mostly  below  —  100°,  while  their  critical  pressure 
is  somewhat  less  than  that  of  carbonic  acid,  ex- 
cepting hydrogen,  which  is  over  100  atmospheres. 
The  essential  parts  of  Cailletet's  apparatus  are 

represented  in  fig.  349.     The  gas  to  be  condensed 

is   contained  in  the  tube  TP,  which  is   fitted,  by 

means  of  a  bronze  screw  A,  into  a  strong  wrought- 

iron  mercury  bath  B.     By  means  of  a  screw  RE, 
and  a  tube  U,  this  is  connected  with  a  hydraulic 

or  a  screw  press  not  represented  in  the  figure.  The 

capillary  part  P  of  the  tube  T  is  placed  in  a  vessel 

M,  in  which  it  can  be  surrounded  by  a  freezing 

mixture,  and  this  again  is  surrounded  by  a  stout 

safety  bell-jar  C. 

When  a  pressure  of  250  to  300  atmospheres  is 

applied   by  meaijs   of  the   hydraulic   press,   after 

waiting  until  the  heat  due  to  the  compression  has 

disappeared,  if  a  screw  arranged  in  the  press   is 

suddenly  opened,  the  pressure  being  diminished, 

the  cold  produced  by  the  sudden  expansion  of  the 

gas  in  the  tube  TP  is  so  great  as  to  liquefy  a  portion  of  the  rest,  as  is  shown 

by  the  production  of  a  mist. 

This  observation  was   first    made  with  nitric    oxide,  but  similar  results 

have  been  obtained  with  marsh  gas,  carbonic  acid,  and  oxygen. 

The  principle  of  Pictet's  method  is  that  of  liberating  the  gas  under  great 

pressure,  combined  with  the  application  of  great  degrees  of  cold.     The 

essential  parts  of   the    apparatus  are   the  following  : — Two  double-acting 

pumps,  A  and  B  (fig.  350),  are  so  coupled  together  that  they  cause  the 


382] 


CailleteVs  and  Pictefs  Researches. 


353 


evaporation  of  liquid  sulphurous  acid  contained  in  the  annular  receiver  C. 
By  the  play  of  the  pumps  the  gas  thus  evaporated  is  forced  into  the  re- 
ceiver D,  where  it  is  cooled  by  a  current  of  water,  and  again  liquefied  under 
a  pressure  of  three  atmospheres.  Thence  it  passes  again  by  the  narrow  tube 
d  to  the  receiver  C,  to  replace  that  which  is  evaporated. 

In  this  way  the  temperature  of  the  liquid  sulphurous  acid  is  reduced  to 
—  65°.  Its  function  is  to  produce  a  sufficient  quantity  of  liquid  carbonic  acid, 
which  is  then  submitted  to  a  perfectly  analogous  process  of  rarefaction  and 
condensation.  This  is  effected  by  means  of  two  similar  pumps  E  and  F. 
The  carbonic  acid  gas,  perfectly  pure  and  dry,  is  drawn  from  a  reservoir 
through  a  tube  not  represented  in  the  figure,  and  is  forced  into  the  condenser 
K,  which  is  cooled  by  the  liquid  sulphurous  acid  to  a  temperature  of  —65°, 
and  is  there  liquefied. 

H  is  a  tube  of  stout  copper  in  connection  with  the  condenser  K  by  a 
narrow  tube  k.  When  a  sufficient  quantity  of  carbonic  acid  has  been  liquefied, 
the  connection  with  the  gasholder  is  cut  off,  and  by  working  the  pumps  E 
and  F  a  vacuum  is  created  over  the  liquid  carbonic  acid  in  H,  which  pro- 
duces so  great  a  cold  as  to  solidify  it. 

L  is  a  stout  wrought-iron  retort  capable  of  standing  a  pressure  of  1,500 
atmospheres.  In  it  are  placed  the  substances  by  whose  chemical  actions 
the  gas  is  produced  : 
potassium  chlorate 
in  the  case  of 
oxygen.  This  re- 
tort is  closed  by  a 
strong  copper  tube 
in  which  the  actual 
condensation  is  ef- 
fected, near  the  end 
of  which  is  a  spe- 
cially constructed 
manometer  R,  and 
which  is  closed  by 
a  stopcock  N. 

When  the  four 
pumps  are  set  in 
action,  for  which  a 
steam-engine  of  1 5 
horse-power  is  re- 
quired, heat  is  ap- 
plied to  the  retort. 
Oxygen  is  liberated 
in  a  calculated 
quantity,  the  tem- 
perature of  the  retort  being  about  485°.  Towards  the  close  of  the  de- 
composition the  manometer  indicates  a  pressure  of  500  atmospheres,  and 
then  sinks  to  320.  This  diminution  is  due  to  the  condensation  of  gas, 
and  at  this  stage  the  tube  contains  liquefied  oxygen.  If  the  cock  N  is 
opened,  the  gas  issues  with  violence,  having  the  appearance  of  a  dazzling 

A  A 


354  On  Heat.  [382- 

white  pencil.  This  lasts  three  or  four  seconds.  On  closing  the  stopcock 
the  pressure,  which  had  diminished  to  400  atmospheres,  now  rises,  and 
again  becomes  stationary,  proving  that  the  gas  is  once  more  being  con- 
densed.    The  density  of  liquid  oxygen  has  been  found  to  be  0-9. 

The  phenomena  presented  by  the  jet  of  oxygen  when  viewed  by  the 
electric  light  showed  that  the  light  it  emits  was  partially  polarised,  indicating 
a  probable  transient  crystallisation  of  the  gas. 

For  hydrogen  the  gas  was  disengaged  by  heating  a  mixture  of  potassic 
formate  and  hydrate,  and  liquid  protoxide  of  nitrogen  was  used  instead  of 
carbonic  acid,  by  which  the  temperature  could  be  reduced  to  — 140°  C. 
When  the  pressure  had  reached  650  atmospheres,  and  the  cock  was  opened, 
a  steel-blue  jet  issued  from  the  aperture  with  a  brisk  noise.  This  suddenly 
became  intermittent,  and  resembled  a  shower  of  hailstones.  As  the  separate 
granules  struck  the  ground  they  produced  a  loud  noise,  and  Pictet  considers 
that  in  all  probability  the  hydrogen  in  the  interior  was  frozen. 

In  some  later  experiments,  the  details  of  which  are  too  complicated  to 
give  here,  Cailletet  has  produced  very  low  temperatures  by  the  use  of  liquid 
ethylene  gas.  This  gas  can  be  liquefied  by  a  pressure  of  45  atmospheres  at 
a  temperature  of  1°.  By  promoting  the  evaporation  of  this  liquid,  by  passing 
through  it  a  current  of  air  or  of  hydrogen  which  has  been  previously  cooled  by 
the  rapid  evaporation  of  chloride  of  methyle,  the  temperature  is  easily  reduced 
to  -  120°.  When  oxygen  gas  is  cooled  to  this  temperature  the  application  of 
pressure  is  sufficient  to  resolve  it  into  a  colourless,  transparent  liquid,  sharply 
separated  from  the  gas  by  a  meniscus. 

By  surrounding  the  gas  under  experiment  by  concentric  tubes  containing 
lic|uid  oxygen  that  boils  under  the  atmospheric  pressure  at  —  181°,  which  in 
turn  is  surrounded  by  liquid  ethylene,  Olszewski  obtained  temperatures  low 
enough  to  solidify  nitrogen,  carbonic  oxide,  marsh  gas,  and  nitric  oxide.  The 
evaporation  of  solid  nitrogen  under  a  pressure  of  4"""  produces  a  tempe- 
rature of  —225°. 

:\IIXTURE   OF   GASES   AND    VAPOURS. 

383.  ]baws  of  the  mixture  of  grases  and  vapours. — Every  mixture  of  a 
gas  and  a  vapour  obeys  the  two  following  laws  : — 

I.  The  pressure,  and,  co7iseqiiently,  the  quantity,  of  vapour  which  saturates 
a  given  space  are  the  same  for  the  same  temperature,  whether  this  space  con- 
tains a  gas  or  is  a  vacuum. 

I I .  TJie  pressure  of  the  mixture  of  a  gas  and  a  vapour  is  equal  to  the  sum 
of  the  pressures  which  each  would  possess  if  it  occupied  the  same  space  a/ofie. 

These  are  known  as  Daltoifs  laws,  from  their  discoverer,  and  are  de- 
monstrated by  the  following  apparatus,  which  was  invented  by  Gay-Lussac  :— 
It  consists  of  a  glass  tube  A  (fig.  351),  to  which  two  stopcocks,  b  and  d,  are 
cemented.  The  lower  stopcock  is  provided  with  a  tubulure  which  connects 
the  tube  A  with  a  tube  B  of  smaller  diameter.  A  scale  between  the  two 
tubes  serves  to  measure  the  heights  of  the  mercurial  columns  in  these  tubes. 

The  tube  A  is  filled  with  mercury,  and  the  stopcocks  b  and  d  are  closed. 
A  glass  globe  M,  filled  with  dry  air  or  any  other  gas,  is  screwed  on  by  means 
of  a  stopcock  in  the  place  of  the  funnel  C.  All  three  stopcocks  are  then 
opened,  and  a  little  mercury  is  allowed  to  escape,  which  is  replaced  by  the 


384] 


Mixture  of  Gases  and   Vapours. 


355 


li^ 


dry  air  of  the  globe.     The  stopcocks  are  then  closed,  and  as  the  air  in  the 

tube  expands  on  leaving  the  globe,  the  pressure  on  it  is  less  than  that  of 

the  atmosphere.     Mercury  is  accordingly  poured  into  the  tube  B  until  it  is 

at  the  same  level  in  both  tubes.     The  globe  is  then  removed,  and  replaced 

by  the  funnel  C,  provided  with  a  stopcock  a  of  a  peculiar  construction.     It  is 

not  perforated,  but  has  a  small  cavity,  as  represented  in  «,  on  the  left  of  the 

figure.     Some  of  the  liquid  to  be  vaporised  is 

poured  into  C,  and  the  height  of  the  mercury 

k  having  been  noted,  the  stopcock  b  is  opened, 

and  a  turned  so  that  its  cavity  becomes  filled 

with   liquid  ;    being   again    turned,    the    liquid 

enters  the  space  A  and  vaporises.     The  liquid 

is  allowed  to  fall  drop  by  drop  until  the  air  in 

the  tube  is   saturated,  which  is  the  case  when 

the  level  k  of  the  mercury  ceases  to  sink  (353). 

As  the  pressure  of  the  vapour  produced  in 
the  space  A  is  added  to  that  of  the  air  already 
present,  the  total  volume  of  gas  is  increased. 
It  may  easily  be  restored  to  its  original  volume 
by  pouring  mercury  into  B.  When  the  mercury 
in  the  large  tube  has  been  raised  to  the  level  k, 
there  is  a  difference  B<9  in  the  level  of  the 
mercury  in  the  two  tubes,  which  obviously  re- 
presents the  pressure  of  the  vapour  ;  for  as  the 
air  has  resumed  its  original  volume,  its  pressure 
has  not  changed.  Now,  if  a  few  drops  of  the 
same  liquid  be  passed  into  the  vacuum  of  a 
barometric  tube,  a  depression  exactly  equal  to 
B<?  is  produced,  which  proves  that,  for  the 
same  temperature,  the  pressure  of  a  saturated 
vapour  is  the  same  in  a  gas  as  in  a  vacuum  : 
from  which  it  is  concluded  that  at  the  same 
temperature  the  quantity  of  vapour  is  also  the 
same. 

The  second  law  is  likewise  proved  by  this 
experiment,  for,  when  the  mercury  has  regained  its  level,  the  mixture  sup- 
ports the  atmospheric  pressure  on  the  top  of  the  column  B,  in  addition  to 
the  weight  of  the  column  of  mercury  B<7.  But  of  these  two  pressures,  one 
represents  that  of  the  dry  air,  and  the  other  that  of  the  vapour.  The  second 
law  is,  moreover,  a  necessary  consequence  of  the  first. 

Experiments  can  only  be  made  with  this  apparatus  at  ordinary  tempera- 
tures ;  but  Regnault,  by  means  of  an  apparatus  which  can  be  used  at  different 
temperatures,  investigated  the  tensions  of  the  vapours  of  water,  ether,  bisul- 
phide of  carbon,  and  benzole,  both  in  a  vacuum  and  in  air.  He  found  that  the 
tension  in  air  is  less  than  it  is  in  a  vacuum,  but  the  differences  are  so  small 
as  not  to  invalidate  Dalton's  law.  Regnault  was  even  inclined  to  consider 
this  law  as  theoretically  true,  attributing  the  differences  which  he  observed 
to  the  hygroscopic  properties  of  the  sides  of  the  tubes. 

384.  Problems  on  mixtures  of  gases  and  vapours.- — i.  A  volume  of 

A  A  2 


356  On  Heat.  [384- 

dry  air  V,  at  the  pressure  H,  being  given,  what  will  be  its  volume  V,  when 

it  is  saturated  with  vapour,  the  temperature  and  the  pressure  remaining  the 

same  ? 

If  F  be  the  elastic  force  of  the  vapour  which  saturates  the  air,  the  latter, 

in  the  mixture,  only  supports  a  pressure  equal  to  H  -  F  (381).    But  by  Boyle's 

law  the  volumes  V  and  V  are  inversely  as  their  pressures,  consequently 

V        H  ,  .,,       VH 

whence   V'= 


V      H-F'  H-F 

ii.  Let  V  be  a  given  volume  of  saturated  air  at  the  pressure  H,  and  the 
temperature  t ;  what  will  be  its  volume  V,  also  saturated,  at  the  pressure  H' 
and  the  temperature  /'  ? 

If/be  the  maximum  tension  of  aqueous  vapour  at  /°,  and/'  its  maximum 
tension  at  /'°,  the  air  alone  in  each  of  the  mixtures  V  and  V  will  be  respec- 
tively under  the  pressures  H  — /  and  H'— _/';  consequently,  assuming  first 
that  the  temperature  is  constant,  we  obtain 
V^_H-/ 
V      W-f 
But  as  the  volumes  V  and  V  of  air,  at  the  temperatures  t'  and  /,  are  in  the 
ratio  of  i  +  at'  to  i  +  a/,  a  being  the  coefficient  of  the  expansion  of  air,  the 
equation  becomes 

V       H'-/''     \^ai 

iii.  What  is  the  weight  P  of  a  volume  of  air  V,  saturated  with  aqueous 
vapour  at  the  temperature  t  and  pressure  H  ? 

If  F  be  the  maximum  pressure  of  the  vapour  at  /°,  the  pressure  of 
the  air  alone  will  be  H-F,  and  the  problem  reduces  itself  to  finding  :  ist, 
the  weight  of  V  cubic  inches  of  dry  air  at  /,  and  under  the  pressure  H  -  F  ; 
and  2nd,  the  weight  of  V  cubic  inches  of  saturated  vapour  at  t°  under  the 
pressure  F. 

To  solve  the  first  part  of  the  problem,  we  know  that  a  cubic  inch  of  dry 
air  at  0°  and  the  pressure  760  millimetres  weighs  0-31  gram,  and  that  at  /°, 

and  the  pressure  H  -  F,  it  weighs  -j^ —    \~ t,     {'hTfl)  \  consequently  V  cubic 

inches  of  dry  air  weigh 

o-3i(H-F)V 

(i+«/)  760        ■  ■         ■         ■         •      ^  ^ 

To  obtain  the  weight  of  the  vapour,  the  weight  of  the  same  volume  of 

dry  air  at  the  same  temperature  and  pressure  must  be  sought,  and  this  is  to 

be  multiplied  by  the  relative  density  of  the  vapour.     Now  as  V  cubic  inches 

of  dry  air  at  t°.  and  the  pressure  F,  weigh   —^ —  ^--  —    V  cubic    inches    of 

aqueous  vapour,  whose  density  is  f  that  of  air  (385),  weigh 

0-31  xVF  ^  5  , 

(i+a/)  760     8        ■ ^"^ 

and  as  the  weight  P  is  equal  to  the  sum  of  the  weights  (i)  and  (2)  we  have 
p_o-3JxV(H-F)_^  0-3IXVF  ^5  _   0-31  xV    .^-^  p^ 
(i+a/)76o        (I  +  a/)  760     8      (i+rt/)76o^        '^     '' 


-385]  Spheroidal  Conditiojz.  357 

SPHEROIDAL   CONDITION. 

385.  Iieidenfrost's  phenomena.  Boutig'ny's  experiments. — When 
liquids  are  thrown  upon  incandescent  metal  surfaces  they  present  remark- 
able phenomena,  which  were  first  observed  by  Leidenfrost  a  century  ago, 
and  have  been  named  after  their  discoverer.  They  have  since  then  been 
studied  by  other  physicists,  and  more  especially  by  Boutigny. 

Figure  352  represents  an  interesting  method  of  illustrating  this.  F  is  a 
small  copper  flask  which  is  heated  to  dull  redness  over  a  spirit  lamp,  and 
a  small  quantity  of  boil- 
ing hot  water  is  carefully 
introduced  ;  a  cork  C 
having  been  loosely  fitted, 
the  lamp  is  removed,  and 
in  a  short  time  steam  is 
formed  rapidly  with  such 
explosive  violence  as  to 
drive  out  the  cork. 

When  a  tolerably 
thick  silver  or  platinum 
dish  is  heated  to  redness, 
and   a   little   water,   pre- 

,  J        .  Fig.  352. 

viously  warmed,  is 
dropped  into  the  dish  by  means  of  a  pipette,  the  liquid  does  not  spread  itself 
out  on  the  dish,  and  does  not  moisten  it,  as  it  would  at  the  ordinaiy  tempera- 
ture, but  assumes  the  form  of  a  flattened  globule,  which  fact  Boutigny  ex- 
presses by  saying  that  it  has  passed  into  the  spheroidal  state.  It  rotates 
rapidly  round  on  the  bottom  of  the  dish,  taking  sometimes  the  form  of  a  star, 
and  not  only  does  it  not  boil,  but  its  evaporation  is  only  about  one-fiftieth 
as  rapid  as  if  it  boiled.  As  the  dish  cools,  a  point  is  reached  at  which  it  is 
not  hot  enough  to  keep  the  water  in  the  spheroidal  state  ;  it  is  accordingly 
moistened  by  the  Hquid,  and  a  violent  ebullition  suddenly  ensues. 

All  volatile  Hquids  can  assume  the  spheroidal  condition  ;  the  lowest 
temperature  at  which  it  can  be  produced  varies  with  each  liquid,  and  is 
more  elevated  the  higher  the  boiling  point  of  the  liquid.  For  water,  the 
dish  must  have  at  least  a  temperature  of  200°  ;  for  alcohol,  134°  ;  and  for 
ether,  61°. 

The  temperature  of  a  liquid  in  the  spheroidal  state  is  always  below  its 
boiling  point.  This  temperature  has  been  measured  by  Boutigny  by  means 
of  a  very  dehcate  thermometer  ;  but  his  method  is  not  free  from  objections, 
and  it  is  probable  that  the  temperatures  he  obtained  were  too  high.  He 
found  that  of  water  to  be  95°  ;  alcohol,  75°  ;  ether,  34°;  and  liquid  sulphu- 
rous acid,  -11°.  But  the  temperature  of  the  vapour  which  is  disengaged 
appears  to  be  as  high  as  that  of  the  vessel  itself. 

This  property  of  liquids  in  the  spheroidal  state  remaining  below  their 
boiling  point  was  applied  by  Boutigny  in  a  remarkable  experiment,  that 
of  freezing  water  in  a  red-hot  crucible.  He  heated  a  platinum  dish  to 
bright  redness,  and  placed  a  small  quantity  of  liquid  sulphurous  acid  in  it. 
It  immediately  assumed  the  spheroidal  condition,  and  its  evaporation  was 


358 


On  Heat. 


[385- 


remarkably  slow.  Its  temperature,  as  has  been  stated,  was  about  -  1 1°,  and 
when  a  small  quantity  of  water  was  added,  it  immediately  solidified,  and  a 
small  piece  of  ice  could  be  thrown  out  of  the  red-hot  crucible.  In  a  similar 
manner  Faraday,  by  means  of  a  mixture  of  solid  carbonic  acid  and  ether, 
succeeded  in  freezing  mercury  in  a  red-hot  crucible. 

In  the  spheroidal  state  the  liquid  is  not  in  contact  with  the  vessel. 
Boutigny  proved  this  by  heating  a  silver  plate  placed  in  a  horizontal  position 
and  dropping  on  it  a  little  dark-coloured  water.  The  liquid  assumed  the 
spheroidal  condition,  and  the  flame  of  a  candle  placed  at   some  distance 


perforated  by  several  fine  holes  be  heated,  a  liquid  will  assume  the  spheroidal 

state  when  pro- 
jected upon  it. 
This  is  also  the 
case  with  a  flat 
helix  of  plati- 
n  u  m  w  i  r  e 

pressed  into  a 
slightly  concave 
shape.  An  ex- 
periment of  an- 
other class,  due 
to  Prof  Church, 
also     illustrates 

the  same  fact.  A  polished  silver  dish  is  made  red-hot,  and  a  few  drops 
of  a  solution  of  sulphide  of  sodium  are  projected  on  it.  The  liquid  passes 
into  the  spheroidal  condition,  and  the  silver  undergoes  no  alteration.  But 
if  the  dish  is  allowed  to  cool,  the  liquid  instantly  moistens  it,  producing  a 
dark  spot,  due  to  the  formation  of  sulphide  of  silver.  In  like  manner  nitric 
acid  assumes  the  spheroidal  state  when  projected  on  a  heated  silver  plate, 
and  does  not  attack  the  metal  so  long  as  the  plate  remains  hot. 

An  analogous  phenomenon  is  observed  when  potassium  is  placed  on 
water.  Hydrogen  is  liberated,  and  burns  with  a  yellow  flame  ;  hydrate  of 
potassium,  which  is  formed  at  the  same  time,  floats  on  the  surface  without 
touching  it,  owing  to  its  high  temperature.  In  a  short  time  it  cools  down, 
and  the  globule,  coming  in  contact  with  water,  bursts  with  an  explosion. 

Similarly,  liquids  may  be  made  to  roll  upon  liquids,  and  solid  bodies 
which  vaporise  without  becoming  liquid  also  assume  a  condition  analogous 
to  the  spheroidal  state  of  liquids  when  they  are  placed  on  a  surface  whose 
temperature  is  sufficiently  high  to  vaporise  them  rapidly.  This  is  seen  when 
a  piece  of  carbonate  of  ammonium  is  placed  in  a  red-hot  platinum  crucible. 
The  phenomena  of  the  spheroidal  state  seem  to  prove  that  the  liquid 
globule  rests  upon  a  sort  of  cushion  of  its  own  vapour,  produced  by  the  heat 
radiated  from  the  hot  surface  against  its  under  side.  As  fast  as  this  vapour 
escapes  from  under  the  globule,  its  place  is  supplied  by  a  fresh  quantity 
formed  in  the  same  way,  so  that  the  globule  is  constantly  buoyed  up  by  it, 
and  does  not  come  in  actual  contact  with  the  heated  surface.  When,  how- 
ever, the  temperature  of  the  latter  falls,  the  formation  of  vapour  at  the  under 
surface  becomes  less  and  less  rapid,  until  at  length  it  is  not  sufficient  to  pre- 


-386] 


Gay-Lussacs  Method. 


359 


vent  the  globule  touching  the  hot  metal  or  liquid  on  which  it  rests.  As  soon 
as  contact  occurs,  heat  is  rapidly  imparted  to  the  globule,  it  enters  into 
ebullition  and  quickly  boils  away. 

This  explanation  is  confirmed  by  the  experiments  of  Budde,  who  found 
that  in  an  exhausted  receiver  water  passes  into  the  spheroidal  state,  even  when 
the  temperature  of  the  support  is  not  more  than  80°  or  90°;  for  then  the 
vapour  has  only  to  support  the  drop,  and  not  the  atmospheric  pressure  also. 

These  experiments  on  the  spheroidal  state  explain  the  fact  that  the  hand 
may  be  dipped  into  melted  lead,  or  even  melted  iron,  without  injury.  It  is 
necessary  that  the  liquid  metal  be  heated  greatly  above  its  solidifying  point. 
Usually  the  natural  moisture  of  the  hand  is  sufficient,  but  it  is  better  to  wipe 
it  with  a  damp  cloth.  In  consequence  of  the  great  heat  the  hand  becomes 
covered  with  a  layer  of  spheroidal  fluid,  which  prevents  the  contact  of  the 
metal  with  the  hand.  Radiant  heat  alone  operates,  and  this  is  principally 
expended  in  forming  aqueous  vapour  on  the  surface  of  the  hand.  If  the 
hand  is  immersed  in  boiling  water,  the  water  adheres  to  the  flesh,  and  con- 
sequently a  scald  is  produced. 

The  tales  of  ordeals  by  fire  during  the  middle  ages,  of  men  who  could 
run  barefooted  over  red-hot  iron  without  being  injured,  are  possibly  true  in 
some  cases,  and  would  find  an  explanation  in  the  preceding  phenomena. 


O 


DENSITY   OF   VAPOURS. 

386.  Gay-Xussac's  method. — The  deftsity  of  a  vapour  is  the  relation 
between  the  weight  of  a  given  volume  of  this  vapour  and  that  of  the  same 
volume  of  air  at  the  same  temperature  and 
pressure. 

The  older  methods  used  in  determining  the 
density  of  vapours  are  :  Gay-Lussac's,  which 
serves  for  liquids  that  boil  at  about  100°,  and 
Dumas',  which  can  be  used  up  to  350°. 

Fig.  354  represents  the  apparatus  used  by 
Gay-Lussac.  It  consists  of  an  iron  vessel  con- 
taining mercury,  in  which  there  is  a  glass 
cylinder  M.  This  is  filled  with  water  or  oil, 
and  the  temperature  is  indicated  by  the  ther- 
mometer T.  In  the  interior  of  the  cylinder  is 
a  graduated  gas  jar  C,  which  at  first  is  filled 
with  mercury. 

The  liquid  whose  vapour-density  is  to  be 
determined  is  placed  in  a  small  glass  bulb  A, 
represented  on  the  left  of  the  figure.  The  bulb 
is  then  sealed  and  weighed  ;  the  weight  of  the 
liquid  taken  is  obviously  the  weight  of  the  bulb 
when  filled,  minus  its  weight  while  empty.  The 
bulb  is  then  introduced  into  the  jar  C,  and  the 
liquid  in  M  gradually  heated  somewhat  higher 
than  the  boiling  point  of  the  liquid  in  the  bulb. 
In  consequence  of  the  expansion  of  this  liquid  the  bulb  breaks,  and  the 


36o  On  Heat.  [386- 

liquid  becoming  converted  into  vapour,  the  mercury  is  depressed,  as  repre- 
sented in  the  figure.  The  bulb  must  be  so  small  that  all  the  liquid  in  it  is 
vaporised.  The  volume  of  the  vapour  is  given  by  the  graduation  on  the  jar. 
Its  temperature  is  indicated  by  the  thermometer  T,  and  the  pressure  is 
shown  by  the  diiTerence  between  the  height  of  the  barometer  at  the  time  of 
the  observation  and  the  height  of  the  column  of  mercury  in  the  gas  jar.  It 
is  only  necessary  then  to  calculate  the  weight  of  a  volume  of  air  equal  to  that 
of  the  vapour  under  the  same  conditions  of  temperature  and  pressure.  The 
quotient,  obtained  by  dividing  the  weight  of  the  vapour  by  that  of  the  air, 
gives  the  required  density  of  the  vapour. 

Let^  be  the  weight  of  the  vapour  in  grains,  v  its  volume  in  cubic  inches, 
and  t  its  temperature  ;  if  H  be  the  height  of  the  barometer,  and  h  that  of 
the  mercury  in  the  gas  jar,  the  pressure  on  the  vapour  will  be  H  —h. 

It  is  required  to  find  the  weight  p'  of  a  volume  of  air  ?',  at  the  tempera- 
ture /,  and  under  a  pressure  H  -h.  At  zero,  under  a  pressure  of  760  milli- 
metres, a  cubic  inch  of  air  weighs  0-31  grain  ;  consequently,  under  the 
same  conditions,  v  cubic  inches  will  weigh  0-317/  grains.  And  therefore 
the  weight  of  v  cubic  inches  of  air,  at  t°  and  the  pressure  760  millimetres,  is 

-^ —  gram  [332,  prob.  n. ]. 
\\  at 

As  the  weight  of  a  volume  of  air  is 
proportional  to  the  pressure,  the  above 
weight  may  be  reduced  to  the  pressure 

TT  J 

Vl—Ji    by   multiplying    by  — - — ,    which 

0-317/ (H-//) 

gives  —^ -^- — — ^ 

*  (i+rt/)76o 

for  the  weight  p'  of  the  volume  of  air  v, 
under  the  pressure  W  —  Ji  and  at  /".  Con- 
sequently, for  the  desired  density  we  have 

T\-P  -P  (^  -^  (it)  760 

~ P'~  0-317/ (H-/^)" 

387.  Hofmann's  metliod. — Hofmann 
has  materially  improved  the  method 
of  Gay-Lussac  by  having  the  mercury 
tube  //5,  in  which  the  vapour  is  pro- 
duced, about  a  metre  in  length  (fig.  355) ; 
it  is,  in  fact,  a  barometer,  and  the  vapour 
is  formed  in  the  Torricellian  vacuum. 
This  tube  is  surrounded  by  another  glass 
tube  a,  which  is  connected,  by  a  bent  tube 
6",  with  a  canister  e,  so  that  water,  amylic 
alcohol,  or  aniline,  or,  indeed,  any  sub- 
stance with  a  constant  boiling  point,  may 
be  distilled  through  the  tube  a,  and  the 
vapour  issues  by  the  tube  d,  which  is 
arrangement  not  represented  in  the  figure.    In 


connected  with  a  condensing 


-388] 


Dumas'  Method. 


361 


this  way  more  constancy  in  the  temperatures  is  ensured  than  with  the  use  of 
a  mercury  bath.  The  hquid  is  contained  in  very  minute  stoppered  tubes,  h, 
holding  from  20  to  100  miUigrammes  of  water  ;  the  stoppers  come  out  in  the 
vacuum,  and  the  tubes  can  be  used  over  again. 

As,  under  the  above  conditions,  the  Hquid  vaporises  into  a  vacuum,  the 
vapour  is  formed  under  a  very  much  lower  pressure  than  that  of  the  atmo- 
sphere, and  therefore  at  a  temperature  much  below  its  ordinary  boiling  point. 
Thus,  the  vapour-density  of  a  body  which  only  boils  at  a  temperature  of 
1 50°  can  be  determined  at  the  temperature  of  boiling  water.  This  is  of  great 
use  in  the  case  of  those  bodies  which  decompose  at  their  boiling  point 
under  the  ordinary  atmospheric  pressure. 

388.  Dumas'  method. — The  original  method  of  Gay-Lussac  cannot  be 
applied  to  liquids  whose  boiling  point  exceeds  150°  or  160°.  In  order  to  raise 
the  oil  in  the  cylinder  to  this  temperature  it  would  be  necessary  to  heat  the 
mercuiy  to  such  a  degree  that  its  vapour  would  be  dangerous  to  the  operator. 
And,  moreover,  the  pressure  of  the  mercurial  vapour  in  the  graduated  jar 
would  add  itself  to  that  of  the  vapour  of  the  liquid,  and  so  far  vitiate  the  result. 

The  following  method,  devised  by  Dumas,  can  be  used  up  to  the  tem- 
perature at  which  glass  begins  to  soften  ;  that  is,  about  400^  A  glass 
globe  is  used  with  the  neck  drawn  out  to  a  fine  point  (fig.  356).  The  globe, 
having  been  dried  externally  and  internally,  is  weighed,  the  temperature  i 
and  barometric  height  h  being  noted.  This  weight,  W,  is  the  weight  of  the 
glass  G  in  addition  to  p,  the  weight  of  the  air  it  contains.  The  globe  is 
then  gently  warmed  and  its  point  immersed  in  the  liquid  whose  vapour- 
density  is  to  be  determined  :  on  cooling,  the  air  contracts,  and  a  quantity 
of  liquid  enters  the  globe.  The  globe  is  then  immersed  in  a  bath,  either 
of  oil  or  fusible  metal,  according  to  the  tempera- 
ture to  which  it  is  to  be  raised.  In  order  to  keep 
the  globe  in  a  vertical  position  a  metal  support, 
on  which  a  movable  rod  slides,  is  fixed  on  the 
side  of  the  vessel.  This  rod  has  two  rings,  be- 
tween which  the  globe  is  placed,  as  shown  in  the 
figure.  There  is  another  rod,  to  which  a  weight 
thermometer,  D  (324),  is  attached. 

The  globe  and  thermometer  having  been  im- 
mersed in  the  bath,  the  latter  is  heated  until 
slightly  above  the  boiling  point  of  the  liquid  in 
the  globe.  The  vapour  which  passes  out  by  the 
point  expels  all  the  air  in  the  interior.  When 
the  jet  of  vapour  ceases,  which  is  the  case  when 
all  the  liquid  has  been  converted  into  vapour,  the 
point  of  the  globe  is  hermetically  sealed,  the 
temperature  of  the  bath  t\  and  the  barometric 
height  h',  being  noted.  When  the  globe  is  cooled 
it  is  carefully  cleaned  and  again  weighed.  This 
weight,  W',  is  that  of  the  glass  G,  plus  p',  the  weight  of  the  vapour  which  fills 
the  globe  at  the  temperature  t\  and  pressure  h';  or  W'  =  G  +p'.  To  obtain 
the  weight  of  the  glass  alone,  the  weight^  of  air  must  be  known,  which  is 
determined  in  the  following  manner  : — The  point  of  the  globe  is  placed  under 


Fig.  356. 


362 


On  Heat. 


[388 


mercury  and  the  extremity  broken  off'  with  a  small  pair  of  pincers  :  the 
vapour  being  condensed,  a  vacuum  is  produced,  and  mercury  rushes  up, 
completely  filling  the  globe,  if,  in  the  experiment,  all  the  air  has  been  com- 
pletely expelled.  The  mercury  is  then  poured  into  a  carefully  graduated 
measure,  which  gives  the  volume  of  the  globe.  From  this  result,  the  volume 
of  the  globe  at  the  temperature  /'  may  be  easily  calculated,  and  consequently 
the  volume  of  the  vapour.  From  this  determination  of  the  volume  of  the 
globe,  the  weight/  of  the  air  at  the  temperature  /  and  pressure  h  is  readily 
calculated,  and  this  result  subtracted  from  W  gives  G,  the  weight  of  the 
glass.  Now  the  weight  of  the  vapour/'  is  W  — G.  We  now  know  the 
weight/'  of  a  given  volume  of  vapour  at  the  temperature  f  and  pressure  h\ 
and  it  is  only  necessary  to  calculate  the  weight  /"  of  the  same  volume  of 
air  under  the  same  conditions,  which  is  easily  accomplished.     The  quotient 

-?—  is  the  required  density  of  the  vapour. 
P" 

Deville  and  Troost  modified  Dumas'  method  so  that  it  can  be  used  for 

determining  the  vapour-density  of  liquids  with  very  high  boiling  points. 
The  globe  is  heated  in  an  iron  cylinder  in  the  vapour  of  mercury  or  of 
sulphur,  the  temperatures  of  which  are  constantrespectively  at  35o°and440°. 
In  other  respects  the  determination  is  the  same  as  in  Dumas'  method. 

For   determinations   at   higher  temperatures,   Deville  and  Troost   em- 
ployed the  vapour  of  zinc,  the  temperature  of  which  is    1040°.      As  glass 
vessels  are  softened  by  this  heat,  they  used  porcelain  globes  with  finely- 
drawn-out  necks,  which  are  sealed  by  means  of 
the  oxyhydrogen  flame. 

In  the  case  of  substances  having  a  high  boiling 
point,  Victor  Meyer  has  advantageously  used  a 
non-volatile  substance.  Wood's  fusible  alloy,  which 
melts  at  70°,  instead  of  mercury.    Habermann  has 
y        ^\  zj  introduced  into  Dumas'  method  Hofmann's  modi- 

'^^       \       =  fication  of  Gay-Lussac's,  by  connecting  the  open 

^''-  ^       "  end  of  the  vessel  B  (fig.  356)  with  a  space  in  which 

a  partial  vacuum  is  made.  Thus  the  vapour- 
density  can  be  determined  for  temperatures  far 
below  the  boiling  point. 

A  method  of  determining  vapour-density,  much 
in  use,  is  that  devised  by  Victor  Meyer.  The 
vessel  b  (fig.  357),  of  about  100  cub.  cent,  capacity, 
is  fused  to  a  narrow  glass  tube  about  60  cm.  in 
length,  provided  with  a  caoutchouc  stopper  </, 
which  is  always  pushed  in  to  the  same  depth,  and 
with  a  narrow  delivery  tube  a. 

This  apparatus  is  hung  in  the  glass  flask  Cy 
the  bulb  of  which  holds  about  80  cm.,  and  con- 
tains a  liquid  of  constant  boiling  point,  such  as  aniline  or  diphenyl. 
This  is  heated  until  it  boils  constantly,  which  is  seen  when  no  air-bubbles 
issue  from  the  delivery  tube.  When  this  is  attained  a  graduated  tube  full 
of  water  is  pushed  over  the  end  of  the  tube  a  ;  the  stopper  d  is  removed 
and   quickly  replaced  after  dropping  in  the  weighed  substance  contained 


-389]  Dissociation.  363 

in  a  small  glass  tube  ;  in  order  to  prevent  a  possible  breakage  some 
asbestos  is  placed  in  the  bottom  of  b.  As  soon  as  the  substance  vaporises 
a  corresponding  volume  of  air  issues  and  is  collected  in  the  tube.  When 
no  more  issues  the  tube  is  placed  in  a  cylinder  of  water  and  is  depressed 
until  the  level  inside  and  outside  is  the  same.  The  volume  v  is  read 
off,  and  also  the  temperature  of  the  water  /,  which  is  also  that  of  the  room, 
and  the  barometric  height  H.  These  data,  together  with  the  weight  of  the 
substance^,  and  h,  the  pi^essure  of  aqueous  vapour  at  ^°,  enable  us  to  calcu- 
late the  density  from  the  formula 

D  =  ^  =         P  X  760  (273  +  t) _;g^  (273+/)  2152 

p'     V  (0-001293)  (H-//)  273  V  (H-/«) 

Thus  neither  the  capacity  of  the  vessel  b  nor  the  temperature  of  the  vapour 
need  be  known,  unless  it  be  desired  to  investigate  in  what  respect  the  density 
varies  with  the  temperature  ;  the  volume  of  the  vapour  is  obtained  in  the 
form  of  an  equal  volume  of  air  measured  at  the  temperature  of  the  room. 

389.  Kelation  of  vapour-density  to  molecular  weigrht.  Dissocia- 
tion.— The  densities  of  \apours,  determined  at  temperatures  a  few  degrees 
above  their  boiling  points,  and  when  they  may  be  considered  as  perfect 
gases,  are  governed  by  a  simple  but  very  important  law,  that  the  densities 
of  vapoitrs  are  proportiottal  to  their  molecular  weights.  If  both  densities 
and  molecular  weights  are  ret'erred  to  the  same  standard,  that  of  hydrogen 
being  taken  as  2  for  instance,  the  vapour-densities  are  equal  to  the  mole- 
cular weights.  If  the  density  of  air  is  taken  at  i,  that  of  hydrogen  is 
0-0693  =  ^,  and  hence  for  all  other  gases  and  superheated  vapours  the 
density  is  5^^^  of  the  molecular  weight. 

This  law  is  of  great  importance  in  chemistry  and  in  fixing  the  molecular 
weights  of  bodies,  more  especially  in  organic  chemistry.  In  some  cases 
exceptions  are  met  with  ;  these,  when  small,  may  be  ascribed  to  imperfection 
of  the  gaseous  state.  A  more  important  cause  is  the  following  : — When  sal- 
ammoniac,  NH^Cl,  for  instance,  is  strongly  heated,  it  is  resolved  into 
ammonia,  NH^,  and  hydrochloric  acid,  HCl,  and  it  then  occupies  a  volume 
double  that  required  by  the  law.  But  there  is  a  partial  decomposition 
even  at  lower  temperatures,  so  that  the  vapour- consists  of  molecules  of 
sal-ammoniac,  mixed  with  molecules  of  free  hydrochloric  acid  and  of  free 
ammonia.  In  such  cases  the  vapour-density  is  said  to  be  abnormal ;  and 
this  partial  decomposition,  in  which  there  is  a  mixture  of  undecomposed 
and  of  decomposed  molecules,  is  spoken  of  as  dissociation.  Thus,  sulphuric 
acid,  SO  |H.,,  at  325°,  consists  of  about  one  half  undecomposed  molecules,  while 
the  other  moiety  decomposes  into  sulphuric  anhydride,  SO,,  and  water,  H.,0. 
The  dissociation  of  water  begins  at  1200°  C,  and  is  complete  at  2500°. 

Dissociation  does  not  take  place  suddenly,  but  gradually  ;  it  increases 
with  the  temperature,  and  is  limited  by  the  tendency  of  the  components  to 
recombine  ;  for  each  temperature  the  quantity  dissociated  is  in  a  constant 
ratio  to  the  whole.  As  the  temperature  sinks,  the  bodies  again  recombine, 
and  at  the  initial  temperature  the  body  is  in  its  original  state.  In  this 
respect  dissociation  differs  from  decomposition.  The  temperature  at  which 
the  decomposition  is  half  complete  is  taken  as  that  of  dissociation. 

Dissociation  is  also  met  with  in  elementary  bodies  ;  thus  at  a  tempera- 


364 


On  Heat. 


[389- 


ture  of  500°  C.  sulphur  has  the  vapour  density  96  (H  =  i),  representing  a 
molecular  weight  of  192  ;  as  the  temperature  increases  this  becomes  less, 
and  from  1000°  it  is  constant,  being  then  32,  which  is  normal,  corresponding 
to  a  molecular  weight  of  64.  At  the  lower  temperature  the  molecule  is  con- 
sidered to  be  an  aggregate  consisting  of  six  atoms  or  three  molecules,  while 
at  higher  temperatures  this  complex  splits  up,  and  at  1000°  consists  of  the 
normal  diatomic  molecule.  In  like  manner  the  density  of  iodine  vapour, 
which  up  to  600°  is  8716,  is  only  4-5,  or  about  half  as  much,  at  1500°,  but 
this  remains  constant.  This  represents  a  dissociation  of  the  iodine  molecule, 
I.,,  into  two  atoms. 

Densities  of  vapours. 


Air        .... 

.     I  -0000     Vapo 

ur  of  carbon  bisul 

abide     2-4476 

Vapour  of  water  . 

.     0-6225 

,         phosphorus 

•     4-3256 

„         alcohol 

.     1-6138 

,         turpentine 

•     5'oi3o 

„         acetic  acid   . 

.     2-0800 

,         sulphur 

.     6-6542 

„         ether    . 

.     2-5860 

,         mercury 

.     6-9760 

„         benzole 

.     2-7290 

„         iodine  . 

.     8-7160 

The  density  of  aqueous  vapour,  when  a  space  is  saturated  with  it,  is  at 
all  temperatures  |,  or,  more  accurately,  0-6225,  of  the  density  of  air  at  the 
same  temperature  and  pressure. 

390.  Relation  between  the  volume  of  a  liquid  and  tbat  of  its 
vapour. — The  density  of  vapour  being  known,  we  can  readily  calculate  the 
ratio  between  the  volume  of  a  vapour  in  the  saturated  state  at  a  given  tem- 
perature and  that  of  its  liquid  at  zero.  We  may  take  as  an  example  the 
relation  between  water  at  zero  and  steam  at  100°. 

The  ratio  between  the  weights  of  equal  volumes  of  air  at  zero,  and  the 
normal  barometric  pressure,  and  of  water  under  the  same  circumstances,  is 
as  I  :  ii})-  But  from  what  has  been  already  said  (332),  the  density  of  air 
at  zero  is  to  its  density  at  100°  as  i  ■\-  at  :  i.  Hence  the  ratio  between  the 
weights  of  equal  volumes  of  air  at  100°  and  water  at  0°  is 
I 


:  773,  or  0-73178  :  -jTi 


I  +0-003665  X  100 

Now  from  the  above  table  the  density  of  steam  at  100°  C,  and  the 
normal  pressure,  compared  with  that  of  air  under  the  same  circumstances, 
is  as  0-62225  •  I-  Hence  the  ratio  between  the  weights  of  equal  volumes  of 
steam  at  100°  and  water  at  o'^  is 

0-73178  X  0-6225  :  113,  or  0-4555  :  773,  or  i  :  1698. 

Therefore,  as  the  volumes  of  bodies  are  inversely  as  their  densities,  one 
volume  of  water  at  zero  expands  into  1-698  volumes  of  steam  at  loo*^  C. 
The  practical  rule,  that  a  cubic  inch  of  water  yields  a  cubic  foot  of  steam, 
though  not  quite  accurate,  expresses  the  relation  in  a  convenient  form. 


-392]  365 


CHAPTER   VI. 

HYGROMETRY. 

391.  Province  of  hygrometry. — The  province  oi  hygrometry\%  to  deter- 
mine the  quantity  of  aqueous  vapour  contained  in  a  given  volume  of  air. 
This  quantity  is  very  variable  ;  but  the  atmosphere  is  seldom  or  never 
completely  saturated  with  vapour,  even  m  our  climate.  Nor  is  it  ever  com- 
pletely dry  ;  for  if  hygrometric  substances — that  is  to  say,  substances  with  a 
great  affinity  for  water,  such  as  chloride  of  calcium,  sulphuric  acid,  &c. — be 
at  any  time  exposed  to  the  air,  they  absorb  aqueous  vapour. 

392.  Kyg-rometrlc  state. — As,  in  general,  the  air  is  never  saturated,  the 
ratio  of  the  quantity  of  aqueous  vapour  actually  present  in  the  atmosphere 
to  that  which  it  would  contain  if  it  were  saturated,  the  temperature  remain- 
ing the  same,  is  called  the  hygrometric  state,  or  degree  of  sattcratio7i. 

The  absolute  inoistiire  is  measured  by  the  weight  of  water  actually  present 
in  the  form  of  vapour  in  the  unit  of  volume. 

We  say  the  '  air  is  dry '  when  water  evaporates  and  moist  objects  dry 
rapidly;  and  the  'air  is  moist'  when  they  do  not  dry  rapidly,  and  when 
the  least  lowering  in  temperature  brings  about  deposits  of  moisture.  The 
air  is  dry  or  moist  according  as  it  is  more  or  less  distant  from  its  point 
of  saturation.  Our  judgment  is,  in  this  respect,  independent  of  the  absolute 
quantity  of  moisture  in  the  air.  Thus,  if  in  summer,  at  a  temperature  of 
25°  C,  we  find  that  each  cubic  metre  of  air  contains  13  grammes  of  vapour, 
we  say  it  is  very  dry,  for  at  this  temperature  it  could  contain  22-5  grammes. 
If,  on  the  other  hand,  in  winter  we  find  that  the  same  volume  contains 
6  grammes,  we  call  it  moist,  for  it  is  nearly  saturated  with  vapour,  and  the 
slightest  diminution  of  temperature  produces  a  deposit.  When  a  room  is 
warmed,  the  quantity  of  moisture  is  not  diminished,  but  the  humidity  of 
the  air  is  lessened,  because  its  point  of  saturation  is  raised.  The  air 
may  thus  become  so  dry  as  to  be  injurious  to  the  health,  and  hence  it  is 
usual  to  place  vessels  of  water  on  the  stoves  used  for  heating  in  France  and 
Germany. 

As  Sonde's  law  applies  to  non-saturated  vapours  as  well  as  to  gases  (354), 
it  follows  that,  with  the  same  temperature  and  volume,  the  weight  of  vapour 
in  an  unsaturated  space  increases  with  the  pressure,  and  therefore  with 
the  pressure  of  the  vapour  itself.  Instead,  therefore,  of  the  ratio  of  the 
quantities  of  vapour,  that  of  the  corresponding  pressures  may  be  substituted, 
and  it  may  be  said  that  the  hygrometric  state  is  the  ratio  of  the  elastic 
force  of  the  aqueous  vapour  •which  the  air  actually  contains,  to  the  elastic 
force  of  the  vapour  which  it  would  contain  at  the  same  temperature  if  it 
were  saturated. 

If/ is  the  actual  pressure  of  aqueous  vapour  in  the  air,  and  F  that  of  satu- 


366 


On  Heat. 


[392- 


rateci  vapour  at  the  same  temperature,  and  E  the  hygrometric  state,  we  have 

E  =  -1^ ;  whence  /=  F  x  E. 
F 

As  a  consequence  of  this  second  definition,  it  is  important  to  notice  that, 
the  temperature  having  varied,  the  air  may  contain  the  same  quantity  of 
vapour  and  yet  not  have  the  same  hygrometric  state.  For,  when  the  tem- 
perature rises,  the  tension  of  the  vapour  which  the  air  would  contain,  if  satu- 
rated, increases  more  rapidly  than  the  tension  of  the  vapour  actually  present 
in  the  atmosphere,  and  hence  the  ratio  between  the  two  forces — that  is  to 
say,  the  hygrometric  state — becomes  smaller. 


Jamin  proposes  to  replace  this 


/ 


ratio  -(-,-,  which    expresses  the  relative 
r 

moisture,  by  the  ratio  ^f-/—^,  in  which  H  is  the  barometric  height ;  he  calls 

this  the  hygrometric  richness,  and  contends  that  it  brings  out  changes  in  the 
quantity  of  moisture  present  in  the  air  with  greater  distinctness. 

It  will  presently  be  explained  (401)  how  the  weight  of  the  vapour  contained 
in  a  given  \olume  of  air  may  be  deduced  from  the  hygrometric  state. 

393.  Different  kinds  of  hygrometers. — Hygrometers  are  instruments  for 
measuring  the  hygrometric  state  of  the  air.  There  are  numerous  varieties  of 
them — chemical  hygrometers,  condensing  hygrometers,  and  psychrometers. 

394.  Chemical  hygrometer. — The  method  of  the  chemical  hygrometer 
consists  in  passing  a  known  volume  of  air  over  a  substance  which  readily 


Fig.  3S8. 

absorbs  moisture — chloride  of  calcium,  for  instance.  The  substance  having 
been  weighed  before  the  passage  of  air,  and  then  afterwards,  the  increase 
in  weight  represents  the  amount  of  aqueous  vapour  present  in  the  air.  By 
means  of  the  apparatus  represented  in  fig.  358  it  is  possible  to  examine  any 


-396]  Danicirs  Hygrometer.  367 

given  volume  of  air.  Two  brass  reservoirs,  A  and  B,  of  the  same  size  and 
construction,  act  alternately  as  aspirators,  by  being  fixed  to  the  same  axis, 
about  which  they  can  turn.  They  are  connected  by  a  central  tubulure,  and 
by  means  of  two  tubulures  in  the  axis  the  lower  reservoir  is  always  in  con- 
nection with  the  atmosphere,  while  the  upper  one,  by  means  of  a  caoutchouc 
tube,  is  connected  with  two  tubes  M  and  N,  filled  either  with  chloride  of 
calcium,  or  with  pumice-stone  impregnated  with  sulphuric  acid.  The  first 
absorbs  the  vapours  in  the  air  drawn  through,  while  the  other,  M,  stops  any 
vapour  which  might  diffuse  from  the  reservoirs  into  the  tube  N. 

The  lower  reservoir  being  full  of  water,  and  the  upper  one  of  air,  the 
apparatus  is  inverted  so  that  the  liquid  flows  slowly  from  A  to  B.  A  partial 
vacuum  being  formed  in  A,  air  enters  by  the  tubes  N  M,  in  the  first  of  which 
all  the  vapour  is  absorbed.  When  all  the  water  is  run  into  B  it  is  inverted  ; 
the  same  flow  recommences,  and  the  same  volume  of  air  is  drawn  through 
the  tube  N.  Thus,  if  each  reservoir  holds  a  gallon,  for  example,  and  the 
apparatus  has  been  turned  five  times,  6  gallons  of  air  have  traversed  the 
tube  N,  and  have  been  dried.  If  then,  before  the  experiment,  the  tube  with 
its  contents  has  been  weighed,  the  increase  of  weight  gives  the  weight  of 
aqueous  vapour  present  in  6  gallons  of  air  at  the  time  of  the  experiment. 

Edelmann  has  devised  a  new  form  of  hygrometer,  the  principle  of  which 
is  to  enclose  a  given  volume  of  air,  and  then  to  absorb  the  aqueous  vapour 
present  by  means  of  strong  sulphuric  acid  ;  in  this  way  a  diminution  in  the 
pressure  is  produced  which  is  determined,  and  which  is  a  direct  measure  of 
the  tension  y  of  the  aqueous  vapour  previously  present. 

Similar  apparatus  have  been  devised  by  Rudorff  and  by  Neesen. 

395.  Condensing-  hygrometers. — When  a  body  gradually  cools  in  a 
moist  atmosphere — as,  for  instance,  when  a  lump  of  ice  is  placed  in  water 
contained  in  a  polished  metal  vessel — the  layer  of  air  in  immediate  contact 
with  it  cools  also,  and  a  point  is  ultimately  reached  at  which  the  vapour 
present  is  just  sufficient  to  saturate  the  air  ;  the  least  diminution  of  tempera- 
ture then  causes  a  precipitation  of  moisture  on  the  vessel  in  form  of  dew^ 
When  the  temperature  rises  again,  the  dew  disappears.  The  mean  of  these 
two  temperatures  is  taken  as  the  dew-poi?it,  and  the  object  of  condensing 
hygrometers  is  to  observe  this  point.  Daniell's  and  Regnault's  hygrometers 
belong  to  this  class. 

396.  Baniell's  hygrrometer. — This  consists  of  two  glass  bulbs  at  the 
extremities  of  a  glass  tube  bent  twice  (fig.  359).  The  bulb  A  is  two-thirds 
full  of  ether,  and  a  very  delicate  thermometer  plunged  in  it ;  the  rest  of  the 
space  contains  nothing  but  the  vapour  of  ether,  the  ether  having  been  boiled 
before  the  bulb  B  was  sealed.  The  bulb  B  is  covered  with  muslin,  and 
ether  is  dropped  upon  it.  The  ether  in  evaporating  cools  the  bulb,  and  the 
vapour  contained  in  it  is  condensed.  The  internal  pressure  being  thus  dimi- 
nished, the  ether  in  A  forms  vapour  which  condenses  in  the  other  bulb  B.  In 
proportion  as  the  liquid  distils  from  the  lower  to  the  upper  bulb,  the  ether  in 
A  becomes  cooler,  and  ultimately  the  temperature  of  the  air  in  immediate 
contact  with  A  sinks  to  that  point  at  which  its  vapour  is  more  than  sufficient 
to  saturate  it,  and  it  is,  accordingly,  deposited  on  the  outside  as  a  ring  of 
dew  corresponding  to  the  surface  of  the  ether.  The  temperature  of  this  point 
is  noted  by  means  of  the  thermometer  in  the  inside.    The  addition  of  ether  to 


368 


On  Heat. 


[396- 


the  bulb  B  is  then  discontinued,  the  temperature  of  A  rises,  and  the  tempera- 
ture at  which  the  dew  disappears  is  noted.     In  order  to  render  the  deposition 
of  dew  more  perceptible,  the  bulb  A  is 
made  of  black  glass. 

These  two  points  having  been  deter- 
mined, their  mean  is  taken  as  that  of  the 
dew-point.  The  temperature  of  the  air 
at  the  time  of  the  experiment  is  indicated 
by  the  thermometer  on  the  stem.  The 
pressure^  corresponding  to  the  tempera- 
ture of  the  dew-point,  is  then  found  in  the 
table  of  pressures  (358).  This  pressure  is 
exactly  that  of  the  vapour  present  in  the 
air  at  the  time  of  the  experiment.  The 
pressure  F  of  vapour  saturated  at  the 
temperature  of  the  atmosphere  is  found 
by  means  of  the  same  table ;  the  quotient 
obtained  by  dividing  _/"  by  F  represents 
the  hygrometric  state  of  the  air  (392). 
For  instance,  the  temperature  of  the  air 
being  15°,  suppose  the  dew-point  is  5°. 
From  the  table  the  corresponding  pres- 
sures are  /=  6-534  millimetres,  and 
F  =  I2"699  millimetres,  which  gives  0-514 
for  the  ratio  of  f  to  F,  or  the  hygro- 
metric state. 
There  are  many  sources  of  error  in  Daniell's  hygrometer.  The  principal 
are  :  ist,  that  as  the  evaporation  in  the  bulb  A  only  cools  the  liquid  on  the 
surface,  the  thermometer  dipping  on  it  does  not  exactly  give  the  dew-point  ; 
2nd,  that  the  observer  standing  near  the  instrument  modifies  the  hygro- 
metric state  of  the  surrounding  air,  as  well  as  its  temperature  ;  the  cold 
ether  vapour  also  flowing  from  the  upper  bulb  may  cause  inaccuracy. 

397.  Regrnault's  hygrometer. — Regnault's  hygrometer  is  free  from  the 
sources  of  error  incidental  to  the  use  of  Daniell's.  It  consists  of  two  very 
thin  polished  silver  thimbles  1-75  inch  in  height,  and  0-75  inch  in  diameter 
(fig.  360).  In  these  are  fixed  two  glass  tubes,  D  and  E,  in  each  of  which  is 
a  thermometer.  A  bent  tube.  A,  open  at  both  ends,  passes  through  the  cork 
of  the  tube  D,  and  reaches  nearly  to  the  bottom  of  the  thimble.  There  is  a 
tubulure  on  the  side  of  D,  fitting  in  a  brass  tube  which  forms  a  support  for 
the  apparatus.  The  end  of  this  tube  is  connected  with  an  aspirator  G.  The 
tube  E  is  not  connected  with  the  aspirator  ;  its  thermometer  simply  indicates 
the  temperature  of  the  atmosphere. 

The  tube  D  is  then  half  filled  with  ether,  and  the  stopcock  of  the  aspirator 
opened.  The  water  contained  in  it  runs  out,  and  just  as  much  air  enters 
through  the  tube  A,  bubbling  through  the  ether,  and  causing  it  to  evaporate. 
This  evaporation  produces  a  diminution  of  temperature,  so  that  dew  is  de- 
posited on  the  silver  just  as  on  the  bulb  in  Daniell's  hygrometer  ;  the  ther- 
mometer T  is  then  instantly  to  be  read,  and  the  stream  from  the  aspirator 
stopped.     The  dew  will  soon  disappear  again,  and  the  thermometer  T  is 


Fig.  359- 


398] 


PsycJu'oineter.      Wet-Bulb  HygrometcT. 


369 


again  to  be  read  ;  the  mean  of  the  two  readings  is  taken  ;  the  thermometer 
/  gives  the  corresponding  temperature  of  the  air,  and  hence  there  are  all  the 
elements  necessary  for 
calculating  the  hygro- 
metric  state. 

As  all  the  ether 
in  this  instrument  is 
at  the  same  tempera- 
ture in  consequence  of 
the  agitation,  and  the 
temperatures  may  be 
read  off  at  a  distance  by 
means  of  a  telescope, 
the  sources  of  error  in 
Daniell's  hygrometer 
are  avoided. 

A  much  simpler 
form  of  the  apparatus 
may  be  constructed 
out  of  a  common  test- 
tube  containing  a 
depth  of  \\  inch  of 
ether.  The  tube  is 
provided  with  a  loosely 
fitting  cork  in  which  are 
a  delicate  thermometer 
and  a  narrow  bent  tube  dipping 
through  a  caoutchouc  tube  of  considerable  length,  a  diminution  of  tempera- 
ture is  caused,  and  dew  is  ultimately  deposited  on  the  glass  ;  after  a  little 
practice  the  whole  process  can  be  conducted  almost  as  well  as  with 
Regnault's  more  complete  instrument.  The  temperature  of  the  air  is 
indicated  by  a  detached  thermometer. 

y^"a.  Sines'  hyg-rometer. —  Dines  has  constructed  a  hygrometer  which 
is  also  one  of  condensation,  but  which  dispenses  with  the  use  of  such  volatile 
liquids  as  ether.  The  principle  of  this  instrument  is  to  have  a  thin  flat 
metal  box,  through  which  a  small  stream  of  cooled  water  is  allowed  to  flow 
for  a  few  seconds.  The  dew  is  deposited  on  the  top  of  the  box,  which  is  of 
thin  dark  polished  metal.  By  alternately  stopping  the  flow  and  allowing  it 
to  continue,  the  disappearance  and  formation  of  the  dew  may  be  very  accu- 
rately observed,  and  the  corresponding  temperatures  read  off  by  a  delicate 
thermometer  placed  inside. 

398.  Psychrometer.  "Wet-bulb  hygrrometer. — A  moist  body  evaporates 
in  the  air  more  rapidly  in  proportion  as  the  air  is  drier,  and  the  temperature 
of  the  body  sinks  in  consequence  of  this  evaporation.  The  psychrometer, 
or  wet-bidb  hygrotfteter,  is  based  on  this  principle,  the  application  of  which 
to  this  purpose  was  first  suggested  by  Leslie.  The  form  usually  adopted  in 
this  country  is  due  to  Mason.  It  consists  of  two  delicate  thermometers 
placed  on  a  wooden  stand  (fig.  361 ).  One  of  the  bulbs  is  covered  with  muslin, 
and  is  kept  continually  moist  by  being  connected  with  a  reservoir  of  water 

P.  R 


Fig   360 

in  the  ether.     On  blowing'  into  the  ether 


370 


On  Heat. 


[398- 


by  means  of  a  string.  Unless  the  air  is  saturated  with  moisture  the  wet-bulb 
thermometer  always  indicates  a  lower  temperature  than  the  other,  and  the 
difference  between  the  indications  of  the  two  thermometers  is  greater  in  pro- 
portion as  the  air  can  take  up  more  moisture.  The  tension  e  of  the  aqueous 
vapour  in  the  atmosphere  may  be  calculated  from  the  indications  of  the  two 
thermometers  by  means  of  the  following  empirical  formula  : — 

t'  =  ^'  — o'ooo77  (/-/')//, 
in  which  e'  is  the  maximum  tension  corresponding  to  the  temperature  of  the 
wet-bulb  thermometer,  0-00077  is  a  constant,  //  is  the  barometric  height,  and 
/  and  /'  the  respective  temperatures  of  the  dry  and  wet  bulb  thermometers. 
If,  for  example,  //  =  750  millimetres,  /=  15°  C,  /'=  10°  C.  ;  ac- 
cording to  the  table  of  pressures  (358),  e'  =  9"i65,  and  we  have 

£?  =  9-165  -0-00077  X  5  X  750  =  6-278. 

This  pressure  corresponds  to  a  dew-point  of  about  4-5°  C. 
If  the  air  had  been  saturated,  the  pressure  would  have  been 
12-699,  <i"d  the  air  is  therefore  about  half  saturated  with 
moisture. 

This  formula  expresses  the  result  with  tolerable  accuracy, 
but  the  above  constant  0-00077  requires  to  be  controlled  for 
different  positions  of  the  instrument  ;  in  small  closed  rooms 
it  is  0-00128,  in  large  rooms  it  is  o-ooioo,  and  in  the  open 
air  without  wind  it  is  0-00090  :  the  number  0-00077  is  its 
value  in  a  large  room  with  open  windows.  Regnault  found 
that  the  difference  in  temperature  of  the  two  bulbs  depends 
on  the  rapidity  of  the  current  of  air  ;  he  also  found  that  at 
a  low  temperature,  and  in  very  moist  air,  the  results  ob- 
tained with  the  psychrometer  differed  from  those  yielded  by 
his  hygrometer.  It  is  probable  that  the  indications  of  the 
psychrometer  are  only  true  for  mean  and  high  temperatures, 
and  when  the  atmosphere  is  not  too  moist. 

A  formula  frequently  used  in  this  country  is  that  given 
by  Dr.  Apjohn.     It  is 

d      h     ^     ^      ,     d      h 


F=/- 


—  ,  or  F  =  /-   - 
88     30'  ■'     96     30 


in  which  d  is  the  difference  of  the  wet  and  dry  bulb  thermometers  in 
Fahrenheit  degrees  ;  h  the  barometric  height  in  i?zches  ;  /  the  pressure  of 
vapour  for  the  temperature  of  the  wet  bulb,  and  F  the  pressure  of  vapour 
at  the  dew-point,  from  which  the  dew-point  may,  if  necessary,  be  found  from 
the  tables.  The  constant  coefficient  88,  for  the  specific  heats  of  air  and 
aqueous  vapour,  is  to  be  used  when  the  reading  of  the  wet  bulb  is  above  32° 
F.,  and  96  when  it  is  below.  • 

According  to  Glaisher  the  temperature  of  the  dew-point  may  be  obtained 
by  multiplying  the  difference  between  the  temperatures  of  the  wet  and  dry 
bulb  by  a  constant  depending  on  the  temperature  of  the  air  at  the  time  of 
observation,  and  subtracting  the  product  thus  obtained  from  this  last-named 
temperature. 


-399]  Absorption  Hygrometers.  371 

The  following  table  gives  the  numbers,  which  are  known  as  ClaisJier's 
factois. 


Dry  bulb 
Temperature  F.° 

Factor 

Dry  bulb 
Temperature  F.° 

Factor 

Below  24° 

8-5 

34  to  35 

2-8 

24  to  25 

6-9 

35-40 

2-5 

25-26 

6-5 

40—45 

2'2 

26 — 27 

6-1 

45-50 

2-1 

27—28 

5-6 

50-55 

2-0 

28—29 

5-1 

55—60 

1-9 

29—30 

4-6 

60—65 

1-8 

30—31 

4-1 

65—70 

1-8 

31—32 

37 

70-75 

17 

32-33 

y}> 

75-80 

17 

33-34 

3-0 

80-85 

1-6 

399.  Absorption  hygrometers. — These  hygrometers  are  based  on  the 
property  which  organic  substances  have  of  elongating  when  moist,  and  of 
again  contracting  as  they  become  dry.  The  most  common  form  is  the  hair 
or  Saiissure's  Jiygrometer. 

It  consists  of  a  brass  frame  (fig.  362),  on  which  is  fixed  a  hair,  f,  fastened 
at  the  top  in  a  clamp,  cz,  provided  with  a  screw,  d.  This  clamp  is  moved  by 
a  screw,  b.  The  lower  part  of  the  hair  passes  round  a 
pulley,  0,  and  supports  a  small  weight,  /.  On  the 
pulley  there  is  a  needle,  which  moves  along  a  graduated 
scale.  When  the  hair  becomes  shorter  the  needle  rises, 
when  it  becomes  longer  the  weight  j?^.  makes  it  sink. 

The  scale  is  graduated  by  calling  that  point  zero  at 
which  the  needle  would  stand  if  the  air  were  completely 
dry,  and  100  the  point  at  which  it  stands  in  air  completely 
saturated  with  moisture.  The  distance  between  these 
points  is  divided  into  100  equal  degrees. 

Regnault  devoted  much  study  in  order  to  render  the 
hair  hygrometer  scientifically  useful,  but  without  much 
success.  The  utmost  that  can  be  claimed  for  it  is  that  it 
can  be  used  as  a  hygroscope ;  that  is,  an  instrument  which 
shows  approximately  whether  the  air  is  more  or  less 
moist,  without  giving  any  indication  as  to  the  quantity  of 
moisture  present.  To  this  class  of  hygroscopes  belong 
the  chimney  ornaments,  one  of  the  most  common  forms 
of  which  is  that  of  a  small  male  and  female  figure,  so 
arranged  in  reference  to  a  little  house,  with  two  doors,  that 
when  it  is  moist  the  man  goes  out  and  the  woman  goes 
in,  and  vice  versa  when  it  is  fine.  They  are  founded  on  the  property  which 
twisted  strings  or  pieces  of  catgut  possess  of  untwisting  when  moist,  and  of 
twisting  when  dry.  As  these  hygroscopes  only  change  slowly,  their  indi- 
cations are  always  behindhand  with  the  state  of  the  weather ;  nor  are  they, 
moreover,  very  exact. 


372  On  Heat.  [399- 

A  strip  of  drawing-paper,  coated  on  one  side  with  gelatine  and  varnished 
on  the  other,  readily  absorbs  moisture,  so  that  the  strip  curves  outwards  on 
the  gelatine  side,  like  the  compensating  strips  in  (320),  when  heated.  If  such 
a  strip  be  coiled  as  a  spiral,  then,  according  to  the  greater  or  less  quantity  of 
moisture  it  absorbs,  this  twists  and  untwists  like  a  Breguet's  thermometer 
(309),  and  thus  serves  as  a  sensitive  hygroscope. 

400.  IMCoisture  of  the  atmosphere. — The  absolute  moisture  varies  with 
the  temperature  in  the  course  both  of  the  year  and  of  the  day.  In  summer 
there  is  a  maximum  at  eight  in  the  morning  and  evening,  and  a  minimum  at 
3  P.M.  and  3  A.M,  because  the  ascending  current  of  air  carries  the  moisture 
upwards.  The  absolute  moisture  is  greatest  in  the  tropics,  where  it  represents 
a  pressure  of  25  mm.,  while  in  our  latitudes  it  does  not  exceed  10  mm.  The 
relative  moisture,  on  the  other  hand,  is  on  the  average  greater  in  high  than 
in  low  latitudes  ;  it  is  at  the  minimum  in  the  hottest  and  at  its  maximum  in 
the  coolest  part  of  the  day.  It  varies  also  in  different  regions.  It  is  greater 
in  the  centre  of  continents  than  it  is  on  the  sea  or  the  sea-coast.  Thus  in 
summer  the  relative  moisture  at  Greenwich  is  "j"]^  at  Venice  64,  Lugano 
58,  and  Uralsk  42*^.  That  the  dryness  increases  with  the  distance  from 
the  sea  is  shown  by  the  clearer  skies  of  continental  regions.  In  Platowskya 
in  Siberia  the  air,  at  a  temperature  of  24°,  was  found  to  contain  a  quantity  of 
moisture  only  sufficient  to  saturate  it  at  —3°;  the  air  might  therefore  have 
been  cooled  through  27°  without  any  deposit  of  moisture.  On  the  ground 
the  absolute  moisture  is  greatest,  and  diminishes  rapidly  as  we  ascend  ;  the 
relative  moisture  however  increases,  so  that  at  a  certain  height  the  air  is 
saturated  with  moisture.  From  this  zone  upwards  the  relative  moisture  de- 
creases, for  the  aqueous  vapour  is  confined  to  the  lower  regions.  In  some 
parts  of  East  Africa  the  springs  of  powder-flasks  exposed  to  the  damp  snap 
like  twisted  quills  ;  on  the  contrary,  paper  becomes  soft  and  sloppy  by  the 
loss  of  its  glaze  ;  and  gunpowder,  if  not  kept  hermetically  sealed,  refuses 
to  ignite.  On  the  other  hand  in  North  America,  where  the  south-west  winds 
blow  over  large  tracts  of  land,  the  relative  moisture  is  less  and  the  evapo- 
ration is  far  more  rapid  than  in  Europe ;  clothes  dry  quickly,  bread  soon 
becomes  hard,  newly  built  houses  can  be  at  once  inhabited,  European  pianos 
soon  give  way  there,  while  American  ones  are  very  durable  on  this  side  of 
the  ocean.  As  regards  the  animal  economy,  liquids  e\'aporate  more  rapidly, 
by  which  the  circulation  and  the  assimilation  are  accelerated,  and  the  whole 
character  is  more  nervous.  For  evaporation  is  quicker  the  drier  the  air,  and 
the  more  frequently  it  is  renewed  ;  it  is,  moreover,  more  rapid  the  higher 
the  temperature,  and  the  less  the  pressure.  This  is  not  in  disaccord  with  the 
statement  that  the  quantity  of  vapour  which  saturates  a  given  space  is  the 
same  however  this  be  filled  with  air  ;  a  certain  space  takes  up  the  same 
weight  of  vapour  whether  it  is  vacuous,  or  filled  with  rarefied  or  dense  air  ; 
the  saturation  with  vapour  takes  place  the  more  rapidly  the  smaller  the 
pressure  of  the  air. 

401.  Problem  on  hygrometry. — To  calculate  the  weight  P  of  a  volume 
of  moist  air  \",  the  hygrometric  state  of  which  is  E,  the  temperature  /,  and 
the  pressure  H,  the  density  of  the  vapour  being  |  that  of  air. 

From  the  second  law  of  the  mixture  of  gases  and  vapours,  it  will  be  seen 
that  the  moist  air  is  nothing  more  than  a  mixture  of  V  cubic  inches  of  dry 


-402]  Correction  for  Loss  of  Weight  in  Air.  2)7?) 

air  at  /°,  under  the  pressure  H  minus  that  of  the  vapour,  and  of  V  cubic 
inches  of  vapour  at  t°  and  the  pressure  given  by  the  hygrometric  state  ; 
these  two  values  must,  therefore,  be  found  separately. 

The  formula /=  F  x  E  (392)  gives  the  pressure /of  the  vapour  in  the  air, 
for  E  has  been  determined,  and  F  is  found  from  the  tables.      The  pressure  / 
being  known,  if/'  is  the  pressure  of  the  air,/+/'  =  H,  from  which 
/'  =  H  -/=  H  -  FE. 

The  question  consequently  resolves  itself  into  calculating  the  weight  of 

V  cubic  inches  of  dry  air  at  /",  and  the  pressure  H  -  FE,  and  then  that  of 

V  cubic  inches  of  aqueous  vapour  also  at  /"",  but  under  the  pressure  FE. 

Now   V   cubic   inches    of  dry  air   under   the  given    conditions    weigh 

°    1 ^-x— "^ )  ^"d  we  readily  see  from  problem  iii.  art.  384,  that  V  cubic 

(i  +at)  760  ^  -^  ^' 

inches  of  vapour  at  t°,  and  the  pressure  FE,  weigh  <  x  -2-=2 .     Adding 

^  "^  '        "^     8     (I  +  a/)  760  ^ 

these  two  weights,  and  reducing,  we  get 

p_o-3i  V(H-|FE) 
(i +0^760 
If  the  air  were  saturated  we  should  have  E  =  i,  and  the  formula  would  thus 
be  changed  into  that  already  found  for  the  mixture  of  gases  and  saturated 
vapours  (384). 

This  formula  contains,  besides  the  weight  P,  many  variable  quantities,  V, 
E,  H,  and  /,  and  consequently,  by  taking  successively  each  of  these  quanti- 
ties as  unknown,  as  many  different  problems  might  be  proposed. 

402.  Correction  for  the  loss  of  \(reigrht  experienced  by  bodies 
weighed  in  the  air. — It  has  been  seen  in  speaking  of  the  balance  that  the 
weight  which  it  indicates  is  only  an  apparent  weight,  and  is  less  than  the 
real  weight.  The  latter  may  be  deduced  from  the  former  when  it  is  remem- 
bered that  every  body  weighed  in  the  air  loses  a  weight  equal  to  that  of  the 
displaced  air  (195).  This  problem  is,  however,  very  complicated,  for  not 
only  does  the  weight  of  the  displaced  air  vary  with  the  temperature,  the 
pressure,  and  the  hygrometric  state,  but  the  volume  of  the  body  to  be 
weighed,  and  that  of  the  weights,  vary  also  with  the  temperature  ;  so  that  a 
double  correction  has  to  be  made  ;  one  relative  to  the  iceights.,  the  other  to 
the  body  weighed. 

Correction  relative  to  tJie  weights. — In  order  to  make  this  correction  let 
P  be  their  weight  in  air,  and  n  their  weight  ifi  vacuo  ;  further,  let  V  be  the 
volume  of  these  weights  at  0°,  D  the  density  of  the  substance  of  which  they 
are  made,  and  K  its  coefficient  of  linear  expansion. 

The  volume  V  becomes  V  (i  +  2,^s.t)  at  t° ;  hence  this  is  the  volume  of  air 
displaced  by  the  weights.    If /x  be  the  weight  of  a  cubic  inch  of  air  at  /,and 
the  pressure  H  at  the  time  of  weighing,  we  have 
P  =  n-MV  (i  +  3l^0- 

From  the  formula  P  =  VD  (125)  V  may  be  replaced  by  _^,  and  the 
formula  becomes 

TV  •  •  •  •  •  \       J 


x.n[ 


374  On  Heat.  [402- 

which  gives  the  value,  in  air,  of  a  weight  n,  when  ix  is  replaced  by  its  value. 
But  since  /x  is  the  weight  of  a  cubic  inch  of  air  more  or  less  moist,  at  the 
temperature  /  and  the  pressure  H,  its  value  may  be  calculated  by  means  of 
the  formula  in  the  foregoing  paragraph. 

Correction  relative  to  the  body  weighed. — Let  p  be  the  apparent  weight 
of  the  body  to  be  weighed,  tt  its  real  weight  in  vacuo.,  d  its  density,  t:  its 
coefficient  of  expansion,  and  /  its  temperature  ;  by  the  same  reasoning  as 
above  we  have 

/-[.-"(-i^] w 

By  using  the  method  of  double  weighing,  and  of  a  counterpoise  whose 
apparent  weight  is^',  the  real  weight  tt',  the  density  d\  and  the  coefficient 
/('',  and  assuming  that  the  pressure  does  not  change,  which  is  usually  the 
case,  we  have  again 

M(i3  +  i-r)l 


P'  =  l.'\^ 


(3) 


If  a  and  b  are  the  two  arms  of  the  beam,  we  have  in  the  first  weighing  ap  =pb  : 
and  in  the  second  aV  =  bp,  whence  p  =  V.  Replacing  P  and  p  by  their  values 
deduced  from  the  above  equations,  we  have 


L  d 

whence 
which  solves  the  problem. 


M(i  +  3^vn  ^r^  _Ki  +  3K/)-| 


d 


-404]  375 


CHAPTER   VII. 

CONDUCTIVITY   OF   SOLIDS,    LIQUIDS,   AND   GASES. 

403.  Transmission  of  beat. — When  we  stand  at  a  little  distance  from  a 
■fire  or  other  source  of  heat  we  experience  the  sensation  of  warmth.  The 
heat  is  not  transmitted  by  the  intervening  air  ;  it  passes  through  it  without 
raising  its  temperature,  for  if  we  place  a  screen  before  the  fire  the  sensation 
ceases  to  be  felt.  The  heat  from  the  sun  reaches  us  in  the  same  manner. 
The  heat,  which,  as  in  this  case,  is  transmitted  to  a  body  from  the  source  of 
heat  without  affecting  the  temperature  of  the  intervening  medium,  is  said  to 
be  radiated. 

That  heat  can  Ije  transmitted  through  a  medium  without  raising  its  tem- 
perature is  proved  by  a  remarkable  experiment  of  Prevost  in  18 11.  Water 
from  a  spring  was  allowed  to  fall  in  a  thin  sheet ;  on  one  side  of  this  was  held 
a  red-hot  iron  ball,  and  on  the  other  a  delicate  thermometer.  The  tempera- 
ture of  the  latter  was  observed  to  rise  steadily,  a  result  which  could  not  have 
been  due  to  any  heating  effect  of  the  water  itself,  as  this  was  cold,  and  was 
being  continually  renewed.  It  could  only  have  been  due  to  heat  which 
traversed  the  water  without  raising  its  temperature.  A  similar  experiment 
has  been  made  by  a  hollow  glass  lens  through  which  cold  water  flowed  in  a 
constant  stream.  The  sun's  rays  concentrated  by  this  arrangement  ignited 
a  piece  of  wood  placed  in  the  focus. 

Heat  is  transmitted  in  another  way.  When  the  end  of  a  metal  bar  is 
heated,  a  certain  increase  of  temperature  is  presently  observed  along  the 
bar.  Where  the  heat  is  transmitted  in  the  mass  of  the  body  itself,  as  in  this 
case,  it  is  said  to  be  conducted.  We  shall  first  consider  the  transmission  of 
heat  by  conduction. 

404.  Conductivity  of  solids. — Bodies  conduct  heat  with  different  de- 
grees of  facility.      Good  condtwtofs  are  those 

which  readily  transmit  heat,  such  as  are  the 
metals  ;  while  bad  cofidiictors,  to  which  class 
belong  the  resins,  glass,  wood,  and  more  espe- 
cially liquids  and  gases,  offer  a  greater  or  less 
resistance  to  the  transmission  of  heat. 

In  order  to  compare  roughly  the  conducting 
power  or  conductivity  of  different  solids,  Ingen- 
haus  constructed  the  apparatus  which  bears  his 
name  and  which  is  represented  in  fig.  363.  It 
is  a  metal  trough,  in  which,  by  means  of  tubu-  '  *"'  " -" 

lures  and  corks,  are  fixed  rods  of  the  same  dimensions,  but  of  different 
materials ;  for  instance,  iron,  copper,  wood,  glass.  These  rods  extend  to 
a  slight  distance  ip  the  trough,  and  the  parts  outside  are  coated  with  wax 
which  melts  at  61'^.  The  box  being  filled  with  boiling  water,  it  is  observed 
that  the  wax  melts  to  a  certain  distance  on  the  metal  rods,  while  on   the 


376 


On  Heat. 


[404- 


others  there  is  no  trace  of  fusion.  The  conducting  power  is  evidently  greater 
in  proportion  as  the  wax  has  fused  to  a  greater  distance.  The  experiment  is 
sometimes  modified  by  attaching  glass  balls  or  marbles  to  the  ends  of  the 
rods  by  means  of  wax.  As  the  wax  melts,  the  balls  drop  off,  and  this  in  the 
order  of  their  respective  conductivities.  The  quickness  with  which  melting 
takes  place  is,  however,  only  a  measure  of  the  conducting  power,  in  case  the 
metals  have  the  same  or  nearly  the  same  specific  heat. 

Despretz  compared  the  conducting  powers  of  solids  by  forming  them  into 
bars  (fig.  364),  in  which  small  cavities  are  made  at  short  intervals  :  these 
cavities  contain  mercury,  and  a  delicate  thermometer  is  placed  in  each  of 
them.     Such  a  bar,  AB,  is  exposed  at  one  end  to  a  constant  source  of  heat, 


such  as  that  of  a  bath  of  paraffin  or  of  fusible  metal  heated  by  a  Bunsen's 
burner  ;  the  thermometers  gradually  rise  until  they  indicate  fixed  tempera- 
tures, which  are  less  according  as  the  thermometers  are  farther  from  the 
source  of  heat  By  this  method  Despretz  verified  the  following  law  : — If  the 
distances  «,  a,  a^  ....  «vi  from  the  source  of  heat  mcrease  in  arithnetical 
progression,  the  excess  of  temperature  over  that  of  the  surrounding  air, 
t,t-^,t^:^    ....  /v  5  decreases  in  geometrical  progression. 

This  law,  however,  only  prevails  in  the  case  of  very  good  conductors, 
such  as  gold,  platinum,  silver,  and  copper  ;  it  is  only  approximately  true  for 
iron,  zinc,  lead,  and  tin,  and  does  not  apply  at  all  to  non-metallic  bodies, 
such  as  marble,  porcelain,  &c. 

Taking  the  conducting  power  of  gold  at  1000,  Despretz  constructed  the 
following  table  of  conductivities  : — 


Platinum  . 

Silver 

Copper 

Iron  .... 

Zinc  .... 

By  making  cavities  in  the  bars,  as  in  Despretz's  metho' 


981 

Tin  . 

97.3 

Lead 

897 

Marble     . 

,374 

Porcelain 

363 

Brick  earth 

•  304 

•  179 

•  23 

12 

1,  their  form  is 


altered,    and   the    continuity  partially  destroyed.      Wiedemann  and   Franz 


;oo-o 

Iron 

73-6 

Steel        . 

S3'~ 

Lead       . 

23-1 

Platinum 

19-0 

Rose's  alloy 

14-5 

Bismuth 

-405]  Coefficient  of  Conductivity.  377 

avoided  this  source  of  error  by  measuring  the  temperature  of  the  bars  in 
different  places  by  applying  to  them  the  junction  of  a  thermo-electric  couple 
(412).  The  metal  bars  were  made  as  regular  as  possible,  one  of  the  ends 
was  heated  to  100°,  the  rest  of  the  bar  being  surrounded  by  air  at  a  constant 
temperature.  The  thermo-electric  couple  was  of  small  dimensions,  in  order 
not  to  abstract  too  much  heat. 

By  this  method  Wiedemann  and  Franz  obtained  results  which  differ  con- 
siderably from  those  of  Despretz.  Representing  the  conductivity  of  silver 
by  100°,  they  found  the  following  numbers  for.  the  other  metals  : — 

Silver      ....     igq-o         Iron         .         .         .         .11-9 

Copper   ....       73-6         Steel        .         .         .         .      ii-6 

Gold       ... 

Brass 

Zinc         .     '    . 

Tin  ... 

These  experimenters  found  that  the  conducting  power  of  the  pure  metals 
for  heat  and  electricity  is  the  same. 

Organic  substances  conduct  heat  badly.  De  la  Rive  and  De  Candolle 
showed  that  woods  conduct  better  in  the  direction  of  their  fibres  than  in  a 
transverse  direction,  and  this  difference  is  greater  with  the  soft  than  with  the 
hard  woods  ;  they  remarked  upon  the  influence  which  this  feeble  conduct- 
ing power,  in  a  transverse  direction,  exerts  in  preserving  a  tree  from  sudden 
changes  of  temperature,  enabling  it  to  resist  alike  a  sudden  abstraction  of 
heat  from  within,  and  the  sudden  accession  of  heat  from  without.  Tyndall 
has  also  shown  that  this  tendency  is  aided  by  the  low  conducting  power  of 
the  bark,  which  in  all  cases  is  less  than  that  of  the  wood.  Cotton,  wool, 
straw,  bran.  &c.,  are  all  bad  conductors. 

Rocks  and  the  earth  are  the  worse  conductors,  the  less  dense  and  homo- 
geneous is  the  mass.  Hence  the  length  of  time  required  for  the  sun's  heat  to 
penetrate  into  the  earth.  The  mean  highest  temperature  of  the  air  near  the 
ground  in  Central  Europe  is  in  the  month  of  July,  but  at  a  depth  of  25  to  28 
feet  in  the  earth  it  is  in  the  month  of  December. 

405.  Coefficient  of  conductivity.— The  numbers  given  in  the  foregoing 
article  only  express  the  relative  conducting  powers  of  the  respective  sub- 
stances. Numerous  experiments  have  been  made  to  determine  the  quantity 
of  heat,  W,  which  passes,  for  instance,  through  a  plate  the  two  sides  of  which 
are  kept  at  a  constant  difference  of  temperature.  This  will  clearly  be  pro- 
portional to  the  area  of  the  plate  A  and  to  the  time  /.  It  is  further  propor- 
tional to  the  excess  of  the  temperature  of  the  one  face  B^  over  that  of  the 
other  6 — that  is,  to  ^j  —  ^  ;  and  as  the  flow  of  heat  is  different  in  different 
substances,  it  will  be  proportional  to  a  constant  k. 

On  the  other  hand  it  will  be  inversely  proportional  to  the  thickness  of  the 
plate  d.     These  results  are  expressed  by  the  formula 

W  =  ^J^i)_A^from  which  ^^  ,,— ^v".  ..• 
d  {01  -  6)  Atd 

On  the  CGS  system  of  units,  the  coefficient  of  thermal  or  calorimetrical 
conductivity^  k,  is  the  quantity  of  heat  which  passes  in  a  second  of  time, 


3/8  On  Heat.  [405- 

betvveen  the  two  opposite  faces  of  a  cube  of  the  substance  one  centimetre  in 
thickness,  and  which  are  kept  at  a  constant  difference  of  one  degree.  The 
mean  values,  as  found  by  Neumann,  are  as  follows: — copper,  i-io8;  zinc, 
0-307  ;  iron,  0-163  ;  argentan,  0-109  ;  ice,  0-0057. 

Thus  if  the  two  opposite  faces  of  a  cube  of  iron  one  centimetre  in  thick- 
ness, that  is  to  say,  a  cubic  centimetre  of  iron,  are  kept  at  a  constant  differ- 
ence of  1°  C,  the  quantity  of  heat  which  passes  in  each  second  of  time  will 
be  sufficient  to  raise  0-163  gramme  of  water  through  1°  C.  From  this,  which 
is  often  called  the  caloriinetrical  measure  of  conductivity.,  we  must  distin- 
guish the  thermometric  measure  of  conductivity  ;  that  is  to  say,  the  number 
of  degrees  through  which  the  cube  in  question  would  be  heated  when  the 
above  quantity  of  heat  passes  through  it  under  the  given  conditions.  This 
is  obtained  from  the  constants  given,  by  dividing  them  by  the  reduced  value 
of  the  cube  c,  or  the  specific  heat  of  unit  volume  ;  that  is,  by  the  product  of 
its  specific  heat  into  its  specific  gravity. 

406.  Senarmont's  experiment. — It  is  only  in  homogeneous  bodies  that 
heat  is  conducted  with  equal  facility  in  all  directions.  If  an  aperture  be 
made  in  a  piece  of  ordinary  glass  covered  with  a  thin  layer  of  wax,  and  a 
platinum  wire  ignited  by  a  voltaic  current  be  held  through  the  aperture,  the 
wax  will  be  melted  round  the  hole  in  a  circular  form.     Senarmont  made,  on 

this  principle,  a  series  of  experiments  on  the  conductivity  of 
heat  in  crystals.  A  plate  cut  from  a  crystal  of  the  regular 
system  was  covered  with  wax,  and  a  heated  metaUic  point 
was  held  against  it.  The  part  melted  had  a  circular  form  ; 
but  when  plates  of  crystals  belonging  to  other  systems  were 
investigated  in  a  similar  manner,  it  was  found  that  the  form 
of  the  isothermal  line  or  line  of  equal  temperature — that  is, 
the  boundary  of  the  melted  part — varied  with  the  different 
systems  and  with  the  position  of  the  axes.  In  plates  of 
uniaxial  crystals  cut  parallel  to  the  principal  axis  it  was  an 
ellipse  (fig.  365),  the  major  axis  of  which  was  in  the  direction 
of  the  principal  axis.  In  plates  cut  perpendicular  to  the 
principal  axis  it  was  a  circle.  In  biaxial  crystals,  for  which 
F'g-  365-  selenite  is  well  adapted,  the  line  was  always  an  ellipse.     The 

isothermal  surface  agrees  in  general  character  with  the  wave  surface  of  the 
extraordinary  ray. 

Instead  of  wax  the  plate  may  be  coated  with  the  double  iodide  of  mercury 
and  copper  ;  this  substance  is  of  a  brick-red  colour,  which  when  heated 
changes  into  a  purplish  black. 

Rontgen  makes  the  experiment  very  simply  by  breathing  on  the  plate, 
and  then  holding  a  hot  steel  point  against  it.  When  a  space  free  from  mois- 
ture has  been  found  about  the  point,  the  whole  plate  is  dusted  with  lyco- 
podium,  which  shows  the  outline  of  the  figure  with  great  sharpness. 

Pfaff  found  the  conductivity  of  rock  crystal  50-3  in  the  direction  of  the 
principal  axis,  and  39-1  in  a  direction  at  right  angles  thereto. 

407.  Conductivity  of  liquids. — The  conductivity  of  liquids  is  very  small, 
as  is  seen  from  the  following  experiment  : — A  delicate  thermoscope  B,  con- 
sisting of  two  glass  bulbs,  joined  by  a  tube  w,  in  which  there  is  a  small 
index  of  coloured  liquid,  is  placed  in  a  large  cylindrical  glass  vessel,  D  (fig. 


-407J 


Conductivity  of  Liquids. 


379 


366).     This  vessel  is  filled  with  water  at  the  ordinary  temperature,  and  a  tin 

vessel,  A,  containing  oil  at  a  temperature  of  two  or  three  hundred  degrees, 

is  dipped  in  it.      The   bulb  near  the  vessel  A  is  J^ 

only  very  slightly  heated,  and  the  index  m  moves 

through  a  very  small  distance.     Other  liquids  give 

the  same  result.     That  liquids  conduct  very  badly 

is  also  demonstrated  by  a  simpler  experiment.     A 

long  test-tube  is  half  filled  with  water,  and  some  ice 

so  placed  in  it  that  it  cannot  rise  to  the  surface. 

By  inclining  the  tube  and  heating  the  surface  of 

the  liquid  by  means  of  a  spirit  lamp,  the  liquid  at 

the  top  may  be  made  to  boil,  while  the  ice  at  the 

bottom  remains  unmelted. 

Despretz  made  a  series  of  experiments  with  an 
apparatus  analogous  to  that  here  described,  but  he 
kept  the  liquid  in  the  vessel,  A,  at  a  constant  tem-  -=^^=-- 

perature,  and  arranged  a  series  of  thermometers  Fig.  366. 

one  below  the  other  in  the  vessel  D.  In  this  manner  he  found  that  the 
conductivity  of  heat  in  liquid  obeys  the  same'^laws  as  in  solids,  but  is  much 
more  feeble.     For  example,  the  conductivity  of  water  is  i  that  of  copper. 

Guthrie  examined  the  conductivity  of  liquids  in  the  following  manner  : — 
Two  hollow  brass  cones  are  placed  near  each  other  so  that  the  top  of  one 


points  upwards,  that  of  the  other  downwards  (fig.  367).  The  distance  of  the 
bases,  which  are  of  platinum,  can  be  regulated  by  a  micrometer  screw.  The 
liquid  to  be  examined  is  introduced  between  the  bases  by  means  of  a  pipette. 
The  lower  cone  is  fitted  with  a  glass  tube  which  dips  in  a  coloured  liquid, 
and  thus  constitutes  an  air  thermometer.  The  base  of  the  upper  cone  is 
kept  at  a  constant  temperature  by  means  of  a  current  of  hot  water  ;  it  thus 


38o  On  Heat.  [407- 

warms  the  liquid,  and  the  base  of  the  lower  cone,  in  consequence  of  which 
the  air  in  the  interior  is  expanded  and  the  column  of  liquid  in  the  stem 
depressed. 

The  bases  of  the  cones  were  first  brought  in  contact  and  the  depression 
of  the  column  of  hquid  was  observed.  A  layer  of  liquid  of  a  given  thick- 
ness was  then  interposed  and  the  depression  observed  after  a  certain  time. 
The  same  thicknesses  of  other  liquids  were  then  successively  introduced, 
and  the  corresponding  depressions  noted.  The  difference  of  the  depressions 
was  a  measure  for  the  resistance  which  the  liquid  offered  to  the  passage  of  heat. 

The  most  complete  researches  on  the  conductivity  of  liquids  are  those  of 
Weber,  who  made  use  of  the  following  method.  A  copper  disc  about  8 
cm.  in  radius  was  separated  from  another  similar  one  by  three  pieces  of 
glass,  about  0'2  cm.  thick.  The  space  thus  formed  between  the  two  is 
filled  with  the  liquid  to  be  examined,  and  the  system  placed  horizontally  on 
a  smooth  block  of  ice.  The  lower  plate  rapidly  assumed  the  temperature  of 
the  ice,  and  heat  travelled  through  the  hquid  from  the  upper  plate,  the 
changes  in  temperature  of  which  were  noted  by  a  thermo-electrical  arrange- 
ment (413).     He  thus  observed  the  following  values  for  k  (405)  : — 


Water 

0-00124 

Carbon  bisu 

Iphide 

.      0-00042 

Solution  of  CuSO., 

Q-OGIlS 

Ether 

.      0-00040 

Solution  of  NaCl 

0-00115 

Olive  oil     . 

.      0-00039 

Glycerine    . 

0-00067 

Chloroform 

.       O-OOO},'] 

Alcohol 

-.pr  HpH.irPrl  frniT.  hiq  i 

0-00049 
p';parrhp'^  th 

Benzole 

p  law  that  fnr 

thp  linilif 

0-00032 
q  pvaminp 

him,  the  conductivity  divided  by  the  specific  heat  of  unit  volume — that  is  to 
say,  the  density  multiplied  by  the  specific  heat — is  an  almost  constant  number. 
408.  IVIanner  in  wtaicli  liquids  are  heated. — When  a  column  of  liquid 
is  heated  at  the  bottom,  ascending  and  descending  currents  are  produced. 
It  is  by  these  that  heat  is  mainly  distributed 
thi-ough  the  hquid,  and  not  by  its  conductivity. 
These  currents  arise  from  the  expansion  of 
the  inferior  layers,  which,  becoming  less 
dense,  rise  in  the  licjuid,  and  are  replaced 
by  colder  and  denser  layers.  They  may  be 
made  visible  by  projecting  bran  or  wooden 
shavings  into  water,  which  rise  and  descend 
with  the  currents.  The  experiment  is 
arranged  as  shown  in  fig.  368.  The  mode 
in  which  heat  is  thus  propagated  in  liquids 
and  in  gases  is  said  to  be  by  co/ivectio/i. 

409.  Conductivity  of  g-ases. —  It  has 
been  a  disputed  question  whether  gases  have 
a  true  conductivity,  that  is  to  say,  a  conduc- 
tion from  layer  to  layer  as  with  the  metals  ; 
but  certainly  when  they  are  restrained  m 
their  motion  their  conductivity  is  very  small. 
All  substances,  for  instance,  between  whose  particles  air  remains  stationary, 
offer  great  resistance  to  the  propagation  of  heat.    This  is  well  seen  in  straw, 


Fig.  368. 


-410]  Applications.  381 

eider-down,  and  furs.  The  propagation  of  heat  in  a  gaseous  mass  is  effected 
by  means  of  the  ascending  and  descending  currents  formed  in  it,  as  is  the 
case  with  hcjuids. 

The  following  experiment,  a  modification  of  one  originally  devised  by 
Sir  W.  Grove,  is  considered  to  prove  that  gases  have  a  certain  conductivity. 

A  glass  tube,  fig.  369,  with  two  lateral  tubes  d  and  e  opening  into  it  at 
one  end,  is  closed  in  the  middle  by  a  cork,  ^,  through  which  a  stout  copper 
wire  passes.  This  is  connected  by  thin  platinum  wires  with  similar  stout 
copper  wires  also  passing  through  the  corks  a  and  c.  When  the  current  of 
a  Grove's  battery  is  passed  through  the  wires,  both  platinums  are  equall)' 
incandescent.  If,  now,  one  half  of  the  tube  is  filled  with  hydrogen  by  con- 
necting one  of  the  small  tubes  with  a  supply  of  that  gas,  and  the  current  is 
again  passed,  the  wire  in  the  hydrogen  is  scarcely  luminous,  while  that  in 
air  is  still  brightly  incandescent. 

This  greater  chilling  of  the  wire  in  hydrogen  than  in  air  was  considered 
by  Magnus  to  be  an  effect  of  conduction  ;  while  Tyndall  ascribes  it  to  the 
greater  mobility  of  the  particles  of  hydrogen. 

Stefan  found  the  value  of  k  for  air  to  be  0-0000558  in  CGS  units,  so 
that  its  conductivity  is  only  J9I55  that  of  copper,  and  j^j  that  of  iron.     He 


Fig.  369. 

also  found  that  hydrogen  conducts  seven  times  as  well  as  air,  and  that 
difference  of  density  seems  to  have  no  influence  on  the  conductivity. 

410,  Applications. — The  greater  or  less  conductivity  of  bodies  meets 
with  numerous  apphcations.  If  a  liquid  is  to  be  kept  warm  for  a  longtime, 
it  is  placed  in  a  vessel  and  packed  round  with  non-conducting  substances, 
such  as  shavings,  straw,  or  bruised  charcoal.  For  this  purpose  water-pipes 
and  pumps  are  wrapped  in  straw  at  the  approach  of  frost.  The  same  means 
are  used  to  hmder  a  body  from  becoming  heated,  Ice  is  transported  in 
summer  by  packing  it  in  bran  or  folding  it  in  flannel. 

Double  walls  constructed  of  thick  planks  having  between  them  any  finely 
divided  materials,  such  as  shavings,  sawdust,  dry  leaves,  &c.,  retain  heat 
extremely  well ;  and  are  likewise  advantageous  in  hot  countries,  for  they 
prevent  its  access.  Pure  sihca  in  the  state  of  rock  crystal  is  a  better  con- 
ductor than  lead,  but  in  a  state  of  powder  it  conducts  very  badly.  If  a  layer 
of  asbestos  is  placed  on  the  hand,  a  red-hot  iron  ball  can  be  held  without 
inconvenience.  Red-hot  cannon-balls  can  be  wheeled  to  the  gun's  mouth  in 
wooden  barrows  partially  filled  with  sand.  Lava  has  been  known  to  flow 
over  a  layer  of  ashes  underneath  which  was  a  bed  of  ice,  and  the  non- 
conducting power  of  the  ashes  has  prevented  the  ice  from  melting. 

The  clothes  which  we  wear  are  not  warm  in  themselves  ;  they  only 
hinder  the  body  from  losing  heat,  in  consequence  of  their  spongy  texture 
and  the  air  they  enclose.  The  warmth  of  bed-covers  and  of  counterpanes 
is  explained  in  a  similar  manner.     Double  windows  are  frequently  used  in 


382  On  Heat.  [410- 

cold  climates  to  keep  a  room  warm — they  do  this  by  the  non-conducting- 
layer  of  air  interposed  between  them.  During  the  night  the  windows  are 
opened,  while  during  the  day  they  are  kept  closed.  It  is  for  the  same  reason 
that  two  shirts  are  warmer  than  one  of  the  same  material  but  of  double  the 
thickness.     Hence,  too,  the  warmth  of  furs,  eider-down,  &c. 

The  small  conducting  power  of  felt  is  used  in  the  North  of  Eui^ope  in  the 
construction  of  the  Norwegian  stove,  which  consists  merely  of  a  wooden 
box  with  a  thick  lining  of  felt  on  the  inside.  In  the  centre  is  a  cavity  in 
which  can  be  placed  a  stew-pan  provided  with  a  cover.  On  the  top  of  this 
is  a  lid,  also  made  of  felt,  so  that  the  pan  is  surrounded  by  a  very  badly 
conducting  envelope.  Meat,  with  water  and  suitable  additions,  is  placed  in 
the  pan,  and  the  contents  are  then  raised  to  boiling  point.  The  whole  is  then 
enclosed  in  the  box  and  left  to  itself ;  the  cooking  will  go  on  without  fire, 
and  after  the  lapse  of  several  hours  it  will  be  quite  finished.  The  cooling 
down  is  very  slow,  owing  to  the  bad  conducting  power  of  the  lining  ;  at  the 
end  of  three  hours  the  temperature  is  usually  not  found  to  have  sunk  more 
than  from  10°  to  15°. 

That  water  boils  more  rapidly  in  a  metallic  vessel  than  in  one  of  porcelain 
of  the  same  thickness  ;  that  a  burning  piece  of  wood  can  be  held  close  to 
the  burning  part  with  the  naked  hand,  while  a  piece  of  iron  heated  at  one 
end  can  only  be  held  at  a  great  distance,  are  easily  explained  by  reference 
to  their  various  conductivities. 

The  sensation  of  heat  or  cold  which  we  feel  when  in  contact  with  certain 
bodies  is  materially  influenced  by  their  conductivity.  If  their  temperature  is 
lower  than  ours,  they  appear  colder  than  they  really  are,  because  from  their 
conductivity  heat  passes  away  from  us.  If,  on  the  contrary,  their  temperature 
is  higher  than  that  of  our  body,  they  appear  warmer  from  the  heat  which 
they  give  up  at  different  parts  of  their  mass.  Hence  it  is  clear  why  carpets, 
for  example,  are  warmer  than  wooden  floors,  and  why  the  latter  again  are 
warmer  than  stone  floors. 

The  closer  the  contact  of  the  hand  with  a  substance,  the  greater  is  the 
difference  of  temperature  felt.  With  smooth  surfaces  there  are  more  points 
of  contact  than  with  rough  ones.  A  hot  glass  rod  feels  hotter  than  a  piece 
of  rusted  iron  of  the  same  temperature,  although  the  latter  is  a  better  con- 
ductor. The  closer  the  substance  is  pressed,  the  more  intimate  the  contact  ; 
an  ignited  piece  of  charcoal  can  be  lifted  by  the  fingers,  if  it  is  not  closely 
pressed. 


-412]  383 


CHAPTER   VIII. 

RADIATION    01^    HEAT. 

411.  Radiant  heat,— It  has  been  already  stated  (403)  that  heat  can  be 
transmitted  from  one  body  to  another  without  aUering  the  temperature  of  the 
intervening  medium,  If  we  stand  in  front  of  a  fire  we  experience  a  sensation 
of  warmth  which  is  not  due  to  the  temperature  of  the  air,  for  if  a  screen  be 
interposed  the  sensation  immediately  disappears,  which  would  not  be  the 
case  if  the  surrounding  air  had  a  high  temperature.  Hence  bodies  can  send 
out  rays  which  excite  heat,  and  which  penetrate  through  the  air  without 
heating  it,  as  rays  of  light  through  transparent  bodies.  Heat  thus  propagated 
is  said  to  be  radiated ;  and  we  shall  use  the  terms  ray  of  heat,  or  thcmial, 
or  calorific  ray,  in  a  similar  sense  to  that  in  which  we  use  the  term  ray  of 
tight,  or  luminous  ray. 

We  shall  find  that  the  property  of  radiating  heat  is  not  confined  to 
luminous  bodies,  such  as  a  fire  or  a  red-hot  ball,  but  that  bodies  of  all  tem- 
peratures radiate  heat.  It  will  be  convenient  to  make  a  distinction  between 
litniinous  and  obscure  rays  of  heat. 

412.  Detection  and  measurement  of  radiant  heat. — In  demonstrating 
the  phenomena  of  radiant  heat,  very  delicate  thermometers  are  required,  and 
the  thermo-electrical  multiplier  of  Melloni  is  used  for  this  purpose  with  great 
advantage  ;  for  it  not  only  indicates  minute  differences  of  temperature,  but 
it  also  measures  them  with  accuracy. 

This  instrument  cannot  be  properly  understood  without  a  knowledge  of 
the  principles  of  thermo-electricity,  for  which  Book  X.  must  be  consulted. 
It  may,  however,  be  stated  here  that  when  two  different  metals  A  and  B  are 
soldered  together  at  one  end  (figs.  370,  371),  the  free  ends  being  joined  by  a 
wire  when  the  soldering 
C    is    heated,    a    current 

of    electricity     circulates  ^  ___  -p^    C  ^ 

through  the    system  ;    if, 
on      the      contrary,     the 


soldering     be    cooled,    a  •"  fU 

current  is  also  produced,  '-g 

but  it  circulates  in  exactly  p.^  ^^^^_  ^.^  ^^^ 

the      opposite     direction. 

This  is  called  a  thermo-electiic  couple  ox  pair.  If  a  number  of  such  pairs  be 
alternately  soldered  together,  as  represented  in  fig.  371,  the  strength  of  the 
current  produced  by  heating  the  ends  is  increased  ;  or,  what  amounts  to  the 
same  thing,  a  smaller  degree  of  heat  will  produce  the  same  effect.  Such  an 
arrangement  of  a  number  of  thermo-electric  pairs  is  called  a  thermo-electric 
battery  ox  pile. 


384 


On  Heat. 


[412 


Melloni's  thermomultiplier  consists  of  a  thermo-electric  pile  connected 
with  a  delicate  galvanometer.  The  thermo-electric  pile  is  constructed  of  a 
number  of  minute  bars  of  bismuth  and  antimony  soldered  together  alternately, 
though  kept  insulated  from  each  other,  and  contained  in  a  rectangular  box 
P  (fig.  372).  The  terminal  bars  are  connected  with  two  binding  screws  in 
and  ;/,  which  in  turn  are  connected  with  the  galvanometer  G  by  means  of  the 
wires  a  and  b. 

The  galvanometer  consists  of  a  quantity  of  fine  insulated  copper  wire 
coiled  round  a  frame,  in  the  centre  of  which  a  delicate  magnetic  needle  is 
suspended  by  means  of  a  silk  thread.  When  an  electric  current  is  passed 
through  this  coil,  the  needle  is  deflected  through  an  angle  which  depends  on 
the  strength  of  the  current.  The  angle  is  measured  on  a  dial  by  an  index 
connected  with  the  needle. 

It  may  then  be  sufficient  to  state  that  the  thermo-electric  pile  being  con- 
nected with  the  galvanometer  by  means  of  the  wires  a  and  ^,  an  excess  of 


temperature  at  one  end  of  the  pile  causes  the  needle  to  be  deflected  through 
an  angle  which  depends  on  the  extent  of  this  excess  ;  and  similarly  if  the 
temperatui-e  is  depressed  below  that  of  the  other  end,  a  corresponding 
deflection  is  produced  in  the  opposite  direction.  By  arrangements  of  this 
kind  Melloni  was  able  to  measure  differences  of  temperature  of  s^joth  of  a 
degree.  The  object  of  the  cone  C  is  to  concentrate  the  thermal  rays  on  the 
face  of  the  pile. 

413.  Itaws  of  radiation. — The  radiation  of  heat  is  governed  by  three 
laws  : — 

I.  Radiation  takes  place  in  all  directions  round  a  body.  If  a  thermometer 
be  placed  in  different  positions  round  a  heated  body,  it  indicates  everywhere 
a  rise  in  temperature. 

II.  In  a  homogeneous  nieditun,  radiation  takes  place  in  a  right  line.  For, 
if  a  screen  be  placed  in  a  right  line  which  joins  the  source  of  heat  and  the 
thermometer,  the  latter  is  not  affected. 


Fig.  373- 


-414]     Catises  zvJiich  Modify  the  Intensity  of  Radimit  Heat.    385 

But  in  passing  obliquely  from  one  medium  into  another,  as  from  air  into 
glass,  calorific  like  luminous  rays  become  deviated,  an  effect  known  as 
refraction.  The  laws  of  this  phenomenon  are  the  same  for 
heat  as  for  light,  and  they  will  be  more  fully  discussed  under 
the  latter  subject. 

III.  Radiant  heat  is  propagated  in  vacuo  as  welt  as  in 
air.     This  is  demonstrated  by  the  following  experiment  : — 

In  the  bottom  of  a  glass  ilask  a  thermometer  is  fixed  in 
such  a  manner  that  its  bulb  occupies  the  centre  of  the  flask 
(fig-  373)-  The  neck  of  the  flask  is  carefully  narrowed  by 
means  of  the  blowpipe,  and  then  the  apparatus  having  been 
suitably  attached  to  an  air-pump,  a  vacuum  is  produced  in 
the  interior.  This  having  been  done,  the  tube  is  sealed  at 
the  narrow  part.  On  immersing  this  apparatus  in  hot  water, 
or  on  bringing  near  it  some  hot  charcoal,  the  thermometer  is 
at  once  seen  to  rise.  This  could  only  rise  from  radiation 
through  the  vacuum  in  the  interior,  for  glass  is  so  bad  a 
conductor  that  the  heat  could  not  travel  with  this  rapidity  through  the  sides 
of  the  flask  and  the  stem  of  the  thermometer, 

414.  Causes  which  modify  the  intensity  of  radiant  heat By  the 

intensity  of  radiant  heat  is  understood  the  quantity  of  heat  received  on  the 
unit  of  surface.  Three  causes  are  found  to  modify  this  intensity  :  the  tem- 
perature of  the  source  of  heat,  its  distance,  and  the  obliquity  of  the  calorific 
rays  in  reference  to  the  surface  which  emits  them.  The  laws  which  regulate 
these  modifications  may  be  thus  stated  : — 

I.  The  intensity  of  radiant  heat  is  proportional  to  the  temperature  of  the 
source. 

II.  The  ititensity  is  inversely  as  the  square  of  the  distance. 

III.  The  ifttensity  is  less,  the  greater  the  obliquity  of  t lie  rays  with  respect 
to  the  radiatijig  surface. 

The  first  law  is  demonstrated  by  placing  a  metal  box  containing  water 
at  10^,  20°,  or  30°  successively  at  equal  distances  from  the  bulb  of  a  differen- 
tial thermometer.  The  temperatures  indicated 
by  the  latter  are  then  found  to  be  in  the  same 
ratio  as  those  of  the  box  :  for  instance,  if  the 
temperature  of  that  corresponding  to  the  box  at 
10°  be  2°,  those  of  others  will  be  4°  and  6°  re- 
spectively. 

The  truth  of  the  second  law  follows  from  the 
geometrical  principle  that  the  surface  of  a  sphere 
increases  as  the  square  of  its  radius.  Suppose 
a  hollow  sphere  ab  (fig.  374)  of  any  given  radius, 
and  a  source  of  heat,  C,  in  its  centre  ;  each  unit 
of  surface  in  the  interior  receives  a  certain  quan-  '"''■  -^''^' 

tity  of  heat.  Now  a  sphere,  ef  of  double  the  radius  will  present  a  surface 
four  times  as  great  ;  its  internal  surface  contains,  therefore,  four  times  as 
many  units  of  surface,  and  as  the  quantity  of  heat  emitted  is  the  same,  each 
unit  must  receive  one-fourth  the  quantity. 

To  demonstrate  the  same  law  experimentally,  a  narrow  tin-plate  box  is 

C  C 


386 


Oit  Heat. 


[414- 


taken  (fig.  375),  filled  with  hot  water,  and  coated  on  one  side  with  lampblack. 
The  thermopile  with  its  conical  reflector  is  placed  so  that  its  face  is  at 
a  certain  definite  distance,  co,  say  9  inches,  from  this  box,  and  the  cover 


having  been  lowered,  the  needle  of  the  galvanometer  is  observed  to  be  de- 
flected, through  80°  for  example. 

If  now  the  pile  is  removed  to  a  distance,  CO  (fig.  376),  double  that  o{  co^ 
the  deflection  of  the  galvanometer  remains  the  same,  which  shows  that 
the  pile  receives    the   same  amount  of  heat  ;    the  same  is  the  case  if  the 


Fig.  376. 

pile  is  removed  to  three  or  four  times  the  distance.  This  result,  though? 
apparently  in  opposition  to  the  second  law,  really  confirms  it.  For  at  first 
the  pile  only  receives  heat  from  the  circular  portion  ab  of  the  side  of  the 
box,  while,  in  the  second  case,  the  circular  portion  AB  radiates  towards  it. 
But,  as  the  two  cones  ACB  and  acb  are  similar,  and  the  height  of  ACB  is- 
double  that  of  acb,  the  diameter  AB  is  double  that  of  ab,  and  therefore  the 


-415]  Mobile  Equilibrium.      Theory  of  Exchanges.  387 

area  AB  is  four  times  as  great  as  that  of  ab.,  for  the  areas  of  circles  are  pro- 
portional to  the  squares  of  the  radii.  But  since  the  radiating  surface  increases 
as  the  square  of  the  distance,  while  the  galvanometer  remains  stationary, 
the  heat  received  by  the  battery  must  be  inversely  as  this  same  square. 

The  third  law  is  demonstrated  by  means  of  the  following  experiment, 
which  is  a  modification  of  one  originally  devised  by  Leslie  (fig.  ■yil)  : — P 


A 

j 

M 

-'"  0  0 

^*^ 

.W. 

da'                                         ^B 

N 

N 

^^^ 

Fig.  377- 

represents  the  thermomultiplier  which  is  connected  with  its  galvanometer, 
and  A  a  metal  cube  full  of  hot  water.  The  cube  being  first  placed  in  such 
a  position,  A,  that  its  front  face,  ac,  is  vertical,  the  deflection  of  the  galvano- 
meter is  noted.  Supposing  it  amounts  to  45°,  this  represents  the  radiation 
from  ac.  If  this  now  be  turned  in  the  direction  represented  by  A',  the 
galvanometer  is  still  found  to  mark  45°. 

The  second  surface  is  larger  than  the  first,  and  it  therefore  sends  more 
rays  to  the  mirror.  But  as  the  action  on  the  thermometer  is  no  greater 
than  in  the  first  case,  it  follows  that  in  the  second  case,  where  the  rays 
are  oblique,  the  intensity  is  less  that  in  the  first  case,  where  they  are 
perpendiculai\ 

In  order  to  express  this  in  a  formula,  let  i  be  the  intensity  of  the  rays 
emitted  perpendicularly  to  the  surface,  and  i'  that  of  the  oblique  rays. 
These  intensities  are  necessarily  inversely  as  the  surfaces  ac  and  a'c',  for  the 
effect  is  the  same  in  both  cases,  and  therefore  i'  x  surface  a'c'  =  i  x  surface  ac  ; 

hence  z"  =  /   '^^'^  -J^  =z'— =zcos.  aoa'  \   which  signifies  that  the  intensity 
surf  a'c         ac 

of  oblique  rays  is  proportional  to  the  cosine  of  the  angle  which  these  rays  form 

with  the  normal  to  the  surface  ;  for  this  angle  is  equal  to  the  angle  aoa'. 

This  law  is  known  as  the  law  of  the  cosine ;  it  is,  however,  not  general  ; 

Desains  and  De  la  Provostaye  have  shown  that  it  is  only  true  within  very 

narrow  limits  ;  that  is,  only  with  bodies  which,  like  lampblack,  are  entirely 

destitute  of  reflecting  power  (423). 

415.  Mobile  equilibrium.     Tbeory  of  exchang-es. — Prevost  of  Geneva 

suggested  the  following  hypothesis  in  reference  to  radiant  heat,  known  as 

Prevost's  theory  of  exchanges,  which  is  now  universally  admitted.    All  bodies, 

whatever  their  temperatures,  constantly  radiate  heat  in  all  directions.     If 

we  imagine  two  bodies  at  different  temperatures  placed  near  each  other, 

the  one  at  a  higher  temperature  will  experience  a  loss  of  heat,  its  temperature 

will  sink,  because  the  rays  it  emits  are  of  greater  intensity  than  those  it 

receives  ;  the  colder  body,  on  the  contrary,  will  rise  in  temperature,  because 

it  receives  rays  of  greater  intensity  than  those  which  it  emits.     Ultimately 

c  c  2 


388  On  Heat.  [415- 

the  temperature  of  both  bodies  becomes  the  same,  but  heat  is  still  exchanged 
between  them,  only  each  receives  as  much  as  it  emits,  and  the  temperature 
remains  constant.    This  state  is  called  the  mobile  eqidlibriiim  of  temperature. 

416.  Ta"ewton's  law  of  cooling-. — A  body  placed  in  a  vacuum  is  only 
cooled  or  heated  by  radiation.  In  the  atmosphere  it  becomes  cooled  or 
heated  by  its  contact  with  the  air,  according  as  the  latter  is  colder  or  hotter 
than  the  radiating  body.  In  both  cases  the  velocity  of  cooling  or  of  heating 
— that  is,  the  qitantity  of  heat  lost  or  gained  in  a  second — is  greater  accord- 
ing as  the  difference  of  temperature  is  greater. 

Newton  enunciated  the  following  law  in  reference  to  the  cooling  or 
heating  of  a  body  : — The  quantity  of  heat  lost  or  gained  by  a  body  in  a  second 
is  proportional  to  the  difference  between  its  temperature  and  that  of  the  sui'- 
roundijig  medium.  Dulong  and  Petit  have  proved  that  this  law  is  not  so 
general  as  Newton  supposed,  and  only  applies  where  the  differences  of 
temperature  do  not  exceed  15°  to  20°.  Beyond  that,  the  quantity  of  heat 
lost  or  gained  is  greater  than  what  is  required  by  this  law. 

Two  consequences  follow  from  Newton's  law  : — 

I.  When  a  body  is  exposed  to  a  constant  source  of  heat,  its  temperature 
does  not  increase  indefinitely,  for  the  quantity  which  it  receives  in  the  same 
time  is  always  the  same  ;  while  that  which  it  loses  increases  with  the  excess 
of  its  temperature  over  that  of  the  surrounding  medium.  Consequently 
a  point  is  reached  at  which  the  quantity  of  heat  emitted  is  equal  to  that 
absorbed,  and  the  temperature  then  remains  stationary. 

II.  Newton's  law,  as  applied  to  the  differential  thermometer,  shows  that 
its  indications  are  proportional  to  the  quantities  of  heat  which  it  receives. 
If  one  of  the  bulbs  of  a  differential  thermometer  receives  rays  of  heat  from 
a  constant  source,  the  instrument  exhibits,  first,  increasing  temperature,  but 
afterwards  becomes  stationary.  In  this  case,  the  quantity  of  heat  which  it 
receives  is  equal  to  that  which  it  emits.  But  the  latter  is  proportional  to  the 
excess  of  the  temperature  of  the  bulb  above  that  of  the  surrounding  atmo- 
sphere— that  is,  to  the  number  of  degrees  indicated  by  the  thermometer  ; 
consequently,  the  temperature  indicated  by  the  differential  thermometer  is 
proportional  to  the  quantity  of  heat  it  receives. 

REFLECTION    OF    HEAT. 

417.  Iiaws  of  reflection. — When  thermal  rays  fall  upon  a  body  they  are, 

speaking  generally,  divided  into  two  portions,  one  of  which  penetrates  the  body 

while  the  other  rebounds  as  if  repelled  from  the 

ID  surface  like  an  elastic  ball.     This  is  said  to  be 

reflected. 

If  jnn  be  a  plane  reflecting  surface  (fig.  378), 
CB  an  incident  ray,  DC  a  line  perpendicular  to 
the  surface  called  the  ?tormal,  and  BA  the  re- 
flected ray,  the  angle  CBD  is  called  the  aiigle 
of  incidence,  and  DBA  the  angle  of  reflection. 
The  reflection  of  heat,  like  that  of  light,  is 
governed  by  the  two  following  laws  : — 
I.    The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 


-418]  Experimental  Demonstration  of  the  Lazvs  of  Reflection.  389 

II.  Botli  tJie  iiicideiif  and  the  refected  ray  are  in  the  same  plane  with  the 
perpendicular  to  the  refecting  surface. 

41S.  Experimental  demonstration  of  the  laws  of  reflection  of  heat. — 

This  may  be  effected  by  means  of  Melloni's  thermopile  and  also  by  the  con- 
jugate mirrors  (420).  Fig.  379  represents  the  arrangement  adopted  in  the 
former  case.  AIN  is  a  horizontal  bar,  about  a  metre  in  length,  graduated  in 
millimetres,  on  which  slide  various  parts,  which  can  be  clamped  by  means 
of  screws.  The  source  of  heat,  S,  is  a  platinum  spiral,  kept  at  a  white  heat  in 
a  spirit  lamp.  A  screen  K,  when  raised,  cuts  off  the  radiation  from  the  source  ; 
a  second  screen,  F,  with  an  aperture  in  the  centre,  cuts  off  all  rays  except  a 
pencil  which  falls  upon  the  mirror  ;//.  At  the  other  end  is  an  upright  rod,  I,  with 
a  graduated  dial,  the  zero  of  which  is  in  the  direction  of  MN,  and  therefore 
parallel  to  the  pencil  S  w.  In  the  centre  of  the  dial  is  an  aperture,  in  which  turns 
an  axis  that  supports  a  metallic  mirror  m.     About  this  axis  turns  an  index,  R, 


on  which  is  fixed  the  thermopile,  P,  in  connection  with  the  galvanometer  G  ; 
H  is  a  screen,  the  object  of  which  is  to  cut  off  any  direct  radiation  from  the 
source  of  heat  towards  the  pile.  In  order  not  to  mask  the  pile,  it  is  not  re- 
presented in  the  position  it  occupies  in  the  experiment. 

By  lowering  the  screen  K,  a  pencil  of  parallel  rays,  passing  through  the 
aperture  F,  falls  upon  the  mirror  in,  and  is  there  reflected.  If  the  index  R 
is  not  in  the  direction  of  the  reflected  pencil,  this  latter  does  not  fall  on 
the  pile,  and  the  needle  of  the  galvanometer  remains  stationary  :  but  by 
slowly  turning  the  index  R,  a  position  is  found  at  which  the  galvanometer 
attains  its  greatest  deviation,  which  is  the  case  when  the  pile  receives  the 
reflected  pencil  perpendicularly  to  its  surface.  Reading  off  then  on  the  dial 
the  position  of  a  small  needle  perpendicular  to  the  mirror,  it  is  observed  that 
this  bisects  the  angle  formed  by  the  incident  and  the  reflected  pencil,  which 
demonstrates  the  first  law. 

The  second  law  is  also  proved  by  the  same  experiment,  for  the  various 
pieces  of  the  apparatus  are  arranged  so  that  the  incident  and  reflected  rays 


390  On  Heat.  [418- 

are  in  the  same  horizontal  plane,  and  therefore  at  right  angles  to  the  reflect- 
ing surface,  which  is  vertical. 

419.  Reflection  from  concave  mirrors. —  Concave  mirrors  ox  reflectors 
are  polished  spherical  or  parabolic  surfaces  of  metal  or  of  glass,  which  are 
used  to  concentrate  luminous  or  calorific  rays  in  the  same  point. 

We  shall  only  consider  the  case  of  spherical  mirrors.  P'ig.  381  represents 
two  of  these  mirrors  ;  fig.  380  gives  a  medial  section,  which  is  called  the 


Fig.  380. 

prmcipal  section.  The  centre  C  of  the  sphere  to  which  the  mirror  belongs 
is  called  the  centre  of  curvature  ;  the  point  A,  the  middle  of  the  reflector,  is 
the  centre  of  the  flgure  ;  the  straight  line  AB  passing  through  these  points, 
is  \\\&  principal  a.xis  of  the  mirror. 

In  order  to  apply  to  spherical  mirrors  the  laws  of  reflection  from  plane 
surfaces,  they  are  considered  to  be  composed  of  an  infinite  number  of  in- 
finitely small  plane  surfaces,  each  belonging  to  the  corresponding  tangent 
plane  ;  the  normals  to  these  small  surfaces  are  all  radii  of  the  same  sphere, 
and  therefore  meet  at  its  centre,  the  centre  of  curvature  of  the  mirror. 

Suppose  now,  on  the  axis  AB  of  the  mirror  MN,  a  source  of  heat  so 
distant  that  the  rays  EK,  PH  ....  which  start  from  it  may  be  considered 
as  parallel.  From  the  hypothesis  that  the  mirror  is  composed  of  an  infini- 
tude of  small  planes,  the  ray  EK  is  reflected  from  the  plane  K  just  as  from 
a  plane  mirror  ;  that  is  to  say,  CK  being  the  normal  to  this  plane,  the 
reflected  ray  takes  a  direction  such  that  the  angle  CKF  is  equal  to  the 
angle  CKE.  The  other  rays,  PH,  GI  .  .  .  .  are  reflected  in  the  same 
manner,  and  all  converge  approximately  towards  the  same  point  F,  on  the 
line  AC.  There  is  then  a  concentration  of  the  rays  in  this  point,  and  conse- 
quently a  higher  temperature  than  at  any  other  point.  This  point  is  called 
the  focus.,  and  the  distance  from  the  focus  to  the  mirror  at  A  is  the  focal 
distance. 

In  the  above  figure  the  heat  is  propagated  along  the  lines  EKF,  LDF,  in 
the  direction  of  the  arrows  ;  but,  conversely,  if  the  heated  body  be  placed  at 
F,  the  heat  is  propagated  along  the  lines  FKE,  FDL,  so  that  the  rays  emitted 
from  the  focus  are  nearly  parallel  after  reflection. 

420.  Verification  of  the  laws  of  reflection. — The  following  experiment, 
which  was  made  for  the  first  time  by  Pictet  and  Saussure,  and  which  is 
known  as  the  expcrinient  of  the  conjugate  mirrors,  demonstrates  not  only 
the  existence  of  the  foci,  but  also  the  laws  of  reflection.  Two  reflectors, 
M  and  N  (fig.  380),  are  arranged  at  a  distance  of  4  to  5  yards,  and  so  that 


-420]  Verification  of  the  Laws  of  Reflection.  391 

their  axes  coincide.  In  the  focus  of  one  of  them,  A,  is  placed  a  small  wire 
basket  containing  a  red-hot  iron  ball.  In  the  focus  of  the  other  is  placed 
B,  an  easily  inflammable  body,  such  as  gun-cotton  or  phosphorus.  The  rays 
emitted  from  the  focus  A  are  first  reflected  from  the  mirror  M,  in  a  direction 
parallel  to  the  axis  (419),  and  impinging  on  the  other  mirror,  N,  are  reflected 
so  that  they  coincide  in  the  focus  B.  That  this  is  so,  is  proved  by  the  fact 
that  the  gun-cotton  at  this  point  takes  fire,  which  is  not  the  case  if  it  is  above 
or  below  it. 

The  experiment  also  serves  to  show  that  light  and  heat  are  reflected  in 
the  same  manner.  For  this  purpose  a  lighted  candle  is  placed  in  the  focus 
of  A,  and  a  ground-glass  screen  in  the  focus  of  B,  when  a  luminous  focus  is 
seen  on  it  exactly  in  the  spot  where  the  gun-cotton  ignites.  Hence  the 
luminous  and  the  calorific  foci  are  produced  at  the  same  point,  and  the 
reflection  takes  place  in  both  cases  according  to  the  same  laws,  for  it  will  be 


afterwards  shown  that  for  light,  the  angle  of  reflection  is  equal  to  the  angle 
of  incidence,  and  that  both  the  incident  and  the  reflected  rays  are  in  the  same 
plane  perpendicular  to  the  plane  I'eflecting  surface. 

In  consequence  of  the  high  temperature  produced  in  the  foci  of  concave 
mirrors  they  have  been  called  burning  mirrors.  It  is  stated  that  Archi- 
medes burnt  the  Roman  vessels  before  Syracuse  by  means  of  such  mirrors. 
Bufifon  constructed  burning  mirrors  of  such  power  as  to  prove  that  the  feat 
attributed  to  Archimedes  was  not  impossible.  The  mirrors  were  made  of  a 
number  of  silver  plane  mirrors  about  8  inches  long  by  5  broad.  They 
could  be  turned  independently  of  each  other  in  such  a  manner  that  the  rays 
reflected  from  each  coincided  in  the  same  point.  With  128  mirrors  and  a 
hot  summei-'s  sun  Bufifon  ignited  a  plank  of  tarred  wood  at  a  distance  of  70 
yards. 


392 


On  Heat. 


[421- 


421.  Reflection  in  a  vacuum.— Heat  is  reflected  in  a  vacuum  as  well  as 
in  air,  as  is  seen  from  the  following  experiment  (fig.  382),  due  to  Sir  Hum- 
hpry  Davy.  Two  small  concave  reflectors  were  placed  opposite  each  other 
under  the  receiver  of  an  air-pump.  In  the  focus  of  one  was  placed  a  delicate 
thermometer,  and  in  the  focus  of  the  other  a  platinum  wire  made  incandescent 
by  means  of  a  galvanic  current.  The  thermometer  was  immediately  seen  to 
rise  several  degrees,  which  could  only  be  due  to  reflected  heat,  for  the  ther- 
mometer did  not  show  any  increase  of 
temperature  if  it  were  not  exactly  in  the 
focus  of  the  second  reflector. 

422.  iLpparent  rejection  of  cold. 
If  two  mirrors  are  arranged  as  repre- 
sented in  fig.  381,  and  a  piece  of  ice  is 
placed  in  one  of  the  foci  instead  of  the 
red-hot  ball,  the  surrounding  tempera- 
ture being  greater  than  zero,  a  diffe- 
rential thermometer  placed  in  the  focus 
of  the  second  reflector  would  exhibit  a 
decrease  in  temperature  of  several  de- 
grees. This  appears  at  first  to  be 
caused  by  the  emission  oi  frigorific  rays 
from  ice.  It  is,  however,  easily  explained 
from  what  has  been  said  about  the 
mobile  equilibrium  of  temperature  (415). 
There  is  still  an  interchange  of  tempera- 
ture, but  here  the  thermometer  is  the 
warmest  body.  As  the  rays  which  the  thermometer  emits  are  hotter  than 
those  emitted  by  the  ice,  the  former  gives  out  more  heat  than  it  receives, 
and  hence  its  temperature  sinks. 

The  sensation  of  cold  experienced  when  we  stand  near  a  plaster  or  stone 
wall  whose  temperature  is  lower  than  that  of  our  body,  or  when  we  stand  in 
front  of  a  wall  of  ice,  is  explained  in  the  same  way. 

423.  Reflecting-  power. — The  reflecting  power  of  a  substance  is  its  pro- 
perty of  throwing  off  a  greater  or  less  proportion  of  incident  heat. 

This  power  varies  in  different  substances.  In  order  to  study  this  power 
in  different  bodies  without  having  recourse  to  as  many  reflectors,  Leslie 
arranged  his  experiment  as  shown  in  fig.  383.  The  source  of  heat  is  a 
cubical  canister,  M,  now  known  as  Leslie's  cube,  filled  with  hot  water.  A 
plate,  a,  of  the  substance  to  be  experimented  upon  is  placed  on  the  axis  of  a 
I'eflecting  mirror  between  the  focus  and  the  mirror.  In  this  manner  the  rays 
emitted  by  the  source  are  first  reflected  from  the  mirror  and  impinge  on  the 
plate  a,  where  they  are  again  reflected  and  converge  to  the  focus  between  the 
plate  and  the  mirror,  at  which  point  a  differential  thermometer  is  placed. 
The  reflector  and  the  thermometer  are  always  in  the  same  position,  and  the 
water  of  the  cube  is  always  kept  at  100°,  but  it  is  found  that  the  temperature 
indicated  by  the  thermometer  varies  with  the  nature  of  the  plate.  This 
method  gives  a  means  of  determining,  not  the  absolute  reflecting  power  of  a 
body,  but  its  power  relatively  to  that  of  some  body  taken  as  a  standard  of 
comparison.     For  from  what  has  been  said  on  the  application  of  Newton's  law 


Fig.  382. 


-423] 


Reflecting  Pozuer. 


393 


to  the  differential  thermometer  (416),  the  temperatures  which  this  instrument 
indicates  are  proportional  to  the  quantities  of  heat  which  it  receives.  Hence, 
if  in  the  above  experiment  a  plate  of  glass  causes  the  temperature  to  rise  1° 
and  a  plate  of  lead  6°,  it  follows  that  the  quantity  of  heat  reflected  by  the 
latter  is  six  times  as  great  as  that  reflected  by  the  former.  For  the  heat 
emitted  by  the  source  remains  the  same,  the  concave  reflector  receives  the 
same  portion,  and  the  difference  can  only  arise  from  the  reflecting"  power  of 
the  plate  a. 


By  this  method  Leslie  determined  the  reflecting  powers  of  the  following 
substances,  relatively  to  that  of  brass,  taken  as  100  : — 


Polished  brass  . 

.     100 

Indian  ink 

Silver 

•       90 

Glass 

Steel 

.       70 

Oiled  glass 

Lead 

.       60 

Lampblack 

The  numbers  only  represent  the  relative  reflecting  power  as  compared 
with  that  of  brass.  Thew  absolute  power  is  the  relation  of  the  quantity  of 
heat  reflected  to  the  quantity  of  heat  received.  Desains  and  De  la  Provostaye, 
who  examined  the  absolute  reflecting  power  of  certain  metals,  obtained  the 
following  results  by  means  of  Melloni's  thermomultiplier  (412),  the  heat 
being  reflected  at  an  angle  of  50°  : — 

.     0-82 
o-Si 

■  077 

■  074 


Silver  plate 

•     0-97 

Steel 

Gold 

.     0-95 

Zinc 

Brass 

■     0-93 

Iron 

Platinum 

•     0-83 

Cast  iron 

394  On  Heat.  [424- 

424.  Absorbing:  power. — The  absorbing powe}-  of  a  body  is  its  property 
of  allowing  a  greater  or  less  quantity  of  the  heat  which  falls  upon  it  to  pass 
into  its  mass.  Its  absolute  value  is  the  ratio  of  the  quantity  of  heat  absorbed 
to  the  quantity  of  heat  received. 

The  absorbing  power  of  a  body  is  always  inversely  as  its  reflecting 
power  :  a  body  which  is  a  good  absorbent  is  a  bad  reflector,  and  vice  versa. 
It  was  formerly  supposed  that  the  two  powers  were  exactly  complementary, 
that  the  sum  of  the  reflected  and  absorbed  heat  was  equal  to  the  total  quan- 
tity of  incident  heat.  This  is  not  the  case  ;  it  is  always  less  :  the  incident 
heat  is  divided  into  three  parts — ist,  one  which  is  absorbed  ;  2nd,  another 
which  is  reflected  regularly — that  is,  according  to  laws  previously  demon- 
strated (417)  ;  and  a  third,  which  is  irregularly  reflected  in  all  directions, 
and  which  is  called  scattered  or  diffused  heat. 

In  order  to  determine  the  absorbing  power  of  bodies,  Leslie  used  the 
apparatus  which  he  employed  in  determining  the  reflecting  powers  (423). 
But  he  suppressed  the  plate  a^  and  placed  the  bulb  of  the  thermometer  in 
the  focus  of  the  reflector.  This  bulb  being  then  covered  successively  with 
lampblack,  or  varnish,  or  with  gold,  silver,  or  copper  foil,  &c.,  the  thermo- 
meter exhibited  a  higher  temperature  under  the  influence  of  the  source  ot 
heat,  M,  according  as  the  substance  with  which  the  bulb  was  covered 
absorbed  more  heat.  Leslie  found  in  this  way  that  the  absorbing  power  of 
a  body  is  greater  the  less  its  reflecting  power.  In  these  exfJeriments,  how- 
ever, the  relation  of  the  absorbing  powers  cannot  be  deduced  from  that  of 
the  temperatures  indicated  by  the  thermometer,  for  Newton's  law  is  not 
exactly  applicable  in  this  case,  as  it  only  prevails  for  bodies  whose  substance 
does  not  vary,  and  here  the  covering  of  the  bulb  varied  with  each  observa- 
tion. But  we  shall  presently  show  (426)  how  the  comparative  absorbing 
powers  may  be  deduced  from  the  ratios  of  the  emissive  powers. 

Taking,  as  a  source  of  heat,  a  canister  filled  with  water  at  100°,  Melloni 
found,  by  means  of  the  thermomultiplier,  the  following  relative  absorbing 
powers  : — 

Lampblack    .         .         .100         Indian  ink     .         .         .         .85 

White  lead     .         .         .100         Shellac 72 

Isinglass         ...       91         Metals 13 

425.  Radiating:  power. — The  radiating  or  emissive  power  of  a  body  is 
its  capability  of  emitting,  at  the  same  temperature,  and  with  the  same  extent 
of  surface,  greater  or  less  quantities  of  heat. 

The  apparatus  represented  in  fig.  382  was  also  used  by  Leslie  in  deter- 
mining the  radiating  power  of  bodies.  For  this  purpose  the  bulb  of  the 
thermometer  was  placed  in  the  focus  of  the  reflector,  and  the  faces  of  the 
canister  M  were  formed  of  difterent  metals,  or  covered  with  difterent 
substances  such  as  lampblack,  paper,  &c.  The  cube  being  filled  with  hot 
water,  at  100°,  and  all  other  conditions  remaining  the  same,  Leslie  turned 
each  face  of  the  cube  successively  towards  the  reflectors,  and  noted  the 
temperature  each  time.  That  face  which  was  coated  with  lampblack  caused 
the  greatest  elevation  of  temperature,  and  the  metal  faces  the  least.  Applying 
Newton's  law,  and  representing  the  heat  emitted  by  lampblack  as  100,  Leslie 
formed  the  following  table  of  radiating  powers  : — 


-426]     Identity  of  the  Absorbi?ig  and  Radiating  Powers.         395 


Lampblack 

.     100 

Tarnished  lead  . 

45 

White  lead 

.     100 

Mercury     .... 

20 

Paper 

.       98 

Polished  lead      . 

19 

Ordinary  white  glass 

■       90 

Polished  iron 

15 

Isinglass   . 

.       80 

Tin, gold,  silver,  copper,  &c. 

12 

It  will  be  seen  that,  in  this  table,  the  order  of  the  bodies  is  exactly  the 
reverse  of  that  in  the  tables  of  reflecting  powers. 

The  radiating  powers  of  several  substances  were  determined  by  Desains 
and  De  la  Provostaye,  who  used  the  thermomultiplier.  They  found,  in  this 
manner,  the  following  numbers  compared  with  lampblack  as  100  : — 


Platinum  foil    . 

Burnished  platinum 

Silver  deposited  chemically 

Copper  foil 

Gold  leaf. 

Pure  silver  laminated 

,,  burnished 

„  deposited  chemically  and  burnished 


io-8o 
9-50 
5-36 
4-90 
4-28 
3-00 
2-50 

2-25 


It  appears,  therefore,  that  the  radiating  power  found  by  Leslie  for  the 
metals  is  too  large. 

426.  Identity  of  the  absorbing-  and  radiating:  powers. — The  absorb- 
ing power  of  a  body  cannot  be  accurately  deduced  from  its  reflecting  power, 
because  the  two  are  not  exactly  complementary.  But  the  absorbing  power 
would  be  determined  if  it  could  be  shown  that  in  the  same  body  it  is  ecjual 
to  the  radiating  power.  This  conclusion  has  been  drawn  by  Dulong  and 
Petit  from  the  following  experiments  : — In  a  large  glass  globe,  blackened  on 
the  inside,  was  placed  a  thermometer  at  a  certain  temperature,  1 5°  for  ex- 
ample ;  the  globe  was  kept  at  zero  by  surrounding  it  with  ice,  and  having 
been  exhausted  by  means  of  a  tubulure  connected  with  an  air-pump,  the  time 
was  noted  which  elapsed  while  the  thermometer  fell  through  5°.  The  experi- 
ment was  then  made  in  the  contrary  direction  :  that  is,  the  sides  of  the  globe 
were  heated  to  15°,  while  the  thermometer  was  cooled  to  zero  :  the  time  was 
then  observed  which  the  thermometer  occupied  in  rising  through  5°.  It  was 
found  that  this  time  was  exactly  the  same  as  that  which  the  thermometer 
had  taken  in  sinking  through  5°,  and  it  was  thence  concluded  that  the 
radiating  power  is  equal  to  the  absorbing  power  for  the  same  body,  and  for 
the  same  difference  between  its  temperature  and  the  temperature  of  the  sur- 
rounding medium,  because  the  quantities  of  heat  emitted  or  absorbed  in  the 
same  time  are  equal. 

This  point  may  also  be  demonstrated  by  means  of  the  following  apparatus 
devised  by  Ritchie.  Fig.  384  represents  what  is  virtually  a  differential 
thermometer,  the  two  glass  bulbs  of  which  are  replaced  by  two  cylindrical 
reservoirs  B  and  C,  of  metal,  and  full  of  air.  Between  them  is  a  third  and 
larger  one  A,  which  can  be  filled  with  hot  water  by  means  of  a  tubulure. 
The  ends  of  B  and  of  A,  which  face  the  right,  are  coated  with  lampblack'; 
those  of  C  and  of  A,  which  face  the  left,  are  either  painted  white,  or  are 


396 


On  Heat. 


[426- 


Fig.  38 


coated  with  silver  foil.  Thus  one  of  the  two  faces  opposite  each  other  is 
black,  and  the  other  white  ;  hence  when  the  cylinder  A  is  filled  with  hot 
water,  its  white  face  radiates  towards  the  black  face  of  B,  and  its  black  face 
towards  the  white  face  of  C.  In  these  circum- 
stances the  liquid  in  the  stem  does  not  move, 
indicating  that  the  two  reservoirs  are  at  the 
same  temperature.  On  the  one  hand,  the 
greater  emissive  power  of  the  black  face  of  A 
is  compensated  by  the  smaller  absorptive  power 
of  the  white  face  of  C  ;  while,  on  the  other 
hand,  the  feebler  radiating  power  of  the  white 
face  of  A  is  compensated  by  the  greater 
absorbing  power  of  the  black  face  of  B. 

The  experiment  may  be  varied  by  replacing 
the  two  white  faces  by  discs,  of  paper,  glass, 
porcelain,  &c. 

427.  Causes  which  modify  the  reflectingr, 
absorbing-,  and  radiating:  powers. — As  the 
radiating  and  absorbing  powers  are  equal,  any 
cause  which  affects  the  one  affects  the  other 
also.  And  as  the  reflecting  power  varies  in 
an  inverse  manner,  whatever  increases  it  dimi- 
nishes the  radiating  and  absorbing  powers,  and 
vice  versa. 

It  has  been  already  stated  that  these  different  powers  vary  with  different 
bodies,  and  that  metals  have  the  greatest  reflecting  power,  and  lampblack 
the  least.  In  the  same  body  these  powers  are  modified  by  the  degree  of 
polish,  the  density,  the  thickness  of  the  radiating  substance,  the  obliquity  of 
the  incident  or  emitted  rays,  and,  lastly,  by  the  nature  of  the  source  of  heat. 
It  has  been  usually  assumed  that  the  reflecting  power  increases  with  the 
polish  of  the  surface,  and  that  the  other  powers  diminish  therewith.  But 
Alelloni  showed  that  by  scratching  a  polished  metaUic  surface  its  reflecting 
power  was  sometimes  diminished  and  sometimes  increased.  This  pheno- 
menon he  attributed  to  the  greater  or  less  density  of  the  reflecting  surface. 
If  the  plate  had  been  originally  hammered,  its  homogeneity  would  be 
destroyed  by  this  process,  the  molecules  would  be  closer  together  on  the 
surface  than  in  the  interior,  and  the  reflecting  power  would  be  increased. 
But  if  the  surface  is  scratched,  the  interior  and  less  dense  mass  becomes 
exposed,  and  the  reflecting  power  diminished.  On  the  contrary,  in  a  plate 
which  has  not  been  hammered,  and  which  is  homogeneous,  the  reflecting 
power  is  increased  when  the  plate  is  scratched,  because  the  density  at  the 
surface  is  increased  by  the  scratches. 

Melloni  found  that  when  the  faces  of  a  cube  filled  with  water  at  a  constant 
temperature  were  varnished,  the  emissive  power  increased  with  the  number 
of  layers  up  to  16  layers,  while  above  that  point  it  remained  constant,  what- 
ever the  number.  The  thickness  of  the  16  layers  was  calculated  to  be 
0-04  mm.  With  reference  to  metals,  gold  leaves  of  0*008,  0*004,  and  0-002 
of  a  millimetre  in  thickness,  having  been  successively  applied  on  the  sides 
of  a  cube  of  glass,  the  diminution  of  radiant  heat  was  the  same  in  each  case. 


429] 


Dynamical  Theory  of  Heat. 


397 


It  appears,  therefore,  that,  beyond  certain  Hmits,  the  thickness  of  the  ra- 
diating layer  of  metal  is  without  influence. 

The  absorbing  power  is  greatest  when  the  rays  are  at  right  angles,  and 
it  diminishes  in  proportion  as  the  incident  rays  deviate  from  the  normal. 
This  is  one  of  the  reasons  why  the  sun  is  hotter  in  summer  than  in  winter, 
because,  in  the  former  case,  the  sun's  rays  are  less  oblique. 

The  radiating  power  of  gaseous  bodies  in  a  state  of  combustion  is  very 
weak,  as  is  seen  by  bringing  the  bulb  of  a  thermometer  near  a  hydrogen 
flame,  the  temperature  of  which  is  very  high.  But  if  a  platinum  spiral  be 
placed  in  this  flame,  it  assumes  the  temperature  of  the  flame,  and  radiates 
a  great  amount  of  heat,  as  is  shown  by  the  thermometer.  For  a  similar 
reason  the  flames  of  oil  and  of  gas  lamps  radiate  more  than  a  hydrogen 
flame  in  consequence  of  the  excess  of  carbon  which  they  contain,  and 
which,  not  being  entirely  burned,  becomes  incandescent  in  the  flame. 

428.  nCelloni's  researcbes  on  radiant  heat. — For  our  knowledge  of 
the  phenomena  of  the  reflection,  emission,  and  absorption  of  heat  which 
have  up  to  now  been  described,  science  is  indebted  mainly  to  Leslie.  But 
since  his  time  the  discovery  of  other  and  far  more  delicate  modes  of  de- 
tecting and  measuring  heat  has  not  only  extended  and  corrected  our 
previous  knowledge,  but  has  led  to  the  discovery  of  other  phenomena  of 
radiant  heat,  which,  without  such  improved  means,  must  have  remained 
unknown. 

This  advance  in  science  is  due  to  an  Italian  philosopher,  Melloni,  who 
first  applied  the  thermo-electric  pile,  invented  by  Nobili,  to  the  measurement 
of  very  small  diff"erences  of  temperature  ;  a  method  of  which  a  preliminary 
account  has  already  been  given  (412). 

In  his  ex- 
periments Mel- 
loni used  five 
sources  of  heat 
— 1st,  a  Loca- 
telli's  lamp  — 
one,  that  is, 
without  a  glass 
chimney,  but 
provided  with 
a    reflector  (fig. 

385)  ;  2nd,  an 
Argand  lamp, 
that  is,  one  with 
a  chimney  and  a 

double  draught  ;  3rd,  a  platinum  spiral,  kept  red  hot  by  a  spirit  lamp  (fig. 

386)  ;  4th,  a  blackened  copper  plate,  kept  at  a  temperature  of  about  400° 
by  a  spirit  lamp  (fig.  387)  ;  5th,  a  copper  tube,  blackened  on  the  outside 
and  filled  with  water  at  100°  (fig.  388). 

429.  Dynamical  theory  of  heat. — Before  describing  the  results  arrived 
at  by  Melloni  and  others,  it  will  be  convenient  to  explain  here  the  view  now 
generally  taken  as  to  the  mode  in  which  heat  is  propagated.  For  additional 
information  the  chapter  on  the  Mechanical  Theory  of  Heat  and  the  book  on 


398  On  Heat.  [429- 

Light  should  be  read.     According  to  what  has  ah-eady  been  stated  (292),  a 
hot  body  is  nothing  more  than  one  whose  pai'ticles  are  in  a  state  of  vibration. 
The  higher  the  temperature  of  the  body,  the  more  rapid  are  these  vibrations, 
and  a  diminution  in  temperature  is  but  a  diminished  rapidity  of  vibration  of 
the  particles.     The  propagation  of  heat  through  a  bar  is  due  to  a  gradual 
communication  of  this  vibratory  motion  from  the  heated  part  to  the  rest  of 
the  bar.     A  good  conductor  is  one  which  readily  takes  up  and  transmits  the 
vibratory  motion  from  particle  to  particle,  while  a  bad  conductor  is  one  which 
takes  up  and  transmits  the  motion  with  difficulty.    But  even  through  the  best 
conductors  the  propagation  of  this  motion  is  comparatively  slow.     How  then 
are  we  to  explain  the  instantaneous  perception  of  heat  experienced  when  a 
screen  is  removed  from  a  fire,  or  when  a  cloud  drifts  from  the  face   of  the 
sun  ?     In  this  case,  the  heat  passes  from  one  body  to  another  without  affect- 
ing the  temperature  of  the  medium  which  transmits  it.     In  order  to  explain 
these  phenomena,  it  is  imagined  that  all  space,  the  interplanetary  spaces  as 
well  as  the  interstices  in  the  hardest  crystal  or  the  heaviest  metal — in  short, 
matter  of  any  kind — is  permeated  by  a  medium  having  the  properties  of  a 
tluid  of  infinite  tenuity,  called  ether.    The  particles  of  a  heated  body,  being  in 
a  state  of  intensely  rapid  vibration,  communicate  their  motion  to  the  ether 
around  them,  throwing  it  into  a  system  of  waves  which  travel  through  space 
and  pass  from  one  body  to  another  with  the  velocity  of  light.    When  the  un- 
dulations of  the  ether  reach  a  given  body,  the  motion  is  again  delivered  up  to 
the  particles  of  that  body,  which  in  turn  begin  to  vibrate  ;  that  is,  the  body 
becomes  heated.     This  process  of  motion  through  the  hypothetical  ether  is 
termed  radiation,  and  what  is  called  a  ray  of  heat  is  merely  one  series  of 
waves  moving  in  a  certain  direction. 

It  will  facilitate  the  understanding  of  this  to  consider  the  analogous  mode 
in  which  sound  is  produced  and  propagated.  A  sounding  body  is  one  whose 
entire  mass  is  in  a  state  of  vibration  (222)  ;  the  more  rapid  the  rate  of  vibra- 
tion, the  more  acute  the  sound  ;  the  slower  the  rate  of  vibration,  the  deeper 
the  sound.  This  vibratory  motion  is  communicated  to  the  surrounding  air,  by 
means  of  which  the  vibrations  reach  the  auditory  nerve,  and  there  produce 
the  sensation  of  sound.  If  a  metal  ball  be  heated,  say,  to  the  temperature 
of  boiling  water,  we  can  ascertain  that  it  radiates  heat,  although  we  cannot 
see  any  luminosity  ;  and  if  its  temperature  be  gradually  raised,  we  see  it 
becomes  successively  of  a  dull  red,  bright  red,  and  dazzling  white.  At  each 
particular  temperature  the  heated  body  emits  waves  of  a  definite  length  ;  in 
other  words,  its  particles  vibrate  in  a  certain  period.  As  its  temperature 
rises  it  sends  out  other  and  more  rapid  vibrations,  which  coexist,  however, 
with  all  those  which  it  had  previously  emitted.  Thus  the  motion  at  each 
successive  temperature  is  compounded  of  all  preceding  ones. 

It  has  been  seen  that  vibrations  of  the  air  below  and  above  a  certain  rate 
do  not  affect  the  auditory  nerve  (244) ;  it  can  only  take  up  and  transmit  to  the 
brain  vibrations  of  a  certain  periodicity.  So  too  with  the  vibrations  which 
produce  light.  The  optic  nerve  is  insensible  to  a  large  number  of  wave- 
lengths. It  can  apprehend  only  those  waves  that  form  the  visible  spectrum. 
If  the  rate  of  undulation  be  slower  than  the  red  or  faster  than  the  violet, 
though  intense  motion  may  pass  through  the  humours  of  the  eye  and  fall 
upon   the   retina,  yet  we    shall  be  utterly  unconscious  of  the  fact,  for  the 


-430]  Thermal  Analysis  of  Solar  Light.  399 

optic  nerve  cannot  take  up  and  respond  to  the  rate  of  vibrations  which  exist 
beyond  the  visible  spectrum  in  both  directions.  Hence,  these  are  termed 
invisible  or  obsctcre  rays.  A  vast  quantity  of  these  obscure  rays  is  emitted 
by  flames  which,  though  intensely  hot,  are  yet  almost  non-luminous,  such 
as  the  oxy-hydrogen  flame,  or  that  of  a  Bunsen's  burner  ;  for  the  vibra- 
tions which  these  emit,  though  capable  in  part  of  penetrating  the  media 
of  the  eye,  are  incapable  of  exciting  in  the  optic  nerve  the  sensation  of 
light. 

430.   Thermal  analysis  of  solar  ligrht. — When  a  beam  of  sunlight  (fig. 
389),  admitted  through  an  aperture  in  a  dark  room,  is  concentrated  on  a 


prism  of  rock  salt  by  means  of  a  lens  of  the  same  material,  and  then,  after 
emerging  from  the  prism,  is  received  on  a  screen,  it  will  be  found  to  present 
a  band  of  colours  in  the  following  order  :  red,  orange,  yellow,  green,  blue, 
and  violet.     This  is  called  the  spectrum  (564). 

If  now  a  narrow  and  delicate  thermopile  be  placed  successively  on  the 
space  occupied  by  each  of  the  colours,  it  will  be  scarcely  affected  on  the 
violet,  but  in  passing  over  the  other  colours  it  will  indicate  a  gradual  rise  of 
temperature,  which  is  greatest  at  the  red.  Painters,  thus  guided  by  a  cor- 
rect but  unconscious  feeling,  always  speak  of  blue  and  green  colours  as  cold, 
and  of  red  and  orange  as  warm  tones.  If  the  pile  be  now  moved  in  the 
same  direction  beyond  the  limits  of  the  luminous  spectrum,  the  temperature 
will  gradually  rise  up  to  CP,  at  which  it  attains  its  maximum.  From  this 
point  the  pile  indicates  a  decrease  of  temperature  until  it  reaches  a  point,  O, 
where  it  ceases  to  be  affected.  This  point  is  about  as  distant  from  R  as  the 
latter  is  from  V  ;  that  is,  there  is  a  region  in  which  thermal  effects  are  pro- 
duced extending  as  far  beyond  the  red  end  of  the  spectrum  in  one  direction 
as  the  entire  length  of  the  visible  spectrum  in  the  other.  In  accordance 
with  what  we  have  stated,  the  sun's  light  consists  of  rays  of  different  rates  of 
vibration  ;  by  their  passage  through  the  prism  they  are  unequally  broken  or 
refracted  ;  those  of  greatest  wave-length  or  slowest  vibrating  period  are  least 
bent  aside,  or  are  said  to  be  the  least  refrangible,  while  those  with  shorter 
wave-lengths  are  the  most  refrangible. 

These  non-luminous  rays  outside  the  red  are  called  the  extra  or  ultra-red 
rays,  or  sometimes  the  Herschelian  rays,  from  Sir  W.  Herschel,  who  first 
discovered  their  existence. 


400  On  Heat:  [430- 

If,  in  the  above  case,  prisms  of  other  materials  than  rock  salt  be  used, 
the  position  of  the  maximum  heat  will  be  found  to  vary  with  the  nature  of 
the  prism,  a  fact  first  noticed  by  Seebeck.  Thus  with  a  prism  of  water  it  is 
in  the  yellow,  with  one  of  crown  glass  in  the  middle  of  the  red,  and  so  on. 
These  changes  are  due  to  the  circumstance  that  prisms  of  different  materials 
absorb  rays  of  different  refrangibility  to  unequal  extents.  But  rock  salt 
practically  allows  heat  of  all  kinds  to  pass  with  equal  facility,  and  thus  gives 
a  normal  spectrum. 

431.  Tyndall's  researches. — Tyndall  investigated  the  spectrum  pro- 
duced by  the  electric  light,  by  the  following  mode  of  experimenting  : — The 
electric  light  was  produced  between  charcoal  points  by  a  Grove's  battery  of 
fifty  cells.  The  beam,  rendered  parallel  by  a  double  rock-salt  lens,  was 
caused  to  pass  through  a  narrow  slit,  and  then  through  a  second  lens  of  rock 
salt  ;  the  slices  of  white  light  thus  obtained  being  decomposed  by  a  prism 
of  the  same  material.  To  investigate  the  thermal  conditions  of  the  spec- 
trum a  linear  thermo-electric  pile  was  used  ;  that  is,  one  consisting  of  a 
number  of  elements  arranged  in  a  line,  and  in  front  of  which  was  a  slit  that 
could  be  narrowed  to  any  extent.  The  instrument  was  mounted  on  a 
movable  bar  connected  with  a  fine  screw,  so  that  by  turning  a  handle  the 
pile  could  be  pushed  forward  through  the  smallest  space.  On  placing  this 
apparatus  successively  in  each  part  of  the  spectrum  of  the  electric  light,  the 
heating  effected  at  various  points  near  each  other  was  determined  by  the 
indications  of  a  very  delicate  galvanometer.  As  in  the  case  of  the  solar 
spectrum,  the  heating  effect  gradually  increased  from  the  violet  end  towards 
the  red,  and  was  greatest  in  the  dark  space  beyond  the  red.  The  position 
of  the  greatest  heat  was  about  as  far  from  the  limit  of  the  visible  red  as  the 
latter  was  from  the  green,  and  the  total  extent  of  the  invisible  spectrum  was 
found  to  be  twice  that  of  the  visible. 

The  increase  of  temperature  in  the  dark  space  is  veiy  considerable.     If 
thermal  intensities  are  represented  by  perpendicular  lines  of  proportionate 
jj  length,     erected 

at  those  parts  of 
the  spectrum  to 
which  they  cor- 
respond, on 
passing  beyond 
the  red  end 
these  lines  in- 
crease rapidly 
and  greatly  in 
length,  reach  a 
maximum,  and 
then  fall  some- 
what more  sud- 
denly.    If  these 

lines  are  connected,  they  form  a  curve  (fig.  390),  which  beyond  the  red 
represents  a  peak,  quite  dwarfing  that  of  the  visible  spectrum.  In  fig.  391, 
the  dark  parts  at  the  end  represent  the  obscure  radiation.  The  curve  is 
based,  in  the  manner  above  stated,  on  the  results  obtained  by  Tyndall  with 


Fig.  390. 


-432] 


Ljiminous  and  Obscure  Radiation. 


401 


the  electric  light.  The  upper  curve  in  fig.  391  represents  the  spectrum  of 
sunlight  with  a  rock-salt  prism,  while  the  lower  curve  represents  the  results 
obtained  with  a  flint-glass  prism,  which  is  thus  seen  to  absorb  some  of  the 
ultra-red  radiation. 

By  interposing  various  substances,  more  especially  water,  in  certain 
thicknesses,  in  the  path  of  the  electric  light,  the  ultra-red  radiation  was 
greatly  diminished.  Now  aqueous  vapour,  like  water,  absorbs  the  obscure 
rays.  And  probably  the  reason  why  the  obscure  part  of  the  spectrum  of 
sunlight  is  not  so  intense  as  in  the  case  of  the  electric  light  is  that  the 
obscure  rays  have  been  already  partially  absorbed  by  the  aqueous  vapour  of 
the  atmosphere.  If  a  solar  spectrum  could  be  produced  outside  the  atmo- 
sphere, it  would  probably  give  a  spectrum  more  like  that  of  the  electric  light, 
which  is  unaffected  by  the  atmospheric  absorption. 

This  has  been  confirmed  in  other  ways.  Melloni  observed  that  the 
position  of  the  maximum  in  the  solar  spectrum  differs  on  different  days  ; 
which  is  probably  due  to  the  varying  absorption  of  the  atmosphere,  in  con- 
sequence of  its  varying  hygrometric  state.  Secchi,  in  Rome,  found  the 
same  shifting  of 
the  maximum  to 
occur  in  the  dif- 
ferent seasons 
of  the  year  ;  for 
in  winter,  when 
there  is  least 
moisture  in  the 
atmosphere,  the 
maximum  is  far- 
ther from  the 
red  than  in  sum- 
mer,    when    the  '^' 

aqueous  vapour  in  the  air  is  most  abundant.  An  important  observation  on 
the  luminous  rays  has  also  been  made  by  Cooke,  in  America,  who  found  that 
the  faint  black  lines  in  the  solar  spectrum  attributed  to  the  absorption  of  light 
by  our  atmosphere  (see  book  on  Optics)  are  chiefly  caused  by  the  presence 
of  aqueous  vapour. 

432.  Iiuminous  and  obscure  radiation. — The  radiation  from  a  luminous 
object,  a  gas  flame  for  example,  is  of  a  composite  character  ;  a  portion  con- 
sists of  what  we  term  light,  but  a  far  greater  part  consists  of  heat  rays, 
which  are  insensible  to  our  eyes,  being  unable  to  affect  the  optic  nerve. 
When  this  mixed  radiation  falls  upon  the  blackened  face  of  a  thermo-electric 
pile,  the  whole  of  it  is  taken  to  be  absorbed,  the  light  by  this  act  beino- 
converted  into  heat,  and  affecting  the  instrument  proportionally  with  the 
purely  calorific  rays.  The  total  radiation  of  a  luminous  source,  expressed 
in  units  of  heat  or  force,  can  thus  be  measured.  By  introducing  into  the 
path  of  the  rays  a  body  capable  of  stopping  either  the  luminous  or  the 
obscure  radiation,  we  can  ascei'tain  by  the  comparative  action  on  the  pile 
the  relative  quantities  of  heat  and  light  radiated  from  the  source.  Melloni 
sought  to  do  this  by  passing  a  luminous  beam  through  a  layer  of  water 
containing  alum  in  solution  ;  a  liquid  which  he  found  in  previous  experi- 

D  D 


Luminous 

Obscure 

.       O 

lOO 

.       O 

loo 

•     3 

97 

•     4 

96 

.     4-6 

95-4 

.       lO 

90 

402  071  Heat.  [432- 

ments  absorbed  all  the  radiation  from  bodies  heated  under  incandescence. 
Comparing  the  transmission  through  this  liquid — which  allowed  the  luminous 
but  not  the  obscure  part  of  the  beam  to  pass — with  the  transmission  through 
a  plate  of  rock  salt — which  atfected  neither  the  luminous  nor  the  obscure 
radiation,  but  gave  the  loss  due  to  reflection — Melloni  found  that  90  per  cent, 
of  the  radiation  from  an  oil  flame  and  99  per  cent,  of  the  radiation  from  an 
alcohol  flame  consist  of  invisible  calorific  rays.  This  proportion  has  been 
still  further  increased  by  the  experiments  of  Tyndall,  who  employed  a  solu- 
tion of  iodine  in  bisulphide  of  carbon,  which  he  found  to  be  impervious  to 
the  most  intense  light,  but  very  pervious  to  radiant  heat  ;  only  a  slight 
absorption  being  effected  by  the  bisulphide.  By  comparing  the  transmission 
through  the  transparent  bisulphide,  and  the  transmission  through  the  same 
liquid  rendered  opaque  by  iodine,  the  value  of  the  luminous  radiation  from 
various  sources  was  found  to  be  as  follows  :— 

Source 

Red-hot  spiral 

Hydrogen  flame 

Oil  flame  .... 

Gas  flame         .... 

White-hot  spiral 

Electric  light  .... 

Here  by  direct  experiment  the  ratio  of  luminous  to  obscure  rays  in  the 
electric  light  is  found  to  be  10  per  cent,  of  the  total  radiation.  By  prismatic 
analysis,  the  curve  shown  in  fig.  390  was  obtained,  graphically  representing 
the  proportion  of  luminous  to  obscure  rays  in  the  electric  light  ;  by  calculating 
the  areas  of  the  two  spaces  in  the  diagram,  the  obscure  portion,  DCBA,  is 
found  to  be  nearly  10  times  as  large  as  the  luminous  one,  DCE. 

433.  Transmutation  of  obscure  rays. — We  shall  find,  in  speaking  of 
the  luminous  spectrum,  that  beyond  the  violet  there  are  rays  which  are  in- 
visible to  the  eye,  but  which  are  distinguished  by  their  chemical  action,  and 
are  spoken  of  as  the  actinic  or  chemical  rays  ;  they  are  also  known  as  the 
Ritteric  rays,  from  the  philosopher  who  first  discovered  their  existence. 

As  we  shall  afterwards  see  in  the  book  on  Optics,  Stokes  has  succeeded 
in  converting  these  rays  into  rays  of  lower  refrangibility,  which  then  become 
visible  ;  so  Tyndall  has  effected  the  corresponding  but  inverse  change,  and 
has  increased  the  refrangibility  of  the  Herschelian  or  extra  red  rays,  and 
thus  rendered  them  visible.  The  charcoal  points  of  the  electric  light  were 
placed  in  front  of  a  concave  silvered  glass  mirror  in  such  a  manner  that 
the  rays  from  the  points  after  reflection  were  concentrated  to  a  focus  about 
6  inches  distant.  On  the  path  of  the  beam  was  interposed  a  cell  full  of  a 
solution  of  iodine  in  bisulphide  of  carbon,  which  (432)  has  the  power  of  com- 
pletely stopping  all  luminous  radiation,  but  gives  free  passage  to  the  non- 
luminous  rays.  On  now  placing  in  the  focus  of  the  beam,  thus  sifted,  a  piece 
of  platinum,  it  was  raised  to  incandescence  by  the  impact  of  perfectly  invisible 
rays.     In  like  manner  a  piece  of  charcoal  iji  vacuo  was  heated  to  redness. 

By  a  proper  arrangement  of  the  charcoal  points  a  metal  may  be  raised 
to  whiteness,  and  the  light  now  emitted  by  the  metal  yields  on  prismatic 
analysis  a  brilliant  luminous  spectrum,  which  is  thus  entirely  derived  from 


-434] 


Transmission  of  Thermal  Rays. 


403 


the  invisible  rays  beyond  the  red.  This  transmutation  of  non-luminous  into 
luminous  heat,  Tyndall  calls  calorescence. 

When  the  eye  was  cautiously  placed  in  the  focus,  guarded  by  a  small 
hole  pierced  in  a  metal  screen,  so  that  the  converged  rays  should  only  enter 
the  pupil  and  not  affect  the  surrounding  part  of  the  eye,  no  impression  of 
light  was  produced,  and  there  was  scarcely  any  sensation  of  heat.  A  con- 
siderable portion  was  absorbed  by  the  humours  of  the  eye,  but  yet  a  power- 
ful beam  undoubtedly  reached  the  retina  ;  for,  as  Tyndall  showed  by  a 
separate  experiment,  about  18  per  cent,  of  the  obscure  radiation  from  the 
electric  light  passed  through  the  humours  of  an  ox's  eye. 

434.  Transmission  of  thermal  rays. — Melloni  was  the  first  who  ex- 
amined extensively  and  accurately  the  absorption  of  heat  by  solids  and 
liquids.     The  apparatus  he  employed  is  represented  in  fig.  392,  where  AB  is 


Fig.  392. 

the  thermo-electric  pile  ;  rt;  is  a  support  for  the  source  of  heat,  in  this  case  a 
Locatelli's  lamp  ;  F  and  E  are  screens,  and  C  is  a  support  for  the  body  ex- 
perimented on  ;  while  m  is  the  support  for  the  pile,  and  D  the  galvanometer. 
To  express  the  power  which  bodies  have  of  transmitting  heat,  Melloni 
used  the  term  diathermancy  :  diathermancy  bears  the  same  relation  to 
radiant  heat  that  transparency  does  to  light  ;  and  in  like  manner  the  power 
of  stopping  radiant  heat  is  called  at/iermancy,  which  thus  corresponds  to 
opacity  for  light.  In  experimenting  on  the  diathermancy  of  hquids,  Melloni 
used  glass  troughs  with  parallel  sides,  the  thickness  of  the  liquid  layer  being 
0-36  in.  The  radiant  heat  of  an  Argand  lamp  with  a  glass  chimney  was 
first  allowed  to  fall  directly  on  the  face  of  the  pile,  and  the  deflection  pro- 
duced in  the  galvanometer  taken  as  the  total  radiation  ;  the  substance  under 
examination  was  then  interposed,  and  the  deflection  noted.  This  corre- 
sponded to  the  quantity  of  heat  transmitted  by  the  substance.  If  t  indicate 
this  latter  number,  and  /'  the  total  radiation,  then 
t'  :  t ::  100  :  x, 

which  is  the  percentage  of  rays  transmitted.    Thus  calling  the  total  radiation 
100,  Melloni  found  that 

D  D  2 


404 


On  Heat. 


[434- 


Bisulphide  of  carbon  transmitted 

Olive  oil  „ 

Ether  „ 

Sulphuric  acid  „ 

Alcohol  „ 

Solution  of  alum  or  sugar  „ 

Distilled  water  „ 


In  experimenting  with  solids  they  were  cut  into  plates  OT  inch  in  thick- 
ness, and  it  was  found  that  of  every  loo  rays  there  was  transmitted  by 
Rock  salt        .         .         .         .92         Selenite  .         .         .20 

Smoky  quartz  .         .         .67         Alum      .         .         .         .12 

Transparent  carbonate  of  lead     52         Sulphate  of  copper         .       o 

The  transmission  of  heat  through  liquids  has  been  re-examined  by  Tyndall, 
who  used  a  cell  consisting  of  parallel  plates  of  rock  salt  separated  by  a  ring 
of  brass  with  an  aperture  on  the  top  through  which  the  liquid  could  be 
poured.  As  this  ring  could  be  changed  at  will,  liquid  layers  of  various 
thicknesses  were  easily  obtainable,  the  apparatus  being  merely  screwed 
together  and  made  liquid-tight  by  paper  washers.  The  instrument  was 
mounted  on  a  support  before  an  opening  in  a  brass  screen  placed  in  front 
of  the  pile.  The  source  of  heat  employed  was  a  spiral  of  platinum  wire 
raised  to  incandescence  by  an  electric  current,  the  spiral  being  enclosed  in  a 
small  glass  globe  with  an  aperture  in  front,  through  which  the  radiation 
passed  unchanged  in  its  character,  a  point  of  essential  importance  overlooked 
by  Melloni.  The  following  table  contains  the  results  of  experiments  made 
with  liquids  in  the  various  thicknesses  indicated,  the  numbers  expressing 
the  absorption  per  cent,  of  the  total  radiation.  The  transmission  per  cent, 
can  be  found  in  each  case  by  subtracting  the  absorption  from  100.  Thus  a 
layer  of  water  0-2  inch  thick  absorbs  807  and  transmits  19-3  per  cent,  of  the 
radiation  from  a  red-hot  spiral. 


Absorptio?i  of  heat  by  liquids. 

Thickness  of  liquids  in  parts  of  an  inch 

Liquid 

o-o. 

o'o4 

0-07 

0-14 

0-27 

Bisulphide  of  carbon 

5-5 

8-4 

12.5 

15-2 

17-3 

Chloroform 

i6-6 

25-0 

35 -o 

40-0 

44-8 

Iodide  of  methyl 

36-1 

46-5 

53-2 

65-2 

68-6 

Benzole     . 

43-4 

557 

62-5 

71-5 

73-6 

Amylene  . 

58-3 

65-2 

73-6 

777 

82-3 

Ether 

63-3 

73-5 

76-1 

78-6 

85-2 

Alcohol     . 

67-3 

78-6 

83-6 

85-3 

89-1 

Water       . 

807 

86-1 

88-8 

91-0 

91-0 

It  appears  from  these  tables  that  there  is  no  connection  between  diather- 
mancy and  transparency.  The  liquids,  except  olive  oil,  are  all  colourless 
and  transparent,  and  yet  vaiy  as  much  as  75  per  cent,  in  the  amount  of  heat 
transmitted.     Among  solids,  smoky  quartz,  which  is  nearly  opaque  to  light. 


-435] 


Influence  of  the  Nature  of  the  Heat. 


405 


transmits  heat  very  well ;  while  alum,  which  is  perfectly  transparent,  cuts  off 
88  per  cent,  of  heat  rays.  As  there  are  different  degrees  of  transparency,  so 
there  are  different  degrees  of  diathermancy  ;  and  the  one  cannot  be  predi- 
cated from  the  other. 

By  studying  the  transmission  of  heat  from  different  parts  of  the  spec- 
trum separately,  the  connection  between  light  and  heat  becomes  manifest. 
With  this  view  Masson  and  Jamin  received  the  spectrum  of  the  solar  light 
given  by  a  prism  of  rock  salt  on  a  movable  screen  provided  with  an  aperture, 
so  that  by  raising  or  lowering  the  screen  the  action  of  any  given  part  of  the 
spectrum  on  different  plates  could  be  investigated.     They  thus  found — 

That  glass,  rock  crystal,  ice,  and  generally  substances  transparent  for 
light,  are  also  diathermanous  for  all  kinds  of  luminous  heat ; 

That  a  coloured  glass,  red,  for  instance,  which  only  transmits  the  red  rays 
of  the  spectrum,  and  extinguishes  the  others,  also  extinguishes  every  kind  of 
luminous  heat,  excepting  that  of  the  red  rays  ; 

That  glass  and  rock  crystal,  which  are  diathermanous  for  luminous  heat, 
also  transmit  the  obscure  heat  near  the  red— that  is,  the  most  refrangible — 
but  extinguish  the  extreme  obscure  rays,  or  those  which  are  the  least  de- 
flected by  the  prism.  Alum  extinguishes  a  still  greater  proportion  of  the 
obscure  spectrum,  and  ice  stops  it  altogether. 

Knoblauch  has  shown  that  very  thin  layers  of  gold,  silver,  and  platinum, 
which  are  known  to  transmit  luminous  rays  of  a  definite  colour,  also  allow 
rays  of  heat  to  pass  ;  so  that  these  substances  are  diathermanous,  though  in 
a  small  degree.     This  is  also  the  case  with  thin  sheets  of  ebonite. 

435.  Influence  of  the  nature  of  the  heat. — The  diathermanous  power 
differs  greatly  with  the  heat  from  different  sources,  as  is  seen  from  the 
following  table,  in  which  the  numbers  express  what  proportion  of  every 
100  rays  from  the  different  sources  of  heat  incident  on  the  plates  is  trans- 
mitted : — 


Locatelli's 
lamp 

Incandescent 
platinum  wire 

Copper  at  400° 

Copper  at  100° 

Rock  salt   . 

92 

92 

92 

92 

Fluor  spar . 

78 

69 

42 

33 

Plate  glass 

39 

24 

6 

0 

Black  glass 

26 

55 

12 

0 

Selenite 

14 

5 

0 

0 

Alum  .... 

9 

2 

0 

0 

Ice     . 

6 

0-5 

0 

0 

These  different  sources  of  heat  correspond  to  light  from  different  sources. 
Rock  salt  is  here  stated  to  transmit  all  kinds  of  heat  with  equal  facility,  and 
to  be  the  only  substance  which  does  so.  It  is  analogous  to  white  glass, 
which  is  transparent  for  light  from  all  sources.  Fluor  spar  transmits  78  per 
cent,  of  the  rays  from  a  lamp,  but  only  -^jT,  of  those  from  a  blackened  surface 
at  100°.  A  piece  of  plate  glass  only  one-tenth  of  an  inch  thick,  and  perfectly 
transparent  to  light,  is  opaque  to  all  the  radiation  from  a  source  of  100°, 
transmits  only  6  per  cent,  of  the  heat  from  a  source  at  400°,  and  but  39  of 
the  radiation  from  the  lamp.     Black  glass,  on  the  contrary,  though  it  cuts 


4o6  .  On  Heat.  [435- 

off  all  heat  from  a  source  at  ioo°,  allows  12  per  cent,  of  the  heat  at  400°  to 
pass,  and  is  equally  transparent  to  the  heat  from  the  spiral,  but  on  account 
of  its  blackness  is  more  opaque  to  the  heat  from  the  lamp.  As  we  have 
already  seen,  every  luminous  ray  is  a  heat  ray  ;  now  as  several  of  the  sub- 
stances in  this  table  are  pervious  to  all  the  luminous  rays,  and  yet,  as  in  the 
case  of  ice,  transmit  about  6  per  cent,  of  luminous  heat,  we  have  an  apparent 
anomaly  ;  which,  however,  is  only  a  confirmation  of  the  remarkably  small 
proportion  which  the  luminous  rays  of  a  lamp  bear  to  the  obscure. 

From  these  experiments  Melloni  concluded  that  as  the  temperature  of 
the  source  rose,  more  heat  was  transmitted.  This  has  been  confirmed  by 
some  experiments  of  Tyndall.  The  platinum  lamp  (434)  was  used  as  the 
source,  the  temperature  of  which  could  be  varied  from  a  dark  to  a  brilliant 
white  heat,  by  a  gradual  augmentation  of  the  strength  of  the  electric  current 
which  heated  the  platinum  spiral.  Instead  of  liquids,  vapours  were  examined 
in  a  manner  to  be  described  subsequently  ;  the  measurements  are  given  in 
the  following  table  : — 

Absorption  of  Jicat  by  vapours. 


Name  of  vapour 

Source,  platinum  spiral 

Barely  visible      Bright  red 

White  hot 

Near  fusion 

Bisulphide  of  carbon 

Chloroform 

Iodide  of  methyl 

Benzole      .... 

Ether          .... 

Formic  ether     . 

Acetic  ether 

6-5        i          47 
9-1                6-3 
12-5                9-6 
26-4                20-6 
43"4              3 1 '4 
45-2              31-9 
49 '6       1       34-6 

2-9 
5-6 
7-8 
i6-5 
25-9 
25-1 
27-2 

2-5 
3-9 

237 
21-3 

The  percentage  of  rays  absorbed  is  here  seen  to  diminish  in  each  case 
as  the  temperature  of  the  source  rises.  Mere  elevation  of  temperature  does 
not,  however,  invariably  produce  a  high  penetrative  power  in  the  rays 
emitted  ;  the  rays  from  sources  of  far  higher  temperature  than  any  of  the 
foregoing  are  more  largely  absorbed  by  certain  substances  than  are  the  rays 
emitted  from  any  one  of  the  sources  as  yet  mentioned.  Thus,  the  radia- 
tion from  a  hydrogen  flame  was  completely  intercepted  by  a  layer  of  water 
only  o'27  of  an  inch  thick,  the  same  layer  transmitting  9  per  cent,  of  the 
radiation  from  the  red-hot  spiral,  a  source  of  much  lower  temperature.  The 
explanation  of  this  is,  that  those  rays  which  heated  water  emits  (and  water,  • 
the  product  of  combustion,  is  the  main  radiant  in  a  hydrogen  flame)  are  the 
very  ones  which  this  substance  most  largely  absorbs.  This  statement,  which 
will  become  clearer  after  reading  the  analogous  phenomena  in  the  case  of 
light,  was  exemplified  by  the  powerful  absorption  of  the  heat  from  a 
carbonic  oxide  flame  by  carbonic  acid  gas.  It  will  be  seen  presently  (438) 
that  of  the  rays  from  a  heated  plate  of  copper,  olefiant  gas  absorbs  10  times 
the  quantity  intercepted  by  carbonic  acid,  whilst  of  the  rays  from  a  carbonic 
oxide  flame  Tyndall  found  carbonic  acid  absorbed  twice  as  much  as  olefiant 
gas.  A  tenth  of  an  atmosphere  of  carbonic  acid,  inclosed  in  a  tube  4  feet 
long,  absorbs  60  per  cent,   of  the  radiation  from  a  carbonic  oxide  flame. 


-436]     Influence  of  the  Thickness  and  Nature  of  Screens.         407 

Radiant  heat  of  this  character  can  thus  be  used  as  a  dehcate  test  for  the 
presence  of  cai'bonic  acid,  the  amount  of  which  may  even  be  accurately 
measured  by  the  same  means.  Prof.  Barrett  made  in  this  way  a  physical 
analysis  of  the  human  breath.  In  one  experiment,  the  carbonic  acid  con- 
tained in  breath  physically  analysed  was  found  to  be  4"65  per  cent,  whilst 
the  same  breath  chemically  analysed  gave  4'66  per  cent. 

436.  Influence  of  the  tbickness  and  nature  of  screens. — It  will  be 
seen  from  the  table  (435)  that  of  every  100  rays  rock  salt  transmits  92.  The 
other  8  may  either  ha\'e  been  absorbed  or  reflected  from  the  surface  of  the 
plate.  According  to  Melloni,  the  latter  is  the  case  ;  for  if,  instead  of  on  one 
plate,  heat  be  allowed  to  fall  on  two  or  more  plates  whose  total  thickness 
does  not  exceed  that  of  the  one,  the  quantity  of  heat  arrested  will  be  propor- 
tional to  the  number  of  reflecting  surfaces.  He  therefore  concluded  that 
rock  salt  was  quite  diathermanous. 

The  experiments  of  later  observers  show  that  this  conclusion  is  not 
strictly  correct ;  rock  salt  does  absorb  a  very  small  proportion  of  obscure 
rays. 

The  quantity  of  heat  transmitted  through  rock  salt  is  practically  the 
same,  whether  the  plate  be  i,  2,  or  4  millimetres  thick.  But  with  other  bodies 
absorption  increases  with  the  thickness,  although  by  no  means  in  direct 
proportion.  This  is  seen  to  be  the  case  in  the  table  of  absorption  by  liquids 
at  diflerent  thicknesses.  The  following  table  tells  what  proportion  of 
1,000  rays  from  a  Locatelli's  lamp  pass  through  a  glass  plate  of  the  given 
thickness  : — 

Thickness  in  millimetres     0-512345678 
Rays  transmitted    .         .  775    T-})})    682    653    634    620    609    600    592 

The  absorption  takes  place  in  the  first  layers  ;  the  rays  which  have  passed 
these  possess  the  property  of  passing  through  other  layers  in  a  higher  degree, 
so  that  beyond  the  first  layers  the  heat  transmitted  approaches  a  certain 
constant  value.  If  a  thin  glass  plate  be  placed  behind  another  glass  plate 
a  centimetre  thick,  the  former  diminishes  the  transmission  by  little  more 
than  the  reflection  from  its  surface.  But  if  a  plate  of  alum  were  placed  be- 
hind the  glass  plate,  the  result  would  be  different,  for  the  latter  is  opaque  for 
much  of  the  heat  transmitted  by  glass. 

Heat,  therefore,  which  has  traversed  a  glass  plate  traverses  another 
plate  of  the  same  material  with  very  slight  loss,  but  is  very  greatly  diminished 
by  a  plate  of  alum.  Of  100  rays  which  had  passed  through  green  glass 
or  tourmaline,  only  5  and  7  were  respectively  transmitted  by  the  same 
plate  of  alum.  A  plate  of  blackened  rock  salt  only  transmits  obscure  rays, 
while  alum  extinguishes  them.  Consequently,  when  these  two  substances 
are  superposed,  a  system  impervious  to  light  and  heat  is  obtained. 

These  phenomena  find  their  exact  analogies  in  the  case  of  light.  The 
different  sources  of  heat  correspond  to  flames  of  different  colours,  and  the 
screens  of  various  materials  to  glasses  of  different  colours.  A  red  flame 
looked  at  through  a  red  glass  appears  quite  bright,  but  through  a  green  glass 
it  appears  dim  or  is  scarcely  visible.  So  in  like  manner  heat  which  has 
traversed  a  red  glass  passes  through  another  red  glass  with  little  diminu- 
tion, but  it  is  almost  completely  stopped  by  a  green  glass.     Rock  salt  at  1 50° 


4o8 


On  Heat. 


[436- 


emits  only  one  kind  of  heat ;  it  is  monothermal,  just  as  sodium  vapour  is 
monochromatic. 

Different  luminous  rays  being  distinguished  by  their  colours.,  Melloni 
gave  the  name  of  therrnocrose  or  heat  coloration  to  these  different  obscure 
calorific  rays.  The  invisible  portion  of  the  spectrum  is  accordingly  mapped 
out  into  a  series  of  spaces,  each  possessing  its  own  peculiar  feature  corre- 
sponding to  the  coloured  spaces  which  are  seen  in  that  portion  of  the  spec- 
trum visible  to  our  eyes. 

Besides  thickness  and  colour,  the  polish  of  a  substance  influences  the 
transmission.  Glass  plates  of  the  same  size  and  thickness  transmit  more 
heat  as  their  surface  is  more  polished.  Bodies  which  transmit  heat  of  any 
kind  very  readily  are  not  heated.  Thus  a  window  pane  is  not  much  heated 
by  the  strongest  sun's  heat  ;  but  a  glass  screen  held  before  a  common  fire 
stops  most  of  the  heat,  and  is  itself  heated  thereby.  The  reason  of  this  is 
that  by  far  the  greater  part  of  the  heat  from  a  fire  is  obscure,  and  glass  is 
opac[ue  to  this  kind  of  heat. 

437.  Diffusion  of  beat. — When  a  ray  of  light  falls  upon  an  unpolished 
surface  in  a  definite  direction,  it  is  decomposed  into  a  variety  of  rays  which 
are  reflected  from  the  surface  in  all  directions.  This  irregular  reflection  is 
called  diffusion^  and  it  is  in  virtue  of  it  that  bodies  are  visible  when  light 
falls  upon  them.  A  further  peculiarity  is,  that  all  solar  rays  are  not  equally 
diffused  from  the  surface  of  bodies.  Certain  bodies  diffuse  certain  rays  and 
absorb  others,  and  accordingly  appear  coloured.  The  red  colour  of  a  gera- 
nium is  caused  by  its  absorbing  all  the  rays,  excepting  the  red,  which  are 
irregularly  reflected.  Just  as  is  the  case  with  transmitted  light  in  transparent 
bodies,  so  with  diffused  light  in  opaque  ones  ;  for  if  a  red  body  is  illuminated 
by  red  light  it  appears  of  a  bright  red  colour,  but  if  green  light  fall  upon  it 
It  is  almost  black.  We  shall  now  see  that  here  again  analogous  phenomena 
prevail  with  heat. 

Various  substances  diffuse  different  thermal  rays  to  a  difterent  extent  ; 
each  possesses  a  peculiar  thermocrose.  Melloni  placed  a  number  of  strips 
of  brass  foil  between  the  source  of  heat  and  the  thermo-pile.  They  were 
coated  on  the  side  opposite  to  the  pile  with  lampblack,  and  on  the  other 
side  with  the  substances  to  be  investigated.  Representing  the  quantity  ot 
heat  absorbed  by  the  lampblack  by  100,  the  absorption  of  the  other  bodies 
was  as  follows  : — 


Incandescent 
platinum 

Copper  at  400° 

Copper  at  100° 

Lampblack        .... 

100 

100 

ICO 

White  lead         .... 

56 

89 

100 

Isinglass 

54 

64 

91 

Indian  ink         .... 

95 

87 

85 

Shellac 

47 

70 

72 

Polished  metal 

13-5 

13 

13 

Hence  white  lead  absorbs  far  less  of  the  heat  radiated  from  incandescent 
platinum  than  lampblack,  but  it  absorbs  the  obscure  rays  from  copper  at 
100°   as  completely  as  lampblack.     Indian  ink   is  the  reverse  of  this  ;   it 


-438]      Relation  of  Gases  and  Vapours  to  Radiant  Heat.        409 

absorbs  obscure  rays  less  completely  than  luminous  rays.  Lampblack 
absorbs  the  heat  from  all  sources  in  equal  quantities,  and  very  nearly  com- 
pletely. In  consequence  of  this  property  all  thermoscopes  which  are  used 
for  investigating  radiant  heat  are  covered  with  lampblack,  as  it  is  the  best- 
known  absorbent  of  heat.  The  behaviour  of  metals  is  the  reverse  of  that  of 
lampblack.  They  reflect  the  heat  of  different  sources  in  the  same  degree. 
They  are  to  heat  what  white  bodies  are  to  light. 

As  coloured  light  is  altered  by  diffusion  from  several  bodies,  so  Knoblauch 
has  shown  that  the  different  kinds  of  heat  are  altered  by  reflection  from  dif- 
ferent surfaces.  The  heat  of  an  Argand  lamp  diffused  from  white  paper 
passes  more  easily  through  calcspar  than  when  it  has  been  diffused  from 
black  paper. 

The  rays  of  heat,  like  the  rays  of  light,  are  susceptible  of  polarisation 
and  double  refraction.  These  properties  will  be  better  understood  after 
treating  of  light. 

438.  Relation  of  grases  and  vapours  to  radiant  beat. — This  subject 
has  been  investigated  by  Tyndall  ;  the  apparatus  he  used  is  represented  in 
the  adjacent  figure,  the  arrangement  being  looked  upon  from  above. 

A  (fi?-  393)  is  a  cylinder  about  4  feet  in  length  and  2\  inches  in  diameter, 
placed  horizontally,  the  ends  of  which  can  be  closed  with  rock-salt  plates  : 


by  means  of  a  lateral  tube  at  r  it  can  be  connected  with  an  air-pump  and 
exhausted  ;  while  at  /  is  another  tube  which  serves  for  the  introduction  of 
gases  and  vapours.  T  is  a  sensitive  thermo-pile  connected  with  an  extremely 
delicate  galvanometer,  M. 

The  deflections  of  this  galvanometer  were  proportional  to  the  degrees  of 
heat  up  to  about  30°  ;  beyond  this  point  the  proportionality  no  longer  held 
good,  and  accordingly,  for  the  higher  degrees,  a  table  was  empirically  con- 
structed, in  which  the  value  of  the  higher  deflections  was  expressed  in  units  ; 
the  unit  being  the  amount  of  heat  necessary  to  move  the  needle  through  one 
of  the  lower  degrees. 

C  was  a  source  of  heat,  which  usually  was  either  a  Leslie's  cube  filled  with 
boiling  water,  or  else  a  sheet  of  blackened  copper  heated  by  gas.  Now, 
when  the  source  of  heat  was  permitted  to  radiate  through  the  exhausted 
tube,  the  needle  made  a  great  deflection  ;  and  in  this  position  a  very  con- 
siderable degree  of  absorption  would  have  been  needed  to  produce  an 
alteration  of  1°  of  the  galvanometer.  And  if  to  lessen  this  deflection  a  lower 
source  of  heat  had  been  used,  the  fraction  absorbed  would  be  correspondingly 
less,  and  might  well  have  been  insensible.  Hence  Tyndall  adopted  the  fol- 
lowing device,  by  which  he  was  enabled  to  use  a  powerful  flux  of  heat,  and  at 
the  same  time  to  discover  small  variations  in  the  quantity  falling  on  the  pile. 


410 


On  Heat. 


[438- 


The  source  of  heat  at  C  was  allowed  to  radiate  through  the  tube  at  the 
end  of  which  the  pile  was  placed  ;  a  deflection  was  produced  of,  say,  70°  ; 
a  second  source  of  heat,  D,  was  then  placed  near  the  other  face  of  the  pile, 
the  amount  of  heat  falling  on  the  pile  from  this  C07npensating  cube  being 
regulated  by  means  of  a  movable  screen  S.  When  both  faces  of  the  pile 
are  warmed,  two  currents  are  produced,  which  are  in  opposite  directions, 
and  tend,  therefore,  to  neutralise  each  other  :  when  the  heat  on  both  faces 
is  precisely  ec^ual,  the  neutralisation  is  perfect,  and  no  current  at  all  is  pro- 
duced, however  high  maybe  the  temperature  on  both  sides.  In  the  arrange- 
ment just  described,  by  means  of  the  screen  S,  the  radiation  from  the 
compensating  cube  was  caused  to  neutralise  exactly  the  radiation  from  the 
source  C  ;  the  needle  consequently  was  brought  down  from  70°  to  zero,  and 
remained  there  so  long  as  both  sources  were  equal.  If  now  a  gas  or  vapour 
be  admitted  into  the  exhausted  tube,  any  power  of  absorption  it  may  possess 
will  be  indicated  by  the  destruction  of  this  equilibrium,  and  preponderance 
of  the  radiation  from  the  compensating  cube,  by  an  amount  corresponding 
to  the  heat  cut  off  by  the  gas.  Examined  in  this  way,  air,  hydrogen,  and 
nitrogen,  when  dried  by  passing  through  sulphuric  acid,  were  found  to  exert 
an  almost  inappreciable  effect ;  their  presence  as  regards  radiant  heat  being 
but  little  different  from  a  vacuum.  But  with  olefiant  and  other  complex  gases 
the  case  was  entirely  different.  Representing  by  the  number  i  the  quantity 
of  radiant  heat  absorbed  by  air,  olefiant  gas  absorbs  970  times,  and  am- 
moniacal  gas  1,195  times,  this  amount.  In  the  following  table  is  given  the 
absorption  of  obscure  heat  by  various  gases,  referred  to  air  as  unity  : — 


Name  of  gas 


Air         .         .         . 

Oxygen 

Nitrogen 

H  ydrogen 

Chlorine 

Hydrochloric  acid 


Absorption 

under  30  inches 

of  pressure 


Name  of  gas 


Carbonic  acid 
Nitrous  oxide 
Marsh  gas     . 
Sulphurous  acid 
Olefiant 
Ammonia 


Absorption    1 

under  30  inches 

of  pressure. 


90 

335 
403 
710 
970 
1195 


If,  instead  of  comparing  the  gases  at  a  common  pressure  of  one  atmo- 
sphere, they  are  compared  at  a  common  pressure  of  an  inch,  their  differences 
in  aljsorption  are  still  more  strikingly  seen.  Thus,  assuming  the  absorption 
by  I  inch  of  dry  air  to  be  i,the  absorption  by  i  inch  of  olefiant  gas  is  7,950, 
and  by  the  same  amount  of  sulphurous  acid  8,800. 

439.  Xnfluence  of  pressure  and  thickness  on  the  absorption  of  heat 
by  g-ases. — The  absorption  of  heat  by  gases  varies  with  the  pressure  ;  this 
variation  is  best  seen  in  the  case  of  those  gases  which  have  considerable 
absorptive  power.  Taking  the  total  absorption  by  atmospheric  air  under 
ordinary  pressure  at  unity,  the  numbers  of  olefiant  gas  under  a  pressure  of  i, 
3,  5,  7,  and  10  inches  of  mercury  are  respectively  90,  142,  168,  182,  and  193. 
Thus  one-thirtieth  of  an  atmosphere  of  olefiant  gas  exerts  90  times  the 
absorption  of  an  entire  atmosphere  of  air.  And  the  absorption,  it  is  seen, 
increases  with  the  density,  though  not  in  a  direct  ratio.     Tyndall  showed. 


-440] 


A  bsorptive  Poiver  of  Vapo7irs. 


411 


however,  by  special  experiments,  that  for  very  low  pressures  the  absorption 
does  increase  with  the  density.  Employing  as  a  unit  volume  of  the  gas  a 
quantity  which  measured  only  ^  of  a  cubic  inch,  and  admitting  succes- 
sive measures  of  olefiant  gas  into  the  experimental  tube,  it  Avas  found  that 
up  to  15  measures  the  absorption  was  directly  proportionate  to  the  density 
in  each  case. 

In  these  experiments  the  length  of  the  experimental  tube  remains  the 
same  whilst  the  pressure  of  the  gas  within  it  was  caused  to  vary  ;  in  subse- 
quent experiments  the  pressure  of  the  gas  was  kept  constant,  whilst  the 
length  of  the  tube  was,  by  suitable  means,  varied  from  o-oi  of  an  inch  up  to 
50  inches.  The  source  was  a  heated  plate  of  copper  ;  of  the  total  radiation 
from  this  nearly  2  per  cent,  was  absorbed  by  a  film  of  olefiant  gas  -oi  of  an 
inch  thick,  upwards  of  9  per  cent,  by  a  layer  of  the  same  gas  ot  of  an  inch 
thick,  -i)^  per  cent,  by  a  layer  2  inches  thick,  68  per  cent,  by  a  column  20 
inches  long,  and  11  per  cent,  by  a  column  rather  more  than  4  feet  long. 

440.  j^bsorptive  power  of  vapours. — The  absorptive  power  of  olefiant 
gas  is  exceeded  by  that  of  several  vapours.  The  liquid  from  which  the 
vapours  were  to  be  produced  was  inclosed  in  a  small  flask,  which  could  be 
attached  with  a  stop-cock  to  the  exhausted  experimental  tube.  The  absorp- 
tion was  then  determined  after  admitting  the  vapours  into  the  tube  in 
quantities  measured  by  the  pressure  of  the  barometer  gauge  attached  to  the 
air-pump. 

The  following  table  shows  the  absorption  of  vapours  under  pressures 
varying  from  o-i  to  ro  inch  of  mercury  : — 


Name  of  vapours 

Absorption  under  pressure  in  inches  of  mercury 

o-i 

o"S 

I'D 

Bisulphide  of  carbon 

Benzole 

Chloroform        .... 

Ether 

Alcohol 

Acetic  ether      .... 

6l 

85 
300 

325 
590 

47 
182- 
182 
710 
622 
980 

62 
267 
236 
870 

I  195 

These  numbers  refer  to  the  absorption  of  a  whole  atmosphere  of  dry  air 
as  their  unit,  and  it  is  thus  seen  that  a  quantity  of  bisulphide  of  carbon 
vapour,  the  feeblest  absorbent  yet  examined,  which  only  exerts  a  pressure  of 
y^Q  of  an  inch  of  mercury,  or  the  gi^  of  an  atmosphere,  gave  fifteen  times  the 
absorption  of  an  entire  atmosphere  of  air  ;  and  j^  of  an  inch  of  acetic  ether 
590  times  as  much.  Comparing  air  at  a  pressure  of  o-i  with  acetic  ether  of 
the  same  pressure,  the  absorption  of  the  latter  would  be  more  than  17,500 
times  as  great  as  that  of  the  former. 

Tyndall  found  that  the  odours  from  the  essential  oils  exercised  a  marked 
influence  on  radiant  heat.  Perfectly  dry  air  was  allowed  to  pass  through  a 
tube  containing  dried  paper  impregnated  with  various  essential  oils,  and 
then  admitted  into  the  experimental  tube.  Taking  the  absorption  of  dry  air 
as  unity,  the  following  were  the  numbers  respectively  obtained  for  air  scented 
with  various  oils  ; — Patchouli  31,  otto  of  roses  -^,1,  lavender  60,  thyme  68, 


412  On  Heat.  [440- 

rosemary  74,  cassia  109,  aniseed  372.  Thus  the  perfume  of  a  flower- 
bed absorbs  a  large  percentage  of  the  heat  of  low  refrangibility  emitted 
from  it. 

Ozone  prepared  by  electrolysing  water  was  also  found  to  have  a  remark- 
able absorptive  effect.  The  small  quantity  of  ozone  present  in  electrolytic 
oxygen  was  found  in  one  experiment  to  exercise  136  times  the  absorption  of 
the  entire  mass  of  the  oxygen  itself. 

But  the  most  important  results  are  those  which  follow  from  his  experi- 
ments on  the  behaviour  of  aqueous  vapour  to  radiant  heat.  The  experimen- 
tal tube  was  filled  with  air,  dried  as  perfectly  as  possible,  and  the  absorption 
it  exercised  was  found  to  be  one  unit.  Exhausting  the  tube,  and  admitting 
the  ordinary  undried,  but  not  specially  moist,  air  from  the  laboratory,  the 
absorption  now  rose  to  72  units.  The  difference  between  dried  and  undried 
air  can  only  be  ascribed  to  the  aqueous  vapour  the  latter  contains.  Thus  on 
a  day  of  average  humidity  the  absorptive  effect  due  to  the  transparent  aque- 
ous vapour  present  in  the  atmosphere  is  72  times  as  great  as  that  of  the  air 
itself,  though  in  quantity  the  latter  is  about  200  times  greater  than  the  former. 
Analogous  results  were  obtained  on  different  days,  and  with  specimens  of 
air  taken  from  various  localities.  When  air  which  had  been  specially  purified 
and  dried  was  allowed  to  pass  through  a  tube  filled  with  fragments  of  moist- 
ened glass  and  examined,  it  was  found  to  exert  an  absorption  90  times  that 
of  pure  air. 

In  some  other  experiments  Tyndall  suppressed  the  use  of  rock-salt 
plates  in  his  experimental  tube,  and  even  the  tube  itself,  and  yet  in  every 
case  the  results  were  such  as  to  show  the  great  power  which  aqueous  vapour 
possesses  as  an  absorbent  of  radiant  heat. 

The  absorptive  action  which  the  aqueous  vapour  in  the  atmosphere  exerts 
on  the  sun's  heat  has  been  established  by  a  series  of  actinometrical  observa- 
tions made  by  Soret  at  Geneva  and  on  the  summit  of  Mont  Blanc  ;  he  found 
that  the  intensity  of  the  solar  heat  on  the  top  of  Mont  Blanc  is  f  of  that 
at  Geneva  ;  in  other  words,  that  of  the  heat  which  is  radiated  at  the  height 
of  Mont  Blanc,  about  |  is  absorbed  in  passing  through  a  vertical  layer  of 
the  atmosphere  14,436  feet  in  thickness.  The  same  observer  has  found  that 
with  virtually  equal  solar  heights  there  is  the  smallest  transmission  of  heat 
on  those  days  on  which  the  tension  of  aqueous  vapour  is  greatest ;  that  is, 
when  there  is  most  moisture  in  the  atmosphere. 

441.  Radiating:  power  of  gpases. — Tyndall  also  examined  the  radiating 
power  of  gases.  A  red-hot  copper  ball  was  placed  so  that  the  current  of 
heated  air  which  rose  from  it  acted  on  one  face  of  a  thermo-pile  ;  this  action 
was  compensated  by  a  cube  of  hot  water  placed  in  front  of  the  opposite  face. 
On  then  allowing  a  current  of  dry  olefiant  gas  from  a  gasholder  to  stream 
through  a  ring  burner  over  the  heated  ball  and  thus  supplant  the  ascending 
current  of  hot  air,  it  was  found  that  the  gas  radiated  energeticalljf.  By  com- 
paring in  this  manner  the  action  of  many  gases  it  was  discovered  that,  as  is 
the  case  with  solids,  those  gases  which  are  the  best  absorbers  are  also  those 
which  radiate  most  freely. 

442.  Dynamic  radiation  and  absorption. — A  gas  when  permitted  to 
enter  an  exhausted  tube  is  heated  in  consequence  of  the  collision  of  its  par- 
ticles against  the  sides  of  the  vessel ;  it  thus  becomes  a  source  of  heat,  which 


-443]  Relation  of  A  bsorption  to  Molecular  State.  4 1 3 

is  perfectly  capable  of  being  measured.  Tyndall  calls  this  dynatiiic  heathtg. 
In  like  manner,  when  a  tube  full  of  gas  or  vapour  is  rapidly  exhausted,  a 
chilling  takes  place  owing  to  the  loss  of  heat  in  the  production  of  motion  ; 
this  he  calls  dynamic  cJiillitig  or  absorption. 

He  could  thus  determine  the  radiation  or  absorption  of  a  gas  without 
any  source  of  heat  external  to  the  gas  itself  An  experimental  tube  was 
taken,  one  end  of  which  was  closed  with  a  polished  metal  plate,  and  the 
other  with  a  plate  of  rock  salt ;  in  front  of  the  latter  was  the  face  of  the  pile. 
The  needle  being  at  zero,  and  the  tube  exhausted,  a  gas  was  allowed  quickly 
to  enter  until  the  tube  was  full,  the  effect  on  the  galvanometer  being  noted. 
This  being  only  a  transitoiy  effect,  the  needle  soon  returned  to  zero  ;  the 
tube  was  then  rapidly  pumped  out,  by  which  a  sudden  chilling  was  produced 
and  the  needle  exhibited  a  deflection  in  the  opposite  direction.  Comparing 
in  this  way  the  dynamic  heating  and  chilling  of  various  gases,  those  gases 
which  are  the  best  absorbers  were  also  found  to  be  the  best  radiators. 

Polished  metallic  surfaces  are,  as  we  have  seen  (427),  bad  radiators, 
but  radiate  freely  when  covered  with  varnish.  Tyndall  made  the  curious 
experiment  of  varnishing  a  metallic  surface  by  a  film  of  gas.  A  Leslie's 
cube  was  placed  with  its  polished  metal  side  in  front  of  the  pile,  and  its  effect 
neutralised  by  a  second  cube  placed  before  the  other  face  of  the  pile.  On 
allowing  a  stream  of  olefiant  or  coal  gas  to  flow  from  a  gasholder  over  the 
metallic  face  of  the  first  cube,  a  copious  radiation  from  that  side  was  pro- 
duced as  long  as  the  flow  of  gas  continued.  Acting  on  the  principle  indi- 
cated in  the  foregoing  experiment,  Tyndall  determined  the  dynamic  radiation 
and  absorption  of  vapours.  The  experimental  tube  containing  a  vapour 
under  a  small  known  pressure,  air  was  allowed  to  enter  until  the  pressure 
inside  the  tube  was  the  same  as  that  of  the  atmosphere.  In  this  way  the 
entering  air,  by  its  impact  against  the  tube,  became  heated  ;  and  its  particles 
mixing  with  those  of  the  minute  quantity  of  vapour  present,  each  of  them 
became,  so  to  speak,  coated  with  a  layer  of  the  vapour.  The  entering  air 
was  in  this  case  a  source  of  heat,  just  as  in  the  above  experiments  the 
Leslie's  cube  was.  Here,  however,  one  gas  varnished  another  ;  the  radia- 
tion and  subsequently  the  absorption  of  \-arious  vapours  could  thus  be 
determined. 

It  was  found  that  vapours  differed  veiy  materially  in  their  power  of 
radiating  under  these  circumstances  ;  of  those  which  were  tried  bisulphide 
of  carbon  vapour  was  the  worst  and  boracic  ether  the  best  radiator.  And  in 
all  cases  those  which  were  the  best  absorbents  were  also  the  best  radiators. 

443.  Relation  of  absorption  to  molecular  state. — ^After  examining  the 
absorption  of  heat  by  vapours,  Tyndall  tried  the  same  substances  in  a  liquid 
form.  The  conditions  of  the  experiments  were  in  both  cases  the  same  ;  the 
source  of  heat  was  a  spiral  of  platinum  heated  to  redness  by  an  electric  cur- 
rent of  known  strength  ;  and  plates  of  rock  salt  were  invariably  employed  to 
contain  both  vapours  and  liquids.  Finally,  the  absorption  by  the  vapours 
was  re-measured  ;  in  this  case  introducing  into  the  experimental  tube,  not, 
as  before,  equal  quantities  of  vapour,  but  amounts  proportional  to  the 
density  of  the  liquid.  When  this  last  condition  had  been  attained,  it  was 
found  that  the  order  of  absorption  by  a  series  of  liquids,  and  by  the  same 
series  when  turned  mto  vapour,  was  precisely  the  same     Thus  the  sub- 


414  On  Heat.  [443- 

stances  tried  stood  in  the  following  order  as  liquid  and  as  vapour,  beginning 
with  the  feeblest  absorbent,  and  ending  with  the  most  powerful  : — 

Liquids  Vapours 

Bisulphide  of  carbon      ....  Bisulphide  of  carbon. 

Chloroform Chloroform. 

Iodide  of  ethyl Iodide  of  ethyl. 

Benzole Benzole. 

Ether Ether. 

Alcohol Alcohol. 

Water 

A  direct  determination  of  aqueous  vapour  could  not  be  made,  on  account 
of  its  low  tension  and  the  hygroscopic  nature  of  the  rock  salt.  But  the  un- 
deviating  regularity  of  the  absorption  by  all  the  other  substances  in  the  list, 
both  as  liquid  and  vapour,  establishes  the  fact,  which  is  corroborated  by 
the  experiments  already  mentioned,  that  aqueous  vapour  is  one  of  the  most 
energetic  absorbents  of  heat. 

In  this  table  it  will  be  noticed  that  those  substances  which  have  the 
simplest  chemical  constitution  stand  first  in  the  list,  with  one  anomalous 
exception,  namely,  that  of  water.  In  the  absorption  of  heat  by  gases,  Tyndall 
found  that  the  elementary  gases  were  the  feeblest  absorbents,  while  the 
gases  of  most  complex  constitution  were  the  most  powerful  absorbents.  Thus 
it  may  be  inferred  that  absorption  is  mainly  dependent  on  chemical  consti- 
tution ;  that  is  to  say,  that  absorption  and  radiation  are  molecular  acts 
independent  of  the  physical  condition  of  the  body. 

Tyndall  discovered  that  the  radiation  of  powders  is  similar  to  that  of  the 
solids  from  which  they  were  derived,  and  therefore  differs  greatly  iftter  se. 
The  absorbent  power  of  powders  was  also  found  to  correspond  with  their 
radiative  power — which,  as  we  have  shown,  is  the  case  with  solids  and  gases, 
and,  though  as  yet  we  have  no  experiments  on  the  subject,  is  doubtless  also 
true  for  liquids.  The  powders  were  attached  to  the  tin  surfaces  of  a  Leslie's 
cube,  in  such  a  manner  that  radiation  took  place  from  the  surface  of  the 
powder  alone.  The  following  table  gives  the  radiation  in  units  from  some  of 
the  powders  examined  by  Tyndall ;  the  metal  surface  of  the  cube  giving  a 
deflection  of  1 5  units  : — 

Radiation  from  powders. 

Rock  salt  .         .         .  35-3  Sulphate  of  calcium  .  777 

Biniodide  of  mercury       .  397  Red  oxide  of  iron     .  .  78-4 

Sulphur  ....  40-6  Hydrated  oxide  of  zinc  .  80-4 

Carbonate  of  calcium      .  70-2  Sulphide  of  iron       .  .  817 

Red  oxide  of  lead    .         .  74-0  Lampblack       .         .  .  84-0 

These  substances  are  of  various  colours.  Some  are  white,  such  as  rock 
salt,  carbonate  and  sulphate  of  calcium,  and  hydrated  oxide  of  zinc  ;  some 
are  red,  such  as  biniodide  of  mercury  and  oxide  of  lead  ;  whilst  others  are 
black,  as  sulphide  of  iron  and  lampblack  ;  we  have  besides  other  colours. 
The  colours,  therefore,  have  no  influence  on  the  radiating  power  :  rock  salt, 


-444]  Applications.  415 

for  example,  is  the  feeblest  radiator,  and  hydrated  oxide  of  zinc  one  of  the 
most  powerful  radiators. 

Nearly  a  century  ago  Franklin  made  experiments  on  coloured  pieces  of 
cloth,  and  found  their  absorption,  indicated  by  their  sinking  into  snow  on 
which  they  were  placed,  to  increase  with  the  darkness  of  the  colour.  But 
all  the  cloths  were  equally  powerful  absorbents  of  obscure  heat,  and  the 
effects  noticed  were  only  produced  by  their  relative  absorptions  of  light.  In 
feet,  the  conclusions  to  be  drawn  from  Franklin's  experiments  only  hold  good 
for  luminous  heat,  especially  sunlight,  such  as  he  employed. 

444.  Applications — The  properties  which  bodies  possess  of  absorbing, 
emitting,  and  reflecting  heat  meet  with  numerous  applications  in  domestic 
economy  and  in  the  arts.  Leslie  stated  in  a  general  manner  that  white 
bodies  reflect  heat  very  well,  and  absorb  very  little,  and  the  contrary  is 
the  case  with  black  substances.  As  we  have  seen,  this  principle  is  not 
generally  true,  as  Leslie  supposed  ;  for  example,  white  lead  has  as  great  an 
absorbing  power  for  non-luminous  rays  as  lampblack  (437).  Leslie's  principle 
applies  to  powerful  absorbents  like  cloth,  cotton,  wool,  and  other  organic 
substances  when  exposed  to  luminous  heat.  Accordingly,  the  most  suitable 
coloured  clothing  for  summer  is  just  that  which  experience  has  taught  us  to 
use,  namely,  white,  for  it  absorbs  less  of  the  sun's  rays  than  black  clothing, 
and  hence  feels  cooler. 

The  polished  fire-irons  before  a  fire  are  cold,  whilst  the  black  fender  is 
often  unbearably  hot.  If,  on  the  contrary,  a  Hquid  is  to  be  kept  hot  as  long 
as  possible,  it  must  be  placed  in  a  brightly  polished  metallic  vessel,  for 
then,  the  emissive  power  being  less,  the  cooling  is  slower.  Hence  it  is 
advantageous  that  the  steam  pipes,  &c.,  of  locomotives  should  be  kept 
bright.  In  the  Alps,  the  mountaineers  accelerate  the  fusion  of  the  snow  by 
covering  it  with  earth,  which  increases  the  absorbing  power. 

In  our  dwellings,  the  outsides  of  stoves  and  of  hot-water  apparatus  ought 
to  be  black,  and  the  insides  of  fireplaces  ought  to  be  lined  with  firebrick,  in 
order  to  increase  the  radiating  power  towards  the  apartment. 

It  is  in  consequence  of  the  great  diathermancy  of  dry  atmospheric  air 
that  the  higher  regions  of  the  atmosphere  are  so  cold,  notwithstanding  the 
great  heat  which  traverses  them  ;  whilst  the  intense  heat  of  the  sun's  direct 
rays  on  high  mountains  is  probably  due  to  the  comparative  absence  of 
aqueous  vapour  at  these  elevations. 

As  nearly  all  the  luminous  rays  of  the  sun  pass  through  water,  and  the 
sun's  radiation  as  we  receive  it  on  the  surface  of  the  earth  consists  of  a 
large  proportion  of  luminous  rays,  accidents  have  often  arisen  from  the  con- 
vergence of  these  luminous  rays  by  bottles  of  water  which  act  as  lenses.  In 
this  way  gunpowder  could  be  fired  by  the  heat  of  the  sun's  rays  concen- 
trated by  a  water  lens  ;  and  the  drops  of  water  on  leaves  in  greenhouses 
have,  it  is  said,  been  found  to  act  as  lenses,  and  burn  the  leaves  on  which 
they  rest. 

Certain  bodies  can  be  used  (436)  to  separate  the  heat  and  light  radiated 
from  the  same  source.  Rock  salt  covered  with  lampblack,  or  still  better 
with  iodine,  transmits  heat,  but  completely  stops  light.  On  the  other  hand, 
alum,  either  as  a  plate  or  in  solution,  or  a  thin  layer  of  water,  is  permeable 
to  light,  but  stops  all  the  heat  from  obscure  sources.     This  property  is  made 


4i6  On  Heat.  [444- 

use  of  in  apparatus  which  are  ilhiminated  by  the  sun's  rays,  in  order  to  sift 
the  rays  of  their  heating  power  ;  and  a  vessel  full  of  water  or  a  solution  of 
alum  is  used  with  the  electric  light  when  it  is  desirable  to  avoid  too  intense 
a  heat. 

In  gardens,  the  use  of  shades  to  protect  plants  depends  partly  on  the 
diathermancy  of  glass  for  heat  from  luminous  rays  and  its  athermancy  for 
obscure  rays.  The  heat  which  radiates  from  the  sun  is  largely  of  the  former 
quality,  but  by  contact  with  the  earth  it  is  changed  into  obscure  heat,  which, 
as  such,  cannot  retraverse  the  glass.  This  explains  the  manner  in  which 
greenhouses  accumulate  their  warmth,  and  also  the  great  heat  experienced 
in  summer  in  rooms  having  glass  roofs,  for  the  glass  in  both  cases  acts,  as 
it  were,  as  a  valve  which  effectually  entraps  the  solar  rays.  On  the  same 
principle  plates  of  glass  are  frequently  used  as  screens  to  protect  us  from  the 
heat  of  a  fire  ;  the  glass  allows  us  to  see  the  cheerful  light  of  the  fire,  but 
intercepts  the  larger  part  of  the  heat  radiated  from  the  fire.  Though  the 
screens  thus  become  warm  by  the  heat  they  have  absorbed,  yet,  as  they 
radiate  this  heat  in  all  directions  towards  the  fire  as  well  as  towards  us,  we 
finally  receive  less  heat  when  they  are  interposed. 

445.  Attraction  and  repulsion  arising^  from  radiation. — Crookes  has 
discovered  a  highly  remarkable  class  of  phenomena  which  are  due  to  the 
radiant  action  of  heated  and  of  luminous  bodies.  These  phenomena  are 
most  conveniently  illustrated  by  means  of  an  instrument  which  he  has 
devised  and  which  is  called  the  radiometer^  the  construction  of  which  is  as 
follows : — A  glass  tube  (fig.  393),  with  a  bulb  blown  on  it,  is  fused  at  the 
bottom  to  a  glass  tube  which  at  one  end  serves  to  rest  the  whole  apparatus 
in  a  wooden  support.  In  the  other  end  is  fused  a  fine  steel  point.  On  this 
rests  a  small  vane  or  fly,  consisting  of  four  arms  of  aluminium  wire  fixed  at 
one  end  to  a  small  cap,  while  at  the  others  are  fixed  small  discs  or  lozenges 
of  thin  mica,  coated  on  one  side  with  lampblack.  The  weight  of  the  fly  is 
not  more  than  two  grains. 

In  order  to  keep  the  fly  on  the  pivot  a  tube  is  fused  in  the  upper  part  of 
the  bulb  which  reaches  down  to  and  just  surrounds  the  top  of  the  cap,  with- 
out, however,  touching  it  ;  the  other  end  of  this  tube  is  drawn  out  and  con- 
nected with  an  arrangement  for  exhausting  the  air  by  the  Sprengel  pump 
(205)  or  by  chemical  means  ;  when  the  desired  degree  of  exhaustion  has  been 
attained  this  can  be  sealed.  By  keeping  the  apparatus  during  exhaustion  in 
a  hot  air  bath  at  a  temperature  of  300°,  the  gases  occluded  on  the  inner  surface 
of  the  glass,  and  by  the  vanes,  are  got  rid  of 

If  a  source  of  light  or  of  heat,  a  candle  for  instance,  is  brought  near  the 
fly,  it  is  attracted,  and  the  fly  rotates  slowly  in  a  direction  showing  that  the 
blackened  side  moves  towards  the  light  ;  this  movement,  indicating  an 
attraction,  depends  on  a  certain  state  of  rarefaction.  If,  however,  the  appa- 
ratus be  connected  with  an  arrangement  which  allows  the  pressure  to  be 
varied,  this  rotation  gradually  diminishes  in  rapidity  as  the  air  within  is 
further  rarefied,  until  a  certain  point  is  reached  at  which  it  ceases.  If 
now  the  rarefaction  is  pushed  further,  the  highly  remarkable  phenomenon 
is  observed  that  repulsion  succeeds  to  attraction,  and  that  the  fly  now  rotates 
in  the  direction  away  from  the  source  of  heat.     In  a  double  radiometer,  in 


-445]     Attraction  and  Repulsion  arising  from  Radiation.        417 

which  two  flys  are  pivoted  independently  one  over  the  other,  having  their 

blackened  sides  opposite  each  other,  the  flys  rotate  in   opposite  directions 

on    the    approach   of    a   lighted    candle. 

When  a  cold  body,  such    as  a   piece   of 

ice,  is  brought  near,  instead  of  a  hot  one, 

exactly  the  opposite  effects  are  observed  ; 

when  the  vessel  contains  air  a  pith  ball 

suspended  at  one  end  of  a  light  arm  is 

repelled,  the   neutral  point    is    observed, 

while     at     high    degrees    of    rarefaction 

attraction  ensues. 

One  of  the  most  important  facts 
brought  to  light  by  these  experiments 
is,  that  what  has  hitherto  been  looked 
upon  as  a  complete  vacuum  is  not  so  in 
reality  ;  the  most  perfect  vacuum  obtain- 
able still  contains  a  certain  residue  of 
gas,  as  has  been  proved  by  the  experi- 
ments of  Crookes  and  others,  among 
which  that  of  Kundt  may  be  mentioned. 
The  latter  placed  on  the  vanes  a  light 
disc  of  mica,  and  at  a  little  distance 
above  it  a  similar  disc  was  arranged  so 
as  to  rotate  freely,  in  a  horizontal  plane 
independently  of  the  first.  When  the 
lower  vane  was  made  to  rotate  by  bring- 
ing a  light  near,  it  was  found  that  the 
upper  disc  was  also  put  in  rotation  in  the 
same  direction,  being  dragged  by  the 
viscosity  of  the  residual  air.  Accordingly 
the  explanation  of  the  phenomena  of  the 
radiometer  must  take  into  account  the 
existence  of  this  gaseous  residue. 

The  nature  of  the  gas  seems  to  have 
no  special  influence  on  the  pheno- 
mena ;  whether  the  vacuum  be  one  of 
hydrogen,     of    aqueous    vapour,    or     of 

iodine  vapour,  seems  immaterial  ;  though  fig- 394- 

with  hydrogen  the   exhaustion  need  not 

l3e  pushed  so  far  as  with  air.  The  repulsion  takes  place  with  all  the  rays 
of  the  spectrum,  the  intensity  diminishing  from  the  ultra  red  to  the  ultra 
violet.  When  the  chemical  rays  act,  the  interposition  of  a  plate  of  alum  has 
no  effect,  while  a  solution  of  iodine  in  bisulphide  of  carbon  diminishes  the 
repulsion.  The  rate  at  which  the  vane  rotates  depends  on  the  intensity  of 
the  source  of  light.  With  a  strong  light  the  rotation  is  so  rapid  that  its  rate 
cannot  be  determined.  With  two  candles  at  the  same  distance  the  rotation 
is  twice  as  rapid  as  with  one.  Two  sources  of  light  which,  successively  placed 
at  the  same  distance,  produce  the  same  rate  of  rotation,  are  ecjual  in  inten- 
sity.    If,  when  placed  at  different  distances,  they  produce  the  same  speed 


41 8  On  Heat.  [445- 

of  rotation,  their  intensities  are  directly  as  the  squares  of  these  distances  from 
the  radiometer.  On  this  is  based  the  use  of  the  instrument  as  a  photometer 
(509)  for  comparing  together  various  sources  of  artificial  light.  It  may  like- 
wise be  used  for  making  comparative  measurements  of  the  intensity  of 
sunhght  ;  and  the  distribution  of  heat  in  the  solar  spectrum  may  be  in- 
vestigated by  its  means. 

It  is  not  difficult  to  understand  that  the  attraction  observed  in  the  experi- 
ments may  be  explained  by  the  action  of  convection  currents  (408),  as  long 
as  the  apparatus  still  contains  air.  For  heat  falling  upon  this  blackened  disc 
would  raise  its  temperature,  and  the  temperature  of  a  layer  of  air  in  im- 
mediate contact  with  the  disc  would  be  raised  too  ;  it  would  expand  and 
rise,  flowing  over  into  the  space  behind  the  disc,  and  would  thus  increase  the 
pressure  there. 

On  the  other  hand  the  repulsion  observed  at  the  higher  degrees  of  ex- 
haustion, approaching  a  vacuum,  is  due  to  a  reaction  between  the  vane  and 
the  crlass  envelope,  and  is  explained  by  reference  to  the  modern  views  as 
to  the  constitution  of  gases,  of  which  it  is  at  once  an  illustration  and  a 
proof 

The  general  nature  of  this  theory  is  that  a  gas  is  an  assemblage  of  in- 
dependent molecules,  which  are  perfectly  elastic,  and  which  move  with  great 
rapidity  ;  their  impacts  against  the  sides  of  the  vessel  in  which  the  gas  is 
contained  are  the  cause  of  the  pressure.  The  impact  of  the  molecules 
against  each  other  is  the  mechanism  by  which  the  equal  transmission  of 
pressure  in  gases  is  effected  (294). 

Crookes  has  calculated  that  the  mechanical  effect  of  the  force  of  repulsion 
is  equal  to  about  the  -^  of  a  milligramme  on  a  square  centimetre,  and  Stoney 
has  shown  that  this  force  is  sufficient  to  account  for  the  effects  observed,  by 
reference  to  admitted  principles  of  the  mechanical  theory  of  gases. 

The  rays  of  heat  pass  through  the  thin  glass  without  raising  its  tempera- 
ture, and,  falling  on  the  blackened  side  of  the  vane,  are  absorbed  by  it  ;  the 
consequence  of  this  is,  that  it  will  become  slightly  hotter.  The  layer  of  ex- 
tremely rarefied  air  in  immediate  contact  with  the  blackened  disc  will  also 
become  somewhat  hotter,  and  the  molecules  will  fly  from  the  disc  with 
greater  velocity.  Under  ordinary  pressures  or  even  at  moderate  degrees  of 
rarefaction  these  more  rapid  motions  would  be  equalised  by  their  impacts 
ao-ainst  other  molecules,  and  a  uniformity  of  pressure — that  is,  of  temperature 

would  be  established.     But  the  frequency  of  these  intramolecular  shocks 

diminishes  rapidly  with  the  increase  of  rarefaction  ;  and  the  consequence  is, 
that  a  great  number  of  molecules,  after  having  been  heated  by  contact  with 
the  blackened  side  of  the  palette,  will  strike  against  the  cold  glass.  The  effect 
of  this  will  be  to  cool  these  molecules— that  is,  to  diminish  their  velocity  ;  it 
will  be  chiefly  molecules  of  this  kind  which  fall  on  the  back  of  the  disc,  and 
on  the  regions  behind  it.  An  excess  of  force  equal  and  opposite  to  that  on 
the  glass  acts  against  the  front  of  the  disc,  and  is  sufficient  to  account  for 
the  phenomena  exhibited  by  Crookes. 

It  follows  from  this  explanation  that,  other  things  being  equal,  a  fly  will 
rotate  more  rapidly  in  a  small  than  in  a  large  bulb.  This  has  been  con- 
clusively proved  by  Crookes,  who  constructed  a  double-bulb  radiometer,  the 
two  bulbs  being  very  different  insize,  and  so  connected  that,  by  dexterous 


-446a]  Viscosity  of  Gases.  419 

manipulation,  the  fly  could  be  transferred  from  the  pivot  of  the  one  to  that 
of  the  other  bulb. 

The  radiometer  is  well  adapted  for  the  lecture  demonstration  of  many 
phenomena  in  heat.  Thus  the  law  of  the  inverse  square  (414)  may  be  illus- 
trated by  counting  the  number  of  rotations  when  the  instrument  is  placed  at 
varying  distances  from  the  source  of  heat. 

446.  Internal  friction  or  viscosity  of  grases. — In  some  recent  experi- 
ments in  connection  with  the  radiometer,  Crookes  used  an  arrangement  con- 
sisting of  a  long  but  light  arm  of  straw  suspended  by  a  delicate  glass  fibre 
in  a  sort  of  T  tube  turned  upside  down ;  in  this  way  even  a  greater  degree 
of  delicacy  was  obtained  than  with  the  radiometer.  Thus  he  was  able  to 
get  a  deflection  by  moonlight,  which  does  not  move  the  fly  of  the  radiometer. 
He  examined  the  internal  friction  or  viscosity  of  the  residual  gas  by  causing 
the  arm  to  oscillate,  and  then  observing  the  rate  at  which  the  oscillations 
diminish  under  various  pressures.  He  thus  found  that  from  ordinary  pres- 
sures down  to  a  pressure  of  0-19  mm.,  or  what  may  be  called  a  TorriceUian 
vacuum,  the  viscosity  is  practically  constant,  only  diminishing  from  0-126  to 
0-II2.  It  now  begins  to  fall  off,  and  at  apressure  of  0-000076  mm.  it  has 
diminished  to  o-oi,  or  about  j\.  Simultaneously  with  this  decrease  in 
viscosity  the  force  of  repulsion  excited  by  a  standard  light  on  a  blackened 
surface  varies.  It  increases  as  the  pressure  diminishes  until  the  exhaus- 
tion is  about  0-05  mm.,  and  attains  its  maximum  at  about  0-03  mm.  It  then 
sinks  veiy  rapidly  until  it  is  at  0*000076  mm.,  when  it  is  less  than  j^  of  its 
maximum. 

The  viscosity  varies  in  different  gases  ;  it  is  considerably  less  in  hydrogen 
than  in  air  ;  and  hence  with  this  gas  it  is  not  necessar^^  to  drive  the  exhaus- 
tion so  far  to  produce  a  considerable  degree  of  repulsion. 

The  researches  of  Crookes  have  opened  the  way  to  an  entirely  new  field 
of  experimental  inquiry  into  the  phenomena  which  occur  in  what  is  called 
the  ultra-gaseous  state  of  matter,  or  that  in  which  the  rarefaction  of  gases  is 
pushed  to  its  utmost  limits.  The  state  in  which  molecular,  as  distinguished 
from  7nolar,  actions  come  into  play,  has  been  aptly  termed  Crookes's  vacuum. 
A  further  account  of  the  researches  requires  too  great  an  amount  of  detail 
for  the  purposes  of  this  work  ;  and  it  must  also  be  added  that  the  explana- 
tions which  have  been  given  are  still  not  beyond  the  range  of  controversy. 

446^.  Relation  of  radiant  heat  to  sound.^This  subject  has  of  late 
engaged  the  attention  of  several  physicists,  among  whom  may  be  particular- 
ised Bell  and  Tainter,  Tyndall,  Preece,  and  Mercadier.  A  convenient  way 
of  showing  the  phenomena  is  by  means  of  an  apparatus  constructed  by 
Duboscq.,  the  essential  features  of  which  are  represented  in  fig.  396.  It  is 
an  arrangement  by  which  an  intermittent  beam  of  radiant  heat  maybe  made 
to  act  on  various  bodies,  and  consists  of  a  disc  D  mounted  on  a  horizontal 
axis,  and  which,  by  means  of  the  multiplying  wheels  P  and  p',  may  be 
rotated  at  any  desired  speed.  In  the  disc  is  a  series  of  holes,  the  numbers 
of  which  are  in  some  multiple  of  the  ratio  4:5:6:8.  This  apparatus  con- 
stitutes in  fact  a  syren  (242),  and  is  very  convenient  for  lecture  purposes. 
If,  while  the  disc  is  rotating  with  uniform  speed,  a  current  of  air  be  succes- 
sively directed  against  the  rows  of  holes  from  the  inside  to  the  outside,  we 
get  the  fundamental  note,  the  third,  the  fifth,  and  the  octave. 

E  E  2 


420 


On  Heat. 


[446£ 


On  the  stand  is  a  support  on  which  the  arrangement  O  may  be  fixed  in 
any  position  by  means  of  the  screw  s  ;  it  consists  of  a  screen  and  wide  tube 
behind  which  is  the  source  of  radiant  heat,  not  represented  in  the  figure. 
To  this  support  may  be  fitted  a  double  convex  lens,  if  the  rays  are  to  be 
concentrated  on  one  line  of  holes,  or  a  cylindrical  lens  when  a  slice  of 
thermal  rays  is  to  be  used  ;  or  the  rays  may  be  concentrated  by  a  mirror,  to 
get  rid  of  the  effects  of  absorption  by  glass.  The  support  S  is  for  holding 
various  pieces  of  apparatus. 

Tyndall  found  that  when  a  flask  like  that  represented  in  fig.  395,  con- 
taining a  small  quantity  of  ether,  was  placed  so  that  the  intermittent  beam 
arising  from  a  lime-light  could  fall  on  it,  and  the  top  was  connected  with  a 
flexible  tube,  a  distinct  musical  note  was  heard  when  the  ear-trumpet  was 
held  to  the  ear.  Other  liquids  being  tried  it  was  found  that  those  which  his 
other  experiments  had  revealed  as  the  best  absorbers  of  heat  (440)  gave  the 
loudest  sounds.  The  vapour  was  the  operative  cause,  for  when  the  beam 
was  caused  to  strike  against  the  liquid  instead  of  against  the  vapour  no 
sound  was  heard  ;  this  was  also  the  case  when  the  rays  fell  on  a  rock-salt 
cell  filled  with  the  liquid.  The  pitch  of  the  note  depended  on  the  velocity 
of  rotation. 

Dry  air  gave  no  sound,  but  air  containing  moisture  did  so  ;  and  the 
more  moisture  was  present  the  louder  was  the  sound.  Other  gases  gave 
sounds  in  the  order  of  their  absorption  for  heat ;  and,  indeed,  all  Tyndall's 
results  in  this  direction  are  most  strikingly  confirmed. 

The  investigations  of  the  other  experimenters,  Preece,  Bell  and  Tainter, 

Fig.  397. 


Y\%  ^96 


and'  Mercadier,    were    chiefly  directed    to    the  eftects  produced  when  the 
intermittent  beam  is  allowed  to  fall  on  solid  bodies.     A  sort  of  an  acoustic 


-446a]  Relation  of  Radiant  Heat  to  Sonnd.  42 1 

trumpet  (fig.  397)  was  used  by  Mercadier,  consisting  of  a  movable  piece  ab 
fitting  over  c  d  ?,o  that  plates  L  of  various  materials  could  be  experimented 
upon.  The  other  end /is  fitted  with  a  flexible  tube  and  bell  so  that  it  could 
be  applied  to  the  ear. 

When  the  intermittent  beam  is  allowed  to  act  on  this  plate  it  is  set  in 
vibration  and  a  sound  is  produced.  This  is  not  due,  at  any  rate  mainly,  to 
transverse  vibrations  of  the  plate,  for  neither  the  pitch  nor  the  quality  of  the 
note  was  altered  when  the  thickness  and  nature  of  the  plate  were  changed  (282), 
nor  was  it  altered  when  the  plate  was  slit.  The  best  effects  were  obtained 
when  the  diaphragm  was  of  thin  metal  foil  coated  with  lampblack  on  the 
side  next  the  rays.  Marked  effects  were  also  obtained  when  a  transparent 
plate  was  used  blackened  on  the  side  away  from  the  rays.  The  effect  is  one 
of  radiant  heat,  and  is  essentially  due  to  alternate  expansions  and  contrac- 
tions of  the  layer  of  air  in  contact  with  the  surfaces  which  absorb  the  i^adiant 
heat.  The  phenomenon  may  be  very  simply  exhibited  by  blackening  half 
the  inside  of  a  test-tube  R,  the  open  end  of  which  is  provided  with  a  flexible 
tube  which  can  be  placed  to  the  ear.  When  the  rays  fall  on  the  blackened 
part  a  loud  sound  is  heard,  but  very  little  when  the  bright  side  is  exposed. 
The  effect  is  also  obtained  when  a  blackened  piece  of  foil  is  placed  in  the 
tube. 


422  On  Heat.  [447- 


CHAPTER   IX. 

CALORIMETRY. 

447.  Calorimetry.  Thermal  unit. — The  object  of  calorimetry  is  to 
measure  the  quantity  of  heat  which  a  body  parts  with  or  absorbs,  when  its 
temperature  sinks  or  rises  through  a  certain  number  of  degrees,  or  when  it 
changes  its  condition. 

Quantities  of  heat  may  l)e  expressed  by  any  of  its  directly  measurable 
effects,  but  the  most  convenient  is  the  alteration  of  temperature,  and  quan- 
tities of  heat  are  usually  defined  by  stating  the  extent  to  which  they  are 
capable  of  raising  a  known  weight  of  a  known  substance,  such  as  water. 
The  unit  chosen  for  comparison,  and  called  the  tJiermal  unit,  is  not  ever)'- 
where  the  same.  In  France  it  is  the  quantity  of  heat  necessary  to  raise  the 
temperature  of  one  kilogramme  of  water  through  07ie  degree  Centigrade  ;  this 
is  called  a  calorie.  In  this  book  we  shall  adopt,  as  a  thermal  unit,  the 
quantity  of  heat  7tecessary  to  raise  otte  pound  of  water  through  one  degree 
Centigrade:  i  calorie  =  1-2  thermal  units,  and  one  thermal  unit  =  0-45  calorie. 

On  the  centimetre-gramme-second  system  of  units  the  heat  required  to 
raise  one  gramme  of  water  through  one  degree  is  taken  as  the  unit.  This  is 
called  the  gramme-degree  or  'wate7'-gramme-degree. 

448.  Specific  heat.— When  equal  weights  of  two  different  substances,  at 
the  same  temperature,  placed  in  similar  vessels,  are  subjected  for  the  same 
length  of  time  to  the  heat  of  the  same  lamp,  or  are  placed  at  the  same 
distance  in  front  of  the  same  fire,  it  is  found  that  their  temperatures  will  A-aiy 
considerably  ;  thus  mercuiy  will  be  much  hotter  than  water.  But  as,  from 
the  conditions  of  the  experiment,  they  have  each  been  receiving  the  same 
amount  of  heat,  it  is  clear  that  the  quantity  of  heat  which  is  sufficient  to 
raise  the  temperature  of  mercury  through  a  certain  number  of  degrees,  will 
raise  the  temperature  of  the  same  quantity  of  water  only  through  a  less 
number  of  degrees  ;  in  other  words,  that  it  requires  more  heat  to  raise  the 
temperature  of  water  through  one  degree  than  it  does  to  raise  the  temperature 
of  mercury  by  the  same  extent.  Conversely,  if  the  same  quantities  of  water 
and  of  mercury  at  100°  C.  be  allowed  to  cool  down  to  the  temperature  of  the 
air,  the  water  will  require  a  much  longer  time  for  the  purpose  than  the 
mercury  ;  hence,  in  cooling  through  the  same  number  of  degrees,  water 
gives  out  more  heat  than  does  mercury. 

It  is  readily  seen  that  all  bodies  have  not  the  same  specific  heat.  If  a 
pound  of  mercury  at  100°  is  mixed  with  a  pound  of  water  at  zero,  the  tem- 
perature of  the  mixture  will  be  about  3°  only  ;  that  is  to  say,  that  while  the 
mercury  has  cooled  through  97°,  the  temperature  of  the  water  has  been  raised 
only  3°.  Consequently  the  same  weight  of  water  requires  about  32  times  as 
much  heat  as  mercury  does,  to  produce  the  same  elevation  of  temperature. 


-449]    Measure  of  the  Sensible  Heat  absorbed  by  a  Body.    423 

If  similar  experiments  are  made  with  other  substances,  it  will  be  found 
that  the  quantity  of  heat  required  to  efifect  a  certain  change  of  temperature 
is  different  for  almost  every  substance,  and  we  speak  of  the  specific  heat,  or 
thermal  or  calorific  capacity,  of  a  body  as  the  quantity  of  heat  which  it  absorbs 
when  its  temperature  rises  through  a  given  range  of  temperature,  from  zero 
to  1°  for  example,  compared  with  the  quantity  of  heat  which  would  be 
absorbed,  in  the  same  circumstances,  by  the  same  weight  of  water  ;  that  is, 
water  is  taken  as  the  standard  for  the  comparison  of  specific  heats.  Thus, 
to  say  that  the  specific  heat  of  lead  is  0-0314,  means  that  the  quantity  of 
heat  which  would  raise  the  temperature  of  any  given  weight  of  lead  through 
1°  C.  would  raise  the  temperature  of  the  same  weight  of  water  through  only 
0-0314°  C. 

Temperature  is  the  vis  viva  of  the  smallest  particles  of  a  body  ;  in 
bodies  of  the  same  temperature  the  atoms  have  the  same  vis  viva,  the 
smaller  mass  of  the  lighter  atoms  being  compensated  by  their  greater 
velocity.  The  heat  absorbed  by  a  body  not  only  raises  its  temperature — that 
is,  increases  the  vis  viva  of  the  progressive  motion  of  the  atoms — but  in  over- 
coming the  attraction  of  the  atoms  it  moves  them  further  apart,  and  along 
with  the  expansion  which  this  represents,  some  external  pressure  is  overcome. 
In  the  conception  of  specific  heat  is  included  not  merely  that  amount  of  heat 
which  goes  to  raise  the  temperature,  but  also  that  necessary  for  the  internal 
work  of  expansion,  and  that  required  for  the  external  work.  If  these  latter 
could  be  separated,  we  should  get  the  true  heat  of  temperature,  that  which  is 
used  solely  in  increasing  the  vis  viva  of  the  atoms.  This  is  sometimes 
called  the  true  specific  heat. 

Three  methods  have  been  employed  for  determining  the  specific  heats  of 
bodies  :  (i.)  the  method  of  the  melting  of  ice,  (ii.)  the  method  of  mixtures, 
and  (iii.)  that  of  cooling.  In  the  latter,  the  specific  heat  of  a  body  is  deter- 
mined by  the  time  which  it  takes  to  cool  through  a  certain  temperature. 
Previously  to  describing  these  methods,  it  will  be  convenient  to  explain  the 
expression  for  the  quantity  of  heat  absorbed  or  given  out  by  a  body  of  known 
weight  and  specific  heat,  when  its  temperature  rises  or  falls  through  a  certain 
number  of  degrees. 

449.  Measure  of  the  sensible  heat  absorbed  by  a  body.— Let  m  be 
the  weight  of  a  body  in  pounds,  c  its  specific  heat,  and  /  its  temperature. 
The  quantity  of  heat  necessary  to  raise  a  pound  of  water  through  one  degree 
being  taken  as  unity,  vi  of  these  units  would  be  required  to  raise  m  pounds 
of  water  through  one  degree,  and  to  raise  it  through  /  degrees,  /  times  as 
much,  or  )nt.  As  this  is  the  quantity  of  heat  necessary  to  raise  through  / 
degrees  m  pounds  of  water,  whose  specific  heat  is  unity,  a  body  of  the  same 
weight,  only  of  different  specific  heat,  would  require  mtc.  Consequentlj-, 
when  a  body  is  heated  through  /  degrees,  the  quantity  of  heat  which  it 
absorbs  is  the  product  of  its  lueigkt  into  the  range  of  tejnperature  into  its 
specific  heat.  This  principle  is  the  basis  of  all  the  formulae  for  calculatmg 
specific  heats. 

If  a  body  is  heated  or  cooled  from  /  to  /'  degrees,  the  heat  absorbed  or 
disengaged  will  be  represented  by  the  formula 

;«(/'  -  t)c,  or  m{t  —  t')c. 


424 


On  Heat. 


[450- 


450.  iwethod  of  the  fusion  of  ice. — This  method  of  determining  specific 
heats  is  based  on  the  fact  that  to  melt  a  pound  of  ice  80  thermal  units  are 
necessary,  or  more  exactly  79"25.     Black's  calorimeter  (fig.  398)  consists  of 
a  block  of  ice  in  which  a  cavity  is  made, 
and  which  is  provided  with  a  cover  of  ice. 
The  substance  whose  specific  heat  is  to  be 
determined  is  heated  to  a  certain  tempera- 
ture, and  is  then  placed  in  the  cavity,  which 
is  covered.     After  some  time  the  body  be- 
comes cooled  to  zero.    It  is  then  opened,  and 
both  the  substance  and  the  cavity  wiped  dry 
with    a  sponge  which   has  been  previously 
weighed.      The  increase  of  weight  of  this 
sponge  obviously  represents  the  ice  which 
has  been  converted  into  water. 
Now,  since  one  pound  of  ice  at  0°  in  melting  to  water  at  0°  absorbs  80 
thermal  units,  P  pounds  absorbs  80  P  units.     On  the  other  hand  this  cjuan- 
tity  of  heat  is  equal  to  the  heat  given  out  by  the  body  in  cooHng  from  t°  to 
zero,  which  is  nitc,  for  it  may  be  taken  for  granted  that  in  cooling  from  t°  to 
zero  a  body  gives  out  as  much  heat  as  it  absorbs  in  being  heated  from  zero 
to  f-     Consequently  from 


Fig.  398. 


It  is  difficult  to  obtain  blocks  of  ice  as  large  and  pure  as  those  used  by 

Black  in  his  experiments,  and  Lavoisier  and  Laplace  replaced  the  block  of 
^^__  ice  by  a  more  complicated 

apparatus  which  is  called 
the  ice  calorimeter.  Fig. 
399  gives  a  perspective, 
view  of  it,  and  fig.  400 
represents  a  section.  It 
consists  of  three  concen- 
tric tin  vessels  ;  in  the 
central  one  is  placed  the 
body  M,  whose  specific 
heat  is  to  be  determined,- 
while  the  other  two  are 
filled  with  pounded  ice. 
The  ice  in  the  compart- 
ment A  is  melted  by  the 
heated  body,  while  the 
ice  in  the  compartment  B 
cuts  off  the  heating  influ- 
ence  of  the   surrounding 

atmosphere.     The  two  stopcocks  E  and  D  give  issue  to  the  water  which 

arises  from  the  liquefaction  of  the  ice. 

In  order  to  find  the  specific  heat  of  a  body  by  this  apparatus,  its  weight, 

w,  is  first  determined  ;  it  is  then  raised  to  a  given  temperature,  /,  by  keeping 


Fig.  399- 


Fig 


Bunsen's  Ice  Caloriinctcr. 


425 


-451] 

it  for  some  time  in  an  oil  or  water  bath,  or  in  a  current  of  steam.  Having 
been  quickly  brought  into  the  central  compartment,  the  lids  are  replaced 
and  covered  with  ice,  as  represented  in  the  figure.  The  water  which  flows 
out  by  the  stopcock  D  is  collected.  Its  weight,  P,  is  manifestly  that  of  the 
melted  ice.  The  calculation  is  then  made  as  in  the  preceding 
case. 

There  are  many  objections  to  the  use  of  this  apparatus. 
From  its  size  it  requires  some  quantity  of  ice,  and  a  body,  M, 
of  large  mass  ;  while  the  experiment  lasts  a  considerable  time. 
A  certain  weight  of  the  melted  water  remains  adhering  to  the 
ice,  so  that  the  water  which  flows  out  from  D  does  not  exactly 
represent  the  weight  of  the  melted  ice. 

451.  Bunsen's  ice  calorimeter. — On  the  very  considerable 
diminution  of  volume  which  ice  experiences  on  passing  into 
water  (347),  Bunsen  has  based  a  calorimeter  which  is  particu- 
larly suitable  when  only  small  quantities  of  a  substance  can 
be  used  in  determinations.  A  small  test-tube  a  (fig.  401) 
intended  to  receive  the  substance  experimented  upon  is  fused 
in  the  wider  tube  B.  The  part  ab  contains  pure  freshly 
boiled  distilled  water,  and  the  prolongation  of  this  tube  BC, 
together  with  the  capillary  tube  d^  contains  pure  mercury. 
This  tube  d  is  firmly  fixed  to  the  end  of  the  tube  C  ;  it  is 
g'raduated,  and  the  value  of  each  division  of  the  graduation  is 
specially  determined  by  calibration.  When  the  apparatus  is 
immersed  in  a  freezing  mixture,  the  water  in  the  part  ab 
freezes.  Hence,  if  afterwards,  while  the  apparatus  is  protected 
against  the  excess  of  heat  from  without,  a  weighed  quantity  of 
a  substance  at  a  given  temperature  is 

introduced  into   the  tube,   it  imparts  ^  _^ 

its  heat  to  this  in  sinking  to  zero.  In 
doing  so  it  melts  a  certain  quantity  of 
ice,  which  is  evidenced  by  a  corre- 
sponding depression  of  the  mercury 
in  the  tube  d.  Thus  the  weight  of 
ice  melted,  and  the  weight  and 
original  temperature  of  the  sub- 
stance experimented  upon,  furnish  all 
the  data  for  calculating  the  specific 
heat. 

For  heating  the  substance  in  this, 
and  also  in  other  calorimetrical  expe- 
riments, the  apparatus  fig.  402  is  well 
adapted.  The  cylindrical  metal  ves- 
sel G  is  narrower  at  the  top,  and  a 
glass  test-tube  R  is  fitted  into  a  cork 
which  closes  G.  In  this  glass  tube, 
which  is  also  closed  by  a  cork  K,  the 

substance  is  placed  which  is  to  be  heated.     The  greater  part  of  the  vessel  is 
covered  by  a  thick  mantle  of  felt,  B.     The  water  in  the  vessel  is  boiled,  the 


Fig.  401. 


426  071  Heat.  [451- 

steam  emerging  at  d,  until  the  substance  has  acquired  the  temperature  of 
boiling  water,  for  which  about  twenty  minutes  is  required.  The  mantle  and 
the  lamp  having  been  taken  away,  the  tube  R  is  rapidly  removed,  and  its 
contents  tipped  into  the  tube  a  of  the  calorimeter  (fig.  399). 

For  this  method  of  determining  specific  heat  a  new  determination  of  the 
latent  heat  of  ice  was  made,  and  it  was  found  to  be  80*025.  ^t  was  also  in  con- 
nection with  these  experiments  that  Bunsen  made  his  determination  of  the 
specific  gravity  of  ice,  which  he  found  to  be  in  the  mean  0-91674. 

By  the  above  method  Bunsen  determined  the  specific  heat  of  several  of 
the  rare  metals  for  which  a  weight  of  only  a  few  grains  could  be  used. 

452.  iMCethod  of  mixtures. — In  determining  the  specific  heat  of  a  solid 
body  by  this  method,  it  is  weighed  and  raised  to  a  known  temperature,  by 
keeping  it,  for  instance,  for  some  time  in  a  closed  place  heated  by  steam  ; 
it  is  then  immersed  in  a  mass  of  cold  water,  the  weight  and  temperature  of 
which  are  known.  From  the  temperature  of  the  water  after  mixture  the 
specific  heat  of  the  body  is  determined. 

Let  M  be  the  weight  of  the  body,  T  its  temperature,  c  its  specific  heat  ; 
and  let  tn  be  the  weight  of  the  cold  water,  and  /  its  temperature. 

As  soon  as  the  heated  body  is  plunged  into  the  water,  the  temperature  of 
the  latter  rises  until  both  are  at  the  same  temperature.  Let  this  temperature 
be  6.  The  heated  body  has  been  cooled  by  T  — ^  ;  it  has,  therefore,  lost  a 
quantity  of  heat,  M  (^  —  &)c.  The  cooling  water  has,  on  the  contrary,  ab- 
sorbed a  quantity  of  heat  equal  to  )ii{Q  - 1),  for  the  specific  heat  of  water  is 
unity.  Now  the  quantity  of  heat  given  out  by  the  body  is  manifestly  equal 
to  the  quantity  of  heat  absorbed  by  the  water  ;  that  is,  M{T  —  6{c  =  m{6  - 1), 
from  which 

M(T-^' 

An  example  will  illustrate  the  application  of  this  formula.  A  piece  of 
iron  weighing  60  ounces,  and  at  a  temperature  of  100°  C,  is  immersed  in 
180  ounces  of  water,  whose  temperature  is  19°  C.  After  the  temperatures 
have  become  uniform,  that  of  the  cooling  water  is  found  to  be  22°  C.  What 
is  the  specific  heat  of  the  iron  ? 

Here  the  weight  of  the  heated  body,  M,  is  60,  the  temperature,  T,  is  100°, 
c  is  to  be  determined  ;  the  temperature  of  mixture,  ^,  is  22°,  the  weight  of 
the  cooling  water  is  180,  and  its  temperature  12°.     Therefore 

i8oi2^-i9)_^  ^0-1153. 
60(100-22)     7?, 

453.  Corrections. — The  vessel  containing  the  cooling  water  is  usually 
a  small  cylinder  of  silver  or  brass,  with  thin  polished  sides,  and  is  supported 
by  some  badly  conducting  arrangement.  It  is  obvious  that  this  vessel,  which 
is  originally  at  the  temperature  of  the  cooling  water,  shares  its  increase  of 
temperature,  and  in  accurate  experiments  this  must  be  allowed  for.  The 
decrease  of  temperature  of  the  heated  body  is  equal  to  the  increase  of 
temperature  of  the  cooling  water,  and  of  the  vessel  in  which  it  is  contained. 
If  the  weight  of  this  latter  be  in',  and  its  specific  heat  c',  its  temperature,  like 
that  of  the  water,  is  /  :  consequently  the  previous  equation  becomes 

Mf(T  - ^)  =  m{6  - /)  +  7n'c\6 - 1)  ; 


-454J  Apparatus  for  Deterviiniiig  Specific  Heats.  427 

from  which,  by  obvious  transformations, 

_{m  +  7n'c')  {6-t) 

Generally  speaking,  the  value  f/i'c'  is  put  =  fx  ;  that  is  to  say,  /x  is  the 
weight  of  water  which  would  absorb  the  same  quantity  of  heat  as  the  vessel. 
This  is  said  to  be  the  reduced  value  in  water  of  the  vessel,  or  the  water-equi- 
valent.    This  expression  accordingly  becomes 

(m-t-M)(^_zl) 

M(T-^)     ■ 

In  accurate  experiments  it  is  necessary  to  allow  also  for  the  heat  absorbed 
by  the  glass  and  mercury  of  the  thermometer,  by  introducing  into  the  equa- 
tion their  values  reduced  on  the  same  principle. 

In  order  to  allow  for  the  loss  of  heat  due  to  radiation,  a  preliminary  experi- 
ment is  made  with  the  body  whose  specific  heat  is  sought,  the  only  object 
of  which  is  to  ascertain  approximately  the  increase  of  temperature  of  the 
cooling  water.  If  this  increase  be  10°,  for  example,  the  temperature  of  the 
water  is  reduced  by  half  this  number — that  is  to  say,  5° — below  the  tempera- 
ture of  the  atmosphere,  and  the  experiment  is  then  carried  out  in  the 
ordinary  manner. 

By  this  method  of  compensation,  first  introduced  by  Rumford,  the  water 
receives  as  much  heat  from  the  atmosphere,  during  the  first  part  of  the 
experiment,  as  it  loses  by  radiation  during  the  second  part. 

454.  Re^nault's  apparatus  for  determining:  specific  heats. — Fig.  403 
represents  one  of  the  forms  of  apparatus  used  by  Regnault  in  determining 
specific  heats  during  the  method  of  mixtures. 

The  principal  part  is  a  water  bath,  AA,  of  which  fig.  404  represents  a 
section.  It  consists  of  three  concentric  compartments  ;  in  the  central  one 
there  is  a  small  basket  of  brass  wire,  t-,  containing  fragments  of  the  substance 
whose  specific  heat  is  to  be  determined,  in  the  middle  of  which  is  placed  a 
thermometer,  T.  The  second  compartment  is  heated  by  a  current  of  steam 
coming  through  the  tube,  e,  from  a  boiler  B,  and  passing  into  a  worm,  a., 
where  it  is  condensed.  The  third  compartment,  z  z,  is  an  air  chamber,  to 
hinder  the  loss  of  heat.  The  water  bath,  AA,  rests  on  a  chamber,  K,  with 
double  sides,  EE,  forming  a  jacket,  which  is  kept  full  of  cold  water,  in  order 
to  exclude  the  heat  from  AA,  and  from  the  boiler,  B.  The  central  compart- 
ment of  the  water  bath  is  closed  by  a  damper,  r,  which  can  be  opened  at 
pleasure,  so  that  the  basket,  6",  can  be  lowered  into  the  chamber,  K. 

On  the  left  of  the  figure  is  represented  a  small  and  very  thin  brass  vessel, 
D,  suspended  by  silk  threads  on  a  small  carriage,  which  can  be  moved  out 
of,  or  into,  the  chamber,  K.  This  vessel,  which  serves  as  a  calorimeter,  con- 
tains water,  in  w-hich  is  immersed  a  thermometer,  /.  Another  thermometer 
at  the  side,  /',  gives  the  temperature  of  the  air. 

When  the  thermometer  T  shows  that  the  temperature  of  the  substance 
in  the  bath  is  stationary,  the  screen,  ^,  is  raised,  and  the  vessel,  D,  moved  to 
just  below  the  central  compartment  of  the  water  bath.  The  damper,  r,  is 
then  withdrawn,  and  the  basket,  c,  and  its  contents  are  lowered  into  the  water 
in   the  vessel,  D,  the  thermometer,  T,  remaining  fixed  in  the  corn.     The 


428 


On  Heat. 


[454- 


carriage  and  the  vessel,  D,  are  then  moved  out,  and  the  water  agitated  until 
the  thermometer,  T,  becomes  stationary.  The  temperature  which  it  indicates 
is  6.  This  temperature  known,  the  rest  of  the  calculation  is  made  in  the 
manner  described  in  art.  449,  care  being  taken  to  make  all  the  necessary 
corrections. 

In  determining  the  specific  heat  of  substances — phosphorus,  for  instance 
— which  could  not  be  heated  without  causing  them  to  melt,  or  undergo  some 
change  which  would  interfere  with  the  accuracy  of  the  result,  Regnault 
adopted  an  inverse  process  :  he  cooled  them  down  to  a  temperature  con- 
siderably below  that  of  the  water  in  the  calorimeter,  and  then  observed  the 
diminution  in  the  temperature  of  the  latter,  which  resulted  from  immersing 
the  cooled  substance  in  it. 

In  determining  the  specific  heat  of  substances,  which,  like  potassium, 
would  decompose  water,  some  other  liquid,  such  as  turpentine  or  benzole, 


Fi-. 


must  be  used.  These  liquids  have  the  additional  advantage  of  having  a 
lower  specific  heat  than  water,  which  has  the  highest  of  any  liquid,  so  that  an 
error  in  determining  the  temperature  of  the  cooling  liquid  has  a  less  influence 
on  the  value  of  the  specific  heat.  With  this  view  use  has  been  made  of 
mercury,  the  specific  heat  of  which  is  only  one-thirtieth  that  of  water. 


-456]  Method  of  Cooling.  429 

455.  Method  of  cooling-. — Equal  weights  of  different  bodies  whose 
specific  heats  are  different,  will  occupy  different  times  in  cooling  through 
the  same  number  of  degrees.  Dulong  and  Petit  applied  this  principle  in 
determining  the  specific  heats  of  bodies  in  the  following  manner  : — A  small 
polished  silver  vessel  is  filled  with  the  substance  in  a  state  of  fine  powder, 
and  a  thermometer  placed  in  the  powder,  which  is  pressed  down.  This 
vessel  is  heated  to  a  certain  temperature,  and  is  then  introduced  into  a 
copper  vessel,  in  which  it  fits  hermetically.  This  copper  vessel  is  exhausted, 
and  maintained  at  the  constant  temperature  of  melting  ice,  and  the  time 
noted  which  the  substance  takes  in  falling  through  a  given  range  of  tem- 
perature, from  1 5°  to  5'^  for  example.  The  times  which  equal  weights  of  dif- 
ferent bodies  require  for  cooling,  through  the  same  range  of  temperature, 
are  directly  as  their  specific  heats. 

Regnault  has  proved  that  with  solids  this  method  does  not  give  trust- 
worthy results  ;  it  assumes,  which  is  not  quite  the  case,  that  the  cooling  in 
all  parts  is  equal,  and  that  all  substances  part  with  their  heat  to  the  silver 
case  with  equal  facility.  The  method  may,  however,  be  employed  with 
success  in  the  determination  of  the  specific  heat  of  liquids. 

In  an  investigation  of  the  specific  heats  of  various  soils,  Pfaundler  found 
that  a  soil  of  low  specific  heat  heats  and  cools  rapidly,  while  earth  of  higher 
specific  heat  undergoes  slow  heating  and  slow  cooling  ;  that  moist  earths 
rich  in  humus  have  a  high  specific  heat,  amounting  in  the  case  of  turf  to  as 
much  as  0-5  ;  while  diy  soils  free  from  humus,  such  as  lime  and  sand,  have 
a  low  specific  heat,  not  more  than  about  0-2. 

456.  Specific  heat  of  liquids — The  specific  heat  of  liquids  may  be 
determined  either  by  the  method  of  cooling,  by  that  of  mixtures,  or  by  that 
of  the  ice  calorimeter.  In  the  latter  case  they  are  contained  in  a  small 
metal  vessel,  or  a  glass  tube,  which  is  placed  in  the  central  compartment 
(fig.  404),  and  the  experiment  then  made  in  the  usual  manner. 

A  method  devised  by  Pfaundler  of  determining  the  specific  heat  of 
liquids,  which  under  certain  circumstances  is  advantageous,  depends  on  a 
property  of  the  electrical  current  of  heating  any  conductor  through  which 
it  passes. 

In  two  equal  calorimeters  containing  the  liquids  to  be  tested,  together 
with  suitable  thermometers  and  stirrers,  two  equal  spirals  of  fine  platinum 
wire  are  placed.  These  are  connected  with  a  voltaic  battery  by  means  of 
copper  wires,  and  if  the  same  current  of  electricity  be  simultaneously 
passed  through  each  of  them,  which  can  be  very  accurately  done,  the  heat 
produced  in  the  wires  will  be  equal,  and  the  rise  in  tem.perature  in  the 
liquids  will  then  be  inversely  as  the  specific  heats.  One  of  the  liquids  is 
usually  water. 

It  will  be  seen  from  the  table  in  the  following  article  that  water  and  oil 
of  turpentine  have  a  much  greater  specific  heat  than  other  substances,  and 
more  especially  than  the  metals.  It  is  from  its  great  specific  heat  that  water 
requires  a  long  time  in  being  heated  or  cooled,  and  that  for  the  same  weight 
and  temperature  it  absorbs  or  gives  out  far  more  heat  than  other  substances. 
This  double  property  is  applied  in  the  hot-water  apparatus,  of  which  we 
shall  afterwards  speak,  and  it  plays  a  most  important  part  in  the  economy  of 
nature. 


430  On  Heat.  [457- 

457.  Specific  heats  of  bodies. — The  list  contained  in  the  next  article 
(458)  gives  the  specific  heats  of  a  great  number  of  elementary  substances. 
We  give  here  the  specific  heats  of  a  few  substances,  mostly  liquids  : — 

Specific  heat  Specific  heat 

Turpentine  .  .  .     0-426  Bisulphide  of  carbon      .  o"245 

Alcohol.  .  .  .     0-062  Thermometer  glass        .  0-198 

Ether     .  .  .  .0-516  Steel       .         .         .         .  o-ii8 

Glycerine  .  .  -0-555  Brass      ....  0-094 

The  specific  heat  of  water  is  commonly  taken  at  unity,  which  is  not 
strictly  correct.  According  to  the  most  recent  determinations  the  7nean 
specific  heat  between  0°  and  /  is  expressed  by  the  formula  i  +0-00015/. 

These  numbers,  as  well  as  the  numbers  in  (458),  represent  the  mean 
specific  heats  between  0°  and  100°.  It  was  shown  by  Dulong  and  Petit 
that  the  specific  heats  increase  with  the  temperature.  Those  of  the  metals, 
for  instance,  are  gi-eater  between  100°  and  200°  than  between  0°  and  100°, 
and  are  still  greater  between  200°  and  300°  ;  that  is  to  say,  a  greater  amount 
of  heat  is  required  to  raise  a  body  from  200°  to  250'^  than  from  100°  to  150"^, 
and  still  more  than  from  0°  to  50°.  For  silver,  the  mean  specific  heat 
between  0°  and  100°  is  0-057,  while  between  0°  and  200°  it  is  0-061 1.  The 
following  table  gives  the  specific  heats  at  various  temperatures  : — 

Copper         .......     0-0910  +  0-000046/ 

Zinc 0-0865+0-000088/ 

Lead 0-0286  +  0-000038/ 

Platinum      .......     0-0317  +  0-0000062/ 

Water i  +  0-00030/ 

The  increase  of  specific  heat  with  the  temperature  is  greater  as  bodies 
are  nearer  their  fusing  point.  Any  action  which  increases  the  density  and 
molecular  aggregation  of  a  body,  diminishes  its  specific  heat.  Thus  hard 
steel  with  the  density  7-798  has  the  sp.  heat  o-i  175  ;  while  that  of  soft  steel 
of  density  7-861  is  o-i  165.  The  specific  heat  of  copper  is  diminished  by  its 
being  hammered,  but  it  regains  its  original  value  after  the  metal  has  been 
again  heated. 

The  specific  heat  of  a  liquid  increases  with  the  temperature  much  more 
rapidly  than  that  of  a  solid.  Water  is,  however,  an  exception  :  its  specific 
heat  increases  less  rapidly  than  does  that  of  solids. 

The  most  remarkable  examples  of  the  influence  of  temperature  on  the 
specific  heat  are  afforded  by  carbon,  boron,  and  'sihcon.  Weber  has  found 
that  at  600°  the  specific  heat  of  carbon  is  7  times,  and  that  of  boron  2\  times, 
as  great  as  their  respective  specific  heats  at  —  50°.  The  specific  heat  of 
diamond  is  0-0635  ^^  —50°,  0-1318  at  '^'^°,  0-2218  at  140°,  and  0-3026  at  247°. 
Although  the  specific  heat  increases  thus  rapidly  between  -  50''  and  250°, 
beyond  that  point  the  rate  of  increase  is  slower  ;  and  beyond  600°,  or  at  an 
incipient  red  heat,  it  seems  to  be  pretty  constant,  or  at  any  rate  to  exhibit 
no  greater  variations  with  the  temperature  than  are  afforded  by  other  sub- 
stances. Thus  while  at  600°  the  specific  heat  is  0-441,  at  985°  it  is  0-459. 
Graphite  also  has  at  22°  the  specific  heat  0-168  ;  this  increases,  but  at  a 
gradually  diminishing  rate,  to  642°,  where  its  specific  heat  is  0-445.     Like 


-457]  Specific  Heats  of  Bodies.  43 1 

diamond,  an  incipient  red  heat  seems  to  be  a  limiting  temperature  beyond 
which  graphite  exhibits  only  the  ordinary  variation  with  the  temperature. 
Weber  has  also  found  that,  in  their  thermal  deportment,  there  are  only  two 
essentially  different  modifications  of  carbon— the  transparent  one  (diamond), 
and  the  opaque  ones  (graphite,  dense  amorphous  carbon,  and  porous  amor- 
phous carbon). 

Crystallised  boron  is  similar  in  its  deportment  to  carbon  ;  its  specific 
heat  increases  from  0-1915  at  -40°  to  0-2382  at  27°,  and  to  0-3663  at  233°. 
The  rate  of  increase  is  very  rapid  up  to  80°  ;  it  increases  beyond  that 
temperature,  but  at  a  gradually  diminished  rate,  and,  no  doubt,  tends  to  an 
almost  constant  value  of  0-5. 

The  specific  heat  of  silicon  also  varies  with  the  temperature  ;  between 
-40°  and  200°  it  increases  from  0-136  to  0-203  ;  the  rate  of  increase  is  less 
rapid  with  higher  temperatures,  being  at  200°  only  ^^  what  it  is  at  10°.  At 
200°  it  reaches  its  limiting  value. 

The  specific  heat  of  substances  is  greater  in  the  liquid  than  in  the  solid 
state,  as  will  be  seen  by  the  following  table  : — 

Solid  Liquid 

Water 0-502  i-qoo 

Sulphur 0-203  0-234 

Bromine 0-084  o-iio 

Iodine 0-054  o-oo8 

Mercury 0-031  0-033 

Phosphorus  .         .         .         .         .         .0-190  0-212 

Tin 0-056  0-064 

Lead 0-031  0-040 

It  also  differs  with  the  allotropic  modification  ;  thus  the  specific  heat  of 
red  phosphorus  is  0-19,  and  that  of  white  0-17;  of  crystallised  arsenic 
0-083,  and  of  amorphous  0*058  ;  of  crystallised  selenium  0-084,  and  of 
amorphous  0-0953  ;  of  wood  charcoal  0-241  5  of  graphite  0-202  ;  and  of 
diamond  0-147. 

Pouillet  used  the  specific  heat  of  platinum  for  measuring  high  decrees  of 
heat.  Supposing  200  ounces  of  platinum  had  been  heated  in  a  furnace  and 
had  then  been  placed  in  1,000  ounces  of  water,  the  temperature  of  which  it 
had  raised  from  13°  to  20°.  From  the  formula  we  have  M  =  200,  in  1000  • 
6  is  20,  and  /  is  13.  The  specific  heat  of  platinum  is  0-033,  and  we  have 
therefore,  from  the  equation — 

yicij-e)  =  m{e-t) 

^  ^  i)i{6-f)  +  M6-g  ^  7000+132  ^  7232  ^ 
Vlc  6-6  6-6 

It  is  found,  however,  that  the  mean  specific  heat  of  platinum  at  tempera- 
tures up  to  about  1200°  is  0-0377  ;  if  this  value,  therefore,  be  substituted  for 
c  in  the  equation,  we  have — 

T  =  7J-5^S  =  948°C. 

7-54 

By  this  method,  which  requires  great  skill  in  the  experimenter,  Pouillet 
determined  a  series  of  high  temperatures.  He  found,  for  example,  the  tem- 
perature of  melting  iron  to  be  1500°  to  1600°  C. 


432  On  Heat.  [458- 

458.  Dulong  and  Petit's  law. — A  knowledge  of  the  specific  heat  of 
bodies  has  become  of  great  importance,  in  consequence  of  Dulong  and  Petit's 
discovery  of  the  remarkable  law,  that  the  product  of  the  specific  heat  of  any 
solid  element  into  its  atomic  weight  is  approximately  a  constant  number,  as 
will  be  seen  from  the  following  table  :  — 


Specific  heat 

Atomic  weight 

Atomic  heat 

Aluminium 

0-2143 

27-4 

5-87 

Antimony 

0-0513 

122 

6-26 

Arsenic   . 

0-0822 

75 

6-17 

Bismuth  . 

0-0308 

210 

6-47 

Bromine . 

0-0843 

80 

6-74 

Cadmium 

0-0567 

112 

6-35 

Cobalt     . 

0-1067 

58-7 

6-26 

Copper   . 

0-0939 

63-5 

5  "99 

Gold        . 

0-0324 

197 

6-38 

Iodine     . 

0-0541 

127 

6-87 

Iron 

O-II38 

56 

6-37 

Lead        . 

0-0314 

207 

6-50 

Magnesium 

0-2475 

24 

5-94 

Mercury . 

0-0332 

200 

6-64 

Nickel     . 

0-1092 

58-7 

6-41 

Phosphorus 

0-1740 

31-0 

5-39 

Platinum 

0-0324 

197-5 

6-40 

Potassium 

0-1655 

39-1 

6-47 

Silver      . 

i         0-0570 

108-0 

6-i6 

Sulphur  . 

0-178 

32 

570 

Tin 

0-0555 

118 

6-55 

Zinc 

0-0950 

65-2 

6-23 

It  will  be  seen  that  the  number  is  not  a  constant,  but  varies  between  5-39 
and  6-87.  These  variations  may  depend  partly  on  the  difficulty  of  getting 
the  elements  in  a  state  of  perfect  purity,  and  partly  on  errors  incidental 
to  the  determination  of  the  specific  heats,  and  of  the  atomic  weights.  Again, 
the  specific  heats  of  bodies  vary  with  the  state  of  aggregation  of  the  bodies, 
and  also  with  the  temperatures  at  which  they  are  determined  ;  some,  such 
as  potassium,  have  been  determined  at  temperatures  very  near  their  fusing 
points  ;  others,  like  platinum,  at  temperatures  much  removed  from  them.  A 
prominent  cause,  therefore,  of  the  discrepancies  is  doubtless  to  be  found  in 
the  fact  that  all  the  determinations  have  not  been  made  under  correspondmg' 
physical  conditions. 

The  atomic  weights  of  the  elements  represent  the  relative  weights  of  equal 
numbers  of  atoms  of  these  bodies,  and  the  product,  pc,  of  the  specific  heat, 
c,  into  the  atomic  weight,  p,  is  the  atomic  heat,  or  the  quantity  of  heat 
necessary  to  raise  the  temperature  of  the  same  number  of  atoms  of  different 
substances  by  one  degree  ;  and  Dulong  and  Petit's  law  may  be  thus  ex- 
pressed :  the  same  quantity  of  heat  is  needed  to  heat  an  atom  of  all  simple 
bodies  to  the  same  extent. 

The  atomic  heat  of  a  body,  when  divided  by  its  specific  heat,  gives  the 


-459]  Specific  Heat  of  Compound  Bodies.  433 

atomic  weight  of  a  body.  Regnault  proposed  to  use  this  relation  as  a 
means  of  determining  the  atomic  weight,  and  it  certainly  is  of  great  service 
in  deciding  on  the  atomic  weight  of  a  body  in  cases  where  the  chemical 
relations  permit  a  choice  between  two  or  more  numbers. 

According  to  modern  views,  the  heat  imparted  to  a  body  is  partly  expended 
in  external  work,  which  in  the  case  of  a  solid  would  be  extremely  small,  be- 
ing only  that  required  for  raising  the  pressure  of  the  atmosphere  through  a 
distance  representing  the  expansion  ;  secondly,  the  internal  work,  or  the  heat 
used  in  overcoming  the  attraction  of  the  atoms  for  each  other,  and  forcing 
them  apart  ;  and  thirdly,  there  is  the  true  specific  heat.,  or  the  heat  applied  in 
increasing  the  temperature — that  is,  in  increasing  the  vis  viva  of  the  molecules 
(448).  By  far  the  most  considerable  of  these  is  the  latter  ;  the  amount  of 
heat  consumed  in  the  two  former  operations  is  small,  and  the  variations 
with  different  bodies  must  be  inconsiderable.  Until,  however,  the  relation 
between  the  various  factors  is  made  out,  absolute  identity  in  the  numbers 
for  the  atomic  specific  heat  cannot  be  expected.  Weber  holds  that  even 
when  due  allowance  has  been  made  for  these  circumstances,  the  variations 
are  too  great  to  be  accounted  for,  and  he  considers  that  they  point  for  their 
explanation  to  an  alteration  in  the  constitution  of  the  atom,  and  render 
probable  a  changing  valency  of  the  atom  of  carbon. 

459.  specific  beat  of  compound  bodies. — In  compound  bodies  the  law 
also  prevails  :  the  product  of  the  specific  heat  into  the  equivalent  is  an  al- 
most constant  number,  which  varies,  however,  with  different  classes  of  bodies. 
Thus,  for  the  class  of  oxides  of  the  general  formula  RO,  it  is  11 -30  ;  for  the 
sesquioxides  R-'O^  it  is  27-15  ;  for  the  sulphides  RS,  it  is  i8-88  ;  and  for  the 
carbonates  RCO^,  it  is  21-54.  The  law,  which  is  known  as  Neiimamis  law., 
maybe  expressed  in  the  following  general  manner: — With  compounds  of 
the  same  fynnula,  and  of  a  similar  chemical  constitution,  the  product  of  the 
atomic  weight  into  the  specific  heat  is  a  consta?it  qiui7itity.  This  includes 
Dulong  and  Petit's  law  as  a  particular  case. 

Kopp  propounded  the  following  law,  which  is  an  extension  of  that  of 
Neumann  : —  The  molecular  heats  of  all  solid  bodies  are  equal  to  the  sum  or 
thfi  molecular  heats  of  the  elements  contained  iii  them.  Dulong  and  Petit's 
law  that  all  elements  have  the  same  atomic  heat  he  does  not  consider  uni- 
versally valid.  He  assigns  the  number  6-4  to  all  elements  excepting  the  fol- 
lowing ;  with  sulphur  and  phosphorus  it  is  5-4,  fluorine  5-0,  oxygen  4-0 
siUcon  3-8,  boron  2-7,  hydrogen  2-3,  and  carbon  rS. 

Even  with  this  modification  it  is  found  that  the  calculated  heats  of  com- 
pounds differ  more  from  the  observed  ones  than  can  be  ascribed  to  errors  in 
the  determination  of  the  specific  heats.  This  is  probably  due  to  the  fact  that 
some  of  the  heat  is  expended  in  internal  work,  and  that  it  is  this  which  brino-s 
about  the  discrepancies. 

With  mixtures  of  alcohol  and  water  in  certain  proportions,  the  specific 
heat  is  greater  than  that  of  the  water  ;  thus,  that  of  a  mixture  containing  20 
per  cent,  of  alcohol  was  found  by  Dupre  and  Page  to  be  1-0456.  No  general 
law  can  be  laid  down  for  solutions  of  acids  or  of  salts  in  water  ;  though  the 
specific  heat  is  most  frequently  less  than  that  calculated  from  the  consti- 
tuents. 


434 


On  Heat. 


[460 


460.  Specific  heat  of  g-ases. — The  specific  heat  of  a  gas  may  be  re- 
ferred either  to  that  of  water  or  to  that  of  air.  In  the  former  case  it  repre- 
sents the  quantity  of  heat  necessary  to  raise  a  given  weight  of  the  gas  through 
one  degree,  as  compared  with  the  heat  necessary  to  raise  the  same  weight 
of  water  one  degree.  In  the  latter  case  it  represents  the  quantity  of  heat 
necessary  to  raise  a  given  volume  of  the  gas  through  one  degree,  compared 
with  the  quantity  necessary  for  the  same  volmne  of  air  treated  in  the  same 
manner. 

De  la  Roche  and  Berard  determined  the  specific  heats  of  gases  in  re- 
ference to  water  by  causing  known  volumes  of  a  given  gas  under  constant 
pressure,  and  at  a  given  temperature,  to  pass  through  a  spiral  glass  tube 
placed  in  water.  From  the  increase  in  temperature  of  this  water,  and  from 
the  other  data,  the  specific  heat  was  determined  by  a  calculation  analogous; 
to  that  given  under  the  method  of  mixtures.  They  also  determined  the 
specific  heats  of  different  gases  relatively  to  that  of  air,  by  comparing  the 
quantities  of  heat  which  equal  volumes  of  a  given  gas,  and  of  air  at  the  same 
pressure  and  temperature,  imparted  to  equal  weights  of  water.  Subsequently 
to  these  researches,  De  la  Rive  and  Marcet  applied  the  method  of  cooling  to 
the  same  determination  ;  and  more  recently  Regnault  made  a  series  of  in- 
vestigations on  the  calorific  capacities  of  gases  and  vapours,  in  which  he 
adopted,  but  with  material  improvements,  the  method  of  De  la  Roche  and 
Berard.  He  thus  obtained  the  following  results  for  the  specific  heats  of  the 
various  gases  and  vapours,  compared  first  with  the  specific  heat  of  an  equal 
weight  of  water  taken  as  unity  ;  secondly,  with  that  of  an  ecjual  volume  of 
air,  referred,  as  before,  to  its  own  weight  of  water  taken  as  unity  : — 

Specific  heats 


Equal 

Equal 

weights 

volumes 

Air         .... 

.       0-2374 

0-2374 

■  Oxygen  .... 

.     0-2I74 

0-2405 

Simple 

Nitrogen 

.     0-2438 

0-2370 

gases 

Hydrogen 

3-4090 

0-2359 

Chlorine 

.       0-I2I0 

0-2962 

/  Binoxide  of  nitrogen      . 

•   0-2315 

0-2406 

Carbonic  oxide 

.    0-2450 

0-2370 

Compound 

Carbonic  acid 

.    0-2163 

0-3307 

gases 

Hydrochloric  acid 

.    0-1845 

0-2333 

Ammonia 

.    0-5083 

0^2966 

>01efiant  gas  . 

.     0-4040 

0-4106 

/Water    .... 

.     0-4805 

0-2984 

Ether     .... 

.    0-4810 

1-2296 

Vapours 

Alcohol. 

•    0-4534 

0-7171 

Turpentine     . 

.    0-5061 

2-3776 

Bisulphide  of  carbon      . 

.    0-1570 

0-4140 

Benzole. 

•    0-3754 

I -01  14 

In  making  these  determinations  the  gases  were  under  a  constant  pressure, 
but  variable  volume  ;  that  is,  the  gas  as  it  was  heated  could  expand,  and 
this  is  called  the  specific  heat  under  co7istant pressure.  But  if  the  gas  when 
being  heated  is  kept  at  a  constant  volume,  its  pressure  or  elastic  force  then 


-461]  Latent  Heat  of  Fusion.  43  5 

necessarily  increasing,  it  has  a  different  capacity  for  heat  ;  this  latter  is 
spoken  of  as  the  specific  heat  imder  constant  volume.  That  this  latter  is  less 
than  the  former  is  evident  from  the  following  considerations  : — 

Suppose  a  given  quantity  of  gas  to  have  had  its  temperature  raised  /" 
while  the  pressure  remained  constant,  this  increase  of  temperature  will  have 
been  accompanied  by  a  certain  increase  in  volume.  Supposing  now  that 
the  gas  is  so  compressed  as  to  restore  it  to  its  original  volume,  the  result  of 
this  compression  will  be  to  raise  its  temperature  again  to  a  certain  extent, 
say  t'°.  The  gas  will  now  be  in  the  same  condition  as  if  it  had  been  heated 
and  had  not  been  allowed  to  expand.  Hence,  the  same  quantity  of  heat  which 
is  required  to  raise  the  temperature  of  a  given  weight  of  gas,  /°,  while  the 
pressure  remains  constant  and  the  volume  alters,  will  raise  the  temperature 
t-^f  degrees  if  it  is  kept  at  a  constant  volume  but  variable  pressure.  The 
specific  heat,  therefore,  of  a  gas  at  constant  pressure,  c,  is  greater  than  the 
specific  heat  under  constant  volume,  t;,  and  they  are  to  each  other  as  /+  /':  /, 

that  IS     = . 

c,  t 
It  is  not  possible  to  determine  by  direct  means  the  specific  heat  of  gases 
under  constant  volume  with  much  approach  to  accuracy  ;  and  it  has  been 
determined  by  some  indirect  method,  of  which  the  most  accurate  is  based 
on  the  theory  of  the  propagation  of  sound  (229).  A  critical  comparison  of 
the  most  accurate  recent  determinations  gives  the  number  i  -405  for  the  value 

of  ^  ,  which  is  usually  designated  by  the  symbol  k.  * 

461.  Xiatent  heat  of  fusion. — Black  was  the  first  to  observe  that  during 
the  passage  of  a  body  from  the  solid  to  the  liquid  state,  a  cjuantity  of  heat 
disappears,  so  far  as  thermometric  effects  are  concerned,  and  which  is 
accordingly  said  to  become  latent. 

In  one  experiment  he  suspended  in  the  room  at  a  temperature  8-5°  two 
thin  glass  flasks,  one  containing  water  at  0°,  and  the  other  the  same  weight 
of  ice  at  0°.  At  the  end  of  half  an  hour  the  temperature  of  the  water  had 
risen  4°,  that  of  the  ice  being  unchanged,  and  it  was  \o\  hours  before  the 
ice  had  melted  and  attained  the  same  temperature.  Now  the  temperature 
of  the  room  remained  constant,  and  it  must  be  concluded  that  both  vessels 
received  the  same  amount  of  heat  in  the  same  time.  Hence  21  times  as 
much  heat  was  required  to  melt  the  ice  and  raise  it  to  4°  as  was  sufficient 
to  raise  the  same  weight  of  water  through  4°.  So  that  the  total  quantity  of 
heat  imparted  to  the  ice  was  21x4  =  84;  and  as  only  4  of  this  was  used  in 
raising  the  temperature,  the  remainder,  80,  was  used  in  simply  melting  the 
ice. 

He  also  determined  the  latent  heat  by  immersing  119  parts  of  ice  at  0° 
in  135  parts  of  water  at  877°  C.  He  thus  obtained  254  parts  of  water  at 
1 1 '6°  C.  Taking  into  account  the  heat  received  by  the  vessel  in  which  the 
liquid  was  placed,  he  obtained  the  number  79*44  as  the  latent  heat  of  lique- 
faction of  ice. 

We  may  thus  say 

Water  at  0°=  Ice  at  0°  + latent  heat  of  liquefaction. 

The  method  which  Black  adopted  is  essentially  that  which  is  now  used 


436  On  Heat.  [461- 

for  the  determination  of  latent  heats  of  Uquids  ;  it  consists  in  placing  the 
substance  under  examination  at  a  known  temperature  in  the  water  (or  other 
Hquid)  of  a  calorimeter,  the  temperature  of  which  is  sufficient  to  melt  the 
substance  if  it  is  solid,  or  to  solidify  it  if  liquid  ;  and  when  uniformity  of 
temperature  is  established  in  the  calorimeter,  this  temperature  is  determined. 
Thus,  to  take  a  simple  case,  suppose  it  is  required  to  determine  the  latent 
heat  of  the  liquidity  of  ice.  Let  M  be  a  certain  weight  of  ice  at  zero,  and  in 
a  weight  of  water  at  f  sufficient  to  melt  the  ice.  The  ice  is  immersed  in 
the  water,  and  as  soon  as  it  has  melted,  the  final  temperature  6°  is  noted. 
The  water,  in  cooling  from  f  to  6°,  has  parted  with  a  quantity  of  heat, 
m  {t-6).  If  X  be  the  latent  heat  of  the  ice,  it  absorbs,  in  liquefying,  a 
quantity  of  heat  M.i" ;  but,  besides  this,  the  water  which  it  forms  has  risen 
to  the  temperature  6°,  and  to  do  so  has  required  a  quantity  of  heat,  repre- 
sented by  M^°.     We  thus  get  the  equation 

from  which  the  value  x  is  deduced. 

By  this  method  Desains  and  De  la  Provostaye  found  that  the  latent  heat 
of  the  liquefaction  of  ice  is  7Q'2  5  :  that  is,  a  pound  of  ice,  in  liquefying, 
absorbs  the  quantity  of  heat  which  would  be  necessary  to  raise  79"25  pounds 
of  water  i°,  or,  what  is  the  same  thing,  one  pound  of  water  from  zero  to 
79-25°.     Bunsen's  most  recent  determination  gives  80-025  (450- 

This  method  is  thus  essentially  that  of  the  method  of  mixtures  :  the  same 
apparatus  may  be  used,  and  the  same  precautions  are  required,  in  the  two 
cases.  In  determining  the  latent  heat  of  liquefaction  of  most  solids,  the  diffe- 
rent specific  heats  of  the  substance  in  the  solid  and  in  the  liquid  state  require 
to  be  taken  into  account.  In  such  a  case,  let  ;//  be  the  weight  of  the  water 
in  the  calorimeter  (the  water  ecjuivalents  of  the  calorimeter  and  thermometer 
supposed  to  be  included)  ;  M  the  weight  of  the  substance  worked  with  ;  /  the 
origmal  and  6  the  final  temperature  of  the  calorimeter  ;  T  the  original  tem- 
perature of  the  substance  ;  C  its  melting  (or  freezing)  point ;  C  the  specific 
heat  of  the  substance  in  the  solid  state  between  the  temperature  %  and  6  ;  c 
its  specific  heat  in  the  liquid  state  between  the  temperatures  T  and  %  ;  and 
let  L  be  the  latent  heat  sought. 

If  the  experiment  be  made  on  a  melted  substance  which  gives  out  heat 
to  the  calorimeter  and  is  thereby  solidified  (it  is  taken  for  granted  that  a 
body  gives  out  as  much  heat  in  solidifying  as  it  absorbs  in  liquefying),  it  is 
plain  that  the  quantity  of  heat  absorbed  by  the  calorimeter,  ;;z(^-/),  ismade 
up  of  three  parts  ;  first,  the  heat  lost  by  the  substance  in  cooling  from  its 
original  temperature  T  to  the  solidifying  point  C  ;  secondly,  the  heat  given 
out  in  solidification,  ML  ;  and,  thirdly,  the  heat  it  loses  in  sinking  from  its 
solidifying  point  €",  to  the  temperature  of  the  water  of  the  calorimeter. 
That  is  : 

;«(^_/)  =  M  r(T-r)6-  +  L  +  ((r-^)c1 

whence,  i^J<Q^t)^^T-^)c-{^-b)Q. 

The  following  numbers  have  been  obtained  for  the  latent  heats  of 
fusion  : — 


-462]       Dcteruiination  of  the  Latent  Heat  of  Vapour.  437 


Water    . 

.     80-03 

Cadmium 

.      13-66 

Nitrate  of  Sodium 

.     62-97 

Bismuth 

.      12-64 

„         „ 

Potassium 

•     47-37 

Sulphur 

•       9-37 

Zinc 

•     28-13 

Lead      . 

■       5-37 

Platinum 

.     27-18 

Phosphorus    . 

•       5-03 

Silver     . 

.     21-07 

D'Arcet's  alloy 

•       4-50 

Tin 

•     14-25 

Mercury 

.       2-83 

These  numbers  represent  the  number  of  degrees  through  which  a  pound 
of  water  would  be  raised  by  a  pound  of  the  body  in  question  in  passing 
from  the  liquid  to  the  solid  state  ;  or,  what  is  the  same  thing,  the  number  of 
pounds  of  water  that  would  be  raised  i^  C.  by  one  of  the  bodies  in  solidi- 
fying. 

On  modern  views  the  heat  expended  in  melting  is  consumed  in  moving 
the  atoms  into  new  positions  ;  the  work,  or  its  equivalent  in  heat  required 
for  this — the  potential  energy  they  thus  acquire,  is  strictly  comparable  to  the 
expenditure  of  work  in  the  process  of  raising  a  weight.  When  the  liquid 
solidifies,  it  reproduces  the  heat  which  had  been  expended  in  liquefying  the 
solid  :  just  as  when  a  stone  falls  it  produces  by  its  impact  against  the  ground 
the  heat,  the  equivalent  of  which  in  work  had  been  expended  in  raising  it, 
and  a  similar  explanation  applies  to  the  latent  heat  of  gasification. 

462.  netermination  of  the  latent  beat  of  vapour. — Liquids,  as  we 
have  seen,  in  passing  into  the  state  of  vapour,  absorb  a  very  considerable 
quantity  of  heat,  which  is  termed 
latent  heat  of  vaporisation.  In  deter- 
mining the  heat  absorbed  in  vapours, 
it  is  assumed  that  a  vapour  in  liquefy- 
ing gives  out  as  much  heat  as  it  had 
absorbed  in  becoming  converted  into 
vapour. 

The  method  employed  is  essentially 
the  same  as  that  for  determining  the 
specific  heat  of  gases.  Fig.  405  repre- 
sents the  apparatus  used  by  Despretz. 
The  vapour  is  produced  in  a  retort, 
C,  where  its  temperature  is  indicated 
by  a  thermometer.  It  passes  into  a 
worm  SS  immersed  in  cold  water, 
where  it  condenses,  imparting  its 
latent  heat  to  the  condensing  water  in  the  vessel  B. 
is  collected  in  a  vessel,  A,  and  its  weight  represents  the  quantity  of  vapour 
which  has  passed  through  the  worm.  The  thermometers  in  B  gi^•e  the 
change  of  temperature. 

Let  M  be  the  weight  of  the  condensed  vapour,  T  its  temperature  on 
entering  the  worm,  which  is  that  of  its  boiling  point,  and  x  the  latent  heat  of 
vaporisation.  Similarly,  let  vi  be  the  weight  of  the  condensing  water  (com- 
prising the  weight  of  the  vessel  B  and  of  the  worm  SS  reduced  va  water),  let 
t°  be  the  temperature  of  the  water  at  the  beginning,  and  6°  its  temperature 
at  the  end  of  the  experiment. 


Fig.  405. 

The  condensed  vapour 


438 


On  Heat. 


[462- 


It  is  to  be  observed  that,  at  the  commencement  of  the  experiment,  the 
condensed  vapour  passes  out  at  the  temperature  /°,  while  at  the  conclusion 
its  temperature  is  6°  ;  we  may,  however,  assume  that  its  mean  temperature 

during   the  experiment  is  ^        '.      The  vapour  M  after  condensation  has 


therefore  parted  with  a  quantity  of  heat  M 


(t-~) 


f,  while  the  heat 


disengaged  in  liquefaction  is  represented  by  yix.  The  quantity  of  heat 
absorbed  by  the  cold  water,  the  worm,  and  the  vessel  is  m{Q  —  t).  There- 
fore, 

/ 


M;i-+ J 


M  ('T-^^^y-  =  ;/<^-/), 


from  which  x  is  obtained.     Despretz  found  that  the  latent  heat  of  aqueous 
vapour  at  ioo°  is  540  ;  that  is,  a  pound  of  water  at  100°  absorbs  in  vaporising 
as  much  heat  as  would  raise   540  pounds  of  water  through  1°.     Regnault 
found  the  number  537,  and  Favre  and  Silbermann  538-8. 
As  in  the  case  of  the  latent  heat  of  water  we  may  say, 

Steam  at  100°  =  water  at  100°  + latent  heat  of  gasification. 

Bertholet  uses  the  veiy  convenient 
apparatus  represented  in  fig.  406,  for  deter- 
mining latent  heats  of  vaporisation.  The 
liquid  in  the  flask  D  is  heated  by  the  ring 
burner  B,  and  the  vapour  which  forms  passes 
through  the  tube  ab  into  the  serpentine  S> 
where  it  condenses  and  collects  in  the  bulb 
R.  These  are  contained  in  the  calorimeter 
C,  the  top  of  which  is  closed  by  a  wooden 
cover  HH  ,  and  a  layer  of  felt,  NN'  ;  they 
cut  off  any  heat  from  the  flask  D  and  from 
the  burner  B.  As  the  serpentine  SR  can 
be  detached  from  ab,  it  is  easy  to  deter- 
mine the  weight  of  the  distillate  ;  from  this, 
and  from  the  rise  in  temperature  of  the  water 
in  the  calorimeter,  the  latent  heat  can  be 
readily  calculated. 

In  the  conversion  of  a  body  from  the 
liquid  into  the  gaseous  state,  as  in  the 
analogous  process  effusion  (461),  one  part  of 
the  heat  is  used  in  increasing  the  temperature 
and  another  in  internal  -work.  For  vaporisation,  the  greater  portion  is  con- 
sumed in  the  internal  work  of  overcoming  the  reciprocal  attraction  of  the 
particles  of  liquid,  and  in  removing  them  to  the  far  greater  distances  apart 
in  which  they  exist  in  the  gaseous  state.  In  addition  to  this  there  is  the 
external  work — namely,  that  required  to  overcome  the  external  pressure, 
usually  that  of  the  atmosphere  :  and  as  the  increase  of  volume  in  vaporisa- 
tion is  considerable,  this  pressure  has  to  be  raised  through  a  greater  space. 
Vaporisation  may  take  place  without  having  external  work  to  perform, 
as  when  it  is  effected  in  \acuo  ;  but  whether  the  evaporation  is  under  a  high 


-463J 


Favre  and  Silba'inami  s  Calorimeter. 


439 


or  under  a  low  pressure,  on  the  surface  of  a  liquid  or  in  the  interior,  there 
is  always  a  great  consumption  of  heat  in  internal  work. 

463.  Pavre  and  Sllbermann's  Calorimeter. — The  apparatus  (fig.  407) 
furnishes  a  very  delicate  means  of  determining  the  calorific  capacity  of 
liquids,  latent  heats  of  evaporation,  and  the  heat  disengaged  in  chemical 
actions. 

The  principal  part  is  a  spherical  iron  reservoir,  A,  full  of  mercury,  of 
which  it  holds  about  50  pounds,  and  represents,  therefore,  a  volume  of  more 
than  half  a  gallon.  On  the  left  there  are  two  tubulures,  B,  in  which  are 
fitted  two  sheet-iron  tubes  or  iimffles,  projecting  into  the  interior  of  the  bulb. 
Each  can  be  fitted  with  a  glass  tube  for  containing  the  substance  experl- 


Fig.  407. 

mented  upon.  In  most  cases  one  muffle  and  one  glass  tube  are  enough  ; 
the  two  are  used  when  it  is  desired  to  compare  the  quantities  of  heat  pro- 
duced in  two  different  operations.  In  a  third  vertical  tubulure,  C,  there  is 
also  a  muffle,  which  can  be  used  for  determining  calorific  capacities  by 
Regnault's  method  (454),  in  which  case  it  is  placed  beneath  the  ?■  of  fig.  403. 
The  tubulure  d  contains  a  steel  piston  ;  a  rod  turned  by  a  handle,  ;?/, 
and  which  is  provided  with  a  screw  thread,  transmits  a  vertical  motion  to 
the  piston  ;  but,  by  a  peculiar  mechanism,  gives  it  no  rotatory  motion.  In 
the  last  tubulure  is  a  glass  bulb,  a,  in  which  is  a  long  capillary  glass  tube,  bo, 
divided  into  parts  of  equal  capacity. 


440 


On  Heat. 


[463- 


It  will  be  seen  from  this  description  that  the  mercury  calorimeter  is 
essentially  a  thermometer  with  a  very  large  bulb  and  a  capillary  stem  :  it 
is  therefore  extremely  delicate.  It  dififers,  however,  from  a  thermometer  in 
the  fact  that  the  divisions  do  not  indicate  the  temperature  of  the  mercury 
in  the  bulb,  but  the  number  of  thermal  units  imparted  to  it  by  the  substances 
placed  in  the  muffle. 

This  graduation  is  effected  as  follows  ; — By  working  the  piston  the 
mercuiy  can  be  made  to  stop  at  any  point  of  the  tube,  bo^  at  which  it  is 
desired  the  graduation  should  commence.  Having  then  placed  in  the  iron 
tube  a  small  quantity  of  mercury,  which  is  not  afterwards  changed,  a  thin 

glass  tube,  e,  is  inserted, 
which  is  kept  fixed  against 
the  buoyancy  of  the  mer- 
cury by  a  small  wedge 
not  represented  in  the 
figure.  The  tube  being 
thus  adjusted,  the  point 
of  a  bulb  tube  (see  fig. 
408)  is  introduced,  con- 
taining water  which  is 
raised  to  the  boiling 
point  :  turning  the  posi- 
tion of  the  pipette,  then, 
as  represented  in  n\  a 
quantity  of  the  liquid  flows 
into  the  test  tube. 

The  heat  which  is  thus  imparted  to  the  mercury  makes  it  expand  ;  the 
column  of  mercury  in  bo  is  lengthened  by  a  number  of  divisions,  which  we 
shall  call  n.  If  the  water  poured  into  the  test  glass  be  weighed,  and  if  its 
temperature  be  taken  when  the  column  bo  is  stationary,  the  product  of  the 
weight  of  the  water  into  the  number  of  degrees  through  which  it  has  fallen 
indicates  the  number  of  thermal  units  which  the  water  gives  up  to  the  entire 
apparatus  (447).  Dividing,  by  n,  this  number  of  thermal  units,  the  quotient 
gives  the  number,  «,  of  thermal  units  corresponding  to  a  single  division  of 
the  tube  bo. 

In  determining  the  specific  heat  of  liquids,  a  given  weight,  M,  of  the 
liquid  in  question  is  raised  to  the  temperature  T,  and  is  poured  into  the  tube 
C.  Calling  the  specific  heat  of  the  liquid  t",  its  final  temperature  ^,  and  71 
the  number  of  divisions  by  which  the  mercurial  column  bo  has  advanced,  we 
have 


Mt-(T  ■ 


«rt,  from  which  c 


M(T-^) 


The  boards  represented  round  the  apparatus  are  hinged  so  as  to  form  a 
box,  which  is  lined  with  eider-down  or  wadding,  to  prevent  any  loss  of  heat. 
It  is  closed  at  the  top  by  a  board,  which  is  provided  with  a  suitable  case, 
also  lined,  which  fits  over  the  tubulures  d  and  a.  A  small  magnifying  glass 
which  slides  along  the  latter,  enables  the  divisions  on  the  scale  to  be  read 


-464]  Examples.  441 

464.  Examples.— I.  What  weight  of  ice  at  zero  must  be  mixed  with  g 
pounds  of  water  at  20°  in  order  to  cool  it  to  5°  ? 

Let  M  be  the  weight  of  ice  necessary  ;  in  passing  from  the  state  of  ice 
to  that  of  water  at  zero,  it  will  absorb  80M  thermal  units  ;  and  in  order  to 
raise  it  from  zero  to  5'^,  5M  thermal  units  will  be  needed.  Hence  the  total 
heat  which  it  absorbs  is  80M  +  5M  =  85M.  On  the  other  hand,  the  heat 
given  up  by  the  water  in  cooling  from  20°  to  5°  is  9  x  (20-5)=  135.  Con- 
sequently, 

85M  =  135  ;  from  which  M  =  1-588  pounds. 

II.  What  weight  of  steam  at  100°  is  necessary  to  raise  the  temperature 
of  208  pounds  of  water  from  14°  to  32°  ? 

Let^  be  the  weight  of  the  steam.  The  latent  heat  of  steam  is  540°,  and 
consequently^  pounds  of  steam  in  condensing  into  water  give  up  a  quantity 
of  heat,  540^,  and  form^  pounds  of  water  at  100°.  But  the  temperature  of 
the  mixture  is  32^,  and  therefore  p  gives  up  a  further  quantity  of  heat 
p  (100- 32)  =  68/,  for  in  this  case  c  is  unity.  The  208  pounds  of  water  in 
being  heated  from  14°  to  32°  absorb  208(32  -  14)  =  3744  units.     Therefore 

540/ +  68/ =  3744  ;  from  which/ =  6-58 1  pounds. 


442  On  Heat.  [465- 


CHAPTER   X. 

STEAM    ENGINES. 

465.  Steam  Eng-ines. — Steam  engines  are  machines  by  which  heat 
energy,  obtained  by  the  combustion  of  some  fuel,  is  turned  into  mechanical 
work,  aqueous  ^•apour  being  used  as  a  working  fluid  for  effecting  the  trans- 
formation. In  all  but  a  few  very  exceptional  cases  the  mechanical  means 
used  for  the  transformation  of  the  one  form  of  energy  into  the  other  are  as 
follows  : — the  heat  of  combustion  is,  as  far  as  possible,  imparted  to  water  in 
a  closed  vessel  called  a  boiler  ;  the  water  is  thereby  converted  into  steam, 
occupying  an  enormously  greater  volume,  and  this  steam  is  allowed  to  pass 
from  the  boiler  as  fast  as  it  is  formed,  and  to  act  alternately  on  the  two  sides 
of  a  movable  piston  working  backwards  and  forwards  in  a  cylinder.  As  soon 
as  the  piston  has  been  pushed  to  either  end  of  the  cylinder  by  the  incoming 
steam  acting  on  one  side  of  it,  the  communication  between  that  side  and  the 
boiler  is  shut  off,  and  another  communication  opened  either  to  a  condenser 
or  to  the  atmosphere.  In  either  case  the  steam  rushes  out  of  the  cylinder 
and  the  pressure  against  the  piston  falls,  so  that  it  can  be  pushed  back  by 
fresh  steam  from  the  boiler  acting  on  its  opposite  side.  If  the  purpose  of 
the  engine  is  merely  to  work  pumps,  or  any  other  apparatus  requiring  only  a 
reciprocating  motion,  a  rod  from  the  piston  can  be  connected  directly,  or 
through  a  lever,  to  the  pump  to  be  worked.  If,  however,  as  in  a  majority  of 
cases,  the  engine  has  to  drive  something  having  a  rotary  motion,  a  simple 
mechanism  is  used  to  change  the  reciprocating  motion  of  the  piston  into  the 
rotation  of  a  crank.  In  this  change  itself  there  is  no  loss  of  work  or  energy 
(471),  the  work  of  the  steam  on  the  piston  being  exactly  equal  to  the  work 
done  at  the  rotating  crank-pin,  minus  only  the  lost  work  spent  in  overcoming 
the  friction  of  the  joints  of  the  mechanism. 

We  shall  first  consider  the  boiler,  or  apparatus  for  generating  steam,  and' 
then  the  engine  itself. 

466.  Steam  boiler. — Figs.  409  and  410  show  one  of  the  forms  of  boiler 
most  commonly  used  in  this  country  for  supplying  steam  to  stationary  engines. 
This  type  of  boiler  is  called  Cornish,  having  been  first  used  for  the  pumping 
engines  in  Cornwall.  Fig.  409  shows  a  longitudinal  section  of  the  boiler  and 
the  brick  flues  in  which  it  is  set,  and  fig.  410  shows  on  the  left  a  half- front 
view  of  the  boiler  and  on  the  right  a  half  cross  section.  The  boiler  consists 
of  an  outer  cylindrical  shell  A  of  wrought  iron  or  steel  plates  riveted  together,, 
and  a  smaller  internal  flue  or  furnace  B.  The  latter  is  open  at  both  ends, 
and  is  crossed  by  a  series  of  vertical  tubes  C,  called  Galloway  tubes,  which 
allow  the  water  to  circulate  from  the  lower  to  the  upper  part  of  the  boiler. 
The  fire  is  placed  on  a  grate  D  in  the  front  part  of  the  flue  and  ending 
in  a  ■  firebrick  ^?7Vi^^  over  which  the  gases  have  to  pass.     These  hot  gases 


-466] 


Steam  Boiler. 


443 


find  their  way  past  the  tubes  to  the  back  of  the  boiler  and  then  are  com- 
pelled to  diverge  sideways  and  return  by  the  side  flues  K  to  nearly  the  front 
of  the  shell  where  the  flues  are  diverted  downwards,  as  shown  in  fig.  410, 
and  thence  they  return  by  the  lower  flue  L  to  the  chimney  M.     By  thus 


,-^ 

-^^- 


WATCR  LIME 


QODOQH 


^ 


^. 


Fig.  4og. 


encircling  the  boiler  with  flues  it  is  endeavoured  to  get  all  the  heat  possible 
from  the  gases  before  they  are  allowed  to  pass  away  up  the  chimney.  The 
principal yf/Z/V/o-j-  or  inoimthtgs  of  the  boiler  are  indicated  in  the  figures  and 
are  as  follows  :  G  is  a  dome  on  which  stands  the  stop-valve  N  through  which 
the  steam  is  carried  to  the  engine.  The  object  of  the  dome  is  to  take  the 
steam  from  a  point  as  far  away  from  the 
water  line  as  possible,  so  as  to  dry  it.  P  is 
a  safety  valve.,  held  down  on  its  seat  by  the 
action  of  a  weighted  lever,  and  so  adjusted 
that  as  soon  as  the  pressure  of  steam  reaches 
its  intended  maximum  and  tends  to  rise 
beyond  it,  the  valve  is  lifted  and  the  steam 
rushes  away  into  the  air.  Q  is  a  manhole 
door  by  which  access  is  had  to  interior  of  the 
boiler,  when  it  is  empty  and  out  of  use,  for 
cleaning  and  repair.  R  is  a  pressure  gauge 
or  indicator,  standing  in  front  of  the  shell, 
showing,  by  a  hand  working  in  front  of  a  dial 
plate,  the  'boiler  pressure'  or  amount  which 
the  pressure  of  steam  inside  the  boiler  ex- 
ceeds that  of  the  atmosphere  surrounding  it.  S  is  a  water  gatige,  a  glass 
tube  connected  at  top  and  bottom  to  the  boiler,  its  upper  end  to  the  steam 
space,  and  the  lower  end  to  the  water  space.  The  water  stands  in  the  glass 
tube  at  the  same  level  as  in  the  boiler,  and  the  fireman  can  see  at  a  glance 
whether  it  is  at  the  right  height.  This  matter  is  of  great  importance, 
because  an  accidental  fall  of  water-level  is  a  frequent  cause  of  boiler  explo- 
sions. If,  for  instance,  the  water  fell  so  low  as  to  leave  the  top  of  the  furnace 
B  uncovered,  the  plates  would  get  red-hot  and  soften  so  much  as  to  collapse 


Fig.  41 


444 


On  Heat. 


[466- 


under  the  action  of  the  steam  pressure,  with  consequences  that  might  be 
most  serious. 

In  marine  boilers,  when  it  is  of  the  greatest  importance  to  get  as  much 
heating  surface  as  possible  into  a  small  space,  and  similarly  in  the  locomotive 
boiler  to  be  presently  described,  the  hot  gases  after  leaving  the  furnace  are 
made  to  pass  through  a  number  of  small  tubes  instead  of  one  large  one  as  in 
fig.  409.     Such  boilers  are  called  multiticbidar  boilers. 

Of  late  years  the  shells  of  large  boilers  have  frequently  been  made  of 
'  mild  steel,'  produced  by  the  Bessemer  or  Siemens-Martin  processes,  rather 
than  of  wrought  iron.  In  locomotive  boilers,  where  the  combustion  is  very 
rapid  and  intense,  the  fire-boxes  are  frequently  made  of  copper,  a  much 
better  conductor  of  heat  than  either  iron  or  steel. 

467.  Cornish  eng-ine. — Fig.  411  shows  the  oldest  of  all  the  types  of 
engines  still  in  use,  the  Cornish  piunping  engine.,  which  is  worth  examina- 
tion both  for  its  historical  interest  and  on  account  of  the  special  way  in 
which  it  works.  (In  the  figure  all  details  except  those  absolutely  necessary 
to  illustrate  the  action  of  the  engine  are  omitted.)    The  engine  has  a  vertical 


Fig.  411. 

cylinder  A  (often  of  very  great  size,  and  with  as  much  as  10  or  11  ft.  stroke), 
in  which  works  a  piston  P,  whose  rod  is  connected  by  a  chain  to  a  sector  on 
the  end  of  a  beam  B.  Beside  the  cylinder  is  a  chamber  C  containing  the 
valves  for  admitting  and  discharging  steam,  whose  mode  of  working  will  be 
presently  described.     At  the  further  end  of  the  beam  a  second  sector  is 


-467]  Cornish  Engine.  445 

connected  with  the  pump-rod,  at  the  upper  end  of  which  is  placed  a  hea\y 
counterweight  Q.  Below  the  cylinder  a  pipe  AI  leads  to  a  chamber  N  called 
the  condejiser^  into  which  a  jet  of  water  from  the  tank  in  which  it  stands 
continually  plays.  The  condenser  in  its  turn  is  connected  with  a  pump 
called  an  air-pump,  worked  from  the  beam  by  the  rod  E,  and  fitted  with 
suction  and  discharge  valves,  and  valves  in  its  piston  in  the  usual  way. 

We  can  follow  the  working  of  the  engine  easily  by  supposing  the  piston 
to  start  at  the  top  of  its  stroke.  The  valves  are  then  in  the  position  shown, 
ni  open,  n  and  0  closed.  Steam  passes  from  the  boiler  through  the  pipe  T 
to  the  top  of  the  piston,  and  forces  it  down  against  the  small  pressure  of  the 
steam  below  it,  this  steam  escaping  into  the  condenser  through  the  valve  o 
and  the  pipe  M.  The  pump-rods  or  pit  work.,  and  the  weight  Q,  are  thus 
lifted  to  the  top  of  their  stroke.  When  the  piston  arrives  at  the  bottom  of 
its  stroke  the  valves  w  and  0  are  shut  and  n  is  opened.  This  allows  free 
communication  between  the  two  sides  of  the  piston,  and  so  puts  it  into 
equilibrium.  The  counter-weight  Q,  together  with  the  pump-rods,  is  made 
somewhat  heavier  than  the  piston  and  rod  plus  the  whole  weight  of  the 
column  of  water  to  be  hfted.  It  therefore  falls  slowly  (the  whole  affair  thus 
becommg  an  Attwood's  machine  ij"])  on  an  enormous  scale),  and  forces 
up  the  water  through  the  pumps.  As  soon  as  the  piston  has  once  more 
got  to  the  top  of  its  stroke,  by  which  time  of  course  all  the  steam  has  been 
transferred  to  its  under  side,  the  position  of  the  valves  is  again  reversed, 
and  the  piston  once  more  begins  to  fall.  The  steam  below  the  piston  is 
suddenly  put  into  communication  with  the  condenser  N,  into  which  a  jet  of 
cold  water  is  always  playing.  It  is  therefore  reduced  in  temperature  almost 
instantaneously,  much  of  it  is  condensed  into  water,  and  the  rest,  which  still 
fills  the  space  below  the  piston,  is  necessarily  reduced  to  a  pressure  of  only 
about  3  pounds  per  square  inch  or  about  \  of  an  atmosphere.  As  the  pres- 
sure of  the  steam  coming  direct  from  the  boiler  in  such  engines  is  often  50 
pounds  per  sq.  inch  above  that  of  the  atmosphere,  it  follows  that  the  differ- 
ence of  pressure  on  the  two  sides  of  the  piston  in  such  a  case,  is  50  -t-  15  -  3 
=  62  pounds  per  square  inch,  and  it  is  this  difference  of  pressure  which 
compels  the  piston  to  move  downwards  and  lift  all  the  weight  at  the  other 
end  of  the  beam.  The  condensed  steam  and  the  condensing  water  fall 
together  at  the  bottom  of  the  condenser,  and  are  continually  removed  (along 
with  the  uncondensed  steam  and  any  air  that  may  be  present)  by  the  air 
pump.,  which  is  a  simple  lift  pump  with  a  valve  in  its  piston  (216). 

In  all  modern  Cornish  engines  the  beams  are  of  iron  and  the  sector  and 
chains  are  replaced  by  an  arrangement  of  iron  links  forming  ?i.  pai-allel  motio7t 
which  it  is  not  necessary  here  to  describe.  The  simple  arrangement  for 
working  the  valves,  shown  in  outline  in  the  figure,  is  also  replaced  by  a  much 
more  complicated  apparatus  in  which,  by  means  of  cataracts.,  any  required 
length  of  pause  can  be  made  between  the  strokes  of  the  engine,  a  matter 
which  is  sometimes  of  importance  in  heavy  pumping  work.  It  will  be 
noticed  that  by  the  peculiar  single-acting  method  of  working  adopted  in 
the  Cornish  engine,  the  velocity  of  the  down  stroke  (also  called  the  steam 
stroke.,  or  the  indoor  stroke)  depends — other  things  being  equal — upon  the 
steam  pressure,  but  the  velocity  of  the  up  stroke  {eqiiilibriuni  or  outdoor 
stroke)  depends  solely  on  the  overplus  weight  put  on  the  outer  end  of  the 


446 


On  Heat. 


[467- 


beam.     In  this  way  a  slow  and  quiet  upward  motion  can  be  given  to  the 
water,  no  matter  how  quickly  the  steam  may  move  the  piston. 

468.  Ordinary  horizontal  engine.- — The  engines  now  most  largely 
used  in  factories  for  driving  machinery  differ  altogether  in  their  action  from 
the  Cornish  engine.  In  them  the  cylinder  is  generally  horizontal,  and  the 
crank  is  driven  through  a  connecting  rod  only,  without  the  intervention  of 
any  beam.     Such  an  engine  is  shown  in  fig.  412.     Here  A  is   the   steam 


Fig.  4 


cylinder,  B  the  valve  chest,  or  chamber  in  which  works  the  valve  whose  mode 
of  action  is  described  in  the  next  article.  D  is  the  main  shaft,  on  the  inner 
end  of  which  is  the  crank  driven  by  the  connecting  rod  E.  C  is  an  eccetitric 
(fig.  414),  which  works  the  valve  by  the  rod  N.  F  is  ?i  governor  controlling 
the  admission  of  steam  to  the  cylinder  by  the  valve  H.  M  is  the  bedplate 
or  frame  of  the  engine,  and  L  the  flywheel. 

A  few  words  are  necessary  about  the  governor.  This  apparatus,  an 
invention  of  James  Watt's,  consists  of  two  weighted  arms  hinged  at  the  top, 
which  fly  outward  when  the  speed  of  rotation  is  increased  and  drop  together 
when  it  is  reduced.  The  outward  or  inward  motion  of  the  arms  is  caused 
by  a  simple  arrangement  to  turn  the  spindle  G  and  so  to  close  or  open  the 
valve  H,  which  admits  steam  through  K  to  the  cylinder.  In  this  way  the 
engine  automatically  controls  its  own  speed  (471). 

469.  Distribution  of  the  steam.  Slide  valves. — Figs.  413  and  414 
show  details  as  to  the  working  of  the  valve  and  the  chstribution  of  the  steam 
in  the  engine  just  described.  The  former  is  a  longitudinal  section  of  the 
cylinder  shown  m  fig.  412.  A  is  the  cylinder  itself,  B  the  piston,  C  the 
piston-rod,  D  the  stuffing-box  through  which  the  piston  passes  steam-tight. 
It  will  be  seen  that  deport  or  passage  L  communicates  between  each  end  of 
the  cylinder  and  the  surface  on  which  the  valve  works,  or  valve  face.  On 
this  face,  and  between  the  two  steam-ports,  comes  a  third  port  M,  communi- 
cating directly  with  the  atmosphere  or  with  a  condenser  as  the  case  may  be. 
The  valve  G  is  shaped  in  section  something  like  an  irregular  D,  and  is  often 


-469] 


Distribution  of  Steam.     Slide    Valves. 


447 


called  a  '  D '  valve  in  consequence.  It  is  moved  continuously  backwards 
and  forwards  upon  the  valve  face  by  the  valve  rod  H  working  in  the  stuffing- 
box  K.  When  in  the  position  shown  in  the  figure  the  steam  enters  by  F, 
and  passes  into  the  left-hand  end  of  the  cylinder  (past  the  edge  of  the 
valve)  and  pushes  the  piston  from  left  to  right.  The  steam  at  present  in 
the  cylinder  (as  shown  by  the  arrows)  passes  out  at  L,  and  through  the 
under  part  of  the  valve  G  to  the  exhaust  port  M.  As  the  piston  moves  on, 
the  valve  at  first  moves  in  the  same  direction,  opening  the  port  a  little  wider, 
then  gradually  moves  back  again  and  closes  the  admission  port  altogether. 


The  point  at  which  this  occurs  is  called  the  point  oi  cut  off.  No  more  steam 
is  allowed  to  enter  the  cylinder  for  that  stroke,  the  piston  being  pushed 
forward  by  the  pressure  of  the  elastic  steam  expanding  behind  it.  By  the 
time  the  piston  has  got  to  the  end  of  its  stroke,  the  position  of  the  valve  is 
just  reversed  from  that  in  which  it  is  shown,  and  steam  passes  into  the 
cylinder  through  the  right-hand  port,  driving  the  piston  from  right  to  left, 
while  the  steam  which  has  already  done  duty  in  the  left-hand  end  of  the 
cylinder  passes  away,  in  its  turn,  through  the  exhaust. 

The  eccentric  from  which  the  valve  receives  its  motion  (lettered  C  in  fig. 
412)  is  shown  in  detail  in  fig.  414.  Here  D  is  the  crank-shaft  and  A  a  disc 
(solid  or  ribbed)  fixed  eccentrically  on  it  so  as  to  revolve  with  it.  Encircling 
this  disc  (which  is  the  eccentric)  is  a  strap  or  ring  B  (made  in  two  pieces  for 
the  sake  of  getting  on  and  off),  rigidly  connected  with  a  rod  C,  which  is 
coupled  by  a  pin  to  the  valve-rod  E.  In  each  revolution  of  the  eccentric 
the  valve-rod  is  moved  backwards  and  forwards  through  a  space  equal  to 
twice  the  eccentricity  of  the  eccentric,  or  distance  between  the  centres  of  D 
and  of  A.  The  eccentric  is  thus  equivalent  exactly  to  a  crank  having  a 
radius  equal  to  its  eccentricity.  It  is  used  instead  of  a  crank  because  it 
does  not  require  any  gap  to  be  left  in  the  shaft,  as  a  crank  would  do,  but 
allows  it  to  be  carried  continuously  on. 

In  locomotive  or  marine  engines  two  eccentrics  are  commonly  used,  one 
so  placed  as  to  give  the  valve  the  right  motion  when  the  shaft  rotates  in 
one  direction,  and  one  rightly  placed  for  the  other.  By  apparatus  called 
reversing  gear  either  one  or  the  other  can  be  caused  to  move  the  valve,  so 
that  the  engine  can  be  made,  at  pleasure,  to  turn  the  shaft  in  one  or  the 
other  direction. 


448 


On  Heat. 


[470- 


470.  a^ocomotives. — Locomotive  engines,  or  simply  locomotives,  are 
steam  engines  which,  mounted  on  a  carriage,  propel  themselves  by  trans- 
mitting their  motion  to  wheels.  The  whole  machine,  fig.  415,  boiler  and 
engine,  is  fixed  to  a  wrought-iron  frame,  which,  therefore,  is  made  strong 


enough  to  carry  the  whole  weight,  and  which  in  turn  transmits  that  weight 
to  the  axle-boxes  (or  bearings  in  which  the  axles  turn),  by  means  of  springs, 
and  thence  through  the  wheels  to  the  rails.  The  boiler  is  of  a  special  type, 
adopted  in  order  to  get  the  greatest  possible  heating  surface  in  a  very  limited 


-470]  Locomotives.  449 

space.  It  consists  of  three  parts — \h.&  fire-box,  barrel,  and  s7noke-box.  The 
fire-box,  in  the  left  of  the  engraving,  is  generally  a  more  or  less  rectangular 
box,  with  a  flat  top,  placed  inside  a  second  box  of  somewhat  similar  shape, 
but  with  a  semi-cylindrical,  or,  as  in  the  figure,  domed  top.  In  the  inner 
fire-box  are  the  fire-bars,  on  which  the  fuel  is  placed  through  a  door  in  front. 
The  space  between  the  inner  and  outer  boxes  is  filled  with  water  to  a  height 
considerably  over  the  top  of  the  inner  one,  and  communicates  freely  with  a 
long  cylindrical  barrel,  closed  at  the  other  end  by  the  smoke-box.  This 
barrel,  which  forms  the  main  bulk  of  the  boiler,  is  filled  with  water  to  within 
nine  or  ten  inches  of  its  upper  side.  It  is  traversed  from  end  to  end  by  a 
great  number  of  small  tubes  (about  i^  inch  in  diameter)  which  communicate 
with  the  inner  fire-box  at  the  one  end,  and  with  the  smoke-box  at  the  other. 
They,  therefore,  are  entirely  immersed  in  the  water  from  end  to  end.  The 
gases  of  combustion,  formed  in  the  inner  fire-box,  pass  through  these  tubes 
to  the  smoke-box,  and  thence  up  the  chimney,  and  impart  most  of  their  heat 
to  the  water  as  they  pass  along.  There  are  two  steam  cylinders,  one  on  each 
side  of  the  frame,  each  one  with  its  piston  and  connecting  rod,  etc.,  being 
simply  an  ordinary  high-pressure  horizontal  engine.  Their  exhaust  steam 
is  discharged  through  a  blast  pipe  into  a  nozzle  inside  the  chimney  near  its 
base,  and  this  serves  to  excite  the  fierce  draught  which  is  required  in  order 
that  the  necessary  heat  may  be  developed  by  the  very  small  furnace.  The 
two  cylinders  work  cranks  at  right  angles  to  each  other,  so  that  one  may  be 
in  full  action  when  the  other  is  at  its  dead  point. 

A  locomotive  such  as  that  shown  in  the  figure  is  called  an  outside 
cylinder  engine,  on  account  of  the  position  of  its  cylinders.  In  England 
many  engines  have  cylinders  placed  inside  the  frames,  which  are  then  called 
inside  cylinder  locomoti\'es.  In  express  engines  the  cylinders  frequently 
dri\e  only  one  very  large  pair  of  wheels,  as  is  shown  in  the  figure.  These 
are  called  driving  -wheels,  those  on  the  front  axle  being  leading  wheels  and 
on  the  rear  axle  trailing  wheels.  In  the  case  of  goods  engines,  however  (as 
well  as  in  many  other  instances),  when  less  speed  but  a  greater  pull  is  re- 
c[uired,  two  or  more  pairs  of  wheels  of  the  same  diameter  are  connected 
together  by  coupling  rods,  so  that  two  or  more  axles  may  be  directly  or 
indirectly  actually  dri\-en  by  the  engine.  Such  engines  are  called  coupled 
engines. 

The  action  of  the  engine  upon  the  wheels  may  cause  them  either  to  slip 
round  on  the  rails  (in  which  case  the  engine,  of  course,  does  not  move 
onwards)  or  to  roll  on  them  in  the  usual  way.  To  prevent  slipping  occurring 
it  is  necessary  to  make  the  friction  between  the  wheels  and  the  rails  as 
great  as  possible.  This  is  done  by  making  as  large  a  proportion  of  the 
whole  weight  as  possible  rest  on  the  driving  or  the  coupled  wheels,  and  also 
— when  bad  weather  causes  the  rails  to  be  greasy  or  otherwise  unusually 
slippery — by  increasing  the  coefficient  of  friction  (47)  between  the  wheels 
and  the  rails  by  pouring  sand  on  the  latter.  All  locomotives  are  furnished 
with  a  sand-box  for  this  purpose. 

The  steam  pressure  in  locomotives  is  greater  than  that  commonly  used 
in  any  other  engines,  being  often  120  to  130  lbs.  per  square  inch  above  the 
atmosphere.  In  marine  engines  70  to  80  lbs.  is  often  used,  in  stationary 
engines  seldom  cpite  so  much. 

G  G 


450  On  Heat.  [471- 

The  following  is  an  explanation  of  the  reference  letters  in  fig.  415  : — A, 
the  main  steam-pipe,  conveying  steam  to  the  cylinder  F,  in  which  works  a 
piston  P,  driving  the  crank  M  through  the  connecting  rod  K,  rr  are  the 
piston-rod  guides,  V  the  stuffing-box.  The  exhaust  steam  is  discharged 
through  the  pipe  E.  (It  will  be  remembered  that  the  cylinder  and  all  this 
gear  are  duplicated  on  the  other  side  of  the  engine.)  D  Z  is  the  outer  fire- 
box and  X  the  barrel  of  the  boiler,  both  covered  with  felt  and  wood  or  sheet 
iron  to  prevent  loss  of  heat  by  radiation.  The  small  tubes  are  seen  at  a, 
Y  is  the  smoke-box,  and  Q  the  chimney  or  funnel.  TT  are  the  springs 
which  transmit  the  weight  of  the  frame  to  the  axle-boxes.  Of  the  smaller 
details,  G  I  is  the  arrangement  for  closing  or  openmg  the  steam-admission 
\'alve,  'BbC  the  reversing  gear,  RR  feed-water  pipes,  N  coupling  rod  for 
attaching  tender  and  rest  of  train,  ci  safety  valves,  g  whistle,  ni  steps,  tt 
water  gauge,  /  cocks  for  blowing  water  out  of  cylinders,  H  cock  for  blowing 
out  boiler  when  necessary. 

It  is  perhaps  hardly  necessary  to  explain  that  the  breaking  away  of  part 
of  the  fire-box,  cylinder,  etc.,  is  done  in  the  drawing  only  for  the  sake  of 
showing  clearly  the  internal  construction. 

471.  Various  kinds  of  steam  eng-ine. — Three  types  of  steam  engine 
have  been  described  ;  the  Cornish  engine,  the  ordinary  horizontal  engine, 
and  the  locomotive  engine.  Others  ought  to  be  mentioned,  although  they 
cannot  be  here  described  in  detail.  Compound  engines  are  those  in  which 
the  steam  is  first  used  in  the  ordinary  way  in  one  cylinder  and  then  trans- 
ferred— of  course  at  a  comparatively  low-  pressure — to  another  cylinder  and 
used  in  it  before  being  sent  away  to  the  condenser.  This  type  is  practically 
uni\ersal  for  marine  purposes,  and  is  very  common  for  stationary  engines. 
Its  main  advantage  is  a  thermodynamic  one.  In  an  ordinary  engine  the 
cylinder  walls  are  exposed  alternately  to  the  hot  steam  from  the  boiler 
and  the  cool  vapour  passing  to  the  condenser.  The  latter  so  reduces  the 
temperature  of  the  iron,  that  when  the  first  rush  of  fresh  steam  comes  into 
the  cylinder,  much  of  it  is  immediately  condensed  on  the  cool  metal,  and  an 
enormous  quantity  of  heat  is  thereby  lost.  By  passing  the  steam  through 
an  intermediate,  or  loiu-pressiire^  cylinder  on  its  way  to  the  condenser,  the 
sides  of  the  first  or  Mgh-p?'essiire  cylinder  are  never  exposed  to  condenser 
temperature,  but  only  to  that  of  the  steam  as  it  passes  to  the  low-pressure 
cylinder  ;  they  therefore  are  not  so  much  cooled,  and  the  loss  of  steam  by 
condensation  on  them  is  very  much  reduced.  There  is  no  mechanical  gain, 
as  has  sometimes  been  stated,  in  the  use  of  two  cylinders  instead  of  one. 

Sometimes  the  cylinder  of  an  engine  is  inclosed  in  a  second,  slightly 
larger,  cylinder,  and  fresh  steam  at  boiler  pressure  admitted  to  the  annular 
space  so  formed  outside  the  working  cylinder.  The  object  of  this  is  to  re- 
duce still  further  the  condensation  in  the  cylinder  just  alluded  to.  Such  an 
engine  is  said  to  be  steam-jacketed. 

A  surface-condensing  engine  is  one  in  which  the  steam  is  condensed  by 
contact  with  the  surface  of  a  number  of  small  tubes  through  which  cold 
water  is  kept  continually  circulating  without  being  itself  actually  mixed  with 
the  condensing  water.  By  this  arrangement  the  condensed  steam  is  kept 
by  itself,  and  being  distilled  water  it  can  be  used  very  advantageously  to  feed 
the  boiler  again.     Compound  marine  engines  are  almost  invariably  surface- 


-472]  Work  of  an  Engine.     Horse-poiver.  451 

condensing.  In  this  case  the  air  pump  only  takes  away  the  condensed 
steam,  a  separate  pump,  called  a  circulating  pump,  being-  used  to  force  the 
condensing  water  through  the  tubes. 

Engines  without  any  condenser,  like  that  shown  in  fig.  414,  in  which  the 
steam  is  exhausted  directly  into  the  atmosphere  after  it  has  done  its  work, 
are  often  called  //^^//-/r^j'«/';r  engines,  but  high  pressures  (of  80  to  90  pounds 
per  square  inch)  are  now  frequently  used  in  condensing  engines,  so  that  the 
name  may  be  somewhat  misleading. 

In  such  an  engine  as  is  shown  in  fig.  414  we  have  seen  that  the  governor 
keeps  the  speed  constant,  by  closing  or  opening  an  exterior  valve  through 
which  the  steam  passes  on  its  way  to  the  main  valve.  An  artificial  resist- 
ance is  in  this  way  opposed  to  the  passage  of  the  steam,  by  increasing 
which  the  pressure  can  be  reduced,  and  therefore  the  work  done  by  the 
steam,  so  that  the  engine  will  not  run  too  fast  if  the  resistance  to  its  motion 
be  diminished  (as  by  the  disconnecting  of  some  of  the  machines  it  is  driving, 
etc).  The  actual  weight  of  steam  passing  into  the  cylinder  at  each  stroke 
remains  unchanged,  but  the  amount  of  useful  work  the  steam  can  do  is 
diminished  artificially  by  giving  it  some  useless  work  to  do  in  addition,  in 
forcing  its  way  through  a  constricted  passage.  This  is  now  known  to  be  a 
wasteful  way  of  controlling  speed.  In  modern  engines,  therefore,  the 
governor  is  frequently  made  to  act  by  regulating  the  quantity  of  steam  ad- 
mitted by  each  stroke,  and  thus  making  the  consumption  of  steam  as  nearly 
as  possible  proportional  to  the  work  done.  Engines  so  arranged,  of  which 
the  Corliss  engine  is  one  of  the  best-known  examples,  are  said  to  be  fitted 
with  automatic  cut-off  gear. 

There  is  a  popular  misconception,  that  somehow  or  other  work  is  lost  in 
an  engine  of  the  ordinary  type  between  the  piston  and  the  crank,  the  latter 
receiving  less  work  than  is  done  on  the  former  in  consequence  of  the  nature 
of  the  mechanism  connecting  them.  It  is  probably  unnecessary  to  point 
out  here  the  fallacy  of  this  notion,  but  it  has  received  sufficient  acceptance 
to  lead  to  the  invention  of  a  host  oi  rotary  engines,  it  which  it  is  endeavoured 
to  obtain  the  desired  rotary  motion  in  a  somewhat  more  direct  fashion, 
Reuleaux  has  shown  that  in  almost  every  case  the  mechanisms  used  in  the 
rotary  engines  are  the  same  as  those  of  ordinary  engines,  although  disguised 
in  form,  so  that  the  idea  of  mechanical  advantage  is  doubly  a  mistake,  while 
in  almost  every  case  the  rotary  engines  possess  such  grave  mechanical 
defects  that  none  of  them  have  practically  come  into  use. 

472.  "Work  of  an  eng-ine.  Horse-power. — The  unit  of  work  by  which 
the  performance  of  an  engine  is  measured  is  in  this  country  always  the  foot- 
pound. The  number  of  foot-pounds  of  work  done  by  the  engine  in  any 
given  time  is  equal  to  the  average  effective  pressure  upon  its  piston  during 
that  time,  multiplied  by  the  total  distance  through  which  the  piston  has 
moved  under  that  pressure.  By  average  effective  pressure  is  meant  the 
average  value  of  the  difference  between  the  pressures  on  its  two  sides. 
Taking  the  time  as  one  minute,  this  quantity  of  work  in  foot-pounds  is 
equal  to  : — 

Area  of  piston  x  jnean  intensity  of  pressure  on  piston  x  length  of  stroke 
X  number  of  strokes  per  minute. 

The  stroke  must  be  taken  in  feet.     If  the  area  is   in  square  feet,  the 

G  G  2 


452  On  Heat.  [473- 

pressure  must  be  in  pounds  per  square  foot  :  if  the  area  is  in  square  inches, 
the  pressure  must  be  in  pounds  per  square  inch.  If  the  strokes  are  double 
strokes,  each  corresponding,  that  is,  to  one  whole  revolution  of  the  shaft,  the 
length  of  stroke  must  be  multiplied  by  2.  To  find,  for  example,  the  work 
done  in  one  minute  by  an  engine  with  cylinder  16  inches  diameter  and  24 
inches  stroke,  making  50  (double)  strokes  per  minute  with  a  mean  pressure 
of  52  pounds  per  square  inch,  we  have 

(8-  X  3-1416)  ;<  52  X  (  "'^  "  "  j  X  50  =2,09 1,000  ft. -lbs. 

The  rate  at  which  an  engine  does  work  is  often  measured  in  /lorse-porue?-  of 
33,000  ft.-lbs.  per  minute,  an  arbitrary  unit  supposed  to  represent  the  maxi- 
mum rate  at  which  work  could  actually  be  done  by  a  horse.     In  the  case 

supposed  the  horse-power  would  be  "'  ^  ' =  63-4. 

33,000 

On  the  Continent  the  unit  of  work  is  a  kilogrammetre,  which  is  very 
closely  equal  to  y\  ft.-lbs.  The  horse-power  used  abroad,  of  75  kilo- 
grammetres  per  second,  is  nearly  2  per  cent,  smaller  than  that  in  use  in  this 
country. 

473.  Indicator.  Brake. — By  the  expression  work  done  by  au  ciigitie  we 
may  mean  either  of  two  things,  viz. — the  total  work  done  by  the  engine,  or 
what  is  called  its  useful,  or  effective,  work.  The  total  work  is  the  actual  work 
done  by  the  steam  on  the  piston  and  obtained  by  calculation,  as  described 
in  the  last  paragraph.  The  useful  work  is  what  remains  of  this  total  after 
deduction  has  been  made  of  the  work  necessary  to  drive  the  engine  itselt 
against  its  own  frictional  resistances.  The  total  work  of  an  engine  is  mea- 
sured by  means  of  an  apparatus  called  an  indicato7%  in\ented  by  Watt,  of 
which  fig.  414  shows  one  of  the  most  recent  forms  (Richard's)  omitting  a 
number  of  constructional  details.  The  steam-engine  indicator  consists  of  a 
small  cylinder  A,  half  a  square  inch  in  area,  in  which  works  a  piston  B,  the 
under  side  of  which  can  be  put  into  full  communication  with  the  cylinder 
of  the  engine  by  opening  the  cock  C.  Between  the  top  side  of  the  piston 
and  the  under  side  of  the  cylinder-cover  is  a  spiral  spring.  The  motion 
of  the  piston-rod  is  transferred  to  a  parallel  motion  DD,  and  so  causes  a 
point  E  to  move  in  a  straight  line  up  and  down,  its  stroke  being  about 
four  times  as  great  as  that  of  the  small  piston.  The  indicator  is  fixed  on  to 
the  cylinder  of  the  steam  engine  near  one  end,  so  that  when  the  cock  C  is 
opened,  there  is  the  same  pressure  of  steam  on  the  indicator  piston  as  on  the 
engine  piston.  This  pressure  forces  up  the  piston,  and  the  amount  of  com- 
pression of  the  spring  so  caused  is  proportionate  to  the  pressure  causing  it. 
The  upward  motion  of  E,  therefore,  is  proportional  to  the  steam  pressure. 
In  front  of  E  is  a  vertical  drum  F  on  which  a  strip  of  paper  can  be  fixed, 
and  this  drum  is  caused  to  rotate  about  its  axis  by  attaching  the  cord  G 
to  any  suitable  part  of  the  engine.  The  paper  thus  moves  horizontally 
under  the  pencil,  with  a  motion  proportional  to  the  stroke  of  the  engine, 
while  the  pencil  moves  up  and  down  on  the  paper  with  a  motion  proportional 
to  the  steam  pressure  on  the  piston.  The  two  motions  occurring  simul- 
taneously, the  pencil  traces  on  the  paper  a  curv'e  whose  horizontal  and 
vertical  ordinates  are  proportional  to  the  two  quantities  just  named,  and 


-473]  Indicator.     Brake.  453 

whose  area  is  therefore  proportional  to  the  product  of  these  quantities,  or, 
which  IS  the  sime  thing,  to  the  work  done  by  the  piston  as  defined  in  the 
last  paia^aiph      The  lui\  e  ib  c  illed  an  indicator  card,  or  indicator  diagram. 


A    B 


Fig.  417. 


B 

■* 

^^.._ 

■^ 



" "~  C 

PI 

\p 

J^ 

■^ 

Fig.  416.  Fig.  41S. 

and  while  its  whole  area  shows  the  whole  work  done  by  the  steam,  \X.s  form 
shows  the  engineer  what  is  happening  within  the  cylinder  at  each  point  of 
the  stroke,  which  he  may  often  require  to  know. 

Figs.  417  and  418  show  two  forms  of  indicator  diagram.  The  curves 
themselves,  as  drawn  by  the  indicators,  are  lettered  ABCD.  Beside  them 
a  scale  of  pressure  in  atmospheres  is  placed.  In  fig.  417  the  steam  is  ex- 
panded about  seven  times,  and  the  back  pressure  is  about  \  of  an  atmo- 
sphere, the  pressure  during  admission  being  five  atmospheres.  The  engine 
is  a  condensing  one,  and  the  diagram  is  fairly  good.  Fig.  418  is  for  a  non- 
condensing  engine,  the  back  pressure  being  above  that  of  the  atmosphere. 
The  steam  is  cut  off  (at  B)  only  at  about  f  of  the  stroke,  so  that  it  is  not 
working  economically,  and  from  the  roundness  of  its  corners  the  diagram 
would  be  considered  a  poor  one. 

The  useful  work  of  an  engine  is  measured  by  an  entirely  different  piece 
of  apparatus,  called  a  dynamometer.  This  is  used  in  many  forms,  but 
fig.  417  shows  the  principle  upon  which  the  majority  act.  The  apparatus 
shown  in  the  figure  is  known  as  a  Pronfs  friction  bratce.  A  is  the  shaft, 
the  usual  work  transmitted  by  which  we  require  to  find.  Upon  the  shaft  is 
a  fixed  pulley  B,  einbraced  by  two  blocks  Bj  and  B,,  which  can  be  tightened 
up  by  the  screws  at  C^  and  C.  To  the  lower  block  is  fixed  a  lever  D,  from 
which  hangs  a  weight,  and  which  has  at  its  extremity  a  small  pointer  work- 
ing against  a  short  scale  F.  If  such  an  apparatus  be  set  in  motion  by 
turning  the  shaft  A,  one  of  two  things  must  happen  ;  either  the  pulley  must 


454 


On  Heat. 


[473- 


slip  round  in  the  blocks,  or  it  must  so  grip  them  as  to  carry  both  them  and 
the  lever  D  round  its  own  axis.  The  moment  of  resistance  to  the  former  is 
r  F,  if  r  be  the  radius  of  the  pulley  and  F  the  frictional  resistance  at  its 


.r^ 


Fig.  419. 

periphery  ;  that  of  the  latter  is  RW,  where  R  is  the  radius  of  the  weight 
and  W  the  weight  itself.     In  practice  the  screw  C.,  is  loosened  just  suffi- 
ciently to  keep  the  weight  just  lifted  from  the  ground,  while  the  pulley  is 
always  turning  round  in  the  blocks,  so  that,  therefore, 
rF  =  RW. 

The  work  done  at  the  brake  per  minute  is  equal  to  the  frictional  resistance 
multiplied  by  the  distance  through  which  it  is  overcome  in  the  same  time, 
or,  if;/  be  the  number  of  revolutions  per  minute, 
=  27rrF«  =  27rRW«. 
It  is  therefore  just  the  same  as  if  a  resistance  =  W  were  continually  being 
overcome  at  the  periphery  of  a  wheel  of  radius  R,  making  n  turns  per  minute. 
As  the  values  of  all  the  quantities  in  the  expression  27rRW«  are  very  readily 
determined,  it  will  be  seen  that  this  brake  affords  a  very  simple  way  of 
measuring  the  net  work  transmitted  through  the  shaft  of  an  engine. 

™,  ^-      useful  work  work  shown  by  brake       •         n   j  .1,       zk  • 

The  ratio --,  or    , — , — ^--r. ,  is  called  the  cfflci- 

total  work  work  shown  by  mdicator 

ency  of  the  engine  as  a  machine,  or  its  mccJiaiiical  efficiojcy.  It  is  often  as 
much  as  0-85,  and  sometimes  even  higher  than  0-9  or  90  per  cent.,  being 
generally  greatest  in  large  engines. 

474.  Efficiency  of  heat  engrines. — There  is  another  ratio  of  efficiency 
connected  with  the  steam  engine,  namely  the  ratio 
Total  work  done  by  engine 
Total  heat  expended 

which  is  called  the  efficiency  of  the  e?tgine  as  a  heat  engine  or  its  thermo- 
dynamic efficiency.  If  T,  and  T.,  be  respectively  the  absolute  temperatures 
(496)  of  the  steam  and  the  feed  water  in  any  engine,  then  it  can  be  shown 


-476]  Gas  Engines.  455 

that  such  an  engine,  if  working  quite  perfectly,  could  transform  no  more 

than  ( — lZ — 2jof  the  heat  which  it  receives  into  work.     This  fraction  in  the 

case  of  a  steam  engine  is  seldom  more  than  about  o'25.  The  value  of  the 
actual  efficiency  of  the  engine  is  often  from  o"io  to  0'i4  ;  while,  therefore, 
an  ordinary  steam  engine,  with  such  an  efficiency,  turns  into  work  only  from 
~~  to  I  of  the  whole  heat  it  receives,  yet  it  may  be  turning  into  work  h  or 
more  of  the  whole  heat  which  it  could  possibly  transform  into  work  if  it 
were  perfect. 

To  increase  the  economy  of  steam  engines  we  require  to  make  the  value 

of  i  -^-^ — ^j  larger.     This  is  done  either  by  raising  Tj  or  by  lowering  Tg,  or 
\     T[     / 

both.     The  chief  difficulty  is  that  we  cannot  raise  Tj  without  increasing  the 

steam  pressure,  which  it  is  often  not  convenient  to  do,  while  we  cannot  lower 

T.,  below  such  a  temperature,  50^  to   60°  F.,  as   can  readily  be  obtained 

naturally  at  all  seasons  of  the  year. 

475.  Hot-air  engines. — The  difficulty  as  to  T,  just  mentioned  is  got  over 
by  the  use  of  some  fluid  whose  pressure  is  not  a  function  of  its  temperature, 
and  naturally  air  is  the  most  convenient  fluid  for  the  purpose.  Many  '  hot- 
air'  engines  have  been  designed,  and  some  have  found  a  considerable 
measure  of  success  commercially,  as  Rider's,  Hock's,  and  Lehmann's.  In 
all  cases  the  engines  consist  essentially  of  one  (or  two)  chambers  placed  so 
that  one  end  can  be  heated  by  a  furnace  and  the  other  cooled  by  a  refrige- 
rator. The  air  is  compelled  to  move  from  the  cold  space  to  the  hot  and  back 
again  continually.  When  hot  it  is  allowed  to  expand  and  push  forward  a 
piston,  when  cold  it  is  compressed  by  pushing  back  the  piston  again  to  its 
original  position.  The  difference  between  these  two  quantities  of  work  is 
the  whole  work  done  by  the  engine.    By  making  T^  a  very  high  temperature, 

(T  -  T  \ 
— L        -j  of  an  air  engine  may  be  made  much 

higher  than  that  of  a  steam  engine.  But  it  is  so  much  more  difficult  to  attain 
the  theoretical  efficiency  in  the  air  than  in  the  steam  engine,  that  its  actual 
efficiency  is  generally  much  lower  than  that  of  a  steam  engine.  There  are 
constructive  difficulties  connected  with  the  hot-air  chambers,  and  with  the 
regulation  of  the  speed,  and  these,  as  well  as  with  the  large  bulk  of  most  air 
engines  in  proportion  to  their  power,  have  stood  greatly  in  the  way  of  their 
development.  No  doubt,  however,  much  more  improvement  would  ha\'e 
taken  place  in  these  engines  had  not  gas  engines  come  into  prominence  of 
late  years  and  proved  much  more  convenient. 

476.  Gas  engines. — Gas  engines,  like  steam  engines  and  air  engines,  are 
heat  engines,  but  in  them  the  working  fluid  is  ordinary  coal  gas  mixed  with 
air,  in  the  proportion  of  about  i  to  1 1  by  volume.  The  principle  of  action 
is  very  simple  : — The  explosive  mixture  after  being  drawn  into  the  cylinder 
is  set  light  to,  the  heat  generated  by  the  very  rapid  combustion  which 
we  call  an  explosion  causes  the  mixed  gases  to  expand  and  drive  forward 
the  piston.  The  great  difficulty  for  many  years  was  that  the  explosion  was 
so  rapid  that  the  comparatively  slow-going  piston  could  not  keep  up  with  it, 
and  the  greater  part  of  the  energy  of  the  explosion  was  lost  by  radiation  and 
conduction.     In  the  more  modern  gas  engines,  however  (Otto's  and  Clerk's 


456 


On  Heat. 


[476- 


and  others),  this  difficulty  is  got  over  by  compressing  the  charge  before 
igniting^  it,  a  treatment  which  is  found  to  decrease  very  much  the  rapidity 
of  the  explosion  and  so  greatly  increase  the  actual  efficiency  of  the  engine. 
Fig.  420  shows  the  principal  parts  of  an  Otto  'Silent'  gas  engine,  as  now  made. 
A  is  the  cylinder,  open  at  front  and  single-acting,  in  which  works  a  deep 
piston  F,  driving  a  crank  in  the  usual  manner.  The  cylinder  is  surrounded 
by  a  water  jacket,  to  prevent  it  from  getting  too  hot.  At  the  back  of  the 
cylinder  is  a  slide  valve  B,  worked  by  a  cam,  not  shown  in  drawing,  on  the 


lay  shaft  G.  The  valve  B  is  kept  up  against  its  face  by  spiral  springs  E. 
D  is  a  chamber  in  which  a  small  jet  of  gas  for  igniting  the  mixture  is  con- 
tinually burning.  C,  is  the  cock  for  admission  of  gas,  and  C,  an  india- 
rubber  bag  to  equalise  the  gas  pressure.  The  working  of  the  engine  is  as 
follows  : — the  piston  moves  from  left  to  right  and  draws  into  the  cylinder  the 
explosive  mixture.  On  the  return  stroke  it  compresses  the  mixture  to  about 
3  atmospheres.  The  igniting  flame  is  then  allowed  to  come  for  an  instant 
into  contact  with  the  compressed  mixture,  which  burns  very  rapidly  (or 
explodes  slowly,  whichever  expression  be  preferred)  and  pushes  the  piston 
forward  again,  the  pressure  rising  to  10  or  12  atmospheres.  On  the  next 
return  stroke  the  burnt  gases  are  pushed  out  through  the  opening  shown  in 
the  drawing,  and  the  process  begins  again  once  more.  There  are  many 
ingenious  arrangements  about  this  type  of  engine  which  our  space  will  not 
allow  us  to  mention  in  detail.  It  must  suffice  to  say  that  the  engine  has 
proved  distinctly  economical,  and  has  such  very  great  conveniences  as  may 
fairly  account  for  the  rapid  way  in  which  its  use  (and  that  of  other  gas 
engines)  has  extended. 

In  conclusion,  it  is  as  well  to  point  out  that,  as  long  as  they  work  between 
the  same  temperatures,  there  is  no  difference  between  steam,  air,  and  gas 
engines  as  to  theoretical  economy.  The  last  two  gain  by  the  possibility  of 
using  higher  limits  of  temperature  than  can  be  employed  in  a  steam  engine, 
but,  so  far,  have  lost  by  constructive  and  mechanical  difficulties  which  pre- 
vent their  theoretical  efficiency  from  being  attained. 


-478J  457 


CHAPTER   XI. 

SOURCES  OF  HEAT  AND  COLD. 

477.  Different  sources  of  beat. — The  following  difterent  sources  of 
heat  may  be  distinguished  :  i.  the  mechanical  sources,  comprising  friction, 
percussion,  and  pressure  ;  ii.  the  physical  sources —thaX  is,  solar  radiation, 
terrestrial  heat,  molecular  actions,  change  of  condition,  and  electricity  ; 
iii.  the  chemical  sources,  or  molecular  combinations,  and  more  especially 
combustion. 

In  what  follows  it  will  be  seen  that  heat  may  be  produced  by  reversing 
its  effects  ;  as,  for  instance,  when  a  liquid  is  solidified  or  a  gas  compressed 
(479)  ;  though  it  does  not  necessarily  follow  that  in  all  cases  the  reversal  of 
its  effects  causes  heat  to  be  produced — instead  of  it,  an  equivalent  of  some 
other  form  of  energy  may  be  generated. 

In  like  manner  heat  may  be  forced  to  disappear,  or  cold  be  produced 
when  a  change  such  as  heat  can  produce  is  brought  about  by  other  means, 
as  when  a  liquid  is  vaporised  or  a  solid  liquefied  by  solution  ;  though  here 
also  the  disappearance  of  heat  is  not  always  a  necessary  consequence  of 
the  production,  by  other  means,  of  changes  such  as  might  be  effected  by 
heat. 

MECHANICAL    SOURCES. 

478.  Heat  due  to  friction. — The  friction  of  two  bodies,  one  against  the 
other,  produces  heat,  which  is  greater  the  graater  the  pressure  and  the  more 
rapid  the  motion.  For  example,  the  axles  of  carriage  wheels,  by  their  fric- 
tion against  the  boxes,  often  become  so  strongly  heated  as  to  take  fire.  By 
rubbing  together  two  pieces  of  ice  in  a  vacuum  below  zero.  Sir  H.  Davy 
partially  melted  them.  In  boring  a  brass  cannon  Rumford  found  that  the 
heat  developed  in  the  course  of  2h  hours  was  sufficient  to  raise  26^  pounds 
of  water  from  zero  to  100^,  which  represents  2,650  thermal  units  (447).  Mayer 
raised  water  from  12°  to  13°  by  shaking  it.  At  the  Paris  Exhibition,  in  1855, 
Beaumont  and  Mayer  exhibited  an  apparatus,  which  consisted  of  a  wooden 
cone  covered  with  hemp,  and  moving  with  a  velocity  of  400  revolutions  in  a 
minute,  in  a  hollow  copper  cone,  which  was  fixed  and  immersed  in  the  water 
of  an  hermetically-closed  boiler.  The  surfaces  were  kept  covered  with  oil. 
By  means  of  this  apparatus  88  gallons  of  water  were  raised  from  10  to  130 
degrees  in  the  course  of  a  few  hours. 

In  the  case  of  flint  and  steel,  the  friction  of  the  flint  against  the  steel 
raises  the  temperature  of  the  metallic  particles,  which  fly  off,  heated  to  such 
an  extent  that  they  take  fire  in  the  air. 

The  luminosity  of  aerolites  is  considered  to  be  due  to  their  friction 
against  the  air,  and  to  their  condensation  of  the  air  in  front  of  them  (479), 
their  velocity  attaining  as  much  as  150  miles  in  a  second. 


458 


On  Heat. 


[478- 


Tyndall  has  devised  an  experiment  by  which  the  great  heat  developed  by 
friction  is  illustrated  in  a  striking  manner.  A  brass  tube  (fig.  421),  about 
7  inches  in  length  and  f  of  an  inch  in  diameter,  is  fixed  on  a  small  wheel. 
By  means  of  a  cord  passing  round  a  much  larger  wheel,  this  tube  can  be 
rotated  with  any  desired  velocity.  The  tube  is  three  parts  full  of  water,  and 
is  closed  by  a  cork.  In  making  the  experiment,  the  tube  is  pressed  between 
a  wooden  clamp,  while  the  wheel  is  rotated  with  some  rapidity.  The  water 
rapidly  becomes  heated  by  the  friction,  and  its  temperature  soon  exceeding 
the  boiling-point,  the  cork  is  projected  to  a  height  of  several  yards  by  the 
elastic  force  of  the  steam. 

479.  Heat  due  to  pressure  and  percussion. — If  a  bady  be  so  com- 
pressed that  its  density  is  increased,  its  temperature  rises  according  as  the 


Fig.  421. 

volume  diminishes.  Joule  has  verified  this  in  the  case  of  water  and  of  oil, 
which  were  exposed  to  pressures  of  15  to  25  atmospheres.  In  the  case  of 
water  at  i  •2°C.,  increase  of  pressure  caused  lowering  of  temperature — a  result 
which  agrees  with  the  fact  that  water  contracts  by  heat  at  this  temperature. 
Similarly,  when  weights  are  laid  on  metallic  pillars,  heat  is  evolved,  and 
absorbed  when  they  are  removed.  So  in  like  manner  the  stretching  of  a 
metallic  wire  is  attended  with  a  diminution  of  temperature. 

The  production  of  heat  by  the  compression  of  gases  is  easily  shown  by 
means  of  the  piieiimatic  syringe  (fig.  422).  This  consists  of  a  glass  tube 
with  thick  sides,  closed  hermetically  by  a  leather  piston.  At  the  bottom  of 
this  there  is  a  cavity  in  which  a  small  piece  of  cotton,  moistened  with 
ether  or  bisulphide  of  carbon,  is  placed.  The  tube  being  full  of  air,  the 
piston  is  suddenly  plunged  downwards  ;  the  air  thus  compressed  disengages 
so  much  heat  as  to  ignite  the  cotton,  which  is  seen  to  burn  when  the  piston 
is  rapidly  withdrawn.  The  ignition  of  the  cotton  in  this  experiment  indicates 
a  temperature  of  at  least  300°. 

The  elevation  of  temperature  produced  by  the  compression  in  the  above 
experiment  is  sufficient  to  effect  the  combination,  and  therefore  the  detona- 
tion, of  a  mixture  of  hydrogen  and  oxygen. 

A  curious  application  of  the  principle  of  the  pneumatic  syringe  is  met 


-479] 


Heat  due  to  Pressure  a)id  Percussion. 


459 


with  in  the  A.vntnc3.n  ^oiuder  nun  for  pile-driving.  On  the  pile  to  be  driven 
is  fixed  a  powder  mortar,  above  which  is  suspended  at  a  suitable  distance  an 
iron  rammer,  shaped  like  a  gigantic  stopper,  which  just  fits  in  the  mortar. 
Gunpowder  is  placed  in  the  mortar,  and  when  the  rammer  is  detached  it 
foils  into  the  mortar,  compresses  the  air,  producing  so  much  heat  that  the 


Fig.  422. 

powder  is  exploded.  The  force  of  the  gases  projects  the  rammer  into  its 
original  position,  where  it  is  caught  by  a  suitable  arrangement ;  at  the  same 
time  the  reaction  of  the  mortar  on  the  pile  drives  this  in  with  far  greater 
force  than  the  fall  of  the  rammer.  After  adding  a  fresh  charge  of  powder, 
the  rammer  is  again  allowed  to  fall,  again  produces  heat,  explosion,  and  so 
forth,  so  that  the  driving  is  effected  in  a  surprisingly  short  time. 

Percussion  is  also  a  source  of  heat.  In  firing  shot  at  an  iron  target,  a 
sheet  of  flame  is  frequently  seen  at  the  moment  of  impact ;  and  Sir  J.  Whit- 
worth  has  used  iron  shells  which  are  exploded  by  the  concussion  on  striking 
an  iron  target.  A  small  piece  of  iron  hammered  on  the  anvil  becomes  very 
hot.  The  heat  is  not  simply  due  to  an  approximation  of  the  molecules — 
that  is,  to  an  increase  in  density — but  arises  from  a  vibratory  motion  im- 
parted to  them  ;  for  lead,  which  does  not  increase  in  density  by  hammering, 
nevertheless  becomes  heated. 

The  heat  due  to  the  impact  of  bodies  is  not  difficult  to  calculate.  When- 
ever a  body  moving  with  a  velocity  v  is  suddenly  arrested  in  its  motion, 
its  vis  viva  is  converted  into  heat.  This  holds  equally  whatever  be  the 
cause  to  which  the  motion  is  due  :  whether  it  be  that  acquired  by  a  stone 
falling  from  a  height,  by  a  bullet  fired  from  a  gun,  or  the  rotation  of  a 
copper  disc  by  means  of  a  turning-table.     The  vis  viva  of  any  moving  body 

is  expressed  by  — "-  or  in  foot-pounds  by -r     ,  where/  is  the  weight  in 

pounds,  v  the  velocity  in  feet  per  second,  and  g  is  about  32  (29) ;  and  if  the 
whole  of  this  be  converted  into  heat,  its  equivalent  in  thermal  units  will  be 

— £- Suppose,  for  instance,  a  lead  ball  weighing-  a  pound   be  fired 

2^^x  1390  ^^       '  sal 

from  a  gun,  and  strike  against  a  target,  what  amount  of  heat  will  it  produce  ? 

We  may  assume  that  its  velocity  will  be  about  1,600  feet  per  second  ;  then 


its  vis  viva  will  be 


1 600' 

7^: 


_  =  40,000  foot-pounds.     Some  of  this  will  ha\e 

been  consumed  in  producing  the  vibrations  which  represent  the  sound  of  the 
shock,  some  of  it  also  in  its  change  of  shape  ;  but  neglecting  these  two,  as 
being  small,  and  assuming  that  the  heat  is  equally  divided  between  the  ball 


460 


On  Heat. 


[479- 


and  the  target,  then,  since  40,000  foot-pounds  is  the  equivalent  of  287 
thermal  units,  the  share  of  the  ball  will  be  14-3  thermal  units  ;  and  if,  for 
simplicity's  sake,  we  assume  that  its  initial  temperature  is  zero,  then,  taking 
its  specific  heat  at  0'03i4,  we  shall  have 

I  X  0-0314  X  /=  14-3  or  ^  =  457°, 

which  is  a  temperature  considerably  above  that  of  the  melting  point  of 
lead  (338). 

By  allowing  a  lead  ball  to  fall  from  various  heights  on  an  iron  plate,  both 
experience  an  increase  of  temperature  which  may  be  measured  by  the 
thermopile  ;  and  from  these  increases  it  may  be  easily  shown  that  the  heat 
is  directly  proportional  to  the  height  of  fall,  and  therefore  to  the  square  of 
the  velocity. 

By  similar  methods  INIayer  has  calculated  that  if  the  motion  of  the  earth 
were  suddenly  arrested  the  temperature  produced  would  be  sufficient  to  melt 
and  even  volatilise  it  ;  while,  if  it  fell  into  the  sun,  as  much  heat  would  be 
produced  as  results  from  the  combustion  of  5,000  spheres  of  carbon  the  size 
of  our  globe. 

PHYSICAL   SOURCES. 
480.   Solar  radiation. — The  most  intense  of  all  sources  of  heat  is  the 
sun.     Difterent  attempts  have  been  made  to  determine  the  quantity  of  heat 

which  it  emits.  Pouillet  made  the  first 
accurate  measurements  of  the  heat  of 
the  sun  by  means  of  an  instrument 
called  the  pyroheliometer.  The  form 
represented  in  fig.  423  consists  of  a 
flat  cylindrical  metal  box  3  inches  in 
diameter  and  i  an  inch  deep,  contain- 
ing a  known  weight  of  water.  To  it  is 
fitted  a  metal  tube  which  contains  the 
stem  of  a  delicate  thermometer,  the 
bulb  of  which  dips  in  the  liquid  of  the 
box,  being  fitted  by  means  of  a  cork. 
The  tube  works  in  two  collars,  so  that 
by  means  of  a  milled  head  it  can  be 
turned,  and  with  it  the  vessel,  and  the 
liquid  thus  be  uniformly  mixed.  The 
face  of  the  vessel  is  coated  with  lamp- 
black, and  is  so  adjusted  that  the 
sun's  rays  fall  perpendicularly  upon  it. 
This  can  be  ascertained  by  observing 
when  the  shadow  exactly  covers  the 
lower  disc  which  is  fitted  to  the  same 
axis. 

The  instrument  was  exposed  for 
five  minutes  at  a  time  to  the  sun's 
rays  ;  knowing  the  weight  of  the  water,  its  rise  m  temperature  could  be  easily 
calculated  (449).  Corrections  were  necessary  for  the  heat  reflected  by  the 
lampblack,  and  also  for  the  heat  absorbed  by  the  air. 


-481]  Terrestrial  Heat.  46 1 

Pouillet  calculated  from  the  results  of  experiments  with  this  apparatus 
that  if  the  total  quantity  of  heat  which  the  earth  receives  from  the  sun  in  the 
course  of  a  year  were  employed  to  melt  ice,  it  would  be  capable  of  melting  a 
layer  of  ice  all  round  the  earth  of  35  yards  in  thickness.  Another  state- 
ment is  that  the  heat  emitted  by  the  sun  is  equal  to  that  produced  by  the 
combustion  of  1,500  pounds  of  coal  in  an  hour  on  each  square  foot  of  its 
surface.  But  from  the  surface  which  the  earth  exposes  to  the  solar  radia- 
tion, and  from  the  distance  which  separates  the  earth  from  the  sun,  the 
quantity  of  heat  which  the  earth  receives  can  only  be  Ta-gfi];;;^^  of  the  heat 
emitted  by  the  sun. 

Viotti  calculated  the  thickness  of  ice  melted  by  the  sun's  heat  at  the 
equator,  apart  from  absorption  by  the  atmosphere,  at  55  metres  in  thickness  ; 
and,  deducting  this  absorption,  at  yj  metres. 

Faraday  calculated  that  the  average  amount  of  heat  radiated  in  a  day  on 
each  acre  of  ground  in  the  latitude  of  London  is  equal  to  that  which  would 
be  produced  by  the  combustion  of  sixty  sacks  of  coal. 

The  heat  of  the  sun  cannot  be  due  to  combustion,  for  even  if  the  sun 
consisted  of  hydrogen,  which  of  all  substances  gives  the  most  heat  in  com- 
bining with  oxygen,  it  can  be  calculated  that  the  heat  thus  produced  would 
not  last  more  than  3,000  years.  Another  supposition  is  that  originally  put 
forth  by  Mayer,  according  to  which  the  heat  which  the  sun  loses  by  radiation 
is  replaced  by  the  fall  of  aerolites  against  its  surface.  One  class  of  these  is 
what  we  know  as  shooting  stars,  which  often  appear  in  the  heavens  with 
great  brilliancy,  especially  on  August  14  and  November  15  ;  the  term  meteoric 
stone  or  aer-olite  being  properly  restricted  to  the  bodies  which  fall  on  the 
earth.  They  are  often  of  considerable  size,  and  are  even  met  with  in  the 
form  of  dust.  Although  some  of  the  sun's  heat  may  be  restored  by  the 
impact  of  such  bodies  against  the  sun,  the  amount  must  be  very  small,  for 
Sir  W.  Thomson  has  proved  that  a  fall  of  0-3  gramme  of  matter  in  a  second 
on  each  square  metre  of  surface  would  be  necessary  for  this  purpose.  The 
effect  of  this  would  be  that  the  mass  of  the  sun  would  increase,  and  the 
velocity  of  the  earth's  rotation  about  the  sun  would  be  accelerated  to  an 
extent  which  would  be  detected  by  astronomical  observations. 

Helmholtz  considers  that  the  heat  of  the  sun  was  produced  originally  by 
the  condensation  of  a  nebulous  mass,  and  is  kept  up  by  a  continuance  of 
this  contraction.  A  sudden  contraction  of  the  primitive  nebular  mass  of  the 
sun  to  its  present  volume  would  produce  a  temperature  of  28  millions  of 
degrees  Centigrade  ;  and  a  contraction  of  jj^,^--  of  its  mass  would  be 
sufficient  to  supply  the  heat  radiated  by  the  sun  in  2,000  years.  This  amount 
of  contraction  could  not  be  detected  even  by  the  most  refined  astronomical 
methods. 

48 1.  Terrestrial  heat. — Our  globe  possesses  a  heat  peculiar  to  it,  which 
is  called  the  tetyestrial  heat.  The  variations  of  temperature  which  occur  at 
the  surface  gradually  penetrate  to  a  certain  depth,  at  which  their  influence 
becomes  too  slight  to  be  sensible.  It  is  hence  concluded  that  the  solar  heat 
does  not  penetrate  below  a  certain  internal  layer,  which  is  called  the  layer  of 
constant  annual  temperature  ;  its  depth  below  the  earth's  external  surface 
varies,  of  course,  in  different  parts  of  the  globe ;  at  Paris  it  is  about  30  yards, 
and  the  temperature  is  constant  at  1 1  -8'  C. 


462 


On  Heat. 


[481- 


Below  the  layer  of  constant  temperature,  the  temperature  is  observed  to 
increase,  on  the  average,  1°  C.  for  every  90  feet.  The  most  rapid  increase 
is  at  Irkutsk  in  Siberia,  where  it  is  1°  for  20  feet,  and  the  slowest  in  the  mines 
at  Mansfield,  where  it  is  about  1°  C.  for  330  feet.  This  increase  has  been 
verified  in  mines  and  artesian  wells.  According  to  this  at  a  depth  of  3,000 
yards,  the  temperature  of  a  corresponding  layer  would  be  100°,  and  at  a 
depth  of  20  to  ■^:^o  miles  there  would  be  a  temperature  sufficient  to  melt  all 
sulDstances  which  exist  on  the  surface.  Hot  springs  and  volcanoes  confirm 
the  existence  of  this  central  heat. 

Various  hypotheses  have  been  proposed  to  account  for  the  existence  of 
this  central  heat.  The  one  usually  admitted  by  physicists  is  that  the  earth 
was  originally  in  a  liquid  state  in  consequence  of  the  high  temperature,  and 
that  by  radiation  the  surface  has  gradually  solidified,  so  as  to  form  a  solid 
crust.  The  thickness  of  this  crust  is  not  believed  to  be  more  than  40  to  50 
miles,  and  the  interior  is  probably  still  in  a  liquid  state.  The  cooling  must 
be  very  slow,  in  consequence  of  the  imperfect  conductivity  of  the  crust.  For 
the  same  reason  the  central  heat  does  not  appear  to  raise  the  temperature 
of  the  surface  more  than  i  of  a  degree. 

Fourier  calculated  that  the  heat  given  off  by  the  earth  in  100  years  would 
be  sufficient  to  melt  a  layer  of  ice  3  metres  in  thickness,  which  therefore  is 
only  -j7^,,^i  of  that  received  by  the  sun  in  the  same  time. 

482.  Heat  produced  by  absorption  and  imbibition. — Molecular  phe- 
nomena, such  as  imbibition,  absorption,  capillary  actions,  are  usually  accom- 
panied by  disengagement  of  heat.  Pouillet  found  that  whenever  a  liquid  is 
poured  on  a  finely- divided  solid,  an  increase  of  temperature  is  produced 
which  varies  with  the  nature  of  the  substances.  With  inorganic  substances, 
such  as  metal,  the  oxides,  the  earths,  the  increase  is  /^  of  a  degree  ;  but  with 
organic  substances,  such  as  sponge,  flour,  starch,, 
roots,  dried  membranes,  the  increase  varies  from  I 
to  10  degrees. 

The  absorption  of  gases  by  solid  bodies  presents, 
the  same  phenomena.  Dobereiner  found  that  when 
platinum,  in  the  fine  state  of  division  known  as 
platinum  black,  is  placed  in  o.xygen,  it  absorbs 
many  hundred  times  its  volume,  and  that  the  gas 
is  then  in  such  a  state  of  density,  and  the  tempera- 
ture so  high,  as  to  give  rise  to  intense  combustions. 
Spongy  platinum  produces  the  same  effect.  A  jet 
of  hydrogen  directed  on  it  takes  fire. 

The  apparatus  known  as  Dobereiner'' s  Lamp 
depends  on  this  property  of  finely-divided  platinum. 
It  consists  of  two  glass  vessels  (fig.  424).  The 
first.  A,  fits  in  the  lower  vessel  by  means  of  a 
tubulure  which  closes  it  hermetically  At  the  end 
of  the  tubulure  is  a  lump  of  zinc,  Z,  immersed  in 
li.;.  4--4-  dilute  sulphuric  acid.     By  the   chemical  action  of 

the  zinc  on  the  dilute  acid  hydrogen  gas  is  gene- 
rated, which,  finding  no  issue,  forces  the  liquid  out  of  the  vessel  B  into  the 
vessel  A,  so  that  the  zinc  is  not  in  contact  with  the  liquid.     The  stopper  of 


-483]  Chemical  Combination.      Combustion.  463 

the  upper  vessel  is  raised  to  give  exit  to  the  air  in  proportion  as  the  water  rises. 
On  a  copper  tube,  H,  fixed  in  the  side  of  the  vessel  B,  there  is  a  small 
cone,  cz,  perforated  by  an  orifice  ;  above  this  there  is  some  spongy  platinum 
in  the  capsule,  c.  As  soon  now  as  the  cock,  which  closes  the  tube,  H,  is 
opened,  the  hydrogen  escapes,  and,  coming  in  contact  with  the  spongy 
platinum,  is  ignited. 

The  condensation  of  vapours  by  solids  often  produces  an  appreciable 
increase  of  temperature.  This  is  particularlj'  the  case  with  humus,  which,  to 
the  benefit  of  plants,  is  warmer  in  moist  air  than  the  air  itself. 

Favre  has  found  that  when  a  gas  is  absorbed  by  charcoal  the  amount  of 
heat  produced  by  the  absorption  of  a  given  weight  of  sulphurous  acid,  or  of 
protoxide  of  nitrogen,  greatly  exceeds  that  which  is  disengaged  in  the  licjue- 
faction  of  the  same  weight  of  gas  ;  for  carbonic  acid,  the  heat  produced  by 
absorption  exceeds  even  the  heat  which  would  be  disengaged  by  the  solidi- 
fication of  the  gas.  The  heat  produced  by  the  absorption  of  these  gases 
cannot,  therefore,  be  explained  by  assuming  that  the  gas  is  licjuefied,  or  even 
solidified  in  the  pores  of  the  charcoal.  It  is  probable  that  it  is  in  part  due  to 
that  produced  by  the  liquefaction  of  the  gas,  and  in  part  to  the  heat  due  to 
the  imbibition  in  the  charcoal  of  the  liquid  so  produced. 

CHEMICAL   SOURCES. 

483.  Chemical  combination.  Combustion, — Chemical  combinations 
are  usually  accompanied  by  a  rise  of  temperature.  When  these  combinations 
take  place  slowly,  as  when  iron  oxidises  in  the  air,  the  heat  produced  is  im- 
perceptible ;  but  if  they  take  place  rapidly,  the  disengagement  of  heat  is  very 
intense.  The  same  quantity  of  heat  is  produced  in  both  cases,  but  when 
evolved  slowly  it  is  dissipated  as  fast  as  formed. 

Co7nbiistio7i  is  chemical  combination  attended  with  the  evolution  of  light 
and  heat.  In  ordinary  combustion  in  lamps,  fires,  candles,  the  carbon  and 
hydrogen  of  the  coal,  or  of  the  oil,  etc.,  combine  with  the  oxygen  of  the  .air. 
But  combustion  does  not  necessarily  involve  the  presence  of  oxygen.  If 
either  powdered  antimony  or  a  fragment  of  phosphorus  be  placed  in  a  vessel 
of  chlorine,  it  unites  with  chlorine,  producing  thereby  heat  and  flame. 

Many  combustibles  burn  with  flame.  A /lame  is  a  gas  or  vapour  raised 
to  a  high  temperature  by  combustion.  Its  illuminating  power  varies  with 
the  nature  of  the  product  formed.  The  presence  of  a  solid  body  in  the  flame 
increases  the  illuminating  power.  The  flames  of  hydrogen,  carbonic  oxide^ 
and  alcohol  are  pale,  because  they  only  contain  gaseous  products  of  com- 
bustion. But  the  flames  of  candles,  lamps,  coal  gas,  have  a  high  illuminating- 
power.  They  owe  this  to  the  fact  that  the  high  temperature  produced  de- 
composes certain  of  the  gases,  with  the  production  of  carbon,  which,  not 
being  perfectly  burnt,  becomes  incandescent  in  the  flame.  Coal  gas,  when 
burnt  in  an  arrangement  by  which  it  obtains  an  adequate  supply  of  air,  such 
as  a  Bunsen's  burner,  is  almost  entirely  devoid  of  luminosity.  A  non-lumi- 
nous flame  may  be  made  luminous  by  placing  in  it  platinum  wire  or  asbestos. 
The  temperature  of  a  flame  does  not  depend  on  its  illuminating  power. 
A  hydrogen  flame,  which  is  the  palest  of  all  flames,  gives  the  greatest 
heat. 


464 


On  Heat. 


[483- 


Clionical  decomposiiion,  in  which  the  attraction  of  heterogeneous  mole- 
cules for  each  other  is  overcome,  and  they  are  moved  further  apart,  is  an 
operation  recjuiring-  an  expenditure  of  work  or  an  equivalent  consumption  of 
heat  ;  and  conversely,  in  chemical  combination,  motion  is  transformed  into 
heat.  When  bodies  attract  each  other  chemically  their  molecules  move 
towards  each  other  with  gradually  increasing  velocity,  and  when  impact  has 
taken  place  the  progressive  motion  of  the  molecules  ceases,  and  is  converted 
into  a  rotating,  vibrating,  or  progressive  motion  of  the  molecules  of  the  new 
body. 

The  heat  produced  by  chemical  combination  of  two  elements  may  be 
compared  to  that  due  to  the  impact  of  bodies  against  each  other.  Thus  the 
action  of  the  atoms  of  oxygen,  which  in  virtue  of  their  progressive  motion, 
and  of  chemical  attraction,  rush  against  ignited  carbon,  has  been  likened  by 
Tyndall  to  the  action  of  meteorites  which  fall  into  the  sun. 

484.  Heat  disengaged  during  chemical  action. — Many  physicists, 
more  especially  Lavoisier,  Rumford,  Dulong,  Despretz,  Hess,  Favre  and 
Silbermann,  Berthelot,  Thomsen,  and  Andrews,  have  investigated  the 
quantity  of  heat  disengaged  by  various  bodies  in  chemical  actions. 

Lavoisier  used  in  his  experiments  the  ice  calorimeter  already  described. 
Rumford  used  a  calorimeter  known  by  his  name,  which  consists  of  a  rect- 
angular copper  canister  filled  with  water.  In  this  canister  there  is  a  worm 
which  passes  through  the  bottom  of  the  box,  and  terminates  below  in  an 
inverted  funnel.     Under  this  funnel  is  burnt  the  substance  experimented 

upon.  The  products  of  combustion, 
in  passing  through  the  worm,  heat 
the  water  of  the  canister,  and  from 
the  increase  of  its  temperature  the 
quantity  of  heat  evolved  is  calculated. 
Despretz  and  Dulong  successively 
modified  Rumford's  calorimeter  by 
allowing  the  combustion  to  take 
place,  not  outside  the  canister,  but 
in  a  chamber  placed  in  the  liquid 
itself;  the  oxygen  necessary  for  the 
combustion  entered  by  a  tube  in  the 
lower  part  of  the  chamber,  and  the 
products  of  combustion  escaped  by 
another  tube  placed  at  the  upper 
part  and  twisted  in  a  serpentine  form 
in  the  mass  of  the  liquid  to  be 
heated.  Favre  and  Silbermann  have 
improved  this  calorimeter  very 
greatly  (463),  not  only  by  avoiding 
or  taking  account  of  all  possible 
^'  sources  of  error,  but  b)'  arranging  it 
for  the  determination  of  the  heat 
evolved  in  such  chemical  actions  as 
take  place  between  gases  and  vapours.  The  gases  enter  by  tubes  BB'  and 
CC,  fig.  425,  into  a  metal  chamber  A,  where  the  reaction  takes  place,  the 


-484] 


Heat  discnrnzed  during  Combustion. 


465 


course  of  which  can  be  watched  through  a  glass  plate  which  closes  a  wider 
tube  FK.  The  gaseous  products  before  passing  into  the  air  traverse  a  long 
serpentine  tube  H,  at  the  lower  end  of  which  is  a  small  box  G  which  receives 
the  liquids  arising  from  the  condensation  of  the  vapours.  The  cylinder  A 
and  the  serpentine  are  contained  in  a  known  mass  of  water  contained  in  a 
calorimeter,  and  from  the  rise  in  temperature  of  this  water  the  heat  developed 
can  be  calculated.  To  avoid  any  loss  of  heat  this  is  placed  within  a  metal 
case  containing  swan's  down.  The  whole  is  contained  in  a  vessel  of  water 
NN  in  which  is  a  thermometer,  to  eliminate  the  influence  of  changes  in  the 
temperature  of  the  air. 

The  experiments  of  Favre  and  Silbermann  are  the  most  trustworthy,  as 
having  been  executed  with  the  greatest  care.  They  agree  very  closely  with 
those  of  Dulong.  Taking  as  thermal  unit  the  heat  necessary  to  raise  the 
temperature  of  a  pound  of  water  through  one  degree  Centigrade,  the  following- 
table  gives  the  thermal  units  in  round  numbers  disengaged  by  a  pound  of 
each  of  the  substances  while  burning  in  o.xygen  : — 

Hydrogen    . 
Marsh  gas   . 
Olefiant  gas 
Oil  of  turpentine 
OHve  oil 
Ether  . 
Anthracite 
Charcoal 
Coal     . 
Tallow 
Graphite 

Bunsen's  calorimeter  (451)  has  been  used  with  advantage  for  studying 
the  heat  produced  in  chemical  reactions,  for  cases  in  which  only  very  small 
quantities  are  available. 

All  chemical  actions,  whether  of  combination  or  of  decomposition,  are 
attended  by  a. disturbance  of  the  thermal  equilibrium  ;  and  the  quantity  of 
heat  disengaged  is  a  measure  of  the  physical  and  chemical  work. 

In  most  cases  the  act  of  chemical  combination  is  attended  by  a  rise  of 
temperature,  and  the  quantity  of  heat  is  a  measure  of  the  energy  developed 
in  the  reaction.  Thus  in  the  formation  of  one  molecule  of  water  there  are 
liberated  68,924  thermal  units,  which  may  be  written  thus, 

Hj  +  O  =  H„0  +  68,924. 

Those  reactions  which  take  place  with  disengagement  of  heat  are  said  to 
be  exothermic  ;  there  are,  however,  cases  where  bodies  do  not  directly  com- 
bine without  the  intervention  of  extraneous  heat — for  instance,  iodine  and 
hydrogen  to  form  hydriodic  acid  ;  the  equation  for  this  is 

I  +  H+6,ooo=IH. 

Such  reactions  called  endothermic. 

Those  bodies  are  most  stable  in  the  formation  of  which  most  heat  is 

H  H 


34,462 

Diamond 

7,770 

13,063 

Absolute  alcohol   . 

7,180 

11,858 

Coke      . 

7,000 

10,852 

Phosphorus    . 

5,750 

9,860 

Wood,  dried  at  120' 

3,616 

9,030 

Bisulphide  of  carbon 

3,401 

8,460 

Wood,  ordinary     . 

2,756 

8, 080 

Carbonic  oxide 

2,400 

8,000 

Sulphur 

2,220 

8,000 

Iron 

1,181 

7,797 

Zinc 

1,300 

466  On  Heat.  [484- 

developed  ;  thus  the  oxides  of  iron  and  zinc,  in  the  formation  of  which  i,iSi 
and  1,300  units  are  respectively  developed,  are  much  more  stable  than  oxide 
of  silver,  m  the  formation  of  which  only  27  units  are  developed.  The  heat 
of  decomposition  is  the  reciprocal  of  that  of  combination  ;  those  bodies 
which  develop  most  heat  in  their  formation  require  conversely  an  equivalent 
quantity  to  decompose  them  ;  decompositions  which  require  an  expenditure 
of  heat  to  produce  them  are  called  etidothermic.  Those  compounds,  on  the 
contrary,  which  absorb  heat  in  their  formation,  develop  an  equivalent 
quantity  in  being  decomposed,  and  the  reactions  are  exot/icnntc  ;  they  often 
take  place  with  explosive  violence,  as  in  the  case  of  the  chlorides  and  iodide  of 
nitrogen.  An  exothermic  reaction  gives  rise  to  an  endothermic  compound  ; 
and,  conversely,  an  endothermic  reaction  forms  an  exothermic  compound. 

If  there  be  any  system  of  bodies  which  act  on  each  other  without  the 
supply  of  extraneous  energy,  then  that  body,  or  set  of  bodies,  results  in 
the  formation  of  which  most  heat  is  produced.  This  is  called  the  principle 
of  greatest  cJieiiiical  actioti. 

The  heat  developed  in  any  chemical  reaction  depends  on  the  relation 
between  the  initial  and  the  final  products,  and  is  independent  of  the  nature 
and  succession  of  the  intermediate  stages.  It  is  equal  to  the  sum  of  the 
quantities  of  heat  produced  in  each  stage,  regard  being  had  to  the  negative 
quantities  produced  in  such  processes  as  solution  and  gasification. 

Thus  a  unit  weight  of  carbon  in  burning  to  carbonic  acid  produces  8,080 
units.  If  the  same  weight  of  carbon  burns  so  as  to  form  carbonic  oxide  it 
forms  2,473  ;  a^rid  the  combustion  of  the  carbonic  oxide  resulting  from  this 
reaction  yields  5,607,  making  together  8,080. 

Potassium  combines  directly  with  chlorine  to  form  potassium  chloride, 
the  heat  of  formation  of  which  is  1 5,000  and  is  equal  to  that  produced  by  the 
same  weight  of  salt,  whether  this  be  formed  by  the  direct  union  of  hydro- 
chloric acid  and  potash,  or  whether  it  be  produced  by  the  action  of  potassium 
on  aqueous  solution  of  hydrochloric  acid. 

The  heat  of  combustion  of  a  compound  is  not  equal  to  the  sum  of  that  of 
each  of  its  constituents.  The  heat  of  combustion  of  bisulphide  of  carbon  is 
3,401,  while  that  calculated  from  its  constituents  is  3,145  ;  the  compound 
accordingly  possesses  more  energy  than  its  constituents,  and,  its  formation 
is  due  to  an  endothermic  reaction. 

Metameric  bodies  are  those  which  contain  the  same  number  of  elements 
but  in  different  groupings  ;  thus  acetic  acid  and  methylic  formate  have 
each  the  composition  C^H^Oo ;  but  the  heat  of  combustion  of  the  latter 
is  4,157,  and  that  of  the  former  3,505  ;  from  this  it  is  to  be  inferred  that  the 
grouping  of  the  atoms  to  form  acetic  acid  has  been  attended  with  the  expendi- 
ture of  more  energy  than  in  the  case  of  methylic  formate. 

Polymeric  bodies  are  those  which  have  the  same  elements  and  the  same 
percentage  composition  but  differ  in  the  number  of  atoms  which  form  a 
molecule.  Thus  the  more  complex  the  molecule  the  smaller  is  the  quantity 
of  heat.  That  of  amylene,  for  instance,  CjH,o,  is  11,401,  and  that  of 
metamylene,  C.,(,H_i,„  is  10,908. 

Many  chemical  elements,  such  as  carbon,  sulphur,  and  phosphorus,  exist 
in  modifications  which  are  essentially  different  from  each  other  in  their 
physical  properties,  iDut  which  form  when  they  enter  into  combination  with 


-485] 


Auiiual  Heat.  467 


other  elements  identical  chemical  products.  Such  bodies  are  said  to  exist 
in  an  allotropic  form.  A  given  weight  of  carbon  produces  the  same  weight  of 
carbonic  acid  when  it  combines  with  oxygen,  whether  it  be  diamond  or  char- 
coal, but  the  heat  produced  is  different,  and  this  difference  corresponds  to  the 
heat  which  represents  the  transformation  from  one  modification  into  another. 

The  temperature  of  combustion.,  or,  in  the  case  of  gases,  the  temperature 
of  the  flame,  is  the  upper  limit  of  the  temperature  which  can  be  attained  by 
the  combustion-  of  a  body.  This  can  be  deduced  from  the  heat  of  combus- 
tion, and  from  the  specific  heats  of  the  bodies  produced.  The  theoretical 
temperature  of  combustion  of  hydrogen  in  oxygen  is  calculated  at  6,715°  ; 
this,  however,  is  never  even  approximately  reached,  for  at  much  lower  tem- 
peratures aqueous  vapour  is  dissociated  (389)  into  its  constituents,  and  the 
combustion  cannot  exceed  a  certain  limit. 

485.  iVnimal  heat. — In  all  the  organs  of  the  human  body,  as  well  as 
those  of  all  animals,  processes  of  oxidation  are  continually  going  on.  Oxygen 
passes  through  the  lungs  into  the  blood,  and  so  into  all  parts  of  the  body.  In 
like  manner  the  oxidisible  bodies,  which  are  principally  hyrocarbons,  pass 
by  the  process  of  digestion  into  the  blood,  and  likewise  into  all  parts  of  the 
body,  while  the  products  of  oxidation,  carbonic  acid  and  water,  are  ehminated 
by  the  skin,  the  lungs,  etc.  Oxidation  in  the  muscle  produces  motions  of  the 
molecules,  which  are  changed  into  contraction  of  the  muscular  fibres ;  all 
other  oxidations  produce  heat  directly.  When  the  body  is  at  rest,  all  its 
functions,  even  involuntary  motions,  are  transformed  into  heat.  When  the 
body  is  at  work,  the  more  vigorous  oxidations  of  the  working  parts  are 
transferred  to  the  others.  Moreover,  a  great  part  of  the  muscular  work  is 
changed  into  heat,  by  friction  of  the  muscle  and  of  the  sinews  in  their  sheaths, 
and  of  the  bones  in  their  sockets.  Hence  the  heat  produced  by  the  body 
when  at  work  is  greater  than  when  at  rest.  The  blood  distributes  heat 
uniformly  through  the  body,  which  in  the  normal  condition  has  a  temperature 
of  yj'^  C.  =  98-6  F.  The  blood  of  mammalia  has  the  same  temperature,  that  of 
birds  is  somewhat  higher.  In  fever  the  temperature  rises  to  42° -43°,  and  in 
cholera,  or  when  near  death,  sink  as  low  as  35°. 

The  function  of  producing  work  in  the  animal  organism  was  formerly  con- 
sidered as  separate  from  that  of  the  production  of  heat.  The  latter  was 
held  to  be  specially  due  to  the  oxidation  of  the  hydrocarbons  of  the  fat,  while 
the  work  was  ascribed  to  the  chemical  activity  of  the  nitrogenous  matter. 
This  view  has  now  been  generally  abandoned  ;  for  it  has  been  found  that 
during  work  there  is  no  increase  in  the  secretion  of  urea,  which  is  the  result 
of  the  oxidation  of  nitrogenous  matter  ;  moreover,  the  organism  while  at 
rest  produces  less  carbonic  acid,  and  requires  less  oxygen  than  when  it  is  at 
work  ;  and  the  muscle  itself,  both  in  the  living  organism  and  also  when 
removed  from  it  and  artificially  stimulated,  requires  more  oxygen  in  a  state 
of  activity  than  when  at  rest.  For  these  reasons  the  production  of  work  is 
ascribed  to  the  oxidation  of  the  organic  matter  generally. 

The  process  of  vegetation  in  the  living  plant  is  not  in  general  connected 
with  any  o.xidation.  On  the  contrary,  under  the  influence  of  the  sun's  rays, 
the  green  parts  of  plants  decompose  the  carbonic  acid  of  the  atmosphere 
into  free  oxygen  gas  and  into  carbon,  which,  uniting  with  the  elements  of 
water,  form  cellulose,  starch,  sugar,  and  so  forth.     In  order  to  effect  this,  an 

H  H  2 


468 


On  Heat. 


[485- 


expenditure  of  heat  is  required  which  is  stored  up  in  the  plant,  and  which 
reappears  duriny  the  combustion  of  the  wood,  or  of  the  coal  arising  from  its 
decomposition. 

At  the  time  of  blossoming  a  process  of  oxidation  goes  on,  which,  as  in 
the  case  of  the  blossoming  of  the  Victofia  regta,  is  attended  with  an  appreci- 
able rise  of  temperature. 


HEATING. 

486.  Different  kinds  of  heating-. — Heating  is  the  art  of  utilising  for 
domestic  and  industrial  purposes  the  sources  of  heat  which  nature  offers  to 
us.  Our  principal  source  of  artificial  heat  is  the  combustion  of  coal,  coke, 
turf,  wood,  and  charcoal. 

487.  Pireplaces Fireplaces  are  open  hearths  built  against  a  wall  under 

a  chimney,  through  which  the  products  of  combustion  escape. 

However  much  they  may  be  improved,  fireplaces  will  always  remain  the 
most  imperfect  and  costly  mode  of  heating,  for  they  only  render  available 
13  per  cent,  of  th-e  total  heat  yielded  by  coal  or  coke,  and  6  per  cent,  of  that 
by  wood.  This  enormous  loss  of  temperature  arises  from  the  fact  that  the 
current  of  air  necessary  for  combustion  always  carries  with  it  a  large  quan- 
tity of  the  heat  produced,  which  is  dissipated  in  the  atmosphere.  Hence 
Franklin  said  'fireplaces  should  be  adopted  in  cases  where  the  smallest 
quantity  of  heat  was  to  be  obtained  from  a  given  quantity  of  fuel.'  Not- 
withstanding their  want  of  economy,  however,  they  will  always  be  preferred 
as  the  healthiest  and  pleasantest  mode  of  heating,  on  account  of  the  cheerful 
light  which  they  emit,  and  the  ventilation  which  they  ensure. 

488.  Braugrht  of  fireplaces. — The  draught  of  a  fire  is  the  upward  cur- 

rent in  the  chimney  caused  by  the  ascent  of 
the  products  of  combustion;  when  the  current 
is  rapid  and  continuous,  the  chimney  is  said 
to  draiv  well. 

The  draught  is  caused  by  the  difference 
between  the  temperature  of  the  inside  and 
that  on  the  outside  of  the  chimney  ;  for,  in 
consequence  of  this  difference,  the  gaseous 
bodies  which  fill  the  chimney  are  lighter 
than  the  air  of  the  room,  and  consequently 
equilibrium  is  impossible.  The  weight  of  the 
column  of  gas  CD,  fig.  426,  in  the  chimney 
being  less  than  that  of  the  external  column 
of  air  AB  of  the  same  height,  there  is  a 
pressure  from  the  outside  to  the  inside  which 
causes  the  products  of  combustion  to  ascend 
the  more  rapidly  in  proportion  as  the  differ- 
ence in  weight  of  the  two  gaseous  masses  is 
greater. 
The  velocity  of  the  draught  of  a  chimney  may  be  determined  theoreti- 
cally by  the  formula 


t  ig.  420. 


-489J  Stoves.  469 

ill  which  g  is  the  acceleration  of  gravity,  a  the  coefficient  of  the  expansion 
of  air,  h  the  height  of  the  chimney,  /'  the  mean  temperature  of  the  air  inside 
the  chimney,  and  t  the  temperature  of  the  surrounding  air. 

The  currents  caused  by  the  difference  in  temperature  of  two  communi- 
cating gaseous  masses  may  be  demonstrated  by  placing  a  candle  near  the 
top  and  near  the  bottom  of  the  partially- opened  door  of  a  warm  room.  At 
the  top,  the  flame  will  be  turned  from  the  room  towards  the  outside,  while 
the  contrary  effect  will  be  produced  when  the  candle  is  placed  on  the 
ground.  The  two  effects  are  caused  by  the  current  of  heated  air  which 
issues  by  the  top  of  the  door,  while  the  cold  air  which  replaces  it  enters  at 
the  bottom. 

In  order  to  have  a  good  draught,  a  chimney  ought  to  satisfy  the  following 
conditions  : — 

i.  The  section  of  the  chimney  ought  not  to  be  larger  than  is  necessary  to 
allow  an  exit  for  the  products  of  combustion  ;  otherwise  ascending  and  de- 
scending currents  are  produced  in  the  chimney,  which  cause  it  to  smoke.  It 
is  advantageous  to  place  on  the  top  of  the  chimney  a  conical  pot  narrower 
than  the  chimney,  so  that  the  smoke  may  escape  with  sufficient  velocity  to 
resist  the  action  of  the  wind. 

ii.  The  chimney  ought  to  be  sufficiently  high,  for,  as  the  draught  is 
caused  by  the  excess  of  the  external  over  the  internal  pressure,  this  excess  is 
greater  in  proportion  as  the  column  of  heated  air  is  longer. 

iii.  The  external  air  ought  to  pass  into  the  chamber  with  sufficient 
rapidity  to  supply  the  wants  of  the  fire.  In  an  hermetically-closed  room 
combustibles  would  not  burn,  or  descending  currents  would  be  formed  which 
would  drive  the  smoke  into  the  room.  Usually  air  enters  in  sufficient 
quantity  by  the  crevices  of  the  doors  and  windows. 

iv.  Two  chimneys  should  not  communicate,  for  if  one  draws  better  than 
the  other,  a  descending  current  of  air  is  produced  in  the  latter,  which  carries 
smoke  with  it. 

For  the  strong  fires  recjuired  by  steam  boilers  and  the  like,  very  high 
chimneys  are  needed :  of  course  the  increase  in  height  would  lose  its  effect 
if  the  hot  column  above  became  cooled  down.  Hence  chimneys  are  often 
made  with  hollow  walls — that  is,  of  separate  concentric  layers  of  masonry 
or  brickwork — the  space  between  them  containing  air. 

489.  Stoves. — Sieves  are  apparatus  for  heating  with  a  detached  fire, 
placed  in  a  room  to  be  heated,  so  that  the  heat  radiates  in  all  directions 
round  the  stove.  At  the  lower  part  is  the  draught-hole  by  which  the  air 
necessary  for  combustion  enters.  The  products  of  combustion  escape  by 
means  of  iron  chimney-pipes.  This  mode  of  heating  is  one  of  the  most 
economical,  but  it  is  by  no  means  so  healthy  as  that  by  open  fireplaces,  for 
the  ventilation  is  very  bad,  more  especially  where,  as  in  Sweden  and  in 
Germany,  the  stoves  are  fed  from  the  outside  of  the  room.  These  stoves 
also  emit  a  bad  smell,  arising  in  part  from  the  decomposition  of  organic  sub- 
stances which  are  always  present  in  the  air  by  their  contact  with  the  heated 
sides  of  the  chimney-pipes  ;  or  possibly,  as  Deville  and  Troost's  researches 
seem  to  show,  from  the  difitusion  of  gases  through  the  heated  sides  of  the 
stove. 

The  heating  is  very  rapid  with  blackened  metal  stoves,  but  they  also 


470  On  Heat.  [489- 

cool  very  rapidly.  Stoves  constructed  of  polished  earthenware,  which  are 
common  on  the  Continent,  heat  more  slowly,  but  more  pleasantly,  and  they 
retain  the  heat  longer. 

490.  Heating  by  steam. — Steam,  in  condensing,  gives  up  its  latent  heat 
of  vaporisation,  and  this  property  has  been  used'^in  heating  baths,  workshops, 
public  buildings,  hothouses,  &c.  For  this  purpose  steam  is  generated  in 
Ijoilers  similar  to  those  used  for  steam-engines,  and  is  then  made  to  circulate 

in  pipes  placed  in  the  room 
to  be  heated.  The  steam 
condenses,  and  in  doing  so 
imparts  to  the  pipes  its  latent 
heat,  which  becomes  free, 
and  thus  heats  the  surround- 
ing air. 

491.  Heating-  by  hot 
air. —  Heating  by  hot  air 
consists  in  heating  the  air  in 
the  lower  part  of  a  building, 
from  whence  it  rises  to  the 
higher  parts  in  virtue  of  its 
lessened  density.  The  appa- 
ratus is  arranged  as  repre- 
sented in  fig.  427. 

A   series    of    tubes,   AB, 
only  one  of  which  is  shown 
in  the  figure,  is  placed  in  a 
Fig.  427.  furnace  F,  in  the  cellar.    The 

air  passes  into  the  tubes 
through  the  lower  end,  A,  where  it  becomes  heated,  and,  rising  in  the  direc- 
tion of  the  arrows,  reaches  the  room  M  by  a  higher  aperture,  B.  The 
various  rooms  to  be  heated  are  provided  with  one  or  more  of  these  aper- 
tures, which  are  placed  as  low  in  the  room  as  possible.  The  conduit  O  is 
an  ordinary  chimney.  These  apparatus  are  more  economical  than  open  fire- 
places, but  they  are  less  healthy,  unless  special  provision  is  made  for  venti- 
lation. 

492.  Heating-  by  hot  -water. — This  consists  of  a  continuous  circulation 
of  water,  which,  having  been  heated  in  a  boiler,  rises  through  a  series  of  tubes, 
and  then,  after  becoming  cool,  passes  into  the  boiler  again  by  a  similar 
series. 

Fig.  428  represents  an  apparatus  for  heating  a  building  of  several 
storeys.  The  heating  apparatus,  which  is  in  the  basement,  consists  of  a 
bell-shaped  boiler,  0  o,  with  an  internal  flue,  F.  A  long  pipe,  M,  fits  in 
the  upper  part  of  the  boiler,  and  also  in  the  reservoir  Q,  placed  in  the 
upper  part  of  the  building  to  be  heated.  At  the  top  of  this  reservoir  there 
is  a  safety  valve,  j-,  by  which  the  pressure  of  the  vapour  in  the  interior  can 
be  regulated. 

The  boiler,  the  pipe  M,  and  a  portion  of  the  reservoir  Q,  being  filled  with 
water,  as  it  becomes  heated  in  the  boiler  an  ascending  current  of  hot  water 
rises  to  the  reservoir  Q,  while  at  the  same  time  descending  currents  of  colder 


-494] 


Cold  produced  by  Expansion  of  Gases. 


47^ 


and  denser  water  pass  from  the  lower  part  of  the  reservoir  Q  into  receivers, 
i,  d,J\  filled  with  water.     The  water  from  these  passes  again  through  pipes 
into    other   receivers, 
a,  c,  e^  and  ultimately 
reaches      the     lower 
part  of  the  boilei'. 

During  this  circu- 
lation the  hot  watei 
heats  the  pipes  and 
the  receivers,  which 
thus  become  true 
water-stoves.  The 
number  and  the  di- 
mensions of  these 
parts  are  determined 
from  the  fact  that  a 
cubic  foot  of  watei 
in  falling  through  a 
temperature  of  one 
degree  can  theoreti- 
cally impart  the  same 
increase  of  tempera- 
ture to  3,200  cubic 
feet  of  air  (460).  In 
the  interior  of  the  re- 
ceivers, a,  b,  c,  d,  e,  /, 
there  are  cast-iron 
tubes  which  commu- 
nicate with  the  outside  by  pipes,  P,  placed  underneath  the  flooring.  The  air 
becomes  heated  in  these  tubes,  and  issues  at  the  upper  part  of  the  receiver. 

The  principal  advantage  of  this  mode  of  heating  is  that  of  giving  a  tem- 
perature which  is  constant  for  a  long  time,  for  the  mass  of  water  only  cools 
slowly.  It  is  much  used  in  hothouses,  baths,  artificial  incubation,  drying 
rooms,  and  generally  wherever  a  uniform  temperature  is  desired. 


SOURCES   OF   COLD. 

493.  Various  sources  ot  cold. — Besides  the  cold  caused  by  the  passage 
of  a  body  from  a  solid  to  the  liquid  state,  of  which  we  have  already  spoken, 
cold  is  produced  by  the  expansion  of  gases,  by  radiation  in  general,  and  more 
especially  by  radiation  at  night. 

494.  Cold  produced  by  the  expansion  of  grases.  Ice  machines. — We 
have  seen  that  when  a  gas  is  compressed  the  temperature  rises.  The  reverse 
of  this  is  also  the  case  :  when  a  gas  is  rarefied,  a  reduction  of  temperature 
ensues,  because  a  quantity  of  sensible  heat  disappears  when  the  gas  becomes 
increased  to  a  larger  volume.  This  may  be  shown  by  placing  a  delicate 
Breguet's  thermometer  under  the  receiver  of  an  air-pump,  and  exhausting  ; 
at  each  stroke  of  the  piston  the  needle  moves  in  the  direction  of  zero,  and 
regains  its  original  position  when  air  is  admitted. 


A72  On  Heat.  [494- 

The  production  of  cold  when  a  gas  is  expanded  has  been  extensively 
applied  in  machines  for  artificial  refrigeration  on  a  large  scale.  By  Wind- 
hausen's  ice  machine,  from  15,000  to  150,000  feet  of  air  can  be  cooled  in  an 
hour,  through  40  to  100  degrees  in  temperature,  by  means  of  a  steam-engine 
of  from  6  to  20  horse-power.  The  essential  parts  of  this  machine  are  repre- 
sented in  fig.  429.  The  piston  B  in  the  cylinder  A  is  worked  to  the  right  by 
a  steam-engine  and  to  the  left  by  a  steam-engine  and  by  the  compressed  air. 
As  it  moves  towards  the  right  the  valve  a  opens,  and  air  under  the  ordinary 
atmospheric  pressure  enters  the  space  A,.  When  this  is  full  the  piston  moves 
towards  the  left,  the  air  in  A  is  compressed  to  about  2  atmospheres,  the 
valve  a  is  closed,  the  valve  b  opens,  and  air  passes  in  the  direction  of  the 
arrows  into  the  cooler,  C.  By  its  compression  it  has  become  strongly 
heated,  and  the  necessary  cooling  is  effected  by  means  of  pipes  through 
which  cold  water  circulates,  entering  at  5  and  emerging  at  6.  The  air,  thus 
compressed  and  cooled,  passes  out  through  the  valve  c,  which  is  automatically 
worked  by  the  machine,  into  the  space  Ao,  where,  in  conjunction  with  the 
steam-engine,  it  moves  the  piston  to  the  left,  and  compresses  the  air  in  A,  ; 


Fig.  429. 


^^^ 


for  at  a  certain  position  of  the  piston  the  valve  c  is  closed,  the  compressed 
air  in  the  cylinder  A.,  expands,  and  thereby  is  cooled  far  below  the  freezing 
point.  As  the  piston  moves  again  to  the  right,  the  valve  d  is  opened  by  the 
working  of  the  machine,  and  the  cooled  air  emerges  through  the  tube  4  to 
its  destination.  If  it  passes  into  an  ordinary  room  it  fills  it  with  snowflakes. 
Machines  of  this  kind  are  extensively  employed  in  the  arts ;  in  breweries, 
oil  refineries,  in  the  artificial  production  of  ice,  and  in  cooling  rooms  for  the 
transport  of  dead  meat,  &c.,  on  board  ship. 

In  the  Linde  machine  the  material  used  is  ammoniacal  gas,  which  is 
liquefied  by  compression  and  surface  condensation.  This  lic|uid  ammonia 
being  allowed  to  evaporate  takes  the  heat  for  this  change  of  state  from  the 
surrounding  bodies,  which  are  thereby  cooled.  The  ammonia  vapour  thus 
formed  is  again  liquefied,  and  flowing  back  to  the  refrigerator  is  again 
evaporated,  so  that  a  small  quantity  of  ammonia  is  always  passing  through 
the  same  cycle  of  operations. 

A  machine  of  this  kind  worked  by  a  steam-engine  of  half  a  horse-power 
can  cool  in  an  hour  3,400  cubic  yards  of  air  from  10°  to  5°  C,  or  1,400  cubic 


-496]  Absolute  Zero  of  Temperature.  473 

yards  from  6°  to  -4°  C.  ;  or  it  will  produce  i  cwt.  of  ice  in  the  same  time. 
The  larger  machines  are  relatively  more  advantageous. 

495.  Cold  produced  by  radiation  at  nigrht. — During  the  day  the 
ground  receives  from  the  sun  more  heat  than  radiates  into  space,  and  the 
temperature  rises.  The  reverse  is  the  case  during  night.  The  heat  which 
the  earth  loses  by  radiation  is  no  longer  compensated  for,  and  consequently 
a  fall  of  temperature  takes  place,  which  is  greater  according  as  the  sky  is 
clearer,  for  clouds  send  towards  the  earth  rays  of  greater  intensity  than 
those  which  come  from  the  celestial  spaces.  In  some  winters  it  has  been 
found  that  rivers  have  not  frozen,  the  sky  having  been  cloudy,  although  the 
thermometer  had  been  for  several  days  below  -  4°  ;  while  in  other  less 
severe  winters  the  rivers  freeze  when  the  sky  is  clear.  The  emissive  power 
exercises  a  great  influence  on  the  cold  produced  by  radiation  ;  the  greater  it 
is,  the  greater  is  the  cold. 

In  Bengal,  the  nocturnal  cooling  is  used  in  manufacturing  ice.  Large 
flat  vessels  containing  water  are  placed  on  non-conductmg  substances,  such 
as  straw  or  dry  leaves.  In  consequence  of  the  radiation  the  water  freezes, 
even  when  the  temperature  of  the  air  is  10°  C.  The  same  method  can  be 
applied  in  all  cases  with  a  clear  sky. 

The  Peruvians,  in  order  to  preserve  the  shoots  of  young  plants  from 
freezing,  light  great  fires  in  their  neighbourhood,  the  smoke  of  which,  pro- 
ducing an  artificial  cloud,  hinders  the  cooling  produced  by  radiation. 

496.  Absolute  zero  of  temperature. — As  a  gas  is  increased  ^^^3  of  its 
volume  for  each  degree  Centigrade,  it  follows  that  at  a  temperature  of  273^ 
C.  the  volume  of  any  gas  measured  at  zero  is  doubled.  In  like  manner,  if 
the  temperature  of  a  given  volume  at  zero  were  lowered  through  —  273°,  the 
contraction  would  be  equal  to  the  volume :  that  is,  the  volume  would  not 
exist.  At  this  temperature  the  motion  of  the  molecules  of  the  gas  would 
completely  cease,  and  the  pressure  thereby  occasioned.  In  all  probability, 
before  reaching  this  temperature,  gases  would  undergo  some  change. 

This  point  on  the  Centigrade  scale  is  called  the  absolute  zero  of  tempera- 
ture ;  the  temperatures  reckoned  from  this  point  are  called  absolute  tem- 
peratures. They  are  clearly  obtained  by  adding  273  to  the  temperature  on 
the  Centigrade  scale.  Thus  -  35°  C.  is  238°  on  the  absolute  scale  of  tem- 
perature, and  +  15°  C.  is  288^. 


474  On  Heat.  [497 


CHAPTER   XII. 

MECHANICAL   EQUIVALENT   OF    HEAT. 

497.  Mechanical  equivalent  of  heat. —  If  the  various  instances  of  the 
production  of  heat  by  motion  be  examined,  it  will  be  found  that  in  all  cases 
mechanical  force  is  consumed.  Thus  in  rubbing  two  bodies  against  each 
other,  motion  is  apparently  destroyed  by  friction  ;  it  is  not,  however,  lost, 
but  appears  in  the  form  of  a  motion  of  the  particles  of  the  body  ;  the  motion 
of  the  mass  is  transformed  into  a  motion  of  the  molecules. 

Again,  if  a  body  be  allowed  to  fall  from  a  height,  it  strikes  against  the 
ground  with  a  certain  velocity.  According  to  older  views,  its  motion  is  de- 
stroyed, vis  viva  is  lost.  This,  however,  is  not  the  case ;  the  vis  viva  of 
the  body  appears  as  vis  viva  of  its  molecules. 

In  the  case,  too,  of  chemical  action,  the  most  productive  artificial  source 
of  heat,  it  is  not  difficult  to  conceive  that  there  is,  in  the  act  of  combining, 
an  impact  of  the  dissimilar  molecules  against  each  other,  an  effect  analogous 
to  the  production  of  heat  by  the  impact  of  masses  of  matter  against  each 
other  (483). 

In  like  manner,  heat  may  be  made  to  produce  motion,  as  in  the  case  of 
the  steam-engine,  and  the  propulsion  of  shot  from  a  gun. 

Traces  of  a  view  that  there  is  a  connection  between  heat  and  motion  are 
to  be  met  with  in  the  older  writers,  Bacon  for  example  ;  and  Locke  says, 
'  Heat  is  a  very  brisk  agitation  of  the  insensible  parts  of  the  object,  which 
produces  in  us  that  sensation  from  whence  we  denominate  the  object  hot ; 
so  that  what  in  our  sensation  is  heat,  in  the  object  is  nothing  but  motion.' 
Rumford,  in  explaining  his  great  experiment  of  the  production  of  heat  by 
friction,  was  unable  to  assign  any  other  cause  for  the  heat  produced  than 
motion  ;  and  Davy,  in  the  explanation  of  his  experiment  of  melting  ice  by 
friction  i)i  vacuo.,  expressed  similar  views.  Carnot,  in  a  work  on  the  steam- 
engine,  published  in  1S34,  also  indicated  a  connection  between  heat  and 
work. 

The  views,  however,  which  had  been  stated  by  isolated  writers  had  little 
or  no  influence  on  the  progress  of  scientific  investigation,  and  it  is  in  the 
year  1 842  that  the  modern  theories  may  be  said  to  have  had  their  origin. 
In  that  year  Dr.  Mayer,  a  physician  in  Heilbronn,  formally  stated  that  there 
exists  a  connection  between  heat  and  work  ;  and  he  it  was  who  first  intro- 
duced into  science  the  expression  '  mechanical  equivalent  of  heat.'  Mayer 
also  gave  a  method  by  which  this  equivalent  could  be  calculated  ;  the  par- 
ticular results,  however,  are  of  no  value,  as  the  method,  though  correct  in 
principle,  is  founded  on  incorrect  data. 

In  the  same  year  too,  Colding  of  Copenhagen  published  experiments  on 


497J 


Mechanical  Equivalent  of  Heat. 


47  S 


the  production  of  heat  by  friction,  from  which  he  concluded  that  the  evolu- 
tion of  heat  was  proportional  to  the  mechanical  energy  expended. 

About  the  same  time  as  Mayer,  but  quite  independently  of  him.  Joule 
commenced  a  series  of  experimental  investigations  on  the  relation  between 
heat  and  work.  These  first  drew  the  attention  of  scientific  men  to  the 
subject,  and  were  admitted  as  a  proof  that  the  transformation  of  heat  into 
mechanical  energy,  or  of  mechanical  energy  into  heat,  always  takes  place  in 
a  definite  numerical  ratio. 

Subsequently  to  Mayer  and  Joule,  several  physicists,  by  their  theoretical 
and  experimental  investigations,  have  contributed  to  establish  the  mechanical 
theory  of  heat  :  namely,  in  this  country.  Sir  W.  Thomson  and  Rankine  ;  in 
(jermany,  Helmholtz,  Clausius,  and  Holtzmann  ;  and  in  France,  Clapeyron, 
and  Regnault.  The  following  are  some  of  the  most  important  and  satis- 
factory of  Joule's  experiments. 

A  copper  vessel,  B  (fig.  430),  was  provided  with  a  brass  paddle-wheel 
(indicated   by  the  dotted  lines),  which   could  be  made  to  rotate  about  a 


vertical  axis.  Two  weights,  E  and  F,  were  attached  to  cords  which  passed 
over  the  pulleys  C  and  D,  and  were  connected  with  the  axis  A.  These 
weights  in  falling  cause  the  wheel  to  rotate.  The  height  of  the  fall,  which  in 
Joule's  experiments  was  about  63  feet,  was  indicated  on  the  scales  G  and  H. 

The  roller  A  was  so  constructed  that  by  detaching  a  pin  the  weights  could 
be  raised  without  moving  the  wheel.  The  vessel  B  was  filled  with  water 
and  placed  on  a  stand,  and  the  weights  allowed  to  sink.  When  they  had 
reached  the  ground,  the  roller  was  detached  from  the  axis,  and  the  weights 
again  raised,  the  same  operations  being  repeated  twenty  times.  The  heat 
produced  was  measured  by  ordinary  calorimetric  methods  (447). 

The  work  expended  is  measured  by  the  product  of  the  weight  into  the 
height  through  which  it  falls,  or  pk,  less  the  v.-ork  lost  by  the  friction  of  the 
various  parts  of  the  apparatus.  This  is  diminished  as  far  as  possible  by  the 
use  of  friction  wheels  {jj),  and  its  amount  is  determined  by  connecting  C 
and  D  without  causing  them  to  pass  over  A,  and  then  determining  the 
weight  necessary  to  communicate  to  them  a  uniform  motion. 


476  On  Heat.  [497 

In  this  way  it  has  been  found  that  a  thermal  unit— that  is,  the  quantity  of 
heat  by  which  a  pound  of  water  is  raised  through  i°  C. — is  generated  by  the 
expenditure  of. the  same  amount  of  work  as  would  be  required  to  raise  1,392 
pounds  through  i  foot,  or  i  pound  through  1,392  feet.  This  is  expressed  by 
saying  that  the  mechanical  equivalent  of  the  thermal  unit  is  1,392  foot- 
pounds. 

The  friction  of  an  iron  paddle-wheel  in  mercury  gave  1,397  foot-pounds, 
and  that  of  the  friction  of  two  iron  plates  gave  1,395  foot-pounds,  as  the 
mechanical  equivalent  of  one  thermal  unit. 

In  another  series  of  experiments,  the  air  in  a  receiver  was  compressed  by 
means  of  a  force-pump,  both  being  immersed  in  a  known  weight  of  water  at 
a  known  temperature.  After  300  strokes  of  the  piston  the  heat,  C,  was 
measured  which  the  water  had  gained.  This  heat  was  due  to  the  compres- 
sion of  the  air  and  to  the  friction  of  the  piston.  To  eliminate  the  latter  in- 
fluence, the  experiment  was  made  under  the  same  conditions,  but  leaving  the 
receiver  open.  The  air  was  not  compressed,  and  300  strokes  of  the  piston 
developed  C  thermal  units.  Hence  C  —  C  is  the  heat  produced  by  the  com- 
pression of  the  gas.     Representing  the  foot-pounds  expended  in  producing 

this  heat  by  W,  we  have  ^^p^  for  the  value  of  the  mechanical  equivalent. 

By  this  method  Joule  obtained  the  number  1,442. 

The  mean  number  which  Joule  adopted  for  the  mechanical  equivalent  of 
one  thermal  unit  on  the  Centigrade  scale  is  1,390  foot-pounds  ;  on  the 
Fahrenheit  scale  it  is  772  foot-pounds.  The  number  is  called /cw/^'j- ^^z«- 
valent,  and  is  usually  designated  by  the  symbol  J. 

On  the  metrical  system  424  metres  usually  are  taken  as  the  height  through 
which  a  kilogramme  of  water  must  fall  to  raise  its  temperature  i  degree 
Centigrade.  This  is  equal  to  42,400,000  ^i:^s  or  4-24  10"  grammes  raised 
through  a  height  of  a  centnnetre. 
^^*>-  ■  Professor  Rowland  of  Baltimore  has  recently  made  a  very  careful  and 
complete  determination  of  the  mechanical  equivalent  of  heat,  by  Joule's 
.  ,c>j,nethod,  in  which  he  has  examined  and  allowed  for  all  possible  sources  of 
error.  His  results  give  426'9  kilogramme-metres  as  the  mean  value  of  this 
constant  for  the  latitude  of  Baltimore. 

Him  made  the  following  determination  of  the  mechanical  equivalent  by 
means  of  the  heat  produced  by  the  compression  of  lead.  A  large  block  of 
sandstone,  CD  (fig.  431),  is  suspended  vertically  by  cords  ;  its  weight  is  P. 
E  is  a  piece  of  lead,  fashioned  so  that  its  temperature  may  be  determined  by 
the  introduction  of  a  thermometer.  The  weight  of  this  is  n,  and  its  specific 
heat  c.  AB  is  a  cylinder  of  cast  iron,  whose  weight  is/.  If  this  be  raised  to 
A'B',  a  height  of  //,  and  allowed  to  fall  again,  it  compresses  the  lead,  E, 
against  the  anvil,  CD.  It  remains  to  measure  on  the  one  hand  the  work 
lost,  and  on  the  other  the  heat  gained. 

The  hammer  AB  being  raised  to  a  height  //,  the  work  of  its  fall  is  ph  ; 
but  as,  by  its  elasticity,  it  rises  again  to  a  height  //,,  the  work  \s  p  (//-//,). 
The  anvil  CD,  on  the  other  hand,  has  been  raised  through  a  height  H 
to  CD'  and  has  recjuired  in  so  doing  PH  units  of  work.  The  work,  W, 
definitely  absorbed  by  the  lead  \s p  (/^-/z,)-  PH.  On  the  other  hand,  the 
lead  has  been  heated  by  6,  it  has  gained  UcO  thermal  units,  c  being  the 


497J 


Mechanical  Equivalent  of  Heat. 


A77 
specific  heat  of  lead,  and  the  mechanical  equivalent  J  is  equal  to  the  c[uotient 

.     A  series  of  six  experiments  gave  1,394  for  the  mechanical  equivalent 

as  thus  obtained. 


\^     '■ 

\^ 

, _^ j 

g       '■-  ^ 

^^^*-;^:^ 

1--- 

The  recent  experiments  of  Cantoni  and  Gerosa  in  this  direction  are  the 
simplest.  They  allowed  mercury  to  fall  from  a  funnel  through  a  narrow 
tube  into  a  vessel  below,  when  its  temperature  was  measured.  In  this  way 
the  number  1,390  was  obtained. 

Experiments  in  the  opposite  direction  have  also  been  made,  in  which  the 
work  produced  by  one  thermal  unit  was  determined.  This  was  done  on  a 
large  scale  by  Hirn  by  means  of  a  steam-engine  of  one  hundred  horse-power. 
He  determined  the  quantity  of  heat  contained  in  the  steam  before  its  action, 
and  then  the  amount  contained  in  the  water  after  its  condensation.  This  was 
less,  for  some  had  been  expended  in  work  ;  and  this  work  as  measured  by 
the  dynamometer  was  equivalent  to  that  which  had  disappeared,  the  number 
13907  being  thus  obtained. 

The  following  is  the  method  which  origmally  Mayer  employed  in  calcu- 
lating the  mechanical  equivalent  of  heat.  It  is  taken,  with  slight  modifica- 
tions, from  Prof.  Tyndall's  work  on  Heat,  who,  while  strictly  following 
Mayei-'s  reasoning,  has  corrected  his  data. 

Let  us  suppose  that  a  rectangular  vessel  with  a  section  of  a  square  foot 
contains  at  0°  a  cubic  foot  of  air  under  the  ordinary  atmospheric  pressure  ; 
and  let  us  suppose  that  it  is  inclosed  by  a  piston  without  weight. 

Suppose  now  that  the  cubic  foot  of  air  is  heated  until  its  volume  is 
doubled  ;  from  the  coefficient  of  expansion  of  air  we  know  that  this  is  the 
case  at  273°  C.  The  gas  in  doubling  its  volume  will  have  raised  the  piston 
through  a  foot  in  height ;  it  will  have  lifted  the  atmospheric  pressure  through 
this  distance.  But  the  atmospheric  pressure  on  a  square  foot  is  in  round 
numbers  15  x  144  =  2,160  pounds.  Hence  a  cubic  foot  of  air  in  doubling  its 
volume  has  hfted  a  weight  of  2,160  pounds  through  a  height  of  a  foot. 

Now,  a  cubic  foot  of  air  at  zero  weighs  1-29  ounce,  and  the  specific  heat 
of  air  under  constant  pressure — that  is,  when  it  can  expand  freely — as  com- 
pared with  that  of  an  equal  weight  of  water,  is  0-24  ;  so  that  the  quantity  of 
heat  which  will  raise  1-29  ounce  of  air  through  273°  will  only  raise  0-24  x  1-29 


478 


On  Heat. 


[497- 


=  0-31  oz.  of  water  through  the  same  temperature  ;  but  0*31  oz.  of  water  raised 
through  273°  is  equal  to  5-29  pounds  of  water  raised  through  1°  C. 

That  is,  the  quantity  of  heat  which  will  double  the  volume  of  a  cubic  foot 
of  air,  and  in  so  doing  will  lift  2,160  pounds  through  a  height  of  a  foot,  is 
5-29  thermal  units. 

Now,  in  the  above  case  the  gas  has  been  heated  under  constant  pressure, 
that  is,  when  it  could  expand  freely.  If,  however,  it  had  been  heated  under 
constant  volume,  its  specific  heat  would  have  been  less  in  the  ratio  :  1-414 
(460),  so  that  the  quantity  of  heat  required  under  these  circumstances  to 

raise  the   temperature   of  a  cubic  foot  of  air  would  be   5"29  < -~  =  374. 

Deducting  this  from  5-29,  the  diffei-ence  1-55  represents  the  weight  of  water 
v\'hich  would  have  been  raised  1°  C.  by  the  excess  of  heat  imparted  to  the 
air  when  it  could  expand  freely.  But  this  excess  has  been  consumed  in  the 
work  of  raising  2,160  pounds  through  a  foot.  Dividing  this  by  P55  we  have 
1 5393-  Hence  the  heat  which  will  raise  a  pound  of  water  through  1°  C.  will 
vaise  a  weight  of  1,393  pounds  through  a  height  of  a  foot ;  a  numerical  value 
of  the  mechanical  equivalent  of  heat  agreeing  as  closely  as  can  be  expected 
with  that  which  Joule  adopted  as  the  most  certain  of  his  experimental 
results. 

The  law  of  the  relation  of  heat  to  mechanical  energy  may  be  thus  stated : — 
Heat  and  mechanical  energy  are  iniitiially  convertible  ',  ajid  Jieat  requires  tor 
rts  production,  and  produces  by  its  disappearance,  mechanical  energy  in  the 
ratio  of  1,2,^0  foot-pouitds  for  every  thermal  unit. 


A  variety  of  experiments  may  in  like  manner  be  adduced  to  show  that 
whenever  heat  disappears  work  is  produced.  For  example,  if  in  a  reservoir 
immersed  in  water  the  air  be  compressed  to  the  extent  of  10  atmospheres  : 
supposing  that  now,  when  the  compressed  air  has  acquired  the  temperature 
of  the  water,  it  be  allowed  to  act  upon  a  piston  loaded  by  a  weight,  the 
weight  is  raised.     At  the  same  time  the  water  becomes  cooler,  showing  that 


497J 


Medianical  Equivalent  of  Heat. 


479 


a  certain  quantity  of  heat  had  disappeared  in  producing  the  mechanical 
effort  of  raising  the  weight.  This  may  also  be  illustrated  by  the  following 
experiment  (fig.  432),  due  to  Prof.  Tyndall  : — 

A  strong  metal  box  is  taken,  provided  with  a  stopcock,  on  which  can  be 
screwed  a  small  condensing  pump.  Having  compressed  the  air  by  its  means 
as  it  becomes  heated  by  this  process,  the  box  is  allowed  to  stand  for  some 
tmie,  until  it  has  acquired  the  temperature  of  the  surrounding  medium.  On 
opening  the  stopcock  the  air  rushes  out :  it  is  expelled  by  the  expansive 
force  of  the  internal  air  ;  in  short,  the  air  drives  itself  out.  Work  is  there- 
fore performed  by  the  air,  and  there  should  be  a  disappearance  of  heat ;  and 
if  the  jet  of  air  be  allowed  to  strike  against  the  thermopile,  the  galvano- 
meter is  deflected,  and  the  direction  of  its  deflection  indicates  a  cooling 
(fig.  432).  The  same  effect  is  observed  when,  on  opening  a  bottle  of  soda 
water,  the  carbonic  gas  which  escapes  is  allowed  to  impinge  against  the 
thermopile. 

If,  on  the  contrary,  the  experiment  is  made  with  an  ordinary  pair  of 
bellows,  and  the  current  of  air  is  allowed  to  strike  against  the  pile,  the 
deflection  of  the  galvanometer  is  in  the  opposite  direction,  indicating  an 


Fig.  433- 

increase  of  temperature  (fig.  433).  In  this  case  the  hand  of  the  experimenter 
performs  the  work,  which  is  converted  into  heat. 

Joule  placed  in  a  calorimeter  two  equal  copper  reservoirs,  which  could 
be  connected  by  a  tirbe.  One  of  these  contained  air  at  22  atmospheres,  the 
other  was  exhausted.  When  they  were  connected,  they  came  into  equi- 
librium under  a  pressure  of  11  atmospheres  ;  but  as  the  gas  in  expanding 
had  done  no  work,  there  was  no  alteration  in  temperature.  When,  however, 
the  second  reservoir  was  full  of  water,  the  air  in  entering  was  obliged  to 
expel  it  and  thus  perform  work,  and  the  temperature  sank,  owing  to  an 
absorption  of  heat. 

For  further  information  the  student  of  this  subject  is  referred  to  the 
following  works  : — Tyndall  on  Heat  as  a  Mode  of  Motion.,  Maxwell  on  Heat., 
Wormell's    Thermodynamics   (Longmans),    and   Tait    on    Thermodynamics 


4So  On  Heat  [497- 

(Edinondston  &  Douglas).  A  condensed,  though  complete  and  systematic 
account  of  the  dynamical  theory  of  heat  is  met  with  in  Professor  Foster's 
articles  on  '  Heat,'  in  Watts'  Dictionary  of  Chemistry. 

498.  Dissipation  of  energry. — Rankine  has  the  following  interesting 
observations  on  a  remarkable  consequence  of  the  mutual  convertibility  which 
has  been  shown  to  exist  between  heat  and  other  forms  of  energy  : — Sir  W. 
Thomson  has  pointed  out  the  fact  that  there  exists,  at  least  in  the  present 
state  of  the  known  world,  a  predominating  tendency  to  the  conversion  of  all 
the  other  forms  of  physical  energy  into  heat,  and  to  the  uniform  diffusion  of 
heat  throughout  all  matter.  The  form  in  which  we  generally  find  energy 
originally  collected  is  that  of  a  store  of  chemical  power  consisting  of  uncom- 
bined  elements.  The  combination  of  these  elements  produces  energy  in  the 
form  known  by  the  name  of  electrical  currents,  part  only  of  which  can  be 
employed  in  analysing  chemical  compounds,  and  thus  reconverted  into  a 
store  of  chemical  power  ;  the  remainder  is  necessarily  converted  into  heat ; 
a  part  only  of  this  heat  can  be  employed  in  analysing  compounds  or  in  re- 
producing electric  currents.  If  the  remainder  of  the  heat  be  employed  in 
expanding  an  elastic  substance,  it  may  be  converted  entirely  into  visible 
motion,  or  into  a  store  of  visible  mechanical  power  (by  raising  weights,  for 
example),  provided  the  elastic  substance  is  enabled  to  expand  until  its 
temperature  falls  to  the  point  which  corresponds  to  the  absolute  privation 
of  heat  ;  but  unless  this  condition  is  fulfilled  a  certain  proportion  only  of 
the  heat,  depending  on  the  range  of  temperature  through  which  the  elastic 
body  works,  can  be  converted,  the  rest  remaining  in  the  state  of  heat.  On 
the  other  hand,  all  visible  motion  is  of  necessity  ultimately  converted  into 
heat  by  the  agency  of  friction.  There  is,  then,  in  the  present  state  of  the 
known  world,  a  tendency  towards  the  conversion  of  all  physical  energy  into 
the  sole  form  of  heat. 

Heat,  moreover,  tends  to  diffuse  itself  uniformly  by  conduction  and  radia- 
tion, until  all  matter  shall  have  acquired  the  same  temperature.  There  is, 
consequently,  so  far  as  we  understand  the  present  condition  of  the  universe, 
a  tendency  towards  a  state  in  which  all  physical  energy  will  be  in  the  state  of 
heat,  and  that  heat  so  diffused  that  all  matter  will  be  at  the  same  temperature  ; 
so  that  there  will  be  an  end  of  all  physical  phenomena. 

V^ast  as  this  speculation  may  seem,  it  appears  to  be  soundly  based  on 
experimental  data,  and  to  truly  represent  the  present  condition  of  the  uni- 
verse as  far  as  we  know  it. 


-499]  Theories  of  Light  481 


BOOK    VII. 

ON    LIGHT. 


CHAPTER    I. 

TRANSMISSION,    VELOCITY,   AND    INTENSITY   OF    LIGHT. 

499.  Theories  of  light Light  is  the  agent  which,  by  its  action  on  the 

retina,  excites  in  us  the  sensation  of  vision.  That  part  of  physics  which  deals 
with  the  properties  of  hght  is  known  as  optics. 

In  order  to  explain  the  origin  of  light,  various  hypotheses  have  been  made, 
the  most  important  of  which  are  the  emission  or  corpuscular  theory,  and  the 
undulatory  theory. 

On  the  emission  theory  it  is  assumed  that  luminous  bodies  emit,  in  all 
directions,  an  imponderable  substance,  which  consists  of  molecules  of  an 
extreme  degree  of  tenuity  :  these  are  propagated  in  right  lines  with  an  almost 
infinite  velocity.  Penetrating  into  the  eye  they  act  on  the  retina,  and  deter- 
mine the  sensation  which  constitutes  vision. 

On  the  undulatory  theory,  all  bodies,  as  well  as  the  celestial  spaces,  are 
filled  by  an  extremely  subtle  elastic  medium,  which  is  called  the  lt(miniferoiis 
ether.  The  luminosity  of  a  body  is  due  to  an  infinitely  rapid  vibratory  motion 
of  its  molecules,  which,  when  communicated  to  the  ether,  is  propagated  in  all 
directions  in  the  form  of  spherical  waves,  and  this  vibratory  motion,  being 
thus  transmitted  to  the  retina,  calls  forth  the  sensation  of  vision.  The 
vibrations  of  the  ether  take  place  not  in  the  direction  of  the  wave,  but  in  a 
plane  at  right  angles  to  it.  The  latter  are  called  the  transversal  vibrations. 
An  idea  of  these  may  be  formed  by  shaking  a  rope  at  one  end.  The  vibra- 
tions, or  to  and  fro  movements,  of  the  particles  of  the  rope,  are  at  right 
angles  to  the  length  of  the  rope,  but  the  onward  motion  of  the  wave's  form 
is  in  the  direction  of  the  length. 

On  the  emission  theory  the  propagation  of  light  is  effected  by  a  motion 
or  translation  of  particles  of  light  thrown  out  from  the  luminous  body,  as  a 
bullet  is  discharged  from  a  gun  ;  on  the  undulatory  theory  there  is  no  pro- 
gressive motion  of  the  particles  themselves,  but  only  of  the  state  of  disturb- 
ance which  was  communicated  by  the  luminous  body  ;  it  is  a  motion  of 
oscillation.,  and,  like  the  propagation  of  waves  in  water,  takes  place  by  a  series 
of  vibrations. 

The  luminiferous  ether  penetrates  all  l)odies,  but  on  account  of  its 
extreme  tenuity  it  is  uninfluenced  by  gravitation  ;  it  occupies  space,  and 
although  it  presents  no  appreciable  resistance  to  the  motion  of  the  denser 
bodies,  it  is  possible  that  it  hinders  the  motion  of  the  smaller  comets.     It  has 


482  On  Light.  [499- 

been  found,  for  example,  that  Encke's  comet,  whose  period  of  revolution  is 
about  3^  years,  has  its  period  diminished  by  about  O'li  of  a  day  at  each 
successive  rotation,  and  this  diminution  is  ascribed  by  some  to  the  resistance 
of  the  ether. 

The  fundamental  principles  of  the  undulatory  theory  were  enunciated  by 
Huyghens,  and  subsequently  by  Euler.  The  emission  theor)^,  principally 
owing  to  Newton's  powerful  support,  was  for  long  the  prevalent  scientific 
creed.  The  undulatory  theory  was  adopted  and  advocated  by  Young,  who 
showed  how  a  large  number  of  optical  phenomena,  particularly  those  of 
diffraction,  were  to  be  explained  by  that  theory.  Subsequently,  too,  though 
independently  of  Young,  Fresnel  showed  that  the  phenomena  of  diffraction, 
and  also  those  of  polarisation,  are  explicable  on  the  same  theory,  which,  since 
his  time,  has  been  generally  accepted. 

The  undulatory  theory  not  only  explains  the  phenomena  of  light,  but  it 
reveals  an  intimate  connection  between  these  phenomena  and  those  of  heat 
r429)  ;  it  shows,  also,  how  completely  analogous  the  phenomena  of  light  are 
to  those  of  sound,  regard  being  had  to  the  differences  of  the  media  in  which 
these  two  classes  of  phenomena  take  place. 

500.  Xiuminous,  transparent,  translucent,  and  opaque  bodies. — Lumi- 
noits  bodies  are  those  which  emit  light,  such  as  the  sun,  and  ignited  bodies. 
Transparent  or  diaphanous  bodies  are  those  which  readily  transmit  light, 
and  through  which  objects  can  be  distinguished  :  water,  gases,  polished  glass 
are  of  this  kind.  Translucent  bodies  transmit  light,  but  objects  cannot  be 
distinguished  through  them :  ground  glass,  oiled  paper,  &c.,  belong  to  this 
class.  Opaque  bodies  do  not  transmit  light ;  for  example,  wood,  metals,  &c. 
No  bodies  are  quite  opaque  ;  they  are  all  more  or  less  translucent  when  cut 
in  sufficiently  thm  leaves. 

Foucault  showed  that  when  the  object-glass  of  a  telescope  is  thinly 
silvered,  the  layer  is  so  transparent  that  the  sun  can  be  viewed  through  it 
without  danger  to  the  eyes,  since  the  metallic  surface  reflects  the  greater 
part  of  the  heat  and  light. 

501.  Iiuminous  ray  and  pencil. — A  luminous  ray  is  the  direction  of  the 
line  in  which  light  is  propagated  ;  a  luminous  pencil  is  a  collection  of  rays 
from  the  same  source  ;  it  is  said  to  be  parallel  when  it  is  composed  of 
parallel  rays,  divergent  when  the  rays  separate  from  each  other,  and  con- 
vergent \\\\^r\  they  tend  towards  the  same  point.  Every  luminous  body  emits 
divergent  rectilinear  rays  from  all  its  points,  and  in  all  directions. 

502.  Propagation  of  light  in  a  homogreneouB  medium. — A  medium  is 
any  space  or  substance  which  light  can  traverse,  such  as  a  vacuum,  air,  water, 
glass,  &c.  A  medium  is  said  to  be  homogeneous  when  its  chemical  compo- 
sition and  density  are  the  same  in  all  parts. 

In  every  homogeneous  medium  light  is  propagated  in  a  right  line.  For, 
if  an  opaque  body  is  placed  in  the  right  line  which  joins  the  eye  and  the 
luminous  body,  the  light  is  intercepted.  The  light  which  passes  into  a  dark 
room  by  a  small  aperture  is  visible  from  the  light  fallin-  on  the  particles  of 
dust  suspended  in  the  atmosphere. 

Light  changes  its  direction  on  meeting  an  object  which  it  cannot  pene- 
trate, or  when  it  passes  from  one  medium  to  another.  These  phenomena 
will  be  described  under  the  heads  rejlection  and  refraction. 


503] 


Shadozv,  Penumbra. 


483 


503.  Sbadow,  penumbra. — When  light  falls  upon  an  opaque  body  it 
cannot  penetrate  into  the  space  immediately  behind  it,  and  this  space  is 
called  the  shadow. 

In  determining  the  extent  and  the  shape  of  a  shadow  projected  by  a  body, 
two  cases  are  to  be  distinguished  ;  that  in  which  the  source  of  light  is  a 
single  point,  and  that  in  which  it  is  a  body  of  any  given  extent. 

In  the  first  case,  let  S  (fig.  434)  be  the  luminous  point,  and  M  a  spherical 
body,  which  causes  the  shadow.      If  an    infinitely  long  straight  line,  SG, 


move  round  the  sphere  M  tangentially,  always  passing  through  the  point  S, 
this  line  will  produce  a  conical  surface,  which,  beyond  the  sphere,  separates 
that  portion  of  space  which  is  in  shadow  from  that  which  is  illuminated.  In 
the  present  case,  on  placing  a  screen,  PQ,  behind  the  opacjue  body  the  limit 
of  the  shadow  HG  will  be  sharply  defined.  This  is  not,  however,  usually 
the  case,  for  luminous  bodies  have  always  a  certain  magnitude,  and  are  not 
merely  luminous  points. 

Suppose  that  the  luminous  and  illuminated  bodies  are  two  spheres,  SL 
and  MN  (fig.  435).     If  an  infinite  straight  line,  AG,  moves  tangentially   to 


both  spheres,  always  cutting  the  line  of  the  centre  in  the  point  A,  it  will  pro- 
duce a  conical  surface  with  this  point  for  a  summit,  and  which  traces  behind 
the  sphere  MN  a  perfectly  dark  space  MGHN.  If  a  second  right  line,  LD, 
which  cuts  the  line  of  centre  in  B,  moves  tangentially  to  the  two  spheres,  so 
as  to  produce  a  new  conical  surface,  BDC,  it  will  be  seen  that  all  the  space 
outside  this  surface  is  illuminated,  but  that  the  part  between  the  two  conical 
surfaces  is  neither  cjuite  dark  nor  quite  light.  So  that  if  a  screen,  PQ,  is 
placed  behind  the  opaque  body,  the  portion  cQdYi  of  the  screen  is  quite  in 
the  shadow,  while  the  space  ab  receives  light  from  certain  parts  of  the  lumi- 
nous body,  and  not  from  others.     It  is  brighter  than  the  true  shadow,  and 


4«4 


On  Lis-ht 


[503- 


not  so  bright  as  the  rest  of  the  screen,  and  it  is  accordingly  called  the 
pcnujitOfa. 

Shadows  such  as  these  are  geometrical  sliadou's ;  physical  shadoiL's,  or 
those  which  are  really  seen,  are  by  no  means  so  sharply  defined.  A  certain 
quantity  of  light  passes  into  the  shadow,  even  when  the  source  of  light  is  a 
mere  point,  and  conversely  the  shadow  influences  the  illuminated  part.  This 
phenomenon,  which  will  be  afterwards  described,  is  known  by  the  name  of 
diffraction  (646). 

The  explanation  of  the  phenomena  of  eclipses  follows  directly  from  the 
theory  of  shadows. 

When  the  opaque  disc  of  the  moon  comes  according  to  the  conditions 
between  the  sun  and  the  earth,  the  shadow  cast  by  the  moon  causes  a  more 
or  less  complete  solar  eclipse  on  those  parts  of  the  earth  which  it  meets. 

Let  S  be  the  sun,  T  the  earth,  and  L  the  moon  placed  in  a  position 
favourable  for  an  eclipse  (fig.  436).     If  we  can  suppose  the  three  bodies 

represented  with  their 
7-clativc  magnitudes  and 
distances  we  need  only 
repeat  the  graphical 
construction  of  fig.  436 
to  determine  the  dimen- 
sions of  the  cone  of  the 
shadow,  and  of  the  pe- 
numbra of  the  moon. 
The  length  LI  of  the 
cone  of  the  shadow 
varies  between  57  and  59  terrestrial  radii,  according  to  the  relative  positions 
of  the  earth  and  its  satellite  ;  the  distance  of  the  two  planets  varies  between 
55  and  62  such  radii  ;  hence  under  favourable  conditions  the  cone  of  the 


Fig.  436. 


shadow  may  reach  the  earth,  and  in  those  points  of  the  earth  thus  touched,  m. 
there  is  a  total  eclipse  of  the  sun.  As  this  area  has  relatively  a  small  extent, 
an  eclipse  which  is  visible  by  the  inhabitants  of  this  area  is  not  so  by  those  in 
the  neighbourhood.     After  the  lapse  of  a  time  which  never  exceeds  3  min. 


-5041 


Images  produced  by  small  Apertures. 


485 


13  sec.  the  cone  will  have  left  the  place  ;«  and  will  pass  to  w',  which  is  not 
necessarily  on  the  same  parallel  of  latitude.  It  will  thus  sweep  over  the 
surface  of  the  earth,  in  virtue  of  the  special  motion  of  the  two  heavenly 
bodies,  along  a  line  which  astronomers  can  determine  beforehand.  On  all 
points  along-  this  line  (fig.  437)  there  will  successively  be  a  total  eclipse ; 
for  adjacent  ones,  which  are  within  the  cone  of  the  penumbra,  the  eclipse 
will  h&  partial. 

If  the  cone  of  the  shadow  does  not  reach  the  earth,  there  will  nowhere  be 
a  total  eclipse  ;  but  on  a  point  in'  (fig.  43S)  there  will  be  no  light  from  the 
central  part  of  the  sun  ;  this  will  then  appear  like  a  black  circle  surrounded 
by  a  bright  ring  (fig.  439)  ;  this  is  what  is  called  an  a/mtilar  eclipse. 


Fig.  439- 


Total  or  partial  eclipses  of  the  moon  are  produced  by  the  total  or  partial 
immersion  of  the  moon  in  the  cone  of  the  shadow  cast  by  the  earth  ;  for  an 
observer  on  the  moon  they  would  constitute  total  or  partial  eclipses  of  the 
sun  ;  total  at  those  parts  of  the  moon  in  the  shadow,  partial  at  those  in  the 
penumbra. 

The  traiisits  of  Venus  or  of  Mercury  over  the  sun  are  phenomena  of  the 
same  kind  as  eclipses,  being  produced  by  the  projection  on  the  earth  of  the 
penumbral  cones  of  shadow  of  those  planets.  The  eclipses  of  the  satellites 
of  certain  planets  such  as  Jupiter  are  identical  with  the  eclipses  of  the  moon. 

504.  Imagres  produced  by  small  apertures. — When  luminous  rays, 
which  pass  into  a  dark  chamber  tJirougJi  a  small  aperture,  are  received  upon 
a  screen,  they  form  images  of  external  objects.     These  images  are  inverted, 


their  shape  is  always  that  of  the  external  objects,  and  is  independent  of  the 
shape  of  the  aperture. 

The  inversion  of  the  images  arises  from  the  fact  that  the  luminous  rays 
proceeding  from  external  objects,  and  penetrating  into  the  chamber,  cross 
one  another  in  passing  the  aperture,  as  shown  in  fig.  440.  Continuing  in  a 
straight  line,  the  rays  from  the  higher  parts  meet  the  screen  at  the  lower 


486  On  Light.  [604- 

parts  ;  and  conversely,  those  which  come  from  the  lower  parts  meet  the 
higher  parts  of  the  screen.  Hence  the  inversion  of  the  image.  In  the 
article  Camera  Obscura  it  will  be  seen  that  the  brightness  and  precision  of 
these  images  are  increased  by  means  of  lenses. 

In  order  to  show  that  the  shape  of  the  image  is  independent  of  that  of 
the  aperture,  when  the  latter  is  sufficiently  small  and  the  screen  at  an  ade- 
quate distance,  imagine  a  triangular  aperture,  O  (fig.  441),  made  in  the  door 


of  a  dark  chamber,  and  let  ab  be  a  screen  on  which  is  received  the  image  of 
a  flame,  AB.  A  divergent  pencil  from  each  point  of  the  flame  passes  through 
the  aperture,  and  forms  on  the  screen  a  triangular  image  resembling  the 
aperture.  But  the  union  of  all  these  partial  images  produces  a  total  image 
of  the  same  form  as  the  luminous  object.  For  if  we  conceive  that  an  infinite 
straight  line  moves  round  the  aperture,  with  the  condition  that  it  is  always 
tangential  to  the  luminous  object  AB,  and  that  the  aperture  is  very  small, 
the  straight  line  describes  two  cones,  the  apex  of  which  is  the  aperture, 
while  one  of  the  bases  is  the  luminous  object  and  the  other  the  luminous 
object  on  the  screen — that  is,  the  image.  Hence,  if  the  screen  is  per- 
pendicular to  the  right  line  joining  the  centre  of  the  aperture  and  the  centre 
of  the  luminous  body,  the  image  is  similar  to  the  body  ;  but  if  the  screen  is 
oblique,  the  image  is  elongated  in  the  direction  of  its  obliquity.  This  is 
what  is  seen  in  the  shadow  produced  by  foliage  ;  the  luminous  rays  passing 
through  the  leaves  produce  images  of  the  sun,  which  are  either  round  or 
elliptical,  according  as  the  ground  is  perpendicular  or  oblique  to  the  solar 
rays  ;  and  this  is  the  case  whatever  be  the  shape  of  the  aperture  through 
which  the  light  passes. 

505.  Velocity  of  ll^bt. — Light  moves  with  such  a  velocity  that  at  the 
surface  of  the  earth  there  is,  to  ordinaiy  observation,  no  appreciable  interval 
between  the  occurrence  of  any  luminous  phenomenon  and  its  perception  by 
the  eye.  And,  accordingly,  this  velocity  was  first  determined  by  means  of 
astronomical  observations.  Romer,  a  Danish  astronomer,  in  1675,  first 
deduced  the  velocity  of  light  from  an  observation  of  the  eclipses  of  Jupiter's 
first  satellite. 

Jupiter  is  a  planet,  round  which  four  satellites  revolve,  as  the  moon 
does  round  the  earth.  This  first  satellite,  E  ^tig.  442),  suflcrs  occultation — 
that  is,  jiasses  into  Jupiter's  shadow — at  equal  intervals  of  time,  which  arc 
42h.  28m.  36s.  While  the  earth  moves  in  that  part  of  its  orbit,  al\  nearest 
Jupiter  its  distance  from  that  planet  docs  not  materially  alter,  and  the 
intervals  between  two  successive  occultations  of  the  satellite  are  approximately 


-506]     Apparatus  for  determining  the    Velocity  of  Light.      487 

the  same  ;  but,  in  proportion  as  the  earth  moves  away  in  its  revolution 
round  the  sun,  S,  the  interval  between  two  occultations  increases,  and  when, 
at  the  end  of  six  months,  the  earth  has  passed  from  the  position  T  to  the 
position  T',  a  total  retardation  of  i6m.  36s.  is  observed  between  the  time  at 
which  the  phenomenon  is  seen  and  that  at  which  it  is  calculated  to  take 
place.  But  when  the  earth  was  in  the  position  T,  the  sun's  light  reflected 
from  the  satellite  E  had  to  traverse  the  distance  ET,  while  in  the  second 
position  the  light  had  to  traverse  the  distance  ET'.  This  distance  exceeds 
the  first  by  the  quantity  TT',  for,  from  the  great  distance  of  the  satellite  E, 


Fig.  442, 

the  rays  ET  and  ET'  may  be  considered  parallel.  Consequently,  light 
requires  i6m.  36s.  to  travel  the  diameter  TT'of  the  terrestrial  orbit,  or  twice 
the  distance  of  the  earth  from  the  sun,  which  gives  for  its  velocity  190,000 
miles  in  a  second. 

The  stars  nearest  the  earth  are  separated  from  it  by  at  least  206,265 
times  the  distance  of  the  sun.  Consequently,  the  light  which  they  send 
requires  more  than  3  years  to  reach  us.  Those  stars,  which  are  only  visible 
by  means  of  the  telescope,  are  possibly  at  such  a  distance  that  thousands 
of  years  would  be  required  for  their  light  to  reach  our  planetaiy  system. 
They  might  have  been  extinguished  fer  ages  without  our  knowing  it. 

506.  Foucault's  apparatus  for  determining:  the  velocity  of  light.— 
Notwithstanding  the  prodigious  velocity  of  light,  Foucault  succeeded  in 
determining  it  experimentally  by  the  aid  of  an  ingenious  apparatus,  based 
on  the  use  of  the  rotating  mirror,  which  was  adopted  by  Wheatstone  in 
measuring  the  velocity  of  electricity. 

In  the  description  of  this  apparatus,  a  knowledge  of  the  principal  pro- 
perties of  mirrors  and  of  lenses  is  presupposed.  Fig.  444  represents  the 
chief  parts  of  Foucault's  arrangement.  The  window  shutter,  K,  of  a  dark 
chamber  is  perforated  by  a  square  aperture,  behind  which  the  platinum 
wire  o  is  stretched  vertically.  A  beam  of  sunlight  reflected  from  the  out- 
side upon  a  mirror  enters  the  dark  room  by  the  square  aperture,  meets  the 
platinum  wire,  and  then  traverses  an  achromatic  lens,  L,  with  a  long  focus, 
placed  at  a  distance  from  the  platinum  wire  less  than  double  the  principal 
focal  distance.  The  image  of  the  platinum  wire,  more  or  less  magnified, 
would  thus  be  formed  on  the  axis  of  the  lens  ;  but  the  pencil  of  light, 
having  traversed  the  lens,  impinges  on  a  plane  mirror, ;;?,  rotating  with  great 
velocity  ;  it  is  reflected  from  this,  and  forms  in  space  an  image  of  the 
platinum  wire,  which  is  displaced  with  an  angular  velocity  double  that  of  the 
mirror  (520).     This  image  is  reflected  by  a  concave  mirror,  M,  whose  centre 


488 


On  Lio-ht. 


[506- 


of  curvature  coincides  with  the  axis  of  rotation  of  the  mirror  tn,  and  with  its 
centre  of  figure.  The  pencil  reflected  from  the  mirror  M  returns  upon  itself, 
is  again  reflected  from  the  mirror  ;«,  traverses  the  lens  a  second  time,  and 
forms  an  image  of  the  platinum  wire,  which  appears  on  the  wire  itself  so 
long  as  the  mirror  Jii  turns  slowly. 

In  order  to  see  this  image  without  hiding  the  pencil  of  light  which  enters 
by  the  aperture  in  K,  a  mirror  of  unsilvered  glass,  V,  with  parallel  faces,  is 
placed  between  the  lens  and  the  wire,  and  is  inclined  so  that  the  reflected 
rays  fall  upon  a  powerful  eyepiece,  P. 

The  apparatus  being  arranged,  if  the  mirror  in  is  at  rest,  the  pencil  after 
meeting  M  is  reflected  to  in,  and  from  thence  returns  along  its  former  path, 
till  it  meets  the  glass  plate  V  in  a,  and  being  partially  reflected,  forms  at  d — 
the  distance  ad  being  equal  to  ao — an  image  of  the  wire,  which  the  eye  is 
enabled  to  observe  by  means  of  the  eyepiece,  P.  If  the  mirror,  insteadjof 
being  fixed,  is  moving  slowly  round — its  axis  being  at  right  angles  to  the 


plane  of  the  paper— there  will  be  no  sensible  change  in  the  position  of  the 
mirror  in  during  the  brief  interval  elapsing  while  light  travels  from  in  to  M 
and  back  again,  but  the  image  will  alternately  disappear  and  reappear.  If 
now  the  velocity  of  Vl  is  increased  to  upwards  of  30  turns  per  second,  the 
interval  between  the  disappearance  and  reappearance  is  so  short  that  the 
impression  on  the  eye  is  persistent,  and  the  image  appears  perfectly  steady. 
Lastly,  if  the  mirror  turns  with  sufficient  velocity,  there  is  no  appreciable 
change  in  its  position  during  the  time  which  the  light  takes  in  making  the 
double  journey  from  ;//  to  M,  and  from  M  to  in  ;  the  return  ray,  after  its 
reflection  from  the  mirror  w,  takes  the  direction  ;///',  and  forms  its  image 
at  /  ;  that  is,  the  image  has  undergone  a  total  deviation  di.  Speaking  pre- 
cisely, there  is  a  deviation  as  soon  as  the  mirror  turns,  even  slowly ;  but  it  is 
only  appreciable  when  it  has  acquired  a  certain  magnitude,  which  is  the  case 
when  the  velocity  of  rotation  is  sufficiently  rapid,  or  the  distance  Mw  suffi- 
(  icntly  great,  for  the  deviation  necessarily  increases  with  the  time  which  the 
light  takes  in  returning  on  its  own  path. 


-507]  Experiments  of  Fizeau.  489 

In  Foucault's  experiment  the  distance  Mw  was  only  13^  feet  ;  when  the 
mirror  rotated  with  a  velocity  of  600  to  800  turns  in  a  second,  deviations  of 
f^  to  ^''-j  of  a  millimetre  were  obtained. 

Taking  M;«  =  /,  L;«  =  /',  cL  =  r,  and  representing  by  n  the  number  of 
turns  in  a  second,  by  S  the  absolute  deviation  di^  and  by  V  the  velocity  of 
light,  Foucault  arrived  at  the  formula 

a(/4-/')' 

from  which  the  velocity  of  light  is  calculated  at  185,157  miles  in  a  second  ; 
this  number,  which  is  less  than  that  ordinarily  assumed,  agrees  remarkably 
well  with  the  value  deduced  from  the  new  determinations  of  the  value  of  the 
solar  parallax. 

The  mechanism  by  which  the  mirror  was  turned  consisted  of  a  small 
steam  turbine,  bearing  a  sort  of  resemblance  to  the  syren,  and,  like  that 
instrument,  giving  a  higher  sound  as  the  rotation  is  more  rapid  :  in  fact,  it 
is  by  the  pitch  of  the  note  that  the  velocity  of  the  rotation  is  determined. 

In  this  apparatus  liquids  can  be  experimented  upon.  For  that  purpose 
a  tube,  AB,  10  feet  long,  and  filled  with  distilled  water,  is  placed  between  the 
turning  mirror  in,  and  a  concave  mirror  M',  identical  with  the  mirror  M. 
The  luminous  rays  reflected  by  the  rotating  mirror,  in  the  direction  ;;zM', 
traverse  the  column  of  water  AB  twice  before  returning  to  V.  But  the  return 
ray  then  becomes  reflected  at  c,  and  forms  its  image  at  h  :  the  deviation  is 
consequently  greater  for  rays  which  have  traversed  water  than  for  those 
which  have  passed  through  air  alone  ;  hence  the  velocity  of  light  is  less  in 
water  than  in  air. 

This  is  the  most  important  part  of  these  experiments.  For  it  had  been 
shown  theoretically  that  on  the  undulator>'  theory  the  velocity  of  light  must 
be  less  in  the  more  highly  refracting  medium  (638),  while  the  opposite  is  a 
necessary  consequence  of  the  emission  theory.  Hence  Foucault's  result  may 
be  regarded  as  a  crucial  test  of  the  validity  of  the  undulatory  theory. 

507.  Szperiments  of  Flzeau. — In  1849  Fizeau  measured  directly  the 
velocity  of  light,  by  ascertaining  the  time  it  took  to  travel  from  Suresnes  to 
Montmartre  and  back  again.  The  apparatus  employed  was  a  toothed  wheel, 
capable  of  being  turned  more  or  less  quickly,  and  with  a  velocity  that  could 
be  exactly  ascertained.  The  teeth  were  made  of  precisely  the  same  width 
as  the  intervals  between  them.  The  apparatus  being  placed  at  Suresnes,  a 
pencil  of  parallel  rays  was  transmitted  through  an  interval  between  two 
teeth  to  a  mirror  placed  at  Montmartre.  The  pencil,  directed  by  a  properly 
arranged  system  of  tubes  and  lenses,  returned  to  the  wheel.  As  long  as  the 
apparatus  was  at  rest  the  pencil  returned  exactly  through  the  same  interval 
as  that  through  which  it  first  set  out.  But  when  the  wheel  was  turned 
sufficiently  fast,  a  tooth  was  made  to  take  the  place  of  an  interval,  and  the 
ray  was  intercepted.  By  causing  the  wheel  to  turn  more  rapidly,  it  re- 
appeared when  the  interval  between  the  next  two  teeth  had  taken  the  place 
of  the  former  tooth  at  the  instant  of  the  return  of  the  pencil. 

The  distance  between  the  two  stations  was  28,334  feet.  By  means  of  the 
data  furnished  by  this  distance,  by  the  dimensions  of  the  wheel,  its  velocity 
of  rotation,  &c.,  Fizeau  found  the  velocity  of  light  to  be  196,000  miles  per 


4SO  On  Light.  [507- 

second — a  result  agreeing  with  that  given  by  astronomical  observation  as 
closely  as  can  be  expected  in  a  determination  of  this  kind. 

Comu  recently  investigated  the  velocity  of  light  by  Fizeau's  method, 
but  with  improvements  so  that  the  probable  error  did  not  exceed  ^]-  of  the  total 
amount  ;  the  two  stations,  which  were  6-4  miles  apart,  were  a  pavilion  of 
the  Ecole  Polytechnique  and  a  room  in  the  barracks  of  Mont  Valerien.  By 
means  of  electromagnetic  arrangements  the  rotation  of  the  toothed  disc, 
and  the  times  of  obscuration  and  illumination,  were  registered  on  a  blackened 
cylinder,  on  the  principle  of  the  method  described  in  (245).  Comu  thus 
obtained  the  number  185,420  miles — a  result  closely  agreeing  with  that 
of  Foucault,  and  which  is  supported  by  calculations  based  on  the  results  of 
astronomical  observations  of  the  transit  of  Venus  in  1874.  Michelson  made 
a  determination  of  the  velocity  of  light  by  Foucault's  method,  by  which  he 
obtained  the  result  186,380,  with  a  possible  error  of  33  miles. 

508.  Xiaws  of  the  intensity  of  llgbt. — The  ifitensify  of  illumination  is 
the  quantity  of  light  received  on  the  unit  of  surface  ;  it  is  subject  to  the 
following  laws  :• — 

I.  T/ic  intensity  of  illumination  on  a  given  surface  is  inversely  as  the 
square  of  its  distance  from  the  source  oj  light. 

II.  The  intensity  of  illumination  which  is  received  obliquely  is  propor- 
tiojial  to  the  cosine  of  the  angle  which  the  Iwninous  rays  make  with  the 
normal  to  the  illuminated  surface. 

In  order  to  demonstrate  the  first  law,  let  there  be  two  circular  screens, 
CD  and   AB  (fig.  445),. one  placed  at  a  certain  distance  from  a  source  of 

light,  L,  and  the  other  at 
double  this  distance,  and 
let  J  and  S  be  the  areas 
of  the  two  screens.  If 
a  be  the  total  quantity  of 
lig'ht  which  is  emitted  by 
the  source  in  the  direc- 
tion of  the  cone  ALB. 
the  intensity  of  the  light 
on  the  screen  CD— that 
is,     the    quantity    which 

and  the  intensity  on  the  screen  AB  is  -. 

S 


falls  on  the  unit  of  surfa 


Now  as  the  triangles  ALB  and  CLD  are  similar,  the  diameter  of  AB  is 
double  that  of  CD  ;  and  as  the  surfaces  of  circles  are  as  the  squares  of  their 

diameters,  the  surface  S  is  four  times  j,  consequently  the  intensity  -^  is  one- 
fourth  that  of  ' . 
s 

The  same  law  may  also  be  demonstrated  by  an  experiment  with  the 
apparatus  represented  in  fig.  447.  It  is  made  by  comparing  the  shadows  of  an 
opaque  rod  cast  upon  a  glass  plate,  in  one  case  I)y  the  light  of  a  single  candle, 
and  in  another  by  tliat  of  a  lamp  equalling  four  candles,  placed  at  double  the 
distance  of  the  first.     In  both  cases  the  shadows  have  the  same  intensity. 

Fig.  445  shows  that  it  is  owing  to  the  divergence  of  the  luminous  rays 


-509] 


Photometers. 


491 


emitted  from  the  same  source  that  the  ntensity  of  hght  is  inversely  as  the 
square  of  the  distance.  The  illumination  of  a  surface  placed  in  a  beam  of 
parallel  luminous  rays  is  the  same  at  all  distances  in  a  vacuum  ;  in  air  and 
in  other  transparent  media  the  intensity  of  light  decreases,  in  consequence 
of  absorption,  more  rapidly  than  the  square  of  the  distance. 

The  second  law  of  intensity  corresponds  to  the  law  which  we  have  found 
to  prevail  for  heat  :  it  may  be  theoretically  deduced  as  follows  : — Let  DA, 
EB  (fig.  446)  be  a  pencil  of  parallel  rays  falling  obliquely  on  a  surface,  AB 
and  let  ovt  be  the  normal  to  this 
surface.     If  S  is  the  section  of  the 
pencil,  a  the  total  quantity  of  light 
which  falls  on  the  surface  AB,  and 
I   that   which  falls  on  the   unit  of 
surface — that    is,    the    intensity   of 


illumination — we  have  I  = 


AB" 


But 


Fig.  446. 


as  S  is  only  the  projection  of  AB 

on  a  plane  perpendicular  to  the  pencil,  we  know  from  trigonometry  that 


S  =  AB  cos  a,  from  which  AB  = 


This  value  substituted  in  the  above 


equation  gives    I  =  --  cos  a 


a  formula  which  demonstrates  the  law  of  the 


cosine,  for  as  a  and  S  are  constant  quantities,  I  is  proportional  to  cos  a. 

The  law  of  the  cosine  applies  also  to  rays  emitted  obliquely  by  a  luminous 
surface  ;  that  is,  the  rays  are  less  intense  in  proportion  as  they  are  more 
inclined  to  the  surface  which  emits  them.  In  this  respect  they  correspond 
to  the  third  law  of  the  intensity  of  radiant  heat. 

509.  Pbotometers. — A  photometer  is  an  apparatus  for  measuring  the 
relative  intensities  of  dififerent  sources  of  light. 

Rumford's  photometer. — This  consists  of  a  ground  glass  screen,  in  front 
of  which  is  fixed  an  opaque  rod  (fig.  447)  ;  the  lights  to  be  compared — for 


Fig.  447. 

instance,  a  lamp  and  a  candle — are  placed  at  a  certain  distance  in  such  a 
manner  that  each  projects  oh  the  screen  a  shadow  of  the  rod.    The  shadows 


492  On  Light.  [509- 

thus  projected  are  at  first  of  unequal  intensity,  but  by  altering  the  position 
of  the  lamp,  it  may  be  so  placed  that  the  intensity  of  the  two  shadows  is  the 
same.  Then,  since  the  shadow  thrown  by  the  lamp  is  illuminated  by  the 
candle,  and  that  thrown  by  the  candle  Is  illuminated  by  the  lamp,  the  illu- 
mination of  the  screen  due  to  each  light  is  the  same.  The  intensities  of  the 
two  lights — that  is,  the  illuminations  which  they  would  give  at  equal  dis- 
tances— are  then  directly  proportional  to  the  squares  of  their  distances  from 
the  shadows ;  that  is  to  say,  if  the  lamp  is  three  times  the  distance  of  the 
candle,  its  illuminating  power  is  nine  times  as  great. 

For  if  i  and  i'  are  the  intensities  of  the  lamp  and  the  candle  at  the  unit 
of  distance,  and  d  and  d'  their  distances  from  the  shadows,  it  follows,  from 
the  first  law  of  the  intensity  of  light,  that  the  intensity  of  the  lamp  at  the 

distance  d  is  --  and  that  of  the  candle  — -;  at  the  distance  d'.     On  the  screen 
d-  d- 

these  two  intensities  are  equal  ;  hence  -r;  =  '7-;  or  ~  = -^^j  ^vhich  was  to  be 

d-d-       I       d- 

proved. 

Biinsen's  photometer. — When  a  grease-spot  is  made  on  a  piece  of  bibu- 
lous paper,  the  part  appears  translucent.  If  the  paper  be  illuminated  by  a 
light  placed  in  front,  the  spot  appears  darker  than  the  surrounding  space  ; 


Fie.  448. 


if,  on  the  contrary,  it  be  illuminated  from  behind,  the  spot  appears  light  on 
a  dark  ground.  If  the  greased  part  and  the  rest  appear  unchanged,  the 
intensity  of  illumination  on  both  sides  is  the  same.  Bunsen's  photometer 
depends  on  an  application  of  this  principle.  Its  essential  features  are  repre- 
sented in  fig.  448.  A  circular  spot  is  made  on  a  paper  screen  by  means  of  a 
solution  of  spermaceti  in  naphtha  :  on  one  side  of  this  is  placed  a  light  of  a 
certain  intensity,  which  serves  as  a  standard  ;  in  London  it  is  a  sperm 
candle  of  six  to  the  pound,  and  burning  120  grains  in  an  hour.  The  light  to 
be  tested,  a  petroleum  lamp  or  a  gas  burner  consuming  a  certain  volume  of 
gas  in  a  given  time,  is  then  moved  in  a  right  line  to  such  a  distance  on  the 
other  side  of  the  screen  that  there  is  no  difference  in  brightness  between  the 
greased  part  and  the  rest  of  the  screen.  By  measuring  the  distances  of 
the  lights  from  the  screen  by  means  of  the  scale,  their  relative  illuminating 
powers  are  resj)cctively  as  the  squares  of  their  distances  from  the  screen. 

The  difficulty  of  getting  more  carefully  constructed  candles  to  give  a 
li).;ht  sufficiently  uniform  for  standard  purposes  has  led  Harcourt  to  adopt 
as  unit  the  light  formed  by  burning  a  mixture  of  7  volumes  pentane  gas  and 


-510]     Relative  Intensities  of  Various  Sources  of  LigJit.      493 

20  volumes  of  air,  at  the  rate  of  half  a  cubic  foot  in  an  hour,  in  a  specially 
constructed  burner  so  as  to  produce  a  flame  of  a  definite  height.  This  has 
been  found  to  answer  well  in  practice.  By  this  kind  of  detemiination  the 
degree  of  accuracy  which  can  be  attained  is  not  so  great  as  in  many  physical 
determinations,  more  especially  when  the  lights  to  be  compared  are  of  dif- 
ferent colours  ;  one,  for  instance,  being  yellow,  and  the  other  of  a  bluish  tint. 
It  gives,  however,  results  which  are  sufficiently  accurate  for  practical  pur- 
poses, and  is  almost  universally  employed  for  determining  the  illuminating 
power  of  coal  gas  and  of  other  artificial  lights. 

The  absolute  unit  of  light  adopted  by  the  International  Congress  of 
Electricians  is  that  emitted  by  a  square  centimetre  of  melted  platinum  at  the 
moment  of  its  solidification.     It  is  equal  to  about  fifteen  standard  candles. 

Whcatstone's  pJwtometer. — The  principal  part  of  this  instrument  is  a 
steel  bead,  P  (fig.  449),  fixed  on  the 
edge  of  a  disc,  which  rotates  on  a 
pinion,  ^,  working  in  a  larger 
toothed  wheel.  The  wheel  fits  in  a 
cylindrical  brass  box  which  is  held 
in  one  hand,  while  the  other  works 
a  handle,  A,  which  turns  a  central 
axis,  the  motion  of  which  is  trans- 
mitted by  a  spoke,  cz,  to  the  pinion 
0.     In  this  way  the  latter  turns  on  ^'^-  ''''■  ^'^-  ^5°- 

itself,  and  at  the  same  time  revolves  round  the  circumference  of  the  box  ; 
the  bead  shares  the  double  motion  and  consequently  describes  a  curve  in 
the  form  of  a  rose  (fig.  450). 

Now,  let  M  and  N  be  the  two  lights  whose  intensities  are  to  be  com- 
pared ;  the  photometer  is  placed  between  them  and  rapidly  rotated.  The 
brilliant  points  produced  by  the  reflection  of  the  light  on  the  two  opposite 
sides  of  the  bead  give  rise  to  two  luminous  bands,  arranged  as  represented 
in  fig.  450.  If  one  of  them  is  more  brilliant  than  the  other — that  which  pro- 
ceeds from  the  light  M,  for  instance— the  instrument  is  brought  nearer  the 
other  light  until  the  two  bands  exhibit  the  same  brightness.  The  distance 
of  the  photometer  from  each  of  the  two  lights  being  then  measured,  their 
intensities  are  proportional  to  the  squares  of  the  distances. 

510.  Relative  intensities  of  various  sources  of  ligrht. — The  light  of  the 
sun  is  600,000  times  as  powerful  as  that  of  the  moon  ;  and  16,000,000,000 
times  as  powerful  as  that  of  a  Centauri,  the  third  in  brightness  of  all  the 
stars.  The  moon  is  thus  27,000  times  as  bright  as  this  star;  the  sun  is  5,500 
million  times  as  bright  as  Jupiter,  and  8a  billion  times  as  bright  as  Neptune. 
Its  light  is  estimated  to  be  670,000  times  that  of  a  wax  candle  at  a  distance 
of  I  foot.  According  to  Fizeau  and  Foucault  the  electric  light  produced  by 
50  Bunsen's  cells  is  about  \  as  strong  as  sunlight. 

The  relative  luminosities  of  the  following  stars  are  as  compared  with 
Vega=i;  Pole  Star  0-13,  Afdebaran  0*30,  Saturn  0-47,  Arcturus  079, 
Mars  2-93,  Sinus  4"29i,  Jupiter  8-24,  Venus  38-9. 

A  difference  in  the  strength  of  light  or  shadow  is  perceived  when  the 
duller  light  is  ^5  of  the  brightness  of  the  other,  and  both  are  near  together, 
especially  when  the  shadow  is  moved  about. 


494 


On  Light. 


[511- 


CHAPTER   II. 

REFLECTION   OF   LIGHT.      MIRRORS. 

511.  laws  of  the  reflection  of  light.— When  a  ray  of  light  meets  a 
pohshed  surface,  it  is  reflected  according  to  the  two  following  laws,  which, 
as  we  have  seen,  also  hold  for  heat. 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

II.  The  incident  and  the  reflected  ray  are  both  in  the  same  plane .^  which 
is  perpendicular  to  the  reflecting  surface. 

The  words  are  here  used  in  the  same  sense  as  in  article  417,  and  need 

no  further  explanation. 

First  proof— The   two   laws   may  be  demonstrated  by  the  apparatus 

represented  in  fig.  451.     It  consists  of  a  graduated  circle  in  a  vertical  plane. 

Two  brass  slides  move  round  the  cir- 
cumference ;  on  one  of  them  there  is 
a  piece  of  ground  glass,  P,  and  on  the 
other  an  opaque  screen,  X,  in  the 
centre  of  which  is  a  small  aperture. 
Fixed  to  the  latter  slide  there  is  also 
a  mirror,  M,  which  can  be  more  or  less 
inclined,  but  always  remains  in  a  plane 
perpendicular  to  the  plane  of  the  gra- 
duated circle.  Lastly,  there  is  a  small 
polished  metallic  mirror,  ;//,  placed 
horizontally  in  the  centre  of  the  circle. 
In  making  the  experiment,  a  pencil 
of  solar  or  any  suitable  artificial  light, 
S,  is  caused  to  fall  on  the  mirror 
M,  which  is  so  inclined  that  the  re- 
flected light  passes  through  the  aper- 
ture in  N,  and  falls  on  the  centre  of 
the  mirror,  ;//.  The  luminous  pencil 
then  experiences  a  second  reflection 
in  a  direction  m\\  which  is  ascertained 


Fig.  451. 


by  moving  P  until  an  image  of  the  aperture  is  found  in  its  centre.  The 
number  of  degrees  comprised  in  the  arc  AN  is  then  read  off,  and  likewise 
that  in  AP  ;  these  being  equal,  it  follows  that  the  angle  of  reflection  .\wP 
is  equal  to  the  angle  of  incidence  .X/z/M. 

The  second  law  follows  from  the  arrangcinonl  of  ihc  apparatus,  the  i)lanc 
of  the  rays  M/«  and  inV  being  parallel  to  the  plane  of  the  graduated  circle, 
and,  consequently,  perpendicular  to  the  mirror  ///. 


-513 J  Fonnation  of  Images  by  Plane  Mirrors.  495 

Second  proof. — The  law  of  the  reflection  of  light  may  also  be  demon- 
strated by  the  following  experiment,  which  is  susceptible  of  greater  accuracy 
than  that  just  described  :— In  the  centre  of  a  graduated  circle,  M  (fig.  452), 
placed  in  a  vertical  position,  there  is  a  small  telescope  movable  in  a  plane 
parallel  to  the  limb  ;  at  a  suitable  distance  there  is  a  vessel  D  full  of  mercury, 
which  forms  a  perfectly  horizontal  plane  mirror.  Some  particular  star  of 
the  first  or  second  magnitude  is  viewed  through  the  telescope  in  the  direc- 
tion AE,  and  the  telescope  is  then  inclined  so  as  to  receive  the  ray  AD  coming 
from  the  star  after  being  reflected  from  the  brilliant  surface  of  the  mercury. 


Fig.  452 

In  this  way  the  two  angles  formed  by  the  rays  EA  and  DA,  with  the  hori- 
zontal AH,  are  found  to  be  equal,  from  which  it  may  easily  be  shown  that 
the  angle  of  incidence  E'DE  is  equal  to  the  angle  of  reflection  EDA.  For 
if  DE  is  the  normal  to  the  surface  of  the  mercuiy,  it  is  perpendicular  to  AH, 
and  AED,  ADE  are  the  complements  of  the  equal  angles  EAH,  DAH  ; 
therefore  AED,  ADE  are  equal  ;  but  the  two  rays  AE  and  DE'  may  be 
considered  parallel,  in  consequence  of  the  great  distance  of  the  star,  and 
therefore  the  angles  EDE'  and  DEA  are  equal,  for  they  are  alternate  angles 
and,  consequently,  the  angle  E'DE  is  equal  to  the  angle  EDA. 

REFLECTION   OF   LIGHT   FROM    PLANE  SURFACES. 

512.  Mirrors.  Xmag-es. — Mirrors  are  bodies  with  polished  surfaces, 
which  show  by  reflection  objects  presented  to  them.  The  place  at  which 
objects  appear  is  their  image.  According  to  their  shape,  mirrors  are  divided 
\r\io  plane,  concave,  convex,  spherical,  parabolic,  cofiical,  &c. 

513.  Formation  of  imagres  by  plane  mirrors. — The  determination  of 
the  position  and  size  of  images  resolves  itself  into  investigating  the  images 
of  a  series  of  points.  And  first,  the  case  of  a  single  point,  A,  placed  in  front 
of  a  plane  mirror,  MN  (fig.  453),  will  be  considered.  Any  ray,  AB,  incident 
from  this  point  on  the  mirror  is  reflected  in  the  direction  BO,  making  the 
angle  of  reflection  DBO  equal  to  the  angle  of  incidence  DBA. 

If,  now,  a  perpendicular,  AN,  be  let  fall  from  the  point  A  on  the  mirror. 


496 


On  Lidit. 


[513- 


and  if  the  ray  015  be  prolonged  below  the  mirror  until  it  meets  this  perpen- 
dicular in  the  point  a,  two  triangles  are  formed,  ABX  and  BXa,  which  are 
equal,  for  they  have  the  side  BX  common  to  both,  and  the  angles  AXB, 
ABX,  equal  to  the  angles  rtXB,  aBX  ;  for  the  angles  AXB  and  aXB  are 
right  angles,  and  the  angles  ABX  and  aBX  are  each  equal  to  the  angle 
OBM.  From  the  equality  of  these  triangles,  it  follows  that  rtX  is  equal  to 
AX  ;  that  is,  that  any  ray,  AB,  takes  such  a  direction  after  being  reflected, 
that  its  prolongation  below  the  mirror  cuts  the  perpendicular  A<z  in  the  point 
a,  which  is  at  the  same  distance  from  the  mirror  as  the  point  A.  This 
applies  also  to  the  case  of  any  other  ray  from  the  point  A  ;  AC.  for  example. 


Fi^.  453- 

From  this  the  important  consequence  follows,  that  all  rays  from  the  point 
A,  reflected  from  the  mirror,  follow,  after  reflection,  the  same  directiQn  as  if 
they  had  all  proceeded  from  the  point  a.  The  eye  is  deceived,  and  sees  the 
point  A  at  a,  as  if  it  were  really  situated  at  a.  Hence  in  plane  mirrors  the 
image  of  any  point  is  formed  behind  the  mirror  at  a  distance  equal  to  that  oj 
the  given  point,  and  on  the  perpendicular  let  fall  from  this  point  on  the 
mirror. 

It  is  manifest  that  the  image  of  any  object  will  be  obtained  by  construct- 
ing, according  to  this  rule,  the  image  of  each  of  its  points,  or,  at  least,  of 
those  which  are  suflicient  to  determine  its  form.  Fig.  454  shows  how  the 
image  ab  of  any  object,  AB,  is  formed. 

It  follows  from  this  construction  that  in  plane  mirrors  the  image  is  of  the 
same  size  as  the  object ;  for  if  the  trapezium  ABCD  be  applied  to  the  trape- 
zium DCab,  they  are  seen  to  coincide,  and  the  object  AB  agrees  with  its  image. 

A  further  consequence  from  the  above  construction  is,  that  in  plane 
mirrors  the  image  is  symmetrical  in  reference  to  the  object,  and  not  inverted. 

514.  virtual  and  real  Imagres. — There  are  two  cases  relative  to  the 
direction  of  rays  reflected  by  mirrors  according  as  the  rays  after  reflection 
are  convergent  or  divergent.  In  the  first  case  the  reflected  rays  do  not  meet, 
but  if  they  are  supposed  to  be  produced  on  the  other  side  of  the  mirror,  their 
jjrolongations  coincide  in  the  same  point,  as  shown  in  figs.  453  and  454. 
The  eye  is  then  aftected  just  as  if  the  rays  proceeded  from  this  point,  and 
it  sees  an  image.  But  the  image  has  no  real  existence,  the  luminous  rays  do 
not  come  from  the  other  side  of  the  mirror  :  this  appearance  is  called  the 
I'irtuul  image.  The  images  of  real  objects  produced  bj-  plane  mirrors  are  of 
this  kind. 

In  the  second  case,  where  the  reflected  rays  converge,  of  which  we  shall 


-516] 


Multiple  Images  from  Tiuo  Plane  Mirrors. 


497 


soon  have  an  example  in  concave  mirrors,  the  rays  coincide  at  a  point  in 
front  of  the  mirror,  and  on  the  same  side  as  the  object.  They  form  there  an 
image  called  the  real  image,  for  it  can  be  received  on  a  screen.  The  dis- 
tinction may  be  expressed  by  saying  that  real  images  are  those  fo7-7ncd  by 
the  reflected  rays  themselves,  and  virtual  images  those  formed  by  their  pro- 
!o)igatio7is. 

515.  IVIultlple  Imagres  formed  by  g^lass  mirrors. — Metal  mirrors 
which  have  but  one  reflecting  surface  give  only  one  image  ;  glass  mirrors 
give  rise  to  several  images,  which  are  readily  ob- 
served when  the  image  of  a  candle  is  looked  at 
obliquely  in  a  looking-glass.  A  very  feeble  image 
IS  first  seen,  and  then  a  very  distinct  one  ;  behind 
this  there  are  several  others,  whose  intensities  gra- 
dually decrease  until  they  disappear. 

This  phenomenon  arises  from  the  looking-glass 
having  two  reflecting  surfaces.  When  the  rays 
from  the  point  A  meet  the  surface,  fig.  456,  a  part  is 
reflected  and  forms  an  image,  a,  of  the  point  A,  on 
the  prolongation  of  the  ray  ^E,  reflected  by  this  '^'  '*^  ' 

surface  ;  the  other  part  passes  into  the  glass  (536),  and  is  reflected  at  c  from 
the  layer  of  metal  which  covers  the  hinder  surface  of  the  glass,  and  reaching 
the  eye  in  the  direction  dW  gives  the  image  a'.  This  image  is  distant  from 
the  first  by  double  the  thickness  of  the  glass.  It  is  more  distinct,  because 
metal  reflects  better  than  glass. 

In  regard  to  other  images  it  will  be  remarked  that  whenever  light  is  trans- 
mitted from  one  medium  to  another — for  instance,  from  glass  to  air— (536), 
only  some  of  the  rays  get  through  ;  the  remainder  are  reflected  at  the  surface 
which  bounds  the  two  media.  Consequently  when  the  pencil  cd,  reflected 
from  f,  attempts  to  leave  the  glass  at  d,  most  of  the  rays  composing  it  pass 
into  the  air,  but  some  are  reflected  at  d,  and  continue  within  the  glass. 
These  are  again  reflected  by  the  metallic  surface,  and  form  a  third  image  of 
A  ;  after  this  reflection  they  come  to  MN,  when  many  emerge  and  render 
the  third  image  visible  ;  but  some  are  again  reflected  within  the  glass,  and 
in  a  similar  manner  give  rise  to  a  fourth,  fifth, 
&c.,  image,  thereby  completing  the  series 
above  described.  It  is  manifest  from  the 
above  explanation  that  each  image  must  be 
much  feebler  than  the  one  preceding  it,  and 
consequently  only  a  small  number  are  visible 
— ordinarily  not  more  than  eight  or  ten  in 
all. 

This  multiplicity  of  images  is  objection- 
able in  observations,  and,  accordingly,  me- 
tal mirrors  are  to  be  preferred  in  optical 
instruments. 


:i6.   Multiple  images  f>om  two  plane 


Fig-  457- 


mirrors.-  When    an    object    is    placed    be- 
tween two  plane  mirrors,  which  form  an  angle  with  each  other,  either  right 
or  acute,  images  of  the  object  are  formed,  the  number  of  which  increases 

K  K 


498 


Oft  Li^ht. 


[516- 


with  the  inclination  of  the  mirrors.  If  they  are  at  right  angles  to  each 
other,  three  images  are  seen,  arranged  as  represented  in  fig.  457.  The  rays 
OC  and  OD  from  the  point  O,  after  a  single  reflection,  give  the  one  an 
image  O',  and  the  other  an  image  O",  while  the  ray  OA,  which  has  under- 
gone two  reflections  at  A  and  B,  gives  the  third  image  O'".  When  the 
angle  of  the  mirrors  is  60°,  five  images  are  produced,  and  seven  if  it  is  45°. 
The  number  of  images  continues  to  increase  in  proportion  as  the  angle 
diminishes,  and  when  it  is  zero — that  is,  when  the  mirrors  are  parallel — the 
number  of  images  is  theoretically  infinite.  In  general,  if  two  mirrors  are 
inclined  to  each  other,  the  number  of  images  they  produce  is  equal  to  the 
number  of  times  the  angle  between  them  is  contained  in  360. 

The  kaleidoscope,  invented  by  .Sir  D.  Brewster,  depends  on  this  property 
of  inclined  mirrors.  It  consists  of  a  tube,  in  which  are  three  mirrors  inclined 
at  60° ;  one  end  of  the  tube  is  closed  by  a  piece  of  ground  glass,  and  the 
other  by  a  cap  provided  with  an  aperture.  Small  irregular  pieces  of  coloured 
glass  are  placed  at  one  end  between  the  ground  glass  and  another  glass  disc, 
and  on  looking  through  the  aperture,  the  other  end  being  held  towards  the 
light,  the  objects  and  their  images  are  seen  arranged  in  beautiful  symme- 
trical forms  ;  by  turning  the  tube,  an  almost  endless  variety  of  these  shapes 
is  obtained. 

517.  Multiple  imag-es  In  two  plane  parallel  mirrors. — In  this  case 
the  number  of  images  of  an  object  placed  between  them  is  theoretically  in- 
finite. Physically  the  number  is  limited,  for  as  the  incident  light  is  never 
totally  reflected,  some  of  it  being  always  absorbed,  the  images  gradually 
become  fainter  and  are  ultimately  quite  extinguished. 

Fig.  457  shows  how  the  pencil  La  reflected  once  from  M  gives  at  I  the 
image  of  the  object  L  at  a  distance  ml  =  ;«L  ;  then  the  pencil  Lb  reflected 
once  from  the  mirror  M,  and  once  from  X,  furnishes 
the  image  I'  at  a  distance  nV  =  n\;  in  like  manner 
the  pencil  Lc,  after  two  reflections  on  M,  and  one 
on  N,  forms  the  image  I"  at  a  distance  }n\"  =  m\\ 
and  so  on  for  an  infinite  series.      The  images  /,  i\  i" 

are     formed 
in    the  same 
manner      by 
rays  of  light 
which,  emit- 
ted   by    the 
object  L,  fall 
first    on    the 
mirror  X. 
5  I  >S.    Xrreg:ular    reflection.       Diffused    llg^bt. — The 
reflection  from  the  surfaces  of  polished  bodies,  the  laws 
of  which  have  just  been  stated,  is  called  the  rci^ular  or 
specular  reflection  ;  but  the  quantity  thus  reflected  is  less 
'^'  ■*'  ■  than  that  of  the  incident  light.     The  light  incident  on  an 

opaque  body  separates,  in  fact,  into  three  parts  :  one  is  reflected  rec^ularly  : 
another  irret^ulitrly — that  is,  in  all  directions  ;  while  a  third  is  extinguished, 
or  r^fAr^rM/ by  the  reflecting  body.  If  lij^ht  falls  on  a  trans|)arcnt  body,  a 
considerable  porliim  is  transmittrd  with  rcj^ularity. 


-520]   Reflection  of  a  Ray  of  Light  in  a  Rotating  Mirror.        499 

The  irregularly  reflected  light  is  called  scattered  light :  it  is  that  which 
makes  bodies  visible  (502).  The  light  which  is  reflected  regularly  does  not 
give  us  the  image  of  the  reflecting  surface,  but  that  of  the  body  from 
which  the  light  proceeds.  If,  for  example,  a  beam  of  sunlight  be  incident  on 
a  well-polished  mirror  in  a  dark  room,  the  more  perfectly  the  light  is  reflected 
the  less  visible  is  the  mirror  in  the  different  parts  of  the  room.  The  eye 
does  not  perceive  the  image  of  the  mirror,  but  that  of  the  sun.  If  the  reflect- 
ing power  of  the  mirror  be  diminished  by  sprinkling  on  it  a  light  powder,  the 
sun's  image  becomes  feebler,  and  the  mirror  is  visible  from  all  parts  of  the 
room.  Perfectly  smooth,  polished  reflecting  surfaces,  if  such  there  were, 
would  be  invisible.  The  beam  of  light  itself  is  only  seen  in  the  room  owing 
to  irregular  reflections  from  the  particles  of  dust,  and  the  like,  which  are 
floating  in  the  air.  Tyndall  has  shown  that  when  this  floating  matter  in  the 
air  in  an  inclosed  space  is  completely  removed,  the  beam  of  sunlight  or  the 
electric  light  is  quite  invisible.  The  atmosphere  diffuses  the  light  which 
falls  on  it  from  the  sun  in  all  directions,  so  that  it  is  light  in  places  which 
do  not  receive  the  direct  rays  of  the  sun.  Thus,  the  upper  layers  of  the  air 
diffuse  the  light  which  they  receive  before  sunrise  and  after  sunset,  and  ac- 
cordingly give  rise  to  the  phenomena  of  tiuilight. 

519.  Intensity  of  reflected  llgrlit.— The  intensity  of  reflected  light  is 
always  less  than  that  of  the  incident  light,  for  some  of  the  original  vibrations 
are  converted  into  vibrations  of  the  reflecting  surfaces.  The  intensity 
increases  with  the  obliquity  of  the  incident  ray.  For  instance,  if  a  sheet 
of  white  paper  be  placed  before  a  candle,  and  be  looked  at  very  obliquely, 
an  image  of  the  flame  is  seen  by  reflection,  which  is  not  the  case  if  the  eye 
receives  less  oblique  rays. 

The  intensity  of  the  reflection  varies  with  different  bodies,  even  when 
the  degree  of  polish  and  the  angle  of  incidence  are  the  same.  Thus  with  a 
perpendicular  incidence  the  reflected  light  is  |  of  the  incident  in  the  case 
of  that  reflected  from  a  metal  mirror,  |  from  mercury,  ^-^  from  glass,  and  i 
from  water.  It  also  varies  with  the  nature  of  the  medium  which  the  ray  is 
traversing  before  and  after  reflection.  Polished  glass  immersed  in  water 
loses  a  great  part  of  its  reflecting  power. 

In  the  case  of  scattered  reflection  the  actual  lustre  or  brightness  of  a 
luminous  surface  is  only  a  fraction  of  the  light 
which  falls  upon  it,  and  depends  on  the  nature  of 
the  surface.  If  we  call  the  incident  light  100, 
we  have  for  the  brightness  of  freshly  fallen  snow 
78,  white  paper  70,  white  sandstone  24,  porphyrj' 
II,  and  ordinar)-  earth  8. 

520.  Reflection  of  a  ray  of  llgrbt  in  a  ro- 
tating mirror. — When  a  horizontal  ray  of  light 
falls  on  a  plane  mirror  which  can  rotate  about 
a  vertical  axis,  if  the  mirror  is  turned  through  an 
angle  a,  the  reflected  ray  is  turned  through 
double  the  angle. 

Let  7im  (fig.  459)  be  the  first  position  of  the  mirror,  n'lii'  its  position  after 
it  has  been  turned  through  the  angle  a  ;  and  let  OD  be  the  fixed  incident 
ray.     If  from  the  centre  of  rotation   C,  with  any  radius   we  describe   the 


500  On  Light.  [520- 

circumference  0;««,  and  from  the  point  O,  where  it  cuts  the  incident  ray, 
chords  00'  and  OO"  are  drawn  perpendicular  respectively  to  mn  and  w/';/'  ; 
the  points  O'  and  O"  are  the  images  of  the  point  O  in  the  two  positions  of 
the  mirror,  and  the  angles  CO'D  and  CO"I)'  are  each  equal  to  COD.  The 
lines  O'D  and  0"D'thus  making  equal  angles  with  O'C  and  0"C,  the  angle 
between  the  two  former  lines  is  equal  to  that  between  the  two  latter  ;  that 
is,  it  will  be  equal  to  O'CO",  and  will  be  measured  by  the  arc  O'O". 
The  rotations  of  the  reflected  ray  and  of  the  mirror  are  thus  measured  by 
the  two  arcs  O'O"  and  ;«/;/'  respectively. 

Now,  the  two  angles  O'OO"  and  wCw'  are  equal,  for  they  have  their 
sides  perpendicular  each  to  each  ;  but  the  angle  O'OO",  which  is  an  angle 
at  the  circumference,  is  measured  by  half  the  arc  O'O",  and  the  angle  wCw' 
by  the  whole  arc  vim'  ;  hence  O'O"  is  the  double  of ;«;«',  which  shows  that 
when  the  mirror  has  turned  through  an  angle  a,  the  reflected  ray  has  turned 
through  2f. 

521.  Radley's  reflecting-  sextant. — The  principal  features  of  this  in- 
strument, which  is  used  to  measure  the  angular  distance  of  any  two  distant 
objects,  are  represented  in  fig.  460.    It  consists  of  a  metal  sector,  the  arc,  cd. 

of  which  is  graduated.  About 
the  centre  of  the  sector,  an 
index  arm,  ab,  turns  ;  this  is 
provided  with  a  vernier  and 
a  micrometer  screw,  by  which 
the  index  may  be  accurately 
adjusted  and  also  clamped. 
.A.  mirror  at  a  is  fixed  perpen- 
dicularly to  the  arm  afy,  and 
therefore  moves  with  it.  A 
telescope  de  is  permanently 
fixed  to  the  arm  at%  and  oppo- 
site to  it  is  a  second  mirror 
in,  also  permanently  fixed  : 
the  lower  half  of  this  is 
silvered,  and  the  axis  of  the 
telescope  just  traverses  the 
boundary  of  the  silvered  and 
unsilvered  part  of  the  mirror. 
In  making  an  observation, 
the  sextant  is  held  so  that  its  plane  may  pass  through  both  the  objects  whose 
angular  distance  is  to  Ije  measured.  The  index  arm  is  at  the  zero  of  the 
graduation,  which  indicates  the  parallelism  of  the  two  mirrors.  One  of  the 
objects  is  then  viewed  in  the  direction  onu  through  the  telescope,  and  the 
unsilvered  part  of  the  mirror  w.  The  index  arm  is  then  moved  until  the 
eye  sees  simultaneously  with  this  the  image  of  another  object  g,  which 
reaches  the  eye  after  successive  reflections  from  the  mirror  a,  and  from  the 
silvered  part  of  the  mirror  w  ;  that  is,  l)y  the  path  i^^anicdo.  The  angle 
ni/ia  which  the  two  mirrors  now  form  is  measured  by  the  graduation  of  the 
sector  cd,Mu\  is  half  the  angle  gout.  For  when  the  two  mirrors  were  parallel 
the  angular  deflection  of  the  ray^rt,  after  two  reflections,  would  be  zero,  and 


■/i 


Fis.  4^0. 


^^ 


-523]  Malice's  Heliograph.  501 

its  deflection  is  now  the  angle  ^r>/«  ;  whence,  by  the  last  article,  the  mirror  a 
must  have  turned  through  half  that  angle,  the  mirror  j/i  having  been  fixed  in 
position  throughout. 

522.  Measurement  of  small  angles  by  reflection  from  a  mirror 

An  important  application  of  the  laws  of  reflection  in  measuring  small 
angles  of  deflection  in 

magnetic  and  other  ob-  ^q 

servations  was  first 
made  by  Gauss.  The 
principle  of  this  method 
will  be  understood  from 
fig.  461,  in  which  AO 
represents  a  telescope, 
underneath  which,  and 
at  right  angles  to  its 
axis,  is  fixed  a  gradu- 
ated scale  ss  ;  the  cen- 
tre of  which,  the  zero, 
corresponds  to  the  axis 
of  the  telescope.  "*'  '^^'" 

Let  XS  be  the  object  whose  angular  deflection  is  to  be  measured,  a  mag- 
net for  instance,  and  let  nuii  represent  a  small  perfectly  plane  mirror  fixed 
rigidly  at  right  angles  to  the  axis  of  the  magnet.  If  now,  at  the  beginning 
of  the  observation,  the  telescope  is  adjusted  so  that  the  image  of  the  zero 
appears  behind  the  cross  wires,  its  axis  is  perpendicular  to  the  mirror.  Now 
when  the  mirror  is  turned,  by  whatever  cause,  through  an  angle  a,  the  eye 
will  see,  through  the  telescope,  the  image  of  another  division  of  the  scale,  a 
for  instance,  the  ray  proceeding  from  which  makes  with  the  line  cOA.  the 
angle  2a. 

From  the  distance  of  this  division  0^  from  the  zero  of  the  scale  and  the 

distance  O^  from  the  mirror  we  have  tan  2a=  -^.  Thus,  for  instance,  if  Oa 
is  12  millimetres  and  Of  5,000  millimetres,  then  tan  2a  = 


5,000 

2a  =  Z'  15".     As  a  practised  eye  can  easily  read  y^„  of  a  millimetre,  it  is  pos- 
sible by  such  an  arrangement  to  read  off  an  angular  deflection  of  two  seconds. 

523.  Mance's  heliograph. — The  reflection  of  light  from  mirrors  has 
been  applied  by  Sir  H.  Alance  in  signalling  at  great  distances  by  means  of 
the  sun's  light. 

The  apparatus  consists  essentially  of  a  mirror  about  4  inches  in  diameter 
mounted  on  a  tripod,  and  provided  with  suitable  adjustments,  so  that  the 
sun's  light  can  be  received  upon  it  and  reflected  to  a  distant  station.  An 
observer  then  can  see  through  a  telescope  the  reflection  of  the  sun's  rays  as 
a  spot  of  light.  The  mirror  has  an  adjustment  by  which  it  can  be  made  to 
follow  the  sun  in  its  apparent  motion.  There  is  also  a  lever  key  by  which 
the  signaller  can  deflect  the  mirror  through  a  very  small  angle  either  to  the 
right  or  left,  and  thus  the  observer  at  the  distant  station  sees  correspondmg 
flashes  to  the  right  or  left.  Under  the  subject  of  Telegraphy  it  will  be  seen 
.how  these  alternate  motions  can  be  used  to  form  an  alphabet. 


502 


On  Liq-ht. 


[523 


The  heliograph  proved  of  essential  service  in  the  campaigns  in  Africa 
and  Afghanistan.  Instead  of  any  special  form  of  apparatus,  an  ordinary 
shaving  mirror  or  handglass  is  frequently  used  ;  and  the  proper  inclination 
having  been  given  so  as  to  send  the  sun's  rays  to  the  distant  station,  which 
is  very  easily  effected,  the  signals  are  produced  by  obscuring  the  mirror  by 
sliding  a  piece  of  paper  over  it  for  varying  lengths  of  time.  In  this  way 
longer  or  shorter  flashes  of  light  are  produced,  which,  properly  combined, 
form  the  alphabet. 

Of  course  this  mode  of  signalling  can  only  be  used  where  the  sun's  light 
is  available,  but  it  has  the  advantage  of  being  cheap,  simple,  and  portable. 
Signals  have  been  sent  at  the  rate  of  12  words  a  minute,  through  distances, 
in  very  fine  weather,  of  40  miles. 

REFLECTION    OF   LIGHT   FROM   CURVED   SURF.-VCES. 

524.  Spherical  mirrors. — It  has  been  already  stated  (512)  that  there 
are  several  kinds  of  curved  mirrors  ;  those  most  frequently  employed  are 
spherical  and  parabolic  mirrors. 

Spherical  mirrors  are  those  whose  curvature  is  that  of  a  sphere  ;  their 
surface  may  be  supposed  to  be  formed  by  the  revolution  of  an  arc  MX  (fig. 
462)  about  the  radius  CA,  which  unites  the  middle  of  the  arc  to  the  centre 
of  the  circle  of  which  it  is  a  part.     According  as  the  reflection  takes  place 

from  the  internal  or  from 
the  e.xternal  face  of  the 
mirror,  it  is  said  to  be 
concave  or  convex.  C,  the 
centre  of  the  hollow  sphere 
of  which  the  mirror  forms 
part,  is  called  the  centre  of 
curiuiiure,  or  geometrical 
!'■'?•  462.  centre  :  the  point  A  is  the 

centre  of  the  figure.  The  infinite  right  line  AL,  which  passes  through  A  and 
C,  is  \\\(t  principal  axis  of  the  mirror;  any  right  line  which  simply  passes 
through  the  centre  C,  and  not  through  the  point  A,  is  a  secondary  axis. 
The  angle  MCN,  formed  by  joining  the  centre  and  extremities  of  the 
mirror,  is  the  aperture.  A  principal  or  meridional  section  is  the  section 
made  by  a  plane  through  its  principal  axis.  In  speaking  of  mirrors  those 
lines  alone  will  be  considered  which  lie  in  the  same  principal  section. 

The  theory  of  the  reflection  of  light  from  curved  mirrors  is  easily  deduced 
from  the  laws  of  reflection  from  plane  mirrors,  by  considering  the  surface  of 
the  former  as  made  up  of  an  infinitude  of  extremely  small  plane  surfaces, 
which  are  its  elements.  The  nornial  to  the  cur\ed  surface  at  a  given  point  is 
the  perpendicular  to  the  corresponding  element,  or,  what  is  the  same  thing, 
to  its  corresponding  tangent  plane.  It  is  shown  in  geometry  that  in  spheres 
all  the  normals  pass  through  the  centre  of  curvature,  so  that  the  normal  may 
readily  be  drawn  to  any  point  of  a  spherical  mirror. 

525.  Focus  of  a  spherical  concave  mirror. — In  a  curved  mirror  the 
J\hus  is  a  point  in  which  the  reflected  rays  meet  or  tend  to  meet,  if  produced 

either  backwards  or  forwards  ;  there  may  either  be  a  real  focus  or  a  virtual 
focus. 


-525]  Focus  of  a  Spherical  Concave  Mirror.  503 

Real  focus. — We  shall  first  consider  the  case  in  which  the  rays  of  light 
are  parallel  to  the  principal  axis,  which  presupposes  that  the  luminous  body 
is  at  an  infinite  distance.     Let  GD  (fig.  462)  be  such  a  ray. 

From  the  hypothesis  that  curved  mirrors  are  composed  of  a  number  of 
infinitely  small  plane  elements,  this  ray  would  be  reflected  from  the  element 
corresponding  to  the  point  D,  according  to  the  laws  of  the  reflection  from 
plane  mirrors  (513);  that  is,  that  CD  being  the  normal  at  the  point  of 
incidence  D,  the  angle  of  reflection  CDF  is  equal  to  the  angle  of  incidence 
GDC,  and  is  in  the  same  plane.  It  follows  from  this,  that  the  point  F,  where 
the  reflected  ray  cuts  the  principal  axis,  divides  the  radius  of  curvature  AC 
very  nearly  into  two  equal  parts.  For  in  the  triangle  DFC  the  angle  DCF 
is  equal  to  the  angle  CDG,  for  they  are  alternate  and  opposite  angles ;  likewise 
the  angle  CDF  is  equal  to  the  angle  CDG,  from  the  laws  of  reflection  ;  there- 
fore the  angle  FDC  is  equal  to  the  angle  FCD,  and  the  sides  FC  and  FD 
are  equal  as  being  opposite  to  equal  angles.  Now  the  smaller  the  arc  AD, 
the  more  nearly  does  DF  equal  AF  ;  and  when  the  arc  is  only  a  small  number 
of  degrees,  the  right  lines  AF  and  FC  may  be  taken  as  approximately  equal, 
and  the  point  F  may  be  taken  as  the  middle  of  AC.  So  long  as  the  aperture 
of  the  mirror  does  not  exceed  8  to  10  degrees,  any  other  ray  HB  will,  after 
reflection,  pass  very  nearly  through  the  point  F.  Hence,  for  practical  pur- 
poses, we  may  say  that  when  a  pencil  of  rays  parallel  to  the  axis  falls  on  a 
concave  mirror  the  rays  intersect  after  reflection  in  the  same  point,  which  is 
at  an  equal  distance  from  the  centre  of  curvature,  and  from  the  mirror.  This 
point  is  called  the  principal  focus  of  the  mirror,  and  the  distance  AF  is  the 
principal  focal  distance. 

All  rays  parallel  to  the  axis  meet  in  the  point  F  ;  and,  conversely,  if  a 
luminous  point  be  placed  at  F,  the  rays  emitted  by  this  point  will  after 
reflection  take  the  directions 
DG,  BH,  parallel  to  the 
principal  axis  ;  for  in  this 
case  the  angles  of  incidence 
and  reflection  have  changed 
places ;  but  these  angles 
always  remain  equal. 

The  case  is  now  to  be 
considered  in  which  the  rays 
are  emitted  from  a  luminous 

point,  L  (fig.  463),  placed  on  the  principal  axis,  but  at  such  a  distance  that 
they  are  not  parallel,  but  divergent.  The  angle  LKC,  which  the  incident 
ray  LK  forms  with  the  normal  KC,  is  smaller  than  the  angle  SKC,  which 
the  ray  SK,  parallel  to  the  axis,  forms  with  the  same  normal ;  and,  conse- 
quently, the  angle  of  reflection  corresponding  to  the  ray  LK  must  be  smaller 
than  the  angle  CKF,  corresponding  to  the  ray  SK.  And  therefore  the  ray 
LK  will  meet  the  axis  after  reflection  in  the  point  /,  between  the  centre  C 
and  the  principal  focus  F.  So  long  as  the  aperture  of  the  mirror  does  not 
exceed  a  small  number  of  degrees,  all  the  rays  from  the  point  L  will  inter- 
sect after  reflection  in  the  point  /.  This  point  is  called  the  conjugate  focus  ; 
for  there  is  this  connection  between  the  points  L  and  /,  that  if  the  luminous 
point  were  transferred  to  /,  its  conjugate  focus  would  be  at  L,  IK  being  the 
incident  and  KL  the  reflected  ray. 


504 


On  Light. 


[525- 


On  considering  the  figure  463  it  will  be  seen  that  when  the  point  L  is 
brought  near  to  or  removed  from  the  centre  C,  its  conjugate  focus  approaches 
or  recedes  in  a  corresponding  manner,  for  the  angles  of  incidence  and  re- 
flection increase  or  decrease  together. 

If  the  point  L  coincides  with  the  centre  C,  the  angle  of  incidence  is 
null,  and  as  the  angle  of  reflection  must  be  the  same,  the  ray  is  reflected  on 
itself,  and  the  focus  coincides  with  the  luminous  point.  When  the  luminous 
point  is  between  the  centre  C  and  the  principal  focus,  the  conjugate  focus  in 
turn  is  on  the  other  side  of  the  centre,  and  is  further  from  the  centre  accord- 
ing as  the  luminous  point  is  nearer  the  principal  focus.  If  the  luminous  point 
coincides  with  the  principal  focus,  the  reflected  rays,  being  parallel  to  the 
axis,  will  not  meet,  and  there  is,  consequently,  no  focus. 

Virtual  focus. — There  is,  lastly,  the  case  in  which  the  point  is  placed  at 
L,  between  the  principal  focus  and  the  mirror  (fig.  464).  Any  ray  LM, 
omitted  from  the  point  L,  makes  with  the  normal  CM  an  angle  of  incidence 
LMC,  greater  than  FMC  ;  the  angle  of  reflection  must  be  greater  than  C.MS, 
and  therefore  the  reflected  ray  ME  diverges  from  the  axis  AK.  This  is  also 
the  case  with  all  rays  from  the  point  L,  and  hence  these  rays  do  not  intersect, 


and,  consecjuently,  form  no  conjugate  focus ;  but  if  they  are  conceived  to  be 
prolonged  on  the  other  side  of  the  mirror,  their  prolongations  will  intersect 
in  the  same  point,  /,  on  the  axis,  and  the  eye  experiences  the  same  impression 
as  if  the  rays  were  directly  emitted  from  the  point  /.  Hence  a  virtual  focus 
is  formed  cjuite  analogous  to  those  formed  by  plane  mirrors  (514). 

In  all  these  cases  it  is  seen  that  the  position  of  the  principal  focus  is 
constant,  while  that  of  the  conjugate  foci  and  of  the  virtual  foci  varies.  The 
principal  and  the  conjugate  foci  are  always  on  the  same  side  of  the  mirror  as 
the  luminous  point,  while  the  7>irtual  focus  is  always  on  the  other  side  of  the 
mirror. 

Hitherto  the  luminous  point  has  always  been  supposed  to  be  placed  on 
the  princi])al  axis  itself,  and  then  the  focus  is  formed  on  this  axis.  In  the 
case  in  whi(  h  the  luminous  point  is  situate  on  a  seconilary  axis,  LB  (fig.  465), 
by  applying  to  this  axis  the  same  reasoning  as  in  the  preceding  case,  it  will 
be  seen  that  the  focus  of  the  point  L  is  formed  at  a  point  /  on  the  secondary 
axis,  and  that,  according  to  the  distance  of  the  point  L,  the  focus  may  be 
either  principal,  conjugate,  or  virtual. 

526.  Pod  of  convex  mirrors. —  In  convex  mirrors  there  are  only  virtual 
foci.  Let  SI,  TK  .  .  .  dig.  466)  be  rays  jiarallcl  to  the  principal  axis  of  a 
convex  mirror.  These  rays,  after  reflection,  take  the  ili\crging  directions 
IM,    KH,  which,  when  continued,  meet  in  a  point  I",  which  is  ihc principal 


527]      Determination  of  tJie  Principal  Focus  of  a  Mirror.         505 

virtual  focus  of  the  mirror.  By  means  of  the  triangle  CKF,  it  may  be  shown, 
in  the  same  manner  as  with  concave  mirrors,  that  the  point  F  is  approxi- 
mately the  centre  of  the  radius  of  curvature,  CA. 


Fig.  4C6. 


If  the  incident  luminous  rays,  instead  of  being  parallel  to  the  axis,  pro- 
ceed from  a  point  L,  situated  on  the  axis  at  a  finite  distance,  it  is  at  once 
seen  that  a  virtual  focus  will  be  formed  at  a  point  /,  between  the  principal 
focus  F  and  the  mirror. 

527.  determination  of  tbe  principal  focus  of  a  mirror. — In  the  appli- 
cations of  concave  and  convex  mirrois  it  is  often  necessary  to  know  the 
radius  of  curvature.  This  is  tantamount  to  finding  the  principal  focus  ;  for 
being  situated  at  the  middle  of  the  radius,  it  is  simply  necessary  to  double 
the  focal  distance. 

To  find  this  focus  with  a  concave  mirror,  it  is  exposed  to  the  sun's  rays, 
so  that  its  principal  axis  is  parallel  to  them,  and  then  with  a  small  screen  of 
ground  glass  the  point  is  sought  at  which  the  image  is  formed  with  the 
greatest  intensity  ;  this  is  the  principal  focus.  The  radius  of  the  mirror  is 
double  this  distance. 

If  the  mirror  is  convex,  it  is  covered  with  paper;  but  two  small  portions, 
H  and  I,  are  left  exposed  at 
equal  distances  from  the 
centre  of  the  figure  A,  and  on 
the  same  principal  section 
(fig.  467).  A  screen  MN,  in 
the  centre  of  which  is  an 
opening  larger  than  the  dis- 
tance HI,  is  placed  before 
the  mirror.  If  a  pencil  of 
solar  rays,  SH,  ST,  parallel 
to  the  axis,  fall  on  the  mirror,  the  light  is  reflected  at  H  and  I,  on  the  parts 
where  the  mirror  is  left  exposed,  and  forms  on  the  screen  two  brilliant  images 
at  h  and  i.  By  moving  the  screen  MN  nearer  to  or  farther  from  the  mirror, 
a  position  is  found  at  which  the  distance  hi  is  double  that  of  HI.  The 
distance  AD  from  the  screen  to  the  mirror  then  equals  the  principal  focal 
distance.     For  the  arc  HAI  does  not  sensibly  differ  from  its  chord ;  and 


because  the  triangles  FHI  and  Yhi  are  similar, 


HI     FA 


,  but  HI  is  half  of 


hi     FD' 
hi,  and  therefore  also  FA  is  the  half  of  FD,  and  therefore  AD  is  equal  to 


5o6 


On  Li  Hit. 


[527- 


AF.  Further,  FA  is  the  principal  focal  distance  ;  for  the  rays  SH  and  S'l 
are  parallel  to  the  axis  ;  consequently  also  twice  the  distance  AD  equals  the 
radius  of  curvature  of  the  mirror. 

528.  rormatlon  of  imagres  in  concave  mirrors. — Hitherto  it  has  been 
supposed  that  the  luminous  or  illuminated  object  placed  in  front  of  the 
mirror  was  simply  a  point  ;  but  if  this  object  has  a  certain  magnitude, 
we  can  conceive  a  secondary  axis  drawn  through  each  of  its  points,  and 
thus  a  series  of  real  or  virtual  foci  could  be  detennined  the  collection  of 
which  composes  the  image  of  the  object.  By  the  aid  of  the  construc- 
tions which  have  served  for  determining  the  foci,  we  shall  investigate 
the  position  and  magnitude  of  these  images  in  concave  and  in  convex 
mirrors. 

Real  image. — We  shall  first  take  the  case  in  which  the  mirror  is  concave, 
and  the  object  AB  (fig.  468)  is  on  the  other  side  of  the  centre.     To  obtain 


the  image  or  the  focus  of  any  point  A,  a  secondary  axis,  AE,  is  drawn  from 
this  point,  and  then  drawing  from  the  point  A  an  incident  ray  AD,  the 
normal  to  this  point,  CD,  is  taken,  and  the  angle  of  reflection  CDa  is  made 
equal  to  the  angle  of  incidence  ADC.  The  point  a,  where  the  reflected  ray 
cuts  the  secondary  axis  AE,  is  the  conjugate  focus  of  the  pomt  A,  because 
every  other  ray  drawn  from  this  point  passes  through  a.  Similarly  if  a 
secondary  axis,  BI,  be  drawn  from  the  point  B,  the  rays  from  this  point 
meet  after  reflection  in  b,  and  form  the  conjugate  focus  of  B.  And  as  the 
images  of  all  the  points  of  the  object  are  formed  between  a  and  b,  ab  is  the 
complete  image  of  AB.  From  what  has  been  said  about  foci  (525),  it 
follows  that  this  image  is  real,  inverted,  smaller  tJuin  the  object,  and phucd 
between  the  centre  of  curvature  and  the  principal  focus.     This  image  may  be 

seen  in  two  ways  :  by  placing 
the  eye  in  the  continuation  of 
the  reflected  rays,  and  then  it  is 
an  aiirial  image  which  is  seen  ; 
or  the  rays  are  collected  on  a 
screen,  on  which  the  image  ap- 
pears to  be  depicted. 

If  the  luminous  or  illuminated 
^''^'  ■''"^'  object  is  ])laccd  at  ab,  between 

the  ])rincipal  focus  and  the  centre,  its  image  is  formed  at  AB.  It  is  then  a 
real  but  inverted  image  ;  it  is  larger  than  the  object,  and  the  larger  as  the 
object,  ab,  is  nearer  the  focus. 


-530] 


Fornmlcs  for  Spherical  Mirrors. 


507 


Fis.  470. 


If  the  object  is  placed  in  the  principal  focus  itself,  no  image  is  produced^ 
for  then  the  rays  emitted  from  each  point  form,  after  reflection,  as  many 
pencils  respectively  parallel  to  the  secondary  axis,  which  is  drawn  through 
the  point  from  which  they  are  emitted  (524),  and  hence  neither  foci  nor 
images  are  formed. 

When  all  points  of  the  object  AB  are  above  the  principal  axis  (fig.  469), 
by  repeating  the  preceding  construction,  it  is  readily  seen  that  the  image  of 
the  object  is  formed  at  ab. 

Vi7-tual  image. — The  case  remains  in  which  the  object  is  placed  between 
the  principal  focus  and  the  mirror.  Let  AB  be  this  object  (fig.  470) ;  the 
incident  rays  after  reflection 
take  the  directions  DI  and  KH, 
and  their  prolongations  form  a 
virtual  image,  a,  of  the  point  A, 
on  the  secondary  axis.  Simi- 
larly, an  image  of  B  is  formed 
at  b  ;  consequently  the  eye  sees 
at  ab  the  imiage  of  AB.  This 
image  is  virtual,  erect,  and 
larger  than  the  object. 

From  what  has  been  stated, 
it  is  seen  that,  according  to  the 
distance  of  the  object,  concave  mirrors  produce  two  kinds  of  images,  or  none 
at  all  ;  a  person  notices  this  by  placing  himself  in  front  of  a  concave  mirror. 
At  a  certain  distance  he  sees  an  image  of  himself  inverted  and  smaller  ;  this 
is  the  real  image  ;  at  a  less  distance  the  image  becomes  confused,  and  dis- 
appears when  he  is  at  the  focus  ;  still  nearer  the  image  appears  erect,  but 
larger — it  is  then  a  virtual  image. 

529.  Formation  of  imaeres  in  convex  mirrors. — Let  AB  (fig.  471)  be 
an  object  placed  in  front  of  a  mirror  at  any  given  distance.  AC  and  BC  are 
secondary  axes,  and  it  follows, 
from  what  has  been  already 
stated,  that  all  the  rays  from  A 
are  divergent  after  reflection, 
and  that  their  prolongations  pass 
through  a  point  a,  which  is  the 
virtual  image  of  the  point  A. 
Similarly  the  rays  from  B  form 
a  virtual  image  of  it  in  the  point  Fig.  471. 

b.     The  eye  which  receives  the 

divergent  rays  DE,  KH  .  .  .  sees  in  ab  an  image  of  AB.  Hence,  whatever 
the  position  of  an  object  in  front  of  a  convex  mirror,  the  image  is  always 
7<irtual,  erect,  and  smaller  than  the  object. 

530.  Formulae  for  spberlcal  mirrors. — The  relation  between  the 
position  of  an  object  and  that  of  its  image  in  spherical  mirrors  may  be 
expressed  by  a  very  simple  formula.  In  the  case  of  concave  mirrors,  let 
R  be  its  radius  of  curvature,  j?^  the  distance  LA  of  the  object  L  (fig.  472), 
and/'  the  distance  /A  of  the  image  from  the  mirror.  In  the  triangle  LM/, 
the  perpendicular  MC  divides  the  angle  LM/  into  two  equal  parts,  and  from. 


5o8  On  Light.  [530- 

geometry  it  follows  that  the  two  segments  LC,  C/  are  to  each  other  as  the 
two  sides  containing  the  angle  ;  that  is, 

C/ _  /M  .  therefore  CL  x  LM  =  C/x  /M. 
CL"LM 

If  the  arc  AM  does  not  exceed  5  or  6  degrees,  the  lines  AIL  and  M/  are 

approximately  equal  to  AL  and  A/  ; 
that  is,  to/  and/'. 
Further,  C/  =  CA  -  A/  =  R  -/', 
and  also  CL  =  AL-AC  --^p  —  K. 

The    value    substituted    in    the 
preceding  equations  gives 
'"''■'''•  {K-p')p  =  {p-K)P'. 

From  which  transposing  and  reducing  we  have 

\<p+\lp'=2pp'. 

If  the  terms  of  this  equation  be  all  divided  by//'R,  we  ol)tain 


(I) 
(2) 


(3) 


ivhich  is  the  usual  form  of  the  equation. 
From  the  equation  (i)  we  get 

P'  =  -^  .         . 

which  gives  the  distance  of  the   image  from  the  mirror,  in   terms  of  the 
distance  of  the  object,  and  of  the  radius  of  curvature. 

531.  Discussion  of  the  formulae  for  mirrors. — We  shall  now  in- 
vestigate the  different  values  of  /',  according  to  the  values  of/  in  the 
formula  (3). 

i.  Let  the  object  be  placed  at  an  infmite  distance  on  the  axis,  in  which 
case  the  incident  rays  are  parallel.  To  obtain  the  value  of  p',  both  terms 
of  the  fraction  (3)  must  be  divided  by/,  which  gives 

R 

R_ 
/ 

;  that  is,  th 


/'  = 


•      (4) 
nage  is  formed 


as  /  is  infinite,       is  zero,  and  we  have/'  : 
/ 

in  the  principal  focus,  as  ought  to   be  the  case,  for  the  incitlent   rays  are 
parallel  to  the  axis. 

ii.  If  the  object  approaches  the  mirror,/  decreases,  and  as  the  denomi- 
nator of  the  formula  (4)  diminishes,  the  value  of/'  increases  ;  consequently 
the  image  approaches  the  centre  at  the  same  time  as  the  object,  but  it  is 
always  between  the  principal  focus  and  the  centre,  for  so  long  as 

/  is  >  R,  we  have    -  ^  .,>  ^   ami  <   R. 

"'/ 
iii.  When  the  object  coincides  with  the  centre, /=  R,  anil,  consei|ucntly, 
/'  -  R  ;  that  is,  the  image  coincides  with  the  object. 


-532]  Calculation  of  the  Magnitude  of  Images.  509 

iv.  When  the  luminous  object  is  between  the  centre  and  the  principal 
focus,  p  <  R,  and  hence  from  the  formula  (4),  /'  >  R  ;  that  is,  the  image  is 
formed  on  the  other  side  of  the  centre.     When  the  object  is  in  the  focus, 

R  R 

p  =  ^  which  gives /'  =  -;-  =  CO  ;  that  is,  tlie  image  is  at  an  infinite  distance, 

for  the  reflected  rays  are  parallel  to  the  axis. 

V.  Lastly,  if  the  object  is  between  the  principal  focus  and  the  mirror,  we 

get  j^  <  ^  ;  p'  \'i  then  negative,  because  the  denominator  of  the  formula  (4) 

is  negative.  Therefore,  the  distance  p'  of  the  mirror  from  the  image  must 
be  calculated  on  the  axis  in  a  direction  opposite  to  /.  The  image  is  then 
virtual,  and  is  on  the  other  side  of  the  mirror. 

Making  p'  negative  in  the  formula  (2),  it  becomes  --  ^  =  — ;  in  this 

p    P'     "K 
form  It  comprehends  all  cases  of  virtual  images  in  concave  mirrors. 

In  the  case  of  convex  mirrors  the  image  is  always  virtual  (526)  ;  p'  and 
R  are  of  the  same  sign,  since  the  image  and  the  centre  are  on  the  same  side 
of  the  mirror,  while  the  object  being  on  the  opposite  side,  /  is  of  the  contrary 
sign  ;  hence  in  the  formula  (2)  we  get 

'p-rk   •   •   •   •   (5) 

as  the  formula  for  convex  mirrors.  It  may  also  be  found  directly  by  the 
same  geometrical  considerations  as  those  which  have  led  to  the  formula  (2) 
for  concave  mirrors. 

It  must  be  obser^'ed  that  the  preceding  formuhc  are  not  rigorously  true, 
inasmuch  as  they  depend  upon  the  assumption  that  the  lines  LM  and  /M 
(fig.  472)  are  equal  to  LA  and  A/:  although  this  is  not  true,  the  error 
diminishes  without  limit  with  the  angle  MCA  ;  and  when  this  angle  does 
not  exceed  a  few  degrees,  the  error  is  so  small  that  it  may,  in  practice,  be 
neglected. 

532.  Calculation  of  the  mag^nltude  of  imagres.— By  means  of  the  above 
formula'  the  magnitude  of  an  image  may  Ise  calculated  when  the  distance 
of  the  object,  its  magnitude, 
and  the  radius  of  the  mirror 
are  given.  For  if  BD  be 
the  object  (fig.  473),  bd  its 
image,  and  if  the  distance 
A  and  the  radius  AC  be 
known,  Ac  can  be  calculated 
by  means  of  formula  (3)  of 
article   530.     Ac  known,  oZ 

can  be  calculated.  But  as  the  triangles  BCD  and  d<Zb  are  similar,  their 
bases  and  heights  are  in  the  proportion  bd:  BD  =  Cc  :  CK,  or 

Length  of  the  image  :  length  of  the  object 
=  distance  from  image  to  centre  :  distance  from  the  object  to  the  centre. 

The  brightness  of  an  image  formed  by  a  concave  mirror  is  nearly  pro- 
portional to  its  surface,  and  to  the  coefiicient  of  reflection  ;  and  is  inversely 
as  the  square  of  the  focal  distance. 


510  On  Light.  [533- 

533.  Spberlcal  aberration.  Caustics. — In  the  foregoing  explanation 
•of  the  formation  of  foci  and  images  of  spherical  mirrors,  it  has  already  been 
observed  that  the  reflected  rays  only  pass  through  a  single  point  when  the 
aperture  of  the  mirror  does  not  exceed  8  or  10  degrees  (525).  With  a  larger 
aperture  the  rays  reflected  near  the  edges  meet  the  axis  nearer  the  mirror 
than  those  that  are  reflected  at  a  small  distance  from  the  neighbourhood 
of  the  centre  of  the  mirror.  Hence  arises  a  want  of  sharpness  in  these 
images,  which  is  called  spherical  aberration  by  re/lcctio/i,  to  distinguish  it 
from  the  spherical  aberratio}t  by  refraction,  which  occurs  in  the  case  of 
lenses. 

Every  reflected  ray  cuts  the  one  next  to  it  (fig.  474),  and  their  points  of 
intersection  form  in  space  a  cun-ed  surface  which  is  called  the  caustic  by 

rejection.  The  curve  FM  repre- 
sents one  of  the  branches  of  a 
section  of  this  surface  made  by  the 
plane  of  the  paper.  When  the 
light  of  a  candle  is  reflected  from 
the  inside  of  a  tea-cup  or  a  glass 
tumbler,  a  section  of  the  caustic 
surface  can  be  seen  by  partly  filling 
'"■  ■*''^'  the  cup  or  tumbler  with  milk. 

534.  Applications  of  mirrors.  Hellostat. — The  applications  of  plane 
mirrors  in  domestic  economy  are  well  known.  Mirrors  are  also  frequently 
used  in  physical  apparatus  for  sending  light  in  a  certain  direction.  We 
have  already  seen  an  application  of  this  in  the  heliograph  (523).  The  light 
of  the  sun  can  only  be  sent  in  a  constant  direction  by  making  the  mirror 
movable.  It  must  have  a  motion  which  compensates  for  the  continual  change 
in  the  direction  of  the  sun's  rays  produced  by  the  apparent  diurnal  motion 
of  the  sun.  This  result  is  obtained  by  means  of  a  clockwork  motion,  to 
which  the  mirror  is  fixed,  and  which  causes  it  to  follow  the  course  of  the 
sun.  Such  an  apparatus  is  called  a  heliostat.  The  reflection  of  light  is  also 
used  to  measure  the  angles  of  crystals  by  means  of  the  instruments  known 
as  reflecting  gonio)iieters. 

Concave  spherical  mirrors  are  also  often  used.  They  are  applied  for 
magnifying  mirrors,  as  in  the  older  forms  of  shaving  mirrors.  They  have 
been  employed  for  burning  mirrors,  and  are  still  used  in  telescopes.  They 
also  serve  as  reflectors,  for  conveying  light  to  great  distances,  by  placing 
a  luminous  object  in  their  principal  focus.  For  this  purpose,  however, 
parabolic  mirrors  are  preferable. 

The  images  of  objects  seen  in  concave  or  convex  mirrors  appear  smaller 
or  larger,  but  otherwise  similar  geometrically,  except  in  the  case  where 
some  parts  of  a  body  are  nearer  the  mirror  than  others.  The  distor- 
tion of  features  observed  on  looking  into  a  spherical  garden  mirror  is  more 
marked  the  nearer  we  are  to  the  glass.  Objects  seen  in  cylindrical  or 
conical  mirrors  appear  ludicrously  distorted.  From  the  laws  of  reflection 
the  shape  of  such  a  distorted  figure  can  be  geometrically  constructed.  In 
like  manner  distorted  images  of  objects  can  be  constructctl  which,  seen  in 
such  mirrors,  appear  in  their  normal  proportions.  They  aif  called  anamor- 
phoses. 


-535] 


Parabolic  Mirrors. 


511 


535.  Parabolic  mirrors. — Parabolic  mirrors  are  concave  mirrors  whose 
surface  is  generated  by  the  revolution  of  the  arc  of  a  parabola,  AM,  about 
its  axis  AX  (fig.  475)- 

It  has  been  already  stated  that  in  spherical  mirrors  the  rays  parallel  to 
the  axis  converge  only  approximately  to  the  principal  focus  ;  and  reciprocally, 
when  a  source  of  light  is  placed  in 
the  principal  focus  of  these  mirrors, 
the  reflected  rays  are  not  exactly 
parallel  to  the  axis.  Parabolic 
mirrors  are  free  from  this  defect  ; 
they  are  more  difficult  to  construct, 
but  are  better  for  reflectors.  It  is 
a  property  of  a  parabola  that  the 
right  line  FM,  drawn  from  the 
focus  F  to  any  point  M  of  the 
curve,  and  the  line  ML,  parallel  to 
the  axis  AF,  make  equal  angles 
with  the  tangent  TT'  at  this  point. 
Hence  all  rays  parallel  to  the  axis  after  reflec- 
tion meet  in  the  focus  of  the  mirror  F  ;  and 
conversely,  when  a  source  of  light  is  placed 
in  the  focus,  the  rays  incident  on  the  mirror 
are  reflected  exactly  parallel  to  the  axis. 
The  light  thus  reflected  tends  to  maintain  its 
intensity  even  at  a  great  distance,  for  it  has 
been  seen  (508)  that  it  is  the  divergence  of  the 
luminous  rays  which  principally  weakens  the 
intensity  of  light. 

From  this  property  parabolic  mirrors  are 
used  in  carriage  lamps,  and  in  the  lamps  placed 
in  front  of  and  behind  railway  trains.  These  re- 
flectors were  formerly  used  for  lighthouses,  but 
have  been  replaced  by  lenticular  glasses. 

When   two  equal   parabolic    mirrors  are  cut 
by  a   plane  perpendicular   to    the   axis   passing 
through  the  focus,  and  are  then  united  at  their 
intersections   as   shown    in    fig.  476,  so   that  their  foe 
of  reflectors   is   obtained   with   which   a   single   lamp 


m 


Fig.  476. 

coincide,  a  system 
illuminates    in    two 


directions  at  once, 
passages. 


This    arrangement  is  used  in  lighting  staircases  and 


512 


On  Ltzht. 


[536 


CHAPTER    III. 

SINGLE   REFRACTION.      LENSES. 


536.  .Phenomenon  of  refraction. — Refraction  is  the  deflection  or  bending 
which  the  rays  of  Hght  experience  in  passing  obliquely  from  one  medium  to 
another  :  for  instance,  from  air  into  water  (fig.  478).  We  say  obHquely 
because  if  the  incident  ray  is  perpendicular  to  the  surface  separating  the  two 
media,  it  is  not  bent,  but  continues  its  course  in  a  right  hne  (fig.  477). 

The  incident  ray  being  represented  by  SO  (fig.  479),  the  refracted  ray  is 


Fig.  477- 


mm 

IH^H 

w^ 

/^"^SSB^Mt^^^^ 

ji!i^ 

' 

'Bh 

■ 

"j'J- 1      ■ 

■ 

^H 

the  direction  OH  which 
Hght  takes  in  the  second 
medium ;  and  of  the 
angles  SOA  and  HOB, 
which  these  rays  form 
with  the  line  AB,  at 
right  angles  to  the  sur- 
face which  separates  the 
two  media,  the  first  is 
the  angle  of  incidence, 
and  the  other  the  angle 
of  refraction.  Accord- 
ing as  the  refracted  ray 
approaches  or  deviates 
from  the  normal,  the 
second  medium  is  said 
to  be  more  or  less  re- 
fringent  or  refracting 
than  the  first. 

All  the  liijht  which 


falls  on  a  refracting  surface  does  not  completely  pass  into  it  ;    one  part  is 
reflected  and  scattered  (518),  while  another  penetrates  into  the  medium. 

Mathematical  analysis  shows  that  the  direction  of  refraction  depends  on 
the  relative  velocity  of  light  in  the  two  media.     On  the  undulatory  theory 


-538] 


Index  of  Refraction. 


513 


the  more  highly  refracting  medium  is  that  in  which  the  velocity  of  propaga- 
tion is  least. 

In  uncrystallised  media,  such  as  air,  licjuids,  ordinary  glass,  the  luminous 
ray  is  singly  refracted  ;  but  in  certain  crystallised  bodies,  such  as  Iceland 
spar,  selenite,  &c.,  the  incident  ray  gives  rise  to  two  refracted  rays.  The 
latter  phenomenon  is  called  double  refraction.,  and  will  be  discussed  in  another 
part  of  the  book.     We  shall  here  deal  e\clusi\-ely  with  single  refraction. 

537.  Xiaws  of  single  refraction. — When  a  luminous  ray  is  refracted  in 
passing  from  one  medium  into  another  of  a  different  refractive  power,  the 
following  laws  prevail  : — 

I,  Whatever  the  obliquity  of  the  incide?it  ray,  the  ratio  which  the  sine  of 
the  incident  angle  bears  to  the  sine  of  the  angle  of  refraction  is  constant  for 
the  same  two  media,  but  varies  with  different  media. 

II.  The  incide7it  and  the  refracted  ray  are  i?i  the  same  plane,  ivhich  is 
perpendicular  to  the  surface  separating  the  two  media. 

These  have  been  known  as  Descartes' s  law  ;  they  are,  however,  really 
due  to  W'illibrod  Snell,  who  discovered  them  in  1620;  they  are  demon- 
strated by  the  same  apparatus  as  that  used  for  the  laws  of  reflection  (511). 
The  plane  mirror  in  the  centre  of  the  graduated  circle  is  replaced  by  a 
semi-cylindrical  glass  vessel,  filled  with  water  to  such  a  height  that  its 
level  is  exactly  the  height  of  the  centre  (fig.  480).  If  the  mirror,  M,  be 
then  so  inclined  that  a  reflected  ray,  MO,  is  directed  towards  the  centre,  it 
is  refracted  on  passing  into  the  water,  but  it  passes  out  without  refraction, 
because  its  direction  is  then  at  right  angles  to  the  curved  sides  of  the 
vessel.  In  order  to  observe  the  course 
of  the  refracted  ray,  it  is  received  on  a 
screen,  P,  which  is  moved  until  the 
image  of  the  aperture  in  the  screen  N 
is  formed  at  its  centre.  In  all  positions 
of  the  screens  N  and  P,  the  sines  of 
the  angles  of  incidence  and  refraction 
are  measured  by  means  of  two  graduated 
rules,  movable  so  as  to  be  always  hori- 
zontal, and  hence  perpendicular  to  the 
diameter  AD. 

On  reading  off  the  length  of  the  sines 
of  the  angles  MOA  and  DO P  in  the  . 
scales  I  and  R,  the  numbers  are  found 
to  vary  with  the  position  of  the  screens, 
but  their  ratio  is  constant  ;  that  is,  if 
the  sine  of  incidence  becomes  twice  or 
three  times  as  large,  the  sine  of  refrac- 
tion increases  in  the  same  ratio,  which 
demonstrates  the  first  law.  The  second 
law  follows  from  the  arrangement  of  the 
apparatus,  for  the  plane  of  the  graduated  1 
of  the  liquid  in  the  semi-cylindrical  vessel 

538.  Index  of  refraction. — The  ratio  between  the  sines  of  the  incident 


Fig.  480. 

imb  is  perpendicular  to  the  surface 


and  refracted  angle  is  called  index  of  refraction,  or  refractive  index. 

L  L 


It 


514 


On  LioJit. 


[638- 


vanes  with  the  media  ;  for  example,  from  air  to  water  it  is  *,  and  from  air  to 
glass  it  is  'i. 

If  the  media  are  considered  in  an  inverse  order — -that  is,  if  light  passes 
from  water  to  air,  or  from  glass  to  air — it  follows  the  same  course,  but  in  a 
contrary  direction,  PO  becoming  the  incident  and  OM  the  refracted  ray. 
Consequently  the  index  of  refraction  is  reversed  ;  from  water  to  air  it  is  then 
I,  and  from  glass  to  air  \. 

539.  Effects  produced  by  refraction. — In  consequence  of  refraction, 
bodies  immersed  in  a  medium  more  highly  refracting  than  air,  appear  nearer 
the  surface  of  this  medium,  but  they  appear  to  be  more  distant  if  immersed 
in  a  less  refracting  medium.  Let  L  (fig.  481)  be  an  object  immersed  in  a 
mass  of  water.  In  passing  thence  into  air,  the  rays  LA,  LB  .  .  .  diverge 
from  the  normal  to  the  point  of  incidence,  and  take  the  direction  AC,  BD 
.  .  .  ,  the  prolongations  of  which  intersect  approximately  in  the  point  L', 
placed  on  the  perpendicular  L'K.  The  eye  receiving  these  rays  sees  the 
object  L  at  L'.  The  greater  the  obhquity  of  the  rays  LA,  LB  .  .  .  the  higher 
the  object  appears. 

It  is  for  the  same  reason  that  a  stick  plunged  obliquely  into  water  appears 
bent  (fig.  482),  the  immersed  part  appearing  raised. 

An  experimental  illustration  of  the  effect  of  refraction  is  the  following  : — 
A  coin  is  placed  in  an  empty  porcelain  basin,  and  the  position  of  the  eye  is 
so  adjusted  that  it  is  just  not  visible.  If  now,  the  position  of  the  eye  re- 
maining unaltered,  water  be  poured  into  the  basin,  the  coin  becomes  visible. 
A  consideration  of  fig.  481  will  suggest  the  explanation  of  this  phenomenon. 

Owing  to  an  effect  of  refraction,  stars  are  visible  to  us  even  when  they 
are  below  the  horizon.     For  as  the  layers  of  the  atmosphere  are  denser  in 


I  .-.  4::].  I'U.  4S:i.  I'.--  .(  3. 

l)roportion  as  they  are  nearer  the  earth,  and  as  the  refractive  power  of  a  gas 
increases  with  its  density  (550),  it  follows  that  on  entering  the  atmosphere 
the  luminous  rays  become  Ijcnt,  as  seen  in  fig.  4S3,  descril)ing  a  curve  before 
reaching  the  eye,  so  that  we  can  see  the  star  at  S'  along  the  tangent  of  this 
curve  instead  of  at  S.  In  our  climate  the  atmospheric  refraction  does  not 
raise  the  stars  when  on  the  horizon  more  than  half  a  degree. 

The  effect  of  refraction  is  that  objects  at  a  distance  appear  higher  than 
ihcy  are  in  reality;  our  horizon  is  thereby  widened.  When  individual  layers 
of  air  refract  more  strongly  than  usual,  objects  may  thercl)y  become  visible 
which  arc  usually  below  the  horizon.  Thus,  from  Hastings,  the  coast  of 
France,  which  is  at  a  distance  of  56  miles,  is  not  unfrequcntly  seen. 


-541] 


Miraze. 


515 


Fig.  435- 


540.  Total  reflection.  Critical  angrle. — When  a  ray  of  light  passes 
from  one  medium  into  another  which  is  less  refracting,  as  from  water  into 
air,  it  has  been 
seen  that  the 
angle  of  inci- 
dence is  less 
than  the  angle 
of  refraction. 
Hence,  when 
light  is  propa- 
gated in  a  mass 
of  water  from  S 
to  O  (fig.  484), 
there  is  always 

a  value  of  the  angle  of  incidence  SOB,  such  that  the  angle  of  refraction  AOR 
is  a  right  angle,  in  which  case  the  refracted  ray  emerges  parallel  to  the 
surface  of  the  water. 

This  angle,  SOB,  is  called  the  ciitical  cutgle,  since  for  any  greater  angle, 
POB,  the  incident  ray  cannot  emerge,  but  undergoes  an  internal  reflection, 
which  is  called  total  reflection  because  the  incident  light  is  entirely  reflected. 
From  water  to  air  the  critical  angle  is  48°  35' :  from  glass  to  air,  41°  48'. 

The  occurrence  of  this  internal  reflection  may  be  observed  by  the  follow- 
ing experiment :— An  object.  A,  is  placed  before  a  glass  vessel  filled  with 
water  (fig.  485)  ;  the  surface  of  the  liquid  is  then  looked  at  as  shown  in  the 
figure,  and  an  image  of  the  object  A  is  seen  at  a,  formed  by  the  rays  reflected 
at  7)1,  in  the  ordinary  manner  of  a  mirror. 

Similar  effects  of  the  total  reflection  of  the  images  of  objects  contained 
in  aquaria  are  frequently  observed,  and  add  much  to  the  interest  of  their 
appearance. 

In  total  reflection  there  is  no  loss  of  light  from  absorption  or  transmission, 
and  accordingly  it  produces  the  greatest  brilliancy.  If  an  empty  test-tube 
be  placed  in  a  slanting  position  in  water,  its  surface,  when  looked  at  from 
above,  shines  as  brilliantly  as  pure  mercury  ;  those  rays  which  fall  obliquely 
on  the  side  cannot  pass  into  the  water,  and  are,  therefore,  totally  reflected 
upwards.  If  a  little  water  be  passed  into  the  tube,  that  portion  of  it  loses  its 
lustre.  Bubbles,  again,  in  water  glisten  like  pearls,  and  cracks  in  transparent 
bodies  like  strips  of  silver,  for  the  oblique  rays  are  totally  reflected.  The 
lustre  of  transparent  bodies  bounded  by  plane  surfaces,  such  as  the  lustre  of 
chandeliers,  arises  mainly  from  total  reflection.  This  lustre  is  the  more 
frequent  and  the  more  brilliant  the  smaller  the  limiting  angle  ;  the  lustre 
of  diamond,  therefore,  is  the  most  brilliant. 

541.  Mirage. — The  mirage  is  an  optical  illusion  by  which  inverted  images 
of  distant  objects  are  seen  as  if  below  the  ground  or  in  the  atmosphere.  This 
phenomenon  is  of  most  frequent  occurrence  in  hot  climates,  and  more  espe- 
cially on  the  sandy  plains  of  Egypt.  The  ground  there  has  often  the  aspect  of 
a  tranquil  lake,  on  which  are  reflected  trees  and  the  surrounding  villages. 
Monge,  who  accompanied  Napoleon's  expedition  to  Egypt,  was  the  first  to 
give  an  explanation  of  the  phenomenon. 

It  is  a  phenomenon  of  refraction,  which  results  from  the  unequal  density 

L  L  2 


5i6  On  Light.  [541- 

of  the  different  layers  of  the  air  when  they  are  expanded  by  contact  with  the 
heated  soil.  The  least  dense  layers  are  then  the  lowest,  and  the  pencil  of  light 
from  an  elevated  object,  A  (fig.  486),  traverses  layers  which  are  gradually  less 
refracting  ;  for,  as  will  be  shown  presently  (550),  the  refracting  power  of  a 
gas  diminishes  with  lessened  density.  The  angle  of  incidence  accordingly 
increases  from  one  layer  to  the  other,  and  ultimately  reaches  the  critical 
angle,  beyond  which  internal  reflection  succeeds  to  refraction  (540).  The 
pencil  then  rises,  as  seen  in  the  figure,  and  undergoes  a  series  of  successive 
refractions,  but  in  the  direction  contrary  to  the  first,  for  it  now  passes 
through  layers  which  are  gradually  more  refracting.    The  pencil  then  reaches 


Fis.  4S6. 

the  eye  with  the  same  direction  as  if  it  had  proceeded  rom  a  point  below 
the  ground,  and  hence  it  gives  an  inverted  image  of  the  object,  just  as  if  it 
had  been  reflected  at  the  point  O,  from  the  surface  of  a  tranquil  lake. 

The  effect  of  the  mirage  may  be  illustrated  artificially,  though  feebly,  as 
Dr.  WoUaston  showed,  by  looking  along  the  side  of  a  red-hot  poker  at  a  word 
or  object  ten  or  twelve  feet  distant.  At  a  distance  less  than  three-eighths  of 
an  inch  from  the  line  of  the  poker,  an  inverted  image  was  seen,  and  within 
and  without  that  an  erect  image.  A  better  arrangement  than  a  red-hot 
poker  is  a  flat  sheet-iron  box,  about  3  feet  in  length  by  5  to  7  inches  in 
height  and  breadth  (fig.  487)  ;  it  is  filled  with  red  hot  charcoal  and  held  at  a 

p^ -Im 


Fig.  487. 

about  the  level  of  the  eye.  Looking  over  the  litl  of  the  box  in  the  direction 
pin  a  ^/>ri/,  and  in  the  direction /;«' an //;7vvYtv/ image  of  a  distant  point,/;/, 
is  seen.     The  same  phenomenon  is  observed  by  looking  along  the  sides. 

Mariners  sometimes  sec  inverted  images  in  the  air  of  ships  and  distant 
objects  which  arc  still  under  the  horizon  ;  this  is  due  to  the  same  cause  as 
the  mirage,  but  is  in  a  contrary  direction.     The  lower  layers  of  the  air  licing 


-543]  Prisms.  5 1 7 

in  contact  with  the  water  are  cold  and  dense.  The  rays  of  an  ol)ject,  a  ship 
for  instance,  bent  in  an  upward  direction  are  more  and  more  bent  away  from 
the  vertical  as  they  are  continually  passing  into  gradually  less  dense  layers, 
and  ultimately  fall  so  obliciuely  on  an  upper  attenuated  layer  that  they  are 
totally  reflected  downwards,  and  can  thus  reach  the  eye  of  an  observer  on  the 
sea  or  on  the  shore.  Scoresby  observed  several  such  cases  in  the  Polar 
seas. 

The  twinkling  or  scintillation  of  the  fixed  stars  is  also  to  be  accounted 
for  by  alterations  in  the  direction  of  the  motion  of  their  light  due  to  refrac- 
tion. 


TRANSMISSION   OF   LIGHT  THROUGH   TRANSPARENT   MEDIA. 

542.  ivxedia  wltb  parallel  faces. — When  light  traverses  a  medium  with 
parallel  faces,  the  cinc>-gcnt  rays  are  parallel  to  the  incident  rays. 

Let  MN  (fig.  488)  be  a  glass  plate  with  parallel  faces,  let  SA  be  the 
incident  and  DB  the  emergent  ray,  i  and  r  the  angles  of  incidence  and  of 
refraction  at  the  entrance  of  the  ray,  and,  lastly,  i'  and  r'  the  same  angles 
at  its  emergence.     At  A  the  light  undergoes 


a  first  refraction,  the  index  of  which  is 


sm  / 
sin  r 
(537)-     At  D  it  is  refracted  a  second  time, 

and  the  index  is  then— ^ — ,.     But  we  have 
smr 

seen  that  the  index  of  refraction  of  glass  to 

air  is  the  reciprocal  of  its  refraction  from  air 

,  1  sin  i'     sm  r 

to  glass  ;  hence— ^ =    . — :. 

smr     sm  z 

But  as  the  two  normals  AG  and  DE  are 
parallel,  the  angles  r  and  i'  are  equal,  as  being  alternate  interior  angles.  As 
the  numerators  in  the  above  equation  are  equal,  the  denominators  must  also 
be  equal  ;  the  angles  ;-'  and  /  are  therefore  equal,  and  hence  DB  is  parallel 
to  SA. 

543.  Prism. — In  optics  a  prism  is  any  transparent  medium  comprised 
between  two  plane  faces  inclined  to  each  other.  The  intersection  of  these 
two  faces  is  the  edge  of  the  prism,  and  their  inclination  is  its  refracting  angle. 
Every  section  perpendicular  to  the  edge  is  called  a.  ptincipal  section. 

The  prisms  used 
for  experiments  are 
generally  right  trian- 
gular prisms  of  glass, 
as  shown  in  fig.  489, 
and  their  principal  sec- 
tion is  a  triangle  (fig. 
490).  In  this  section 
the  point  A  is  called 
the  sunimit  of  the 
prism,  and  the  right  line  BC  is  called  the  base  :  these  expressions  have 
reference  to  the  triangle  ABC,  and  not  to  the  prism. 


Fig.  489. 


Fi^.  490. 


5i8 


On  Light. 


[544- 


544.  Path  of  rays  In  prism.  Angle  of  deviation. — When  the  laws 
of  refraction  are  known,  the  path  of  the  rays  in  a  prism  is  readily  determined. 
Let  O  be  a  luminous  point  (fig.  490)  in  the  same  plane  as  the  principal  sec- 
tion ABC  of  a  prism,  and  let  OD  be  an  incident  ray.  This  ray  is  refracted 
at  D,  and  approaches  the  normal,  because  it  passes  into  a  more  highly 
refracting  medium.  At  K  it  experiences  a  second  refraction,  but  it  then 
deviates  from  the  normal,  for  it  passes  into  air,  which  is  less  refractive  than 
glass.  The  light  is  thus  refracted  twice  in  the  same  direction,  so  that  the  ray 
is  dcjiected  towards  the  base,  and  consequently  the  eye  which  receives  the 
emergent  ray  KH  sees  the  object  O  at  O' ;  that  is,  objects  seen  through  a 
prism  appear  deflected  towards  its  suvunit.  The  angle  OEO',  which  the 
incident  and  emergent  rays  form  with  each  other,  expresses  the  deviation  of 
light  caused  by  the  prism,  and  is  called  tlie  angle  of  dc7'iation. 

Besides  this,  objects  seen  through  a  prism  appear  in  all  the  colours  of 
the  rainbow  :  this  phenomenon,  known  as  dispersion,  will  be  afterwards 
described  (564). 

This  angle  increases  with  the  refractive  index  of  the  material  of  the  prism, 
and  also  with  its  refracting  angle.    It  also  varies  with  the  angle  under  which 


Fig.  491 


Fig.  492. 


the  luminous  ray  enters  the  prism.  The  angle  of  deviation  increases  up  to 
a  certain  limit,  which  is  determined  by  calculation,  knowing  the  angle  of 
incidence  of  the  ray,  and  the  refracting  angle  of  the  prism. 

That  the  angle  of  deviation  increases  with  the  refractive  index  may  be 
shown  by  means  of  the  polyp) is)n.  This  name  is  given  to  a  prism  formed 
of  several  prisms  of  the  same  angle  connected  at  their  ends  (fig.  491).  These 
prisms  are  made  of  substances  unequally  refringcnt,  such  as  flint  glass,  rock 
crystal,  or  crown  glass.  If  any  object— a  line,  for  instance — be  looked  at 
through  the  polyprism,  its  different  parts  are  seen  at  unequal  heights.  The 
highest  portion  is  that  seen  through  the  flint  glass,  the  refractive  index  of 


-546]  Coiiditio7is  of.  Emergence  in  Prisms.  519 

which  is  greatest  ;  then  the  rock  crystal ;  and  so  on  in  the  order  of  the 
decreasing  refractive  indices. 

The  piisin  with  variable  atigle  (fig.  492)  is  used  for  showing  that  the 
angle  of  deviation  increases  with  the  refracting  angle  of  the  prism.  It  con- 
sists of  two  parallel  brass  plates,  B  and  C,  fixed  on  a  support.  Between 
these  are  two  glass  plates,  moving  on  a  hinge,  with  some  friction  against  the 
plates,  so  as  to  close  it.  When  water  is  poured  into  the  vessel  the  angle 
may  be  varied  at  will.  If  a  ray  of  light,  S,  be  allowed  to  fall  upon  one  of 
them,  by  inclining  the  other  more  the  angle  of  the  prism  increases,  and  the 
deviation  of  the  ray  is  seen  to  increase. 

545-  Application  of  rigbt-angrled  prisms  in  reflectors. — Prisms  whose 
principal  section  is  an  isosceles  right-angled  triangle  afford  an  important 
application  of  total  reflection  (540).  For  let 
ABC  (fig.  493)  be  the  principal  section  of 
such  a  prism,  O  a  luminous  point,  and  OH 
a  ray  at  right  angles  to  the  face  BC.  This 
ray  enters  the  glass  without  being  refracted, 
and  makes  with  the  face  AB  an  angle 
equal  to  B — that  is,  to  45  degrees — and 
therefore  greater  than  the  limiting  angle  of 
glass,  which  is  41°  48'  (540).     The  ray  OH  f"'s-  493- 

undergoes,  therefore,  at  H  total  reflection,  which  imparts  to  it  a  direction 
HI  perpendicular  to  the  second  face  AC.  Thus  the  hypotenuse  surface  of 
this  prism  produces  the  effect  of  the  most  perfect  plane  mirror,  and  an  eye 
placed  at  I  sees  O',  the  image  of  the  point  O.  This  property  of  right-angle 
prisms  is  frequently  used  in  optical  instruments  such  as  the  camera  lucida 
(603)  and  the  prismatic  compass  (697)  instead  of  metal  reflectors,  which  so 
readily  tarnish.     The  newer  lighthouse  lenses  are  made  up  of  such  prisms. 

546.  Conditions  of  emergrence  in  prisms. — In  order  that  any  luminous 
rays  refracted  at  the  first  face  of  a  prism  may  emerge  from  the  second,  it 
is  necessary  that  the  refractive  angle  of  the  prism  be  less  than  twice  the 
critical  angle  of  the  substance  of  which  the  prism  is  composed.  For  if  LI 
(fig.  494)  be  the  ray  incident  on  the  first  face,  IE  the  refracted  ray,  PI  and 
PE  the  normals,  the  ray  IE  can  only  emerge  from  the  second  face  when 
the  incident  angle  lEP  is  less  than 
the  critical  angle  (540).  But  as  the 
incident  angle  LIN  increases,  the 
angle  EIP  also  increases,  while  lEP 
diminishes.  Hence,  according  as  the 
direction  of  the  ray  LI  tends  to  be- 
come parallel  with  the  face  AB,  does 
this  ray  tend  to  emerge  at  the  second 
face. 

Let  LI  be  now  parallel  to  AB,  the 
angle  r  is  then  equal  to  the  critical 
angle  /  of  the  prism,  because  it  has  its 
maximum  value.  Further,  the  angle 
EPK,  the  exterior  angle  of  the  triangle  IPE,  is  equal  to  ?  +/';  but  the 
angles  EPK  and  A  are  ecjual,  because  their  sides  are  perpendicular,  and 


Fig.  494. 


520  On  Light.  [546- 

therefore  A  =  r  +  /' ;  therefore  also  P^  =  l  +  i\  for  in  this  case  r  =  l.  Hence,  if 
A  =  2/  or  is  >2/,  we  shall  have  i'  =  /  or  >/,  and  therefore  the  ray  would  not 
emerge  at  the  second  face,  but  would  be  parallel  to  AC  or  would  undergo 
internal  reflection,  and  emerge  at  a  third  face,  BC.  This  would  be  much 
more  the  case  with  rays  whose  incident  angle  is  less  than  BIN,  because  we 
have  already  seen  that  i'  would  continually  increase.  Thus  in  the  case  in 
which  the  refracting  angle  of  a  prism  is  equal  to  2/  or  is  greater,  no  luminous 
ray  could  pass  through  the  faces  of  the  refracting  angle. 

As  the  critical  angle  of  glass  is  41°  48',  twice  this  angle  is  less  than  90°, 
and,  accordingly,  objects  cannot  be  seen  through  a  glass  prism  whose  re- 
fracting angle  is  a  right  angle.  As  the  critical  angle  of  water  is  48^  35', 
light  could  pass  through  a  hollow  rectangular  prism  formed  of  three  glass 
plates  and  filled  with  water. 

If  we  suppose  A  to  be  greater  than  /  and  less  than  2/,  then  of  rays  inci- 
dent at  I,  some  within  the  angle  NIB  will  emerge  from  AC,  others  will  not 
emerge,  nor  will  any  emerge  that  are  incident  within  the  angle  NIA.  If  we 
suppose  A  to  have  any  magnitude  less  than  /,  all  rays  incident  at  I  within 

the  angle  NIB  will 
emerge  from  AC, 
as  also  will  some  of 
those  incident  with- 
in the  angle  NIA. 

547.  Mlniinuin 
deviation.- — \\'hen 
a  pencil  of  sunlight 
passes  through  an 
aperture  A,  in  the 
side  of  a  dark  cham- 
I''s-4U5.  ber  (fig.   495),   the 

pencil  is  projected  in  a  straight  line  AC,  on  a  distant  screen.  But  if  a  ver- 
tical prism  be  interposed  between  the  aperture  and  the  screen,  the  pencil  is 
deviated  towards  the  base  of  the  prism,  and  the  image  is  projected  at  D,  at 
some  distance  from  the  point  C.  If  the  prism  be  turned  so  that  the  incident 
angle  decreases,  the  disc  of  light  approaches  the  point  C  up  to  a  certain 
position,  E,  from  which  it  reverts  to  its  original  position  even  when  the  prism 
is  rotated  in  the  same  direction.  Hence  there  is  a  deviation,  EBC,  less  than 
any  other.  It  may  be  demonstrated  mathematically  that  this  mittimum 
deviation  takes  place  when  the  angles  of  incidence  and  of  emergence  are 
equal. 

The  angle  of  minimum  deviation  may  be  calculated  when  the  incident 
angle  and  the  refracting  angle  of  the  prism  are  known.  For  when  the 
deviation  is  a  minimum,  then  since  the  angle  of  emergence  ;•' is  equal  to  the 
incident  angle  /(fig.  494), r  must  et|ual/'.  But  it  has  been  shown  above  (546) 
that  A  =  r  +  /■' ;  consequently 

A  =  2;- (I) 

angle  of  deviation  LI)/  be  called  </,  this  angle  being  ex- 
c  DIE,  we  readily  obtain  the  ctiuation 

(t  =  i ~r+r'  —  i'  =  li -  2r, 


If  the  minunui 
terior  to  the  trianjj 


-550]      Measurement  of  tJie  Rcfractii'c  Index  of  Liquids.         521 

whence  d=2i  —  A. (2) 

which  gives  the  angle  d,  when  i  and  A  are  known. 

From  the  formulas  (i)  and  (2)  a  third  may  be  obtained,  which  serves  to 
calculate  the  index  of  refraction  of  a  prism  when  its  refracting  angle  and  the 
minimum  of  deviation  are  known.     The  index  of  refraction,  ?i,  is  the  ratio 

of  the  sines  of  the  angles  of  incidence  and  refraction  ;  hence  n  =  filLi ;  re- 

sm  r 
placing  i  atid  r  from  their  values  in  the  above  equations  (i)  and  (2)  we  get 


/A  +  (/x 


(3) 


548.  AXeasurement  of  tlie  refractive  Index  of  solids. — By  means  of 
the  preceding  formula  (3)  the  refractive  index  of  a  solid  may  be  calculated 
when  the  angles  A  and  d  are  known. 

In  order  to  determine  the  angle  A,  the  substance  is  cut  in  the  form  of  a 
triangle  prism,  and  the  angle  measured  by  means  of  a  goniometer  (534). 

The  angle  d  \s  measured  in  the  following  manner  ;— A  ray,  LI,  emitted 
from  a  distant  object  (fig.  496),  is  received  on  the  prism,  which  is  turned 
in  order  to  obtain  the 
minimum  deviation 
EDL'.  By  means  of 
a  telescope  with  a 
graduated  circle  the 
angle  EDL'  is  read 
off,  which  the  re- 
fracted ray  DE  makes 
with  the  ray  DL', 
coming  directly  from 
the  object  ;  now  this  is  the  angle  of  minimum  deviation,  assuming  that  the 
object  is  so  distant  that  the  two  rays  LI  and  L'D  are  approximately  parallel. 
These  values  then  only  need  to  be  substituted  in  the  equation  (3)  to  give  the 
value  of  n. 

549.  Measurement  of  the  refractive  index  of  liquids. — Biot  applied 
Newton's  method  to  determining  the  refractive  index  of  liquids.  For  this 
purpose  a  cylmdrical  cavity  O,  of  about  075 
in  diameter,  is  perforated  in  a  glass  prism, 
PQ  (fig.  497),  from  the  incident  face  to  the 
face  of  emergence.  This  cavity  is  closed  by 
two  plates  of  thin  glass  which  are  cemented 
on  the  sides  of  this  prism.  Liquids  are 
introduced  through  a  small  stoppered  aper- 
ture, B.  The  refracting  angle  and  the 
minimum  deviation  of  the  liquid  prism  in 
the  cavity  O  having  been  determined,  their 
values  are  introduced  into  the  formula  (3),  which  gives  the  index. 

550.  Measurement  of  the  retractive  index  of  gases.— A  method  for 
this  purpose,  founded  on  that  of  Newton,  was  devised  by  Biot  and  Arago. 


fig-  497- 


522 


On  Light 


[550- 


The  apparatus  which  they  used  consists  of  a  glass  tube  (fig.  498),  bevelled  at 
its  two  ends,  and  closed  by  glass  plates,  which  are  at  an  angle  of  143°. 
This  tube  is  connected  with  a  bell-jar,  H,  in  which  there  is  a  siphon  barometer, 
and  with  a  stopcock  by  means  of  which  the  apparatus  can  be  exhausted,  and 
different  gases  introduced.  After  having  ex- 
hausted the  tube  AB,  a  ray  of  light,  SA,  is  trans- 
mitted, which  is  bent  away  from  the  normal 
through  an  angle  r  =  z  at  the  first  incidence,  and 
towards  it  through  an  angle  /'  -  r'  at  the  second. 
These  two  deviations  being  added,  the  total 
deviation  d  is  r  —  i-^i'  —  r'.  In  the  case  of  a 
minimum  deviation,  i  =  r'  and  r  =  i\  whence 
</=  A  -  2/,  since  r  -t-  z  =  A  (547).     The  index  from 

vacuum    to   air,  which 


is  evidently-^"-, 

sm  I 


has 


therefore  the  value 


(^) 


(4) 


Hence,  in   order   to   deduce   the   refractive 
'^'  "^^  ■  index   n   from  vacuum    into   air,  which    is    the 

absolute  index  or  principal  itidex,  it  is  merely  necessary  to  know  the  re- 
fracting angle  A,  and  the  angle  of  minimum  deviation  d.  To  obtain  the 
absolute  index  of  any  other  gas,  after  having  produced  a  vacuum,  this  gas  is 
mtroduced  ;  the  angles  A  and  d  having  been  measured,  the  above  formula 
gives  the  index  of  refraction  from  gas  to  air.  Dividing  the  index  of  refrac- 
tion from  vacuum  to  air  by  the  index  of  refraction  from  the  gas  to  air,  we 
obtain  the  index  of  refraction  from  vacuum  to  the  gas  ;  that  is,  its  absolute 
index. 

The  square  of  the  refractive  index  of  a  substance,  less  unity,  that  is  «'  —  i, 
measures  what  is  called  the  refractive  action.  On  the  undulatory  theory  ti- 
is  the  density  of  the  ether  in  the  medium,  when  i  is  the  density  of  the  ether 
in  a  vacuum.  The  refractive  action  is  therefore  a  measure  of  the  excess  of 
the  density  of  the  ether  in  the  refracting  medium.     The  refractive  action 


divided  by  the  density  or 


is  called  the  absolute  refractive  po^i'er. 


Table  of  refractive  indices. 

Diamond     . 

2-470  to  2750 

Plate  glass,  St.  Gobin 

•     1-587 

Rutile 

.     2-6i6 

Rock  crystal  . 

•      1-548 

Phosphorus 

.       2-224 

Rock  salt 

•      1-545 

.Sulphur 

•     2-215 

Turpentine 

•      I  471 

Ruby  . 

•      1779 

Alcohol  . 

•      I  -363 

Flint  glass  . 

.      1-702 

Albumen 

.      1-360 

bisulphide  of 

carbon  .         .      1-678 

Ether      . 

•      1-358 

Iceland  spar, 

ordinary  ray  .      1-654 

Crystalline  lens 

.      1384 

-551] 


Different  Kinds  of  Lenses. 


Iceland  spar,  extraordinary  Vitreous  lens 

ray i'483  Aqueous     „    . 

Crown  glass         .         .         .  i-6o8  Water     . 

Oil  of  cassia        .         .         .  i-6oo  Ice 


1-339 
1-357 
1-336 
1-310 


Vacuum 

Hydrogen 

Oxygen . 

Air 

Nitrogen 

Ammonia 


Refractive  indices  of  gases. 
I  -000000         Carbonic  acid 


1-000138 
1-000272 
I  -000294 
I  -000300 
1-000385 


Hydrochloric  acid 
Nitrous  oxide    . 
Sulphurous  acid 
Olefiant  gas 
Chlorine    . 


I  -000449 
I  -000449 
1-000503 
I  -000665 
I  -000678 
1-000772 


LENSES.      THEIR   EFFECTS. 

551.  Different  kinds  Of  lenses. — Lettscs  are  transparent  media  which, 
from  the  curvature  of  their  surfaces,  have  the  property  of  causing  the  luminous 
rays  which  traverse  them  either  to  converge  or  to  diverge.  According  to 
their  curvature  they  are  either  spherical,  cylindrical,  elliptical,  or  parabolic. 
Those  used  in  optics  are  always  exclusively  spherical.  They  are  commonly 
made  either  of  croiun  glass,  which  is  free  from  lead,  or  of  flint  glass,  which 
contains  lead,  and  is  more  refractive  than  crown  glass. 

The  combination  of  spherical  surfaces,  either  with  each  other  or  with 
plane  surfaces,  gives  rise  to  six  kinds  of  lenses,  sections  of  which  are  repre- 
sented in  fig.  499  ;  four  are  formed  by  two  spherical  surfaces,  and  two  by  a 
plane  and  a  spherical  surface. 

M  is  a  double  convex,  N  is  a  plano-convex,  O  is  a  converging  concavo- 
convex,  P  is  a  double  concave,  Q  is  a  plano-concave,  and  R  is  a  diverging 
concavo-coftvex.  The  lenses  O  and  R  are  also  called  meniscus  lenses,  from 
their  resemblance  to  the  crescent-shaped  moon. 

The  first  three,  which  are  thicker  at  the  centre  than  at  the  borders,  are 
convergijtg ;  the  others,  which  are  thinner  in  the  centre,  are  diverging.  In 
the  first  group  the  double  convex  lens  only  need  be  considered,  and  in  the 


Fig.  499. 

second  the  double  concave,  as  the  properties  of  each  of  these  lenses  apply 
to  all  those  of  the  same  group. 

In  lenses  whose  two  surfaces  are  spherical,  the  centres  for  these  surfaces 
are  called  cetitres  of  curvature,  and  the  right  line  which  passes  through 


524 


On  Li  ill  It. 


[551- 


these  two  centres  is  i\\t  f)ritjcipal  axis.     In  a  plano-concave  or  plano-convex 
lens  the  principal  axis  is  the  perpendicular  let  fall  from  the  centre  of  the 

spherical  face  on  the  plane  face. 

In  order  to  compare  the  path  of 
a  luminous  ray  in  a  lens  with  that 
in  a  prism,  the  same  hypothesis  is 
made  as  for  curved  mirrors  (525)  ; 
that  is,  the  surfaces  of  these  lenses 
are  supposed  to  be  formed  of  an 
infinity  of  small  plane  surfaces  or 
elements  (fig.  500)  :  the  normal  at 
any  point  is  then  the  perpendicular 
to  the  plane  of  the  corresponding 
element.  It  is  a  geometrical  principle 
that  all  the  normals  to  the  same 
spherical  surface  pass  through  its 
centre.  On  the  above  hypothesis 
we  can  always  concei\e  two  plane 
surfaces  at  the  points  of  incidence 
and  emergence,  which  are  inclined 
to  each  other,  and  thus  produce 
the  efilect  of  a  prism.  Pursuing 
this  comparison,  the  three  lenses 
M,  N,  and  O  may  be  compared  to 
a  succession  of  prisms  having  their 
summits  outwards,  and  the  lenses 
P,  Q,  and  R  to  a  series  having 
their  summits  inwards  :  from  this 
we  see  that  the  first  ought  to  con- 
dense the  rays,  and  the  latter  to 
disperse  them,  for  we  have  already 
seen  that  when  a  luminous  ray  traverses  a  prism  it  is  deflected  towards  the 
base  (544). 

552.  VocX  in  double  convex  lenses. — The  focus  of  a  lens  is  the  pomt 
where    the    refracted    rays,    or   their  prolongations,  meet.     Double  convex 

lenses  have  both  real 
and  virtual  foci,  like  con- 
cave mirrors. 

Real  /od.—W'e  shall 
first  consider  the  case 
m  which  the  luminous 
rays  which  fall  on  the 
lens  are  parallel  to  its 
l)rincipal  axis,  as  shown 
in  fig  501.  In  this  case, 
any  incident  ray,  LI5,  in 
approaching  the  normal  ot  the  point  of  incidence  B,  and  in  diverging  from 
it  at  the  point  of  emergence  D,  is  twice  refracted  towards  the  axis,  which  it 
cuts  at  F.     As  all  rays  parallel  to  the  axis  are  refracted  in  the  same  manner. 


Fig.  5" 


I'ig.  501. 


-552] 


Foci  in  Double  Convex  Lenses. 


525 


it  can  be  shown  by  calculation  that  they  all  pass  very  nearly  through  the 
point  F,  so  long  as  the  arc  DE  does  not  exceed  10°  to  12°.  This  point  is 
called  the  principal  focus,  and  the  distance  FA  is  xhe  pri?tcipal  focal  dis- 
tatice.  It  is  constant  in  the  same  lens,  but  varies  with  the  radii  of  curvature 
and  the  index  of  refraction.  In  ordinary  lenses,  which  are  of  crown  glass, 
and  in  which  the  radii  of  the  two  surfaces  are  nearly  equal,  the  principal 
focus  coincides  very  closely  with  the  centre  of  curvature. 

We  shall  now  consider  the  case  in  which  the  point  of  light  is  outside  the 
principal  focus, 
but  so  near  that 
all  incident  rays 
form  a  divergent 
pencil,  as  shown 
in  fig.  502.  The 
point  of  light 
being  at  L,  by 
comparing  the 
path  of  a  di- 
verging ray,  LB, 

with  that  of  a  ray,  SB,  parallel  to  the  axis,  the  former  is  found  to  make  with 
the  normal  an  angle,  LB;/,  greater  than  the  angle  SB«  ;  consequently,  after 
traversing  the  lens,  the  ray  cuts  the  axis  at  a  point,  /,  which  is  more  distant 
than   the    principal 

focus     F.      As    all 

rays  from  the  point 

L  intersect  approxi- 
mately in  the  same 

point    /,  this   latter 

is      the      conjugate 
focus   of  the   point 

L ;    this    term   has 

the  same   meaning 

here  as  in  the  case 

of  mirrors,  and  expresses  the  relation  existing  between  the  two  points  L 

and  /,  which  is  of  such  a  nature  that,  if  the  luminous  point  is  moved  to  /, 

the  focus  passes  to  L. 

According  as  the  point  of  light  comes  nearer  the  lens,  the  convergence 

of  the  emergent  rays  decreases,  and  the  focus  /  becomes  more  distant  ; 

when  the  point  L  coin- 
cides   with  the    principal 

focus,  the  emergent  rays 

on    the    other    side    are 

parallel  to  the  axis,  and 

there  is  no  focus,  or,  what 

is    the    same  thing,   it  is 

infinitely  distant.     As  the 

refracted  rays  are  parallel 
in  this  case,  the  intensity 
of  light  only  decreases  slowly  and  a  simple  lamp  can  illuminate  great  dis- 


Fig. 


526 


On  Light. 


[552 


tances.  It  is  merely  necessarj^  to  place  it  in  the  focus  of  a  double  convex 
lens,  as  shown  in  fig.  504. 

Virtual  foci. — A  double  convex  lens  has  a  virtual  focus  when  the  luminous 
object  is  placed  between  the  lens  and  the  principal  focus,  as  shown  in  fig.  504. 
In  this  case  the  incident  rays  make  with  the  normal  greater  angles  than  those 
made  with  the  rays  FI  from  the  principal  focus  ;  hence,  when  the  fonner 
rays  emerge,  they  move  farther  from  the  axis  than  the  latter,  and  fomi  a 
diverging  pencil,  HK,  GM.  These  rays  cannot  produce  a  real  focus,  but 
their  prolongations  intersect  in  some  point,  /,  on  the  axis,  and  this  point  is 
the  virtual  focus  of  the  point  L  (514). 

553.  Poci  In  double  concave  lenses. — In  double  concave  lenses  there 
are  only  virtual  foci,  whatever  the  distance  of  the  object.  Let  SS'  be  any 
pencil  of  rays  parallel  to  the  axis  (fig.  505)  ;  any  ray  SI  is  refracted  at  the 


point  of  incidence  I,  and  approaches  the  normal  CI.  At  the  point  of  emer- 
gence it  is  also  refracted,  but  diverges  from  the  normal  GC',  so  that  it  is 
twice  refracted  in  a  direction  which  moves  it  from  the  axis  CC'.  As  the 
same  thing  takes  place  for  every  other  ray,  S'KMN,  it  follows  that  the  rays, 
after  traversing  the  lens,  form  a  diverging  pencil,  GHMN.  Hence  there  is 
no  real  focus,  but  the  prolongations  of  these  rays  cut  one  another  in  a  point 
F,  which  is  the  principal  virtual  focus. 

In  the  case  in  which  the  rays  proceed  from  a  point,  L  (fig.  506),  on  the 
axis,  it  is  found  by  the  same  construction  that  a  virtual  focus  is  formed  at  /, 
which  is  between  the  principal  focus  and  the  lens. 

554.  Experimental  determination  of  the  principal  focus  offenses. — 
To  determine  the  principal  focus  of  a  convex  lens,  it  may  be  exposed  to 
the  sun's  rays  so  that  they  are  parallel  to  its  axis.  The  emergent  pencil 
being  received  on  a  ground  glass  screen,  the  point  to  which  the  rays  con- 
verge is  readily  seen  ;  it  is  the  principal  focus. 

Or  an  image  of  an  object  is 
formed  on  a  screen,  their  respective 
distances  from  which  are  then  mea- 
sured, and  from  these  distances  the 
focus  is  calculated  from  the  dioptric 
formula  (561). 

With  a  double  concave  lens,  the 
lace  (xb  (fig.  507)  is  covered  with  an 
opaque  substance,  such  as  lamp- 
black, two  small  apertures  a  and  b 
being  left  in  the  same  principal  section,  and  at  an  equal  distance  from  the 
axis  ;   a  pencil  of  sunlight  is  then   received   on  the  other  face,  and   the 


-655]  Optical  Centre,  Secondary  Axis.  527 

screen  P,  which  receives  the  emergent  rays,  is  moved  nearer  to  or  farllier 
from  the  lens,  until  A  and  B,  the  spots  of  light  from  the  small  apertures  a 
and  h,  are  distant  from  each  other  by  twice  ab.  The  distance  DI  is  then 
equal  to  the  focal  distance  FD,  because  the  triangles  Yab  and  FAB  are 
similar.  Another  method  of  determinmg  the  focus  of  a  concave  lens  is 
given  in  article  560. 

555.  Optical  centre,  secondary  axis. — In  every  lens  there  is  a  point 
called  the  optical  centre,  which  is  situate  on  the  axis,  and  which  has  the 
property  that  any  luminous  ray  passing  through  it  experiences  no  angular 
deviation  ;  that  is,  that  the  emergent  ray  is  parallel  to  the  incident  ray. 
The  existence  of  this  point  may  be  demonstrated  in  the  following  manner : — 
Let  two  parallel  radii  of  cur%^ature,  CA  and  C'A'  (fig.  508),  be  drawn  to  the 


two  surfaces  of  a  double  convex  lens.  Since  the  two  plane  elements  of  the 
lens  A  and  A'  are  parallel,  as  being  perpendicular  to  two  parallel  right  lines, 
it  will  be  granted  that  the  refracted  ray  AA'  is  propagated  in  a  medium 
with  parallel  faces.  Hence  a  ray  KA,  which  reaches  A  at  such  an  inclination 
that  after  refraction  it  takes  the  direction  AA',  will  emerge  parallel  to  its  first 
direction  (542);  the  point  O,  at  which  the  right  line  cuts  the  axis,  is  there- 
fore the  optical  centre.  The  position  of  this  point  may  be  determined  for 
the  case  in  which  the  curvature  of  the  two  faces  is  the  same,  which  is  the 
usual  condition,  by  observing  that  the  triangles  COA  and  C'OA'  are  equal, 
and  therefore  that  OC  =  OC,  which  gives  the  point  O.  If  the  curvatures  are 
unequal,  the  triangles  COA  and  COA'  are  similar,  and  either  CO  or  CO  may 
be  found,  and  therefore  also  the  point  O. 

In  double  concave  or  concavo-convex  lenses  the  optical  centre  may  be 
determined  by  the  same  construction.  In  lenses  with  a  plane  face  this  point 
is  at  the  intersection  of  the  axis  by  the  curved  face. 

Every  right  line  PP'  (fig.  509),  which  passes  through  the  optical  centre 
without  passing  through  the  centres  of  cur\-ature,  is  a  secondary  axis.  From 
this  property  of  the  optical  centre,  every  secondary  axis  represents  a  luminous 
rectilinear  ray  passing  through  this  point  :  for,  from  the  slight  thickness  of 
the  lenses,  it  may  be  assumed  that  rays  passing  through  the  optical  centre 
are  in  a  right  line  ;  that  is,  that  the  small  deviation  may  be  neglected  which 
rays  experience  in  traversing  a  medium  with  parallel  faces  (fig.  508). 

So  long  as  the  secondary  axes  only  make  a  small  angle  with  the  principal 
axis,  all  that  has  hitherto  been  said  about  the  principal  axis  is  applicable  to 
them  ;  that  is,  that  rays  emitted  from  a  point  P  (fig.  509)  on  the  secondaiy 
axis  PP'  nearly  converge  to  a  certain  point  of  the  axis  P',  and  according  as 
the  distance  from  the  point  P  to  the  lens  is  greater  or  less  than  the  principal 


528  On  Light.  [555- 

focal  distance,  the  focus  thus  formed  will  be  conjugate  or  virtual.     This 
principle  is  the  basis  of  what  follows  as  to  the  formation  of  images. 

556.  Formation  of  imag-es  In  double  convex  lenses. — In  lenses,  as  well 
as  in  mirrors,  the  image  of  an  object  is  the  collection  of  the  foci  of  its  several 
points  ;  hence  the  images  furnished  by  lenses  are  real  or  virtual  in  the  same 

case  as  the  foci,  and 
their  construction 
resolves  itself  into 
determining  the 
position  of  a  series 
of  points,  as  was 
the  case  with  mir- 
rors (528). 

i.    Real   image. 
Fig.  510.  Let   AB   (fig.    510) 

be  placed  beyond 
the  principal  focus.  It  a  secondary  axis,  A«,  be  drawn  from  the  outside 
point  A,  any  ray  AC,  from  this  point,  will  be  twice  refracted  at  C  and 
D,  and  both  times  in  the  same  direction  approaching  the  secondary  axis, 
which  it  cuts  at  a.  From  what  has  been  said  in  the  last  paragraph,  the 
other  rays  from  the  point  A  will  intersect  in  the  point  «,  which  is  accordingly 
the  conjugate  focus  of  the  point  A.  If  the  secondary  axis  be  drawn  from 
the  point  B,  it  will  be  seen,  in  like  manner,  that  the  rays  from  this  point 
intersect  in  the  point  b  ;  and  as  the  points  between  A  and  B  have  their 
foci  between  a  and  b,  a  real  but  inverted  image  of  AB  will  be  formed  at  ab. 
To  see  this  image,  it  may  be  received  on  a  white  screen,  on  which  it  will 
be  depicted,  or  the  eye  may  be  placed  in  the  path  of  the  rays  emerging 
from  it. 

Conversely,  if  ab  were  the  luminous  or  illuminated  object,  its  image 
would  be  formed  at  AB.  Two  consequences  important  for  the  theory 
of  optical  instruments  follow  from  this  :  that,  ist,  if  aft  object,  even  a  very 
large  one,  is  at  a  sufficient  distance  from  a  double  convex  lens,  the  real  and 
inverted  image  wJnch  is  obtained  of  it  is  very  sfnall — //  is  near  the  prin- 
cipal focus,  but  somewhat  fartlicr  from  the  lens  titan  this  is  ;  2nd,  if  a  very 
small  object  be  placed  near  the  principal  focus,  but  a  little  in  front  of  it,  the 
image  which  is  formed  is  at  a  great  distance — it  is  much  larger,  and  that  in 
propo7-tion  as  the  object  is  tiear  the  principal  focus.  In  all  cases  the  object 
and  the  image  are  in  the  same  proportion  as  their  distances  from  the  lens. 

These  two  principles  are  experimentally  confirmed  by  receiving  on  a 
screen  the  image  of  a  lighted  candle,  placed  successively  at  various  distances 
from  a  doable  convex  lens. 

ii.  Virtual  image.  There  is  another  case  in  which  the  object  .\B  (fig.  511) 
is  placed  between  the  lens  and  its  principal  focus.  If  a  secondary  axis  On 
be  drawn  from  the  point  A,  every  ray  AC,  after  having  been  twice  refracted, 
diverges  from  this  axis  on  emerging,  since  the  point  A  is  at  a  less  distance 
than  the  principal  focal  distance  (552).  This  ray,  continued  in  an  opposite 
direction,  will  cut  the  axis  Oa  in  the  point  a,  which  is  the  virtual  focus  of  the 
point  A.  Tracing  the  secondary  axis  of  the  point  B,  it  will  be  found, 
in  the  same  manner,  that  the  virtual   focus  of  this  point   is  formed  at  b. 


Caustics.  529 

This  is  a  virtual  image ;  it  is 

proportion    as   the  lens  is  more 


- 558]  SpJierical  A  ber ration. 

There  is,  therefore,  an  image  of  Al)  at  ab. 
erect.,  and  larger  than  the  object. 

The  magnifying  power  is  greater 
convex,  and  the 
object  nearer 
the  principal 
focus.  We  shall 
presently  show- 
how  the  magni- 
fying power  may 
be  calculated 
by  means  of  the 
formula?  relating 
to  lenses  (561). 
Double    convex 

lenses,  used  in  this  manner  as  magnifying  glasses,  are  called  simple  micro- 
scopes. 

557.  Formation  of  imag-es  in  double  concave  lenses. — Double  con- 
cave lenses,  like  convex  mirrors,  only  give  virtual  images,  whatever  the 
distance  of  the  object. 

Let  AB  (fig.  512)  be  an  object  placed  in  front  of  such  a  lens.  If  the 
secondary  axis  AO  be  drawn  from 
the  point  A,  all  rays,  AC,  AI,  from 
this  point  are  twice  refracted  in  the 
same  direction,  diverging  from  the 
axis  AO  ;  so  that  the  eye,  receiving 
the  emergent  rays  DE  and  GH, 
supposes  them  to  proceed  from  the 
point  where  their  prolongations  cut 
the  secondary  axis  AO  in  the  point 
a.  In  like  manner,  drawing  a 
secondary  axis  from  the  point  B, 
the  rays  from  this  point  form  a  pen- 
cil of  divergent  rays,  the  directions  of  which,  prolonged,  intersect  in  b.  Hence 
the  eye  sees  at  ab  a  virtual  image  of  AB,  which  is  always  erect.,  and  smaller 
than  the  object. 

558.  Spherical  aberration.  Caustics. — In  speaking  about  foci,  and 
about  the  images  formed  by  different  kinds  of  spherical  lenses,  it  has  been 
hitherto  assumed  that  the  rays  emitted  from  a  single  point  intersect  also 
after  refraction  in  a  single  point.  This  is  virtually  the  case  with  a  lens  whose 
aperture— 'CciTi.X.  is,  the  angle  obtained  by  joining  the  edges  to  the  principal 
focus — does  not  exceed  10°  or  12°. 

Where,  however,  the  aperture  is  larger,  the  rays  which  traverse  the  lens 
near  the  edge  are  refracted  to  a  point  F  nearer  the  lens  than  the  point  G, 
which  is  the  focus  of  the  rays  which  pass  near  the  axis.  The  phenomenon 
thus  produced  is  named  spherical  aberration  by  refraction  ;  it  is  analogous 
to  the  spherical  aberration  produced  by  reflection  (533).  The  luminous  sur- 
faces fonned  by  the  intersection  of  the  refracted  rays  are  termed  caustics  by 
refraction. 

M  M 


Fig.    512. 


530 


On  Light. 


[558- 


Spherical  aberration  is  prejudicial  to  the  sharpness  and  definition  of  an 
image.     If  a  ground  glass  screen  be  placed  exactly  in  the  focus  of  a  lens, 

the  image  of  an  ob- 
ject will  be  sharply- 
defined  in  the 
centre,  but  indis- 
tinct at  the  edges ; 
and,  vice  versa,  if 
the  image  is  sharp 
at  the  edges,  it  will 
be  indistinct  in  the 
centre.  This  defect 
is  very  objection- 
able, more  espe- 
cially in  lenses  used 
for  photography.   It 


Fig.  513 


is  partially  obviated  by  placing  in  front  of  the  lenses  diaphragms  provided 
with  a  central  aperture,  called  stops,  which  admit  the  rays  passing  near  the 
centre,  but  cut  off  those  which  pass  near  the  edges.  The  image  thereby 
becomes  sharper  and  more  distinct,  though  the  illumination  is  less. 

If  a  screen  be  held  between  the  light  and  an  ordinary  double  convex 
lens  which  quite  covers  the  lens,  but  has  two  concentric  series  of  holes, 
two  images  are  obtained,  and  may  be  received  on  a  sheet  of  paper.  By 
closing  one  or  the  other  series  of  holes  by  a  flat  paper  ring  it  can  be 
easily  ascertained  which  image  arises  from  the  central,  and  which  from 
the  marginal  rays.  When  the  paper  is  at  a  small  distance  the  marginal  rays 
produce  the  image  in  a  point,  and  the  central  ones  in  a  ring  ;  the  former  are 
converged  to  a  point,  and  the  latter  not.  At  a  somewhat  greater  distance 
the  marginal  rays  produce  a  ring,  and  the  central  ones  a  point.  It  is  thus 
shown  that  the  focus  of  the  marginal  rays  is  nearer  the  lens  than  that  of  the 
central  rays. 

Mathematical  investigation  shows  that  convex  lenses  whose  radii  of  cur- 
vature stand  in  the  ratio  expressed  by  the  formula 
r  _4-2«^-H« 


are  most  free  from  spherical  aberration,  and  are  called  lenses  of  best  form  : 
in  this  formula  r  is  the  radius  of  curvature  of  the  foci  turned  to  the  parallel 
rays,  and  r,  that  of  the  other  face,  while  n  is  the  refractive  index.     Thus, 

with  a  glass  whose  refractive  index  is  "^j  r,  =  6r.     Spherical  aberration  is 

2 

also  destroyed  by  substituting  for  a  lens  of  short  focus  two  lenses  of  double 
focal  length,  which  are  placed  at  a  little  distance  apart."  Greater  length  of 
focus  has  the  result  that  for  the  same  diameter  the  aperture  and  also  the 
aberration  arc  less  ;  and  as  it  is  not  necessary  to  stop  a  great  part  of  the 
lens  there  is  a  gain  in  luminosity,  which  is  not  purchased  by  indistinctness 
of  the  images,  while  the  combination  of  the  two  lenses  has  the  same  focus 
as  that  of  the  single  lens  (560).  Lenses  which  are  free  from  spherical  aber- 
ration are  called  aplanatic. 


-559]  Fornmlce  relating  to  Lenses.  531 

559.  Formulae  relating:  to  lenses. — In  all  lenses  the  relations  between 
the  distances  of  the  image  and  object,  the  radii  of  curvature,  and  the  refrac- 
tive index  may  be  expressed  by  a  formula.  In  the  case  of  a  double  convex 
lens,  let  P  be  a  luminous  point  situate  on  the  axis  (fig.  514),  let  PI  be  an  in- 
cident ray,  IE  its  direction  within  the  lens,  EP'  the  emergent  ray,  so  that  P' 
is  the  conjugate  focus  of  P.     Further,  let  CI  and  CE  be  the  normals  to  the 


points  of  incidence  and  emergence,  and  I  PA  be  put  equal  to  a,  EP'A'  =  /3 
ECA'  =  y,  IC'A  =  S,  NIP  =  z,  EIO  =  r,  IEO  =  z',  N'EP'  =  r. 

Because  the  angle  i  is  the  exterior  angle  of  the  triangle  PIC,  and  the 
angle  r'  the  exterior  angle  of  the  triangle  CEP',  therefore  z  =  a-t-S,  and 
r'  =  7  +  /3,  whence 

z+r'  =  a-i-8  +  y-l-S ^l) 

But  at  the  point  I,  sin  i  =  7i  sin  r,  and  at  the  point  E,  sin  r'  =  n  sin  i  (538),  n 
being  the  refractive  index  of  the  lens.  Now  if  the  arc  AI  is  only  a  small 
number  of  degrees,  these  sines  may  be  considered  as  proportional  to  the 
angles  z,  r,  z'  and  r' ;  whence,  m  the  above  formula  we  may  replace  the  sines 
by  their  angles,  which  gives  i^nr  and  r'  =  m',  from  which  i  +  r'  =  n  {r^-i'). 
Further,  because  the  two  triangles  lOE  and  COC  have  a  common  equal 
angle  O,  therefore  r  +  i'  =  y  +  b,  from  which  z-t-r'  =  7z  {y+b).  Introducing 
this  value  into  the  equation  (i)  we  obtain 

/z  (y -(•  S)  =  a -(•  jS  H- y -I- S,  from  which  (;z  -  I )  (y -I- S)  =  a  + /3         .  (2) 

Let  CA'  be  denoted  by  R,  CA  by  R',  PA  by^,  and  P'A'  hy  p'.     Then 
with  centre  P  and  radius  PA  describe  the  arc  A^,  and  with  centre  P'  and 
radius  P'A'  describe  the  arc  A'«.     Now  when  an  angle  at  the  centre  of  a 
circle  subtends  a  certain  arc  of  the  circumference,  the  quotient  of  the  arc 
divided  by  the  radius  measures  the  angle  ;  consequently 
A^  ^^  Ad  „     k-'n        A'E   ^.  .     AI 
''  =  AP°'^^''^  =  >-'^=    R'^^^^^-R'- 
Therefore  by  substitution  in  (2),  («-i)  f^'^+^h  =  — +— • 

V    K        YL  /      p        p' 

Now  since  the  thickness  of  the  lens  is  very  small,  the  angles  are  also  small, 
and  A</,  AI,  A'E,  A'«  differ  but  little  from  coincident  straight  lines,  and  are 
therefore  virtually  equal.     Hence  the  above  equation  becomes 

(«-')(^R>)%-%-' (3) 


532  On  Light.  [559- 

This  is  the  formula  for  double  convex   lenses  ;  if/  be  =  :/o — that  is,  if  the 
rays  are  parallel— we  have 

/'  being  the  principal  focal  distance.     Calling  this/  we  get 

("-)(i-R.)V      .....        (4) 

from  which  the  value  of/  is  easily  deduced.     Considered  in  reference  to 
equation  (4),  the  equation  (3)  assumes  the  form 

'*■,=;. (5) 

P  P    J 

which  is  that  in  which  it  is  usually  employed.     When  the  image  is  virtual, 
p'  changes  its  sign,  and  formula  (5)  takes  the  form 

'-'  ^\ (6) 

P    P'    f  ^  ^ 

In  double  concave  lenses /'and  /  retain  the  same  sign,  but  that  of/ 
changes  ;  the  equation  (5)  becomes  then 

III  ,  , 

rj'-f    ■■■•■■    (7) 

The  equation  (7)  may  be  obtained  by  the  same  reasonings  as  the  other. 

560,  Combination  of  lenses. —  If  parallel  rays  fall  on  a  conve.x  lens  A, 
which  has  the  focal  distance/  and  then  on  a  similar  lens  B  with  the  focal 
distance/',  at  a  distance  d  from  A,  the  distajice  from  the  lens  B  at  which 
the  image  is  formed  at  F  is 

V     f    J-d 
If  the  lenses  are  close  together,  so  that  d=o,  then 

¥    f    f 

If  the  lenses  have  the  same  curvature,  that  is  /"=/',  then  „-  =  ^  ;  that  is  to 

say,  the  focal  distance  of  the  combination  is  half  that  of  a  single  lens. 

If  the  second  lens  is  a  dispersing  one  of  the  focal  distance  /',  then 

L  =     ^     _  '  ;  and  if  the  lenses  are  close  together,  then  ^  =^  -  }  ^. 

This  formula  can  be  used  to  determine  the  focal  distance  of  a  concave 
lens,  by  combining  it  with  a  convex  lens  of  longer  focus,  and  then  deter- 
mining the  focal  distance  of  the  combination. 

561.  Relative  masroltudes  of  Imasre  and  object.  Determination  of 
focus. — From  the  similarity  of  the  triangles  AOB,  aOb  (fig.  510),  we  get 

for  the  relative  magnitudes  of  image  and  object  the  proportion         =P  ; 

lib     p' 

whence        =-^  ,  where  AB  =  0  is  the  magnitude  of  the  object,  and  ab  =  \ 
O    / 


-563  J  Laryngoscope.  533 

that  of  the  image;  while/ and/' are  their  respective  distances  from  the 

lens.     Replacing/'  by  its  value  from  the  equation    -+-  =  i    where    the 

P    P' 

image  is  real,  or  from  the  equation  —  —     =  —  where  it  is  virtual,  we  shall 

P    P'     f 

obtain  the  different  values  of  the  ratio  —  for  various  positions  of  the  object. 
In  the  first  case  we  have  -  ^  ^^• 

Thus  if  p>2f    I>0 

/  =  2/    1  =  0 
/<2/     I>0 

In  the  second  case  when  the  image  is  virtual  we  shall  have 

-  =  /    .  so  that  in  all  cases  I  >0. 
O    /-/ 

By  using  the  above  formula  we  may  easily  deduce  the  focal  length  of  a 
convex  lens  where  direct  sunlight  is  not  available  For  if  it  be  placed  in 
front  of  a  scale,  and  if  a  screen  be  placed  on  the  other  side,  then  by  altering 
the  relative  positions  of  the  lens  and  the  screen,  a  position  may  be  found  by 
trial,  such  that  an  image  of  the  object  is  formed  on  the  screen  of  exactly  the 
same  size.  Dividing  now  by  4  the  total  distance  between  the  object  and 
the  screen,  we  get  the  focal  distance  of  the  lens. 

Another  method  is  to  place  on  one  side  of  the  lens,  and  a  little  beyond 
its  principal  focus,  a  brightly  illuminated  scale,  which  is  best  of  glass,  on  which 
a  strong  light  falls  ;  on  the  other  side  a  screen  is  placed  at  such  a  distance 
as  to  produce  a  greatly  magnified  distinct  image  of  the  scale  Then  if/  and 
L  are  the  lengths  of  the  scale  and  its  image  respectively,  and  d  the  distance 
of  the  screen  from  the  lens, 

562.  Determination  of  the  refractive  index  of  a  liquid. — By  measure- 
ments of  focal  distance  the  refractive  index  of  a  liquid  may  be  ascertained  in 
cases  in  which  only  small  quantities  of  liquid  are  available. 
One  face  of  a  double  convex  lens  of  known  focal  distance  yj 
and  known  curvature  r,  is  pressed  against  a  drop  of  the  liquid 
in  question  on  a  plate  glass  (fig.  515).  The  liquid  forms 
thereby  a  plano-concave  lens  whose  radius  of  curvature  is  r. 
The  focal  distance  F  of  the  whole  system  is  then  determined 
experimentally  ;  this  gives  the  focal  length  of  the  liquid  lens 

/'  from  the  formula  Fig.  515. 

I  _  i_  I 

while  from  the  formula  -  =  («—  i)     we  get  the  value  of  n. 

f  r 

563.  Karyng-oscope. — As  an  application  of  lenses  may  be  adduced  the 
laryngoscope,  which  is  an  instrument  invented  to  facilitate  the  investigation 


534 


On  Lio-ht. 


[563- 


of  the  larynx  and  the  other  cavities  of  the  mouth.  It  consists  of  a  plano- 
convex lens  L,  and  a  concave  reflector  M,  both  fixed  to  a  ring  which  can  be 
adjusted  to  any  convenient  lamp  (fig.  516).  The  flame  of  a  lamp  is  in  the 
principal  focus  of  the  lens,  and  at  the  same  time  is  at  the  centre  of  curvature 
of  the  reflector.     Hence  the  divergent  pencil  proceeding  from  the  lamp  to 


Fig.  516. 

the  lens  is  changed  after  emerging  into  a  parallel  pencil.  Moreover,  the 
pencil  from  the  lamp,  impinging  upon  the  mirror,  is  reflected  to  the  focus  ot 
the  lens,  and  traverses  the  lens,  forming  a  second  parallel  pencil  which  is 
superposed  on  the  first.  This  being  directed  into  the  mouth  of  a  patient, 
its  condition  may  be  readily  observed. 


564] 


535 


CHAPTER    IV. 

DISPERSION   AND   ACHROMATISM. 


564.  Becomposltlon  of  wblte  Ugrht.  Solar  spectrum. — The  pheno- 
menon of  refraction  is  by  no  means  so  simple  as  we  have  hitherto  assumed 
When  -vhite  Hght,  or  that  which  reaches  us  from  the  sun,  passes  from  one 
medium  into  another,  it  is  decomposed  into  several  kinds  of  light,  a  pheno- 
menon to  which  the  name  dispersion  is  given. 

In  order  to  show  that  white  light  is  decomposed  by  refraction,  a  pencil  of 
the  sun's  rays  SA  (fig.  517)  is  allowed  to  pass  through  a  small  aperture  in  the 
window  shutter  of  a 
dark  chamber.  This 
pencil  tends  to  form  a 
round  and  colourless 
image  of  the  sun  at 
K  ;  but  if  a  flint  glass 
prism  arranged  hori- 
zontally be  interposed 
in  its  path,  the  beam, 
on  emerging  from  the 
prism,  becomes  re- 
fracted towards  its 
base,  and  produces 
on  a  distant  screen  a 
vertical  band  rounded  '^'  ^'^' 

at  the  ends,  coloured  in  all  the  tints  of  the  rainbow,  which  is  called  the  solar 
spectriun  (see  Plate  I.).  In  this  spectrum  there  is,  in  reality,  an  infinity  of  diffe- 
rent tints,  which  imperceptibly  merge  into  each  other,  but  it  is  customary  to 
distinguish  seven  principal  colours.  These  are  violet,  indigo,  blue,  green, 
yellow,  orange,  red ;  they  are  arranged  in  this  order  in  the  spectrum,  the 
violet  being  the  most  refrangible,  and  the  red  the  least  so.  They  do  not  all 
occupy  an  equal  extent  in  the  spectrum,  violet  having  the  greatest  extent, 
and  orange  the  least. 

With  transparent  prisms  of  different  substances,  or  with  hollow  glass 
prisms  filled  with  various  liquids,  spectra  are  obtained  formed  of  the  same 
colours,  and  in  the  same  order  ;  but  when  the  deviation  produced  is  the 
same,  the  length  of  the  spectrum  varies  with  the  substance  of  which  the 
prism  is  made.  The  angle  of  separation  of  two  selected  rays  (say  in  the  red 
and  the  violet)  produced  by  a  prism  is  called  the  dispersion,  and  the  ratio  of 


536  On  Light.  [564- 

this  angle  to  the  mean  deviation  of  the  two  rays  is  called  the  dispersive  power. 
This  ratio  is  constant  for  the  same  substance  so  long  as  the  refracting  angle 
of  the  prism  is  small.  For  the  deviation  of  the  two  rays  is  proportional  to 
the  refracting  angle  ;  their  difference  and  their  mean  vary  in  the  same 
manner,  and  therefore  the  ratio  of  their  difference  to  their  mean  is  constant. 
For  flint  glass  this  is  0-043  J  for  crown  glass  it  is  0-0246,  since  the  dispersive 
power  of  flint  is  almost  double  that  of  crown  glass. 

The  spectra  which  are  formed  by  artificial  lights  rarely  contain  all  the 
colours  of  the  solar  spectrum  ;  but  their  colours  are  found  in  the  solar 
spectrum,  and  in  the  same  order.  Their  relative  intensity  is  also  modified. 
The  shade  of  colour  which  predominates  in  the  flame  predominates  also  in 
the  spectrum  ;  yellow,  red,  and  green  flames  produce  spectra  in  which  the 
dominant  tint  is  yellow,  red,  or  green. 

565.  Production  of  a  pure  solar  spectrum. — In  the  above  experiment, 
when  the  light  is  admitted  through  a  wide  slit,  the  spectrum  formed  is  built 
up  of  a  series  of  overlapping  spectra,  and  the  colours  are  confused  and  indis- 
tinct. In  order  to  obtain  a  pure  spectrum,  the  slit,  in  the  shutter  of  the  dark 
room  through  which  light  enters,  should  be  from  15  to  25  mm.  in  height  and 
from  I  to  2  mm.  in  breadth.  The  sun's  rays  are  directed  upon  the  slit  by  a 
mirror,  or  still  better  by  a  heliostat  (534).  An  achromatic  double  convex 
lens  is  placed  at  a  distance  from  the  slit  of  double  its  own  focal  length, 
which  should  be  about  a  metre,  and  a  screen  is  placed  at  the  same  distance 
from  the  lens.  An  image  of  the  slit  of  exactly  the  same  size  is  thus  formed 
on  the  screen  (561).  If  now  there  is  placed  near  the  lens,  between  it  and 
the  screen,  a  prism  with  an  angle  of  about  60°,  and  with  its  refracting  edge 
parallel  to  the  slit,  a  very  beautiful,  sharp,  and  pure  spectrum  is  formed  on 
the  screen.  The  prism  should  be  free  from  strias,  and  should  be  placed  so 
that  it  produces  the  minimum  deviation. 

566.  The  colours  of  tbe  spectrum  are  simple,  and  unequally  refran- 
gible.— If  one  of  the  colours  of  the  spectrum  be  isolated  by  intercepting  the 
others  by  means  of  a  screen  E,  as  shown  in  fig.  518,  and  if  the  light  thus 

isolated  be  allowed  to 
p:iss  through  a  second 
])rism,  B,  a  refraction 
will  be  observed,  but 
the  light  remains  un- 
changed ;  that  is,  the 
image  received  on  the 

screen  H  is  violet  if  the 

violet  pencil  has  been 
'*'■  ^'  ■  allowed  to  pass,  blue 

if  the  blue  pencil,  and  so  on.  Mence  the  colours  of  the  spectrum  ?i.ic  simple ; 
that  is,  they  cannot  be  further  decomposed  by  the  prism. 

Moreover,  the  colours  of  the  spectrum  are  unequally  refrangible  ;  that 
is,  they  possess  different  refractive  indices.  The  elongated  shape  of  the 
spectrum  would  be  sufficient  to  prove  the  unequal  rcfrangibility  of  the  simple 
colours,  for  it  is  clear  that  the  violet,  which  is  most  deflected  towards  the 
base  of  the  prism,  is  also  most  refrangible  ;  and  that  red,  which  is  least  de- 
flected, is  least  refrangible.    Hut  the  unequal  rcfrangibility  of  simple  colours 


-566] 


The  Colours  of  the  Spectrum. 


537 

may  be  shown  by  numerous  experiments,  of  which  the  two  following  may  be 
adduced  : — 

i.  Two  narrow  strips  of  coloured  paper,  one  rctl  and  the  other  violet,  are 
fastened  close  to  each  other  on  a  sheet  of  black  paper.  On  looking  at  them 
through  a  prism,  they  are  seen  to  be  unequally  displaced,  the  red  band  to  a 
less  extent  than  the  violet  ;  hence  the  red  rays  are  less  refrangible  than  the 
violet. 

ii.  The  same  conclusion  may  be  drawn  from  Newton's  experiment  with 
crossed  prisms.     On  a  prism  A  (fig.  519),  in  a  horizontal  jjosition,  a  pencil 


Fijj.  519. 

of  white  light,  S,  is  received,  which,  if  it  had  merely  traversed  the  prism  A, 
would  form  the  spectrum  r?',  on  a  distant  screen.  But  if  a  second  prism,  B, 
be  placed  in  a  vertical  position  behind  the  first,  in  such  a  manner  that  the 
refracted  pencil  passes  through  it,  the  spectrum  rv  becomes  deflected  towards 
the  base  of  the  vertical  prism  ;  but,  instead  of  being  deflected  in  a  direction 
parallel  to  itself,  as  would  be  the  case  if  the  colours  of  the  spectrum  were 
equally  refracted,  it  is  obliquely  refracted  in  the  direction  r'v\  proving  that 
from  red  to  violet  the  colours  are  more  and  more  refrangible. 

These  different  experiments  show  that  the  refractive  index  differs  in 
different  colours  ;  even  rays  which  arc  to  j)erception  undistinguishablc  have 
not  the  same  refractive  index.     In  the  rcil  hand,  for  instance,  the  rays  at  the 


extremity  of  the  spectrum  are  less  refracted  than  those  which  are  nearer  the 
orange  zone.  In  determining  indices  of  refraction  (538),  it  is  usual  to  take, 
as  the  index  of  any  particular  substance,  the  refrangibility  of  the  yellow  ray 
in  a  prism  formed  of  that  substance. 


S38 


On  Light. 


[567- 


567.  Recomposition  of  wbite  ligrbt. — Not  merely  can  white  light  be 
resolved  into  lights  of  various  colours,  but  by  combining  the  different  pencils 
separated  by  the  prism  white  light  can  be  reproduced.  This  maybe  effected 
in  various  ways. 

\.  If  the  spectrum  produced  by  one  prism  be  allowed  to  fall  upon  a  second 
prism  of  the  same  material  and  the  same  refracting  angle  as  the  first,  but 
inverted,  as  shown  in  fig.   521,  the  latter  reunites  the  different  colours  of 
the  spectrum,  and  it  is  seen  that  the  emer- 
gent pencil  E,  which  is  parallel  to  the  pencil 
S,  is  colourless. 

ii.    If  the  spectrum  falls  upon  a  double 

convex  lens  (fig.  520),  a  white  image  of  the 

sun  will  be  formed  on  a  white  screen  placed 

in  the  focus  of  the  lens  ;  a  glass  globe  filled 

j.,j^  _^  with  water  produces  the  same  effect  as  the 

lens. 

iii.  When  the  spectrum  falls  upon  a  concave  mirror,  a  white  image  is 

formed  on  a  screen  of  ground  glass  placed  in  its  focus  (fig.  522), 

iv.  Light  may  be  recomposed  by  means  of  a  pretty  experiment,  which 
consists  in  receiving  the  seven  colours  of  the  spectrum  on  seven  small  glass 


I'ig-  523- 

mirrors  with  plane  faces,  and  which  can  be  so  inclined  in  all  positions  that 
the  reflected  light  may  be  transmitted  in  any  given  direction  (fig.  523\ 
When  these  mirrors  are  suitably  arranged,  the  seven  reflected  pencils  may 
be  caused  to  fall  on  the  ceiling,  in  such  a  manner  as  to  form  seven  distinct 
images — red,  orange,  yellow,  &c.  When  the  mirrors  are  moved  so  that  the 
separate  images  become  superposed,  a  single  image  is  obtained,  which  is 
white. 

V.  By  means  oi  Newton's  disc  (fig.  524)  it  may  be  shown  that  the  seven 
colours  of  the  spectrum  form  white.  This  is  a  cardboard  disc  of  about  a 
foot  in  diameter  ;  the  centre  and  the  edges  are  covered  with  black  paper, 
while  in  the  space  between  there  arc  pasted  strii)s  of  paper  of  the  colours  of 
the  spectrum.     They  proceed  from  the  centre  to  the  circumference,  and  their 


-568]         Neivton's  Tlieory  of  the  Compositio7i  of  LigJit.  539 

relative  dimensions  and  tints  are  such  as  to  represent  five  spectra  (fig.  525). 
When  this  disc  is  rapidly  rotated,  the  effect  is  the  same  as  if  the  retina 
received  simultaneously  the  impression  of  the  seven  colours. 

vi.  If  by  a  mechanical  arrangement  a  prism,  on  which  the  sun's  light 
falls,  is  made  to  oscillate  rapidly,  so  that  the  spectrum  also  oscillates,  the 
middle  of  the  spectrum  appears  white. 

These  latter  phenomena  depend  on  the  physiological  fact  that  sensation 
always  lasts  a  little  longer  than  the  impression  from  which  it  results  (625). 
If  a  new  impression  is  allowed  to  act,  before  the  sensation  arising  from  the 
former  one  has  ceased,  a  sensation  is  obtained  consisting  of  two  impressions. 
And  by  choosing  the  time  short  enough,  three,  four,  or  more  impressions 
may  be  mixed  with  each  other.     With  a  rapid  rotation  the  disc  (fig.  524) 


Fig.  S24. 


is  nearly  white.  It  is  not  quite  so,  for  the  colours  cannot  be  exactly  arranged 
in  the  same  proportions  as  those  in  which  they  exist  in  the  spectrum,  and 
moxe.Q\&r pigtne?it  colours  are  not  pure  (571). 

568.  Newton's  theory  of  the  composition  of  light. — Newton  was  the 
first  to  decompose  white  light  by  the  prism,  and  to  recompose  it.  From  the 
various  experiments  which  we  have  described,  he  concluded  that  white  light 
was  not  homogeneous,  but  formed  of  seven  lights  unequally  refrangible, 
which  he  called  simple  or  primitive  lights.  Owing  to  the  difference  in 
refrangibility  they  become  separated  in  traversing  the  prism. 

The  designation  of  the  various  colours  of  the  spectrum  is  to  a  very  great 
extent  arbitrary  ;  for,  in  strict  accuracy,  the  spectrum  is  made  up  of  an  in- 
finite number  of  simple  colours,  which  pass  into  one  another  by  imperceptible 
graduations  of  colour  and  refrangibility. 


540  On  Light.  [569- 

569.  Colour  of  bodies. — The  natural  colour  of  bodies  results  from  the 
fact  that  one  portion  of  the  coloured  rays  contained  in  white  light  is 
absorbed  at  the  surface  of  the  body.  If  the  unabsorbed  portion  traverses 
the  body,  it  is  coloured  and  transparent  ;  if,  on  the  contrary,  it  is  reflected, 
it  is  coloured  and  opaque.  In  both  cases  the  colour  results  from  the 
constituents  which  have  not  been  absorbed.  Those  which  reflect  or 
transmit  all  colours  in  the  proportion  in  which  they  exist  in  the  spectrum 
are  white  :  those  which  reflect  or  transmit  none  are  black.  Between  these 
two  Imiits  there  are  infinite  tints  according  to  the  greater  or  less  extent  to 
which  bodies  reflect  or  transmit  some  colours  and  absorb  others.  Thus  a 
body  appears  yellow  because  it  absorbs  all  colours  with  the  exception  of 
yellow.  In  like  manner,  a  solution  of  ammoniacal  oxide  of  copper  absorbs 
preferably  the  red  and  yellow  rays,  transmits  the  blue  rays  almost  completely, 
the  green  and  violet  less  so  ;  hence  the  light  seen  through  it  is  blue. 

Accordingly  bodies  have  no  colour  of  their  own  ;  the  colour  of  the  body 
changes  with  the  nature  of  the  incident  light.  Thus,  if  a  white  body  in  a 
dark  room  be  successively  illuminated  by  each  of  the  colours  of  the  spectrum, 
it  has  no  special  colour,  but  appears  red,  orange,  green,  &c.,  according  to  the 
position  m  which  it  is  placed.  If  homogeneous  light  falls  upon  a  body,  it 
appears  brighter  in  the  colour  of  this  light,  if  it  does  not  absorb  this  colour  ; 
but  black  if  it  does  absorb  it.  In  the  light  of  a  lamp  fed  by  spirit  in  which 
some  common  salt  is  dissolved,  everything  white  and  yellow  seems  bright, 
while  other  colours,  such  as  vermilion,  ultramarine,  and  malachite,  are 
black.  This  is  well  seen  in  the  case  of  a  stick  of  red  sealing-wax  viewed  in 
such  a  light.  In  the  light  of  lamps  and  of  candles,  which  from  the  want  of 
blue  rays  appear  yellow,  yellow  and  white  appear  the  same,  and  blue  seems 
like  green.  In  bright  twilight  or  in  moonshine  the  light  of  gas  has  a  reddish 
tint. 

570.  Mixed  colours.  Complementary  colours. — By  mixed  colours  we 
understand  the  impression  of  colour  which  results  from  the  coincident  action 
of  two  or  more  colours  on  the  same  position  of  the  retina.  This  new  im- 
pression is  single  ;  it  cannot  be  resolved  into 
its  components  ;  in  this  respect  it  differs  from 
a  complex  sound,  in  which  the  ear,  by  practice, 
can  learn  to  distinguish  the  constituents.  Mixed 
colours  may  be  produced  by  Lamherfs  method, 
which  consists  in  lookmg  in  an  oblique  direction 
through  a  vertical  glass  plate  P  (fig.  526)  at  a 
coloured  wafer  b,  while,  at  the  same  time,  a  wafer 

J,..        ,  of  another  colour  g  sends  its  light  by  reflection 

towards  the  observer's  eye  ;  if  ^  is  placed  in  a 
proper  position,  which  is  easily  found  by  trial,  its  image  exactly  coincides 
with  that  of  b.  The  method  of  the  colour  disc  (567)  affords  another  means 
of  producing  mixed  colours. 

.•\  very  convenient  way  of  investigating  the  phenomena  of  mixed  colours 
is  that  o{  Maxiueirs  colour-discs.  These  consist  of  discs  of  cardboard  with 
an  aperture  in  the  centre,  by  which  they  can  be  fastened  on  the  spindle  of  the 
turning-table  (fig.  527).  Each  disc  is  painted  with  a  separate  colour,  and, 
having  a  radial  slit,  tlicy  may  be  slid  over  each  other  so  as  to  overlap  to  any 


-570] 


Mixed  Colours.     Complementary  Colours. 


541 

desired  extent  (figs.  528  and  529)  ;  and  thus,  when  in  this  way  two  such  discs 
are  rotated,  we  get  the  efifect  due  to  this  mixture  of  these  two  colours.  It  is 
clear  also  that  the  eftect  of  three  colours  may  be  investigated  in  the  same  way. 


Fig.  529. 


If  in  any  of  the  methods  by  which  the  impression  of  mixed  spectral 
colours  is  produced,  one  or  more  colours  be  suppressed,  the  residue  corre- 
sponds to  one  of  the  tints  of  the  spectrum  ;  and  the  mixture  of  the  colours 
taken  away  produces  the  impression  of  another  spectral  colour.  Thus,  if  in 
fig.  526  the  red  rays  are  cut  off  from  the  lens  L,  the  light  on  the  focus  is  no 
longer  white,  but  greenish  blue.  In  like  manner,  if  the  violet,  indigo,  and 
blue  of  the  colour  disc  be  suppressed,  the  rest  seems  yellow,  while  the  mixture 
of  that  which  has  been  taken  out  is  a  bluish  violet.  Hence  white  can  always 
be  compounded  of  two  tints  ;  and  two  tints  which  together  give  white  are 
called  complementary  colours.  Thus  of  spectral  tints  red  zxvdi greenish  yellow 
are  complementary,  so  are  oraftge  and  Prussian  blue ;  yellow  and  indigo 
blue ;  greenis/i  yellozu  and  violet. 

The  method  by  which  Helmholtz  investigated  the  mixture  of  spectral 
colours  is  as  follows  : — Two  very  narrow  slits,  A  and  B  (fig.  530),  at  right 


angles  to  each  other,  are  made  in  the  shutter  of  a  dark  room  ;  at  a  distance 
from  this  is  placed  a  powerfully  dispersing  prism  with  its  refracting  edge 
vertical.  When  this  is  viewed  through  a  telescope,  the  slit  B  gives  the 
oblique  spectrum  LM,  while  the  sHt  A  gives  the  spectrum  ST.  These  two 
spectra  partially  overlap,  and  when  this  is  the  case  two  homogeneous  spectral 
colours  mix.  Thus  at  i  the  red  of  one  spectrum  coincides  with  the  green  of 
the  other  ;  at  3,  indigo  and  yellow  coincide  ;  and  so  forth. 

When  the  experiment  is  made  with  suitable  precautions,  the  colours  ob- 
tained by  mixing  the  spectral  colours  are  given  in  the  table  on  the  next  page, 
where  the  fundamental  spectra  to  be  mixed  are  given  in  the  first  horizontal 
and  vertical  column,  and  the  resultant  colours  where  these  cross. 

The  mixture  of  mixed  colours  gives  rise  to  no  new  colours.  Only  the 
same  colours  are  obtained  as  a  mixture  of  the  primitive  spectral  colours  would 
yield,  except  that  they  are  less  saturated,  as  it  is  called  ;  that  is,  more  mixed 
with  white. 


542  On  Light.  [571- 

571.  Spectral  colours  and  plerment  colours. — A  distinction  must  be 
made  between  spectral  colours  and  pig!?ie?it  colours.  Thus  a  mixture  of 
pigment  yellow  and  pigment  blue  produces  green,  and  not  white,  as  is  the 
case  when  the  blue  and  yellow  of  the  spectrum  are  mixed.  The  reason  of 
this  is  that  in  the  mixture  of  pigments  we  have  a  case  of  subtraction  of 
colours,  and  not  of  addition.  For  the  pigment  blue  in  the  mixture  absorbs 
almost  entirely  the  yellow  and  red  light  ;  and  the  pigment  yellow  absorbs 
the  blue  and  violet  light,  so  that  only  the  green  remains. 

In  the  above  series  are  two  spectral  colours  veiy  remote  in  the  spectrum, 
which  have  nearly  the  same  complementary  tints  ;  these  are  red,  the  com- 
plementary colour  to  which  is  greenish  blue  ;  and  violet,  whose  complementary 
colour  is  greenish  yellow.  Now  when  two  pairs  of  complementary  colours 
are  mixed  together  they  must  produce  white,  just  as  if  only  two  comple- 
mentary colours  were  mixed.  But  a  mixture  of  greenish  blue  and  of  greenish 
yellow  is  green.  Hence  it  follows  that  from  a  mixture  of  red,  green,  and 
violet,  white  must  be  formed.  This  may  easily  be  ascertained  to  be  the  case 
by  means  of  a  colour  disc  on  which  are  these  three  colours  in  suitable  pro- 
portions. 


! 

Violet 

Blue      Green    Yellow      Red 

Red 



Yellow 
Green 

Purple 

Rose 

X        Orange 

Red 

Rose 

White 

^^-     Ye„ow 

Pale  blue 

Bluish 
green 

Green 

Blue 

Indigo 

Blue 

Violet 

Violet 

From  the  above  facts  it  follows  that  from  a  mixture  of  red,  green,  and 
violet  all  possible  colours  may  be  constructed,  and  hence  these  three  spectral 
colours  are  called  the  fundamental  colours.  It  must  be  remarked  that  the 
tints  resulting  from  the  mixture  of  these  three  have  never  the  saturation  of 
the  individual  spectral  colours. 

We  have  to  discriminate  three  points  in  regard  to  colour.  In  the  first 
place,  the  /////,  or  colour  proper,  by  which  we  mean  that  special  property 
which  is  due  to  a  definite  refrang^ibility  of  the  rays  producing  it  ;  secondly, 
the  saturation,\s\\\c\\  depends  on  the  greater  or  less  admixture  of  white  light 
with  the  colours  of  the  spectrum,  these  being  colours  which  are  fully  satu- 
rated ;  and  thirdly,  there  is  the  intensity,  which  depends  on  the  amplitude  of 
vibration. 


-573]  Properties  of  tJie  Spectrum.  543 

572.  Homogreneous  llgrbt. — The  light  emitted  from  luminous  bodies  is 
seldom  or  never  quite  pure  ;  on  being  examined  by  the  prism  it  will  be  found 
to  contain  more  than  one  colour.  In  optical  researches  it  is  frequently  of 
great  importance  to  procure  homogeneous  or  monochromatic  light.  Common 
salt  in  the  flame  of  a  Bunsen's  lamp  gives  a  yellow  of  great  purity.  For  red 
light,  ordinary  light  is  transmitted  through  glass  coloured  with  suboxide  of 
copper,  which  absorbs  nearly  all  the  rays  excepting  the  red.  A  very  pure 
blue  is  obtained  by  transmitting  ordinary  light  through  a  glass  trough  con- 
taining an  ammoniacal  solution  of  sulphate  of  copper,  and  a  nearly  pure  red 
by  transmitting  it  through  a  solution  of  sulphocyanide  of  iron. 

573.  Properties  of  tbe  spectrum.— Besides  its  luminous  properties,  the 
spectrum  is  found  to  produce  calorific  and  chemical  effects. 

Luminous  properties.  It  appears  from  the  experiments  of  Fraunhofer 
and  of  Herschel,  that  the  light  in  the  yellow  part  of  the  spectrum  has  the 
greatest  intensity,  and  that  in  the  violet  the  least. 

Heating  effects.  It  was  long  known  that  the  various  parts  of  the  spectrum 
differed  in  their  calorific  effects.  Leslie  found  that  a  thermometer  placed  in 
different  parts  of  the  spectrum  indicated  a  higher  temperature  as  it  moved 
from  violet  towards  red.  Herschel  fixed  the  maximum  intensity  of  the 
heating  effects  just  outside  the  red  ;  Berard  in  the  red  itself  Seebeck 
showed  that  those  different  effects  depend  on  the  nature  of  a  prism  ;  with  a 
prism  of  water  the  greatest  calorific  effect  is  produced  in  the  yellow  ;  with 
one  of  alcohol  it  is  in  the  orange-yellow  ;  and  with  a  prism  of  crown  glass  it 
is  in  the  middle  of  the  red. 

Melloni,  by  using  prisms  and  lenses  of  rock  salt,  and  by  availing  himself 
of  the  extreme  delicacy  of  the  thermo-electric  apparatus,  first  made  a  com- 
plete investigation  of  the  calorific  properties  of  the  thermal  spectrum.  This 
result  led,  as  we  have  seen,  to  the  confirmation  and  extension  of  Seebeck's 
observations. 

Chemical  properties.  In  numerous  phenomena,  light  exerts  a  chemical 
action.  For  instance,  chloride  of  silver  blackens  under  the  influence  of  light ; 
transparent  phosphorus  becomes  opaque  ;  vegetable  colouring  matters  fade  - 
hydrogen  and  chlorine  gases,  when  mixed,  combine  slowly  in  diffused  light,^ 
and  with  explosive  violence  when  exposed  to  direct  sunlight.  The  chemical 
action  differs  in  different  parts  of  the  spectrum.  Scheele  found  that  when 
chloride  of  silver  was  placed  in  the  violet,  the  action  was  more  energetic 
than  in  any  other  part.  Wollaston  observed  that  the  action  extended  beyond 
the  violet,  and  concluded  that,  besides  the  visible  rays,  there  are  some  in- 
visible and  more  highly  refrangible  rays.  These  are  the  chemical  or  actinic 
rays. 

The  most  remarkable  chemical  action  which  light  exerts  is  in  the  growth 
of  plant  life.  The  vast  masses  of  carbon  and  hydrogen  accumulated  in  the 
vegetable  world  owe  their  origin  to  the  carbonic  acid  and  aqueous  vapour 
present  in  the  atmosphere.  The  light  which  is  absorbed  by  the  green  parts 
of  plants  acts  as  a  reducing  agent.  The  reduction  does  not  extend  to  the 
complete  isolation  of  carbon  and  hydrogen,  and  the  individual  stages  of  the 
process  are  unknown  to  us  ;  but  the  general  result  is,  undoubtedly,  that  under 
the  influence  of  the  sun's  rays  the  chemical  attraction  which  holds  together 
the  carbon  and  oxygen  is  overcome  ;  the  carbon,  which  is  set  free,  assimilates 


544  On  Light.  [573- 

at  that  moment  the  elements  of  water,  forming  cellulose  or  woody  fibre, 
while  the  oxygen  returns  to  the  atmosphere  in  the  form  of  gas.  The 
equivalent  of  the  sunlight  which  has  been  absorbed  is  to  be  sought  in  the 
chemical  energy  of  the  separated  constituents.  When  we  burn  petroleum 
or  coal,  we  reproduce,  in  some  sense,  the  light  which  the  sun  has  expended 
in  former  ages  in  the  production  of  a  primeval  vegetable  growth. 

The  researches  of  Bunsen  and  Roscoe  show  that  whenever  chemical 
action  is  induced  by  light,  an  absorption  of  light  takes  place,  preferably  of 
the  more  refrangible  parts  of  the  spectrum.  Thus,  when  chlorine  and 
hydrogen  unite,  under  the  action  of  light,  to  form  hydrochloric  acid,  light  is 
absorbed,  and  the  quantity  of  chemically  active  rays  consumed  is  directly 
proportional  to  the  amount  of  chemical  action. 

There  is  a  curious  difference  in  the  action  of  the  different  spectral  rays. 
Moser  placed  an  engraving  on  an  iodised  silver  plate,  and  exposed  it  to  the 
light  until  an  action  had  commenced,  and  then  placed  it  under  a  violet  glass 
in  the  sunlight.  After  a  few  minutes  a  picture  was  seen  with  great  distinct- 
ness, while  when  placed  under  a  red  or  yellow  glass  it  required  a  very  long 
time,  and  was  very  indistinct.  When,  however,  the  iodised  silver  plate  was 
first  exposed  in  a  camera  obscura  to  blue  light  for  two  minutes,  and  was  then 
brought  under  a  red  or  yellow  glass,  an  image  quickly  appeared,  but  not 
when  placed  under  a  green  glass.  It  appears  as  if  there  are  vibrations  of  a 
certain  velocity  which  could  commence  an  action,  and  that  there  are  others 
which  are  devoid  of  the  property  of  commencing,  but  can  continue  and 
complete  an  action  when  once  set  up.  Becquerel,  who  discovered  these 
properties  in  luminous  rays,  called  the  former  exciting  rays  and  the  latter 
continuing  or  phosp/wrogenic  rays.  The  phosphorogenic  rays,  for  instance, 
have  the  property  of  rendering  certain  objects  self-luminous  in  the  dark 
after  they  have  been  exposed  for  some  time  to  the  light.  Becquerel  found 
that  the  phosphorogenic  spectrum  extended  from  indigo  to  beyond  the 
violet. 

574.  Dark  lines  of  the  spectrum. — The  colours  of  the  solar  spectrum 
are  not  continuous.  For  se\'eral  grades  of  refrangibility  rays  are  wanting, 
and,  in  consequence,  throughout  the  whole  extent  of  the  spectrum  there  are  a 
great  number  of  very  narrow  dark  lines.  To  observe  them,  a  pencil  of  solar 
rays  is  admitted  into  a  darkened  room,  through  a  narrow  slit.  At  a  distance 
of  three  or  four  yards  we  look  at  this  slit  through  a  prism  of  flint  glass, 
which  must  be  very  free  from  flaws,  taking  care  to  hold  its  edge  parallel  to 
the  slit.  We  then  observe  a  great  number  of  very  delicate  dark  lines  parallel 
to  the  edge  of  the  prism,  and  at  very  unequal  intervals. 

The  existence  of  the  dark  lines  was  first  observed  by  Wollaston  in  1802  ; 
but  PVaunhofer,  a  celel)rated  optician  of  Munich,  first  studied  and  gave  a 
detailed  description  of  them.  Fraunhofer  mapped  the  lines,  and  indicated 
the  most  marked  of  them  by  the  letters  A,  a,  li,  C,  1),  E,  b,  F,  G,  H  ;  they 
are  therefore  generally  known  as  Fraun/io/cr's  tines. 

The  dark  line  A  (see  fig.  2  of  Plate  I.)  is  at  the  middle  and  B  halfway 
between  this  and  the  end  of  the  red  ray  ;  C  at  the  boundary  of  the  red  and 
orange  ray  ;  D  is  in  the  yellow  ray  ;  E,  in  the  green  ;  F,  in  the  blue  ;  G,  in 
the  indigo  ;  H,  in  the  violet.  There  are  certain  other  noticcalile  dark  lines, 
such  as  a  in  the  red  and  /'  in  the  green.     In  the  case  of  sunlight  the  positions 


-576]  Spectroscope.  545 

of  the  dark  lines  are  fixed  and  definite  ;  on  this  account  they  are  used  for 
obtaining  an  exact  determination  of  the  refractive  index  (538)  of  each  colour  ; 
for  example,  the  refractive  index  of  the  blue  ray  is,  strictly  speaking,  that  of 
the  dark  line  F.  In  the  spectra  of  artificial  lights,  and  of  the  stars,  the 
relative  positions  of  the  dark  lines  are  changed.  In  the  electric  light  the 
dark  lines  are  replaced  by  brilliant  lines.  In  coloured  flames — that  is  to 
say,  flames  in  which  certain  chemical  substances  undergo  evaporation — the 
dark  lines  are  replaced  by  very  brilliant  lines  of  light,  which  differ  for  dif- 
ferent substances.  Lastly,  some  of  the  dark  lines  are  constant  in  position 
and  distinctness,  such  as  Fraunhofei-'s  lines  ;  but  some  of  the  lines  only 
appear  as  the  sun  nears  the  horizon,  and  others  are  strengthened.  They  are 
also  influenced  by  the  state  of  the  atmosphere.  The  fixed  lines  are  due  to 
the  sun  ;  the  variable  lines  have  been  proved  by  Jannsen  and  Secchi  to  be 
due  to  the  aqueous  \apour  in  the  air,  and  are  called  atmospheric  or  telluric 
lines. 

Fraunhofer  counted  in  the  spectrum  more  than  600  dark  lines,  more  or 
less  distinct,  distributed  irregularly  from  the  extreme  red  to  the  extreme 
violet  ray.  Brewster  counted  2,000.  By  causing  the  refracted  rays  to  pass 
successively  through  several  analysing  prisms  (576),  not  merely  has  the 
existence  of  3,000  dark  lines  been  ascertained,  but  several  which  had  been 
supposed  to  be  single  have  been  shown  to  be  compound. 

575.  Applications  of  Fraunbofer's  lines. — Subsequently  to  Fraunhofer, 
several  physicists  studied  the  dark  lines  of  the  spectrum.  In  1822  Sir  J. 
Herschel  remarked  that  by  volatilising  substances  in  a  flame  a  very  delicate 
means  is  afforded  of  detecting  certain  ingredients  by  the  colours  they  impart 
to  certain  of  the  dark  lines  of  the  spectrum  ;  and  Fox  Talbot  in  1834  sug- 
gested optical  analysis  as  probably  the  most  delicate  means  of  detecting 
minute  portions  of  a  substance.  To  Kirchhoff"  and  Bunsen,  however,  is 
really  due  the  merit  of  basing  a  method  of  analysis  on  the  observation  of  the 
lines  of  the  spectrum.  They  ascertained  that  the  salts  of  the  same  metal, 
when  introduced  into  a  flame,  always  produced  lines  identical  in  colour  and 
position,  but  that  lines  different  in  colour,  position,  or  number  were  produced 
by  different  metals  ;  and  finally,  that  an  exceedingly  small  quantity  of  a 
metal  suffices  to  disclose  its  existence.  Hence  has  arisen  a  new  and  power- 
ful method  of  analysis,  known  by  the  name  of  spectrum  analysis. 

576.  Spectroscope. — The  name  of  spectroscope  has  been  given  to  the 
apparatus  employed  by  Kirchhoff"  and  Bunsen  for  the  study  of  the  spectrum. 
One  of  the  forms  of  this  apparatus  is  represented  in  fig.  531.  It  is  composed 
of  three  telescopes  mounted  on  a  common  foot,  and  whose  axes  converge 
towards  a  prism,  P,  of  flint  glass.  The  telescope  A  is  the  only  one  which 
can  turn  round  the  prism.  It  is  fixed  in  any  required  position  by  a  clamping 
screw  71.  The  screw-head  m  is  used  io  focus  the  eyepiece.  The  screw-head 
71  serves  to  change  the  inclination  of  the  axis. 

To  explain  the  use  of  the  telescopes  B  and  C  we  must  refer  to  fig.  532, 
which  shows  the  passage  of  the  light  through  the  apparatus.  The  rays 
emitted  by  the  flame  G  fall  on  the  lens  a,  and  are  caused  to  converge  to  a 
point  b,  which  is  the  principal  focus  of  a  second  lens  c.  .  Consequently  the 
pencil,  on  leaving  the  telescope  B,  is  formed  of  parallel  rays  (552).  This  pencil 
enters  the  prism  P.     On  leaving  the  prism  the  light  is  decomposed,  and  in 

N  N 


546  On  Light.  [576- 

this  state  falls  on  the  lens  x.  By  this  lens  x  a  real  and  reversed  image  of 
the  spectrum  is  formed  at  i.  This  image  is  seen  by  the  observer  through  a 
magnifying  glass,  which  forms  at  ss'  a  virtual  image  of  the  spectrum  magni- 
fied about  eight  times. 


V'lg.  531- 

The  telescope  C  serves  to  measure  the  relative  distances  of  the  lines 
of  the  spectrum.     For  this  purpose  a  micrometer  is  placed  at  ;«,  divided 


Fig.  532- 

A  micrometer  is  formed  thus  : — A  scale  of  250  milli- 
metres is  divided  with  great  exactness  into  25  equal  parts.     A  photographic 

taken,  reduced  to   11;  millimetres.     The 


into  25  equal  parts, 
metres  is  divided  w 
negative  on  glass  of  this  scale 


-576  J 


Spectroscope. 


547 


•"■'g-  533- 


negative  is  taken  because  then  the  scale  is  light  on  a  dark  ground.  The 
scale  is  then  placed  at  m  in  the  principal  focus  of  the  lens  e  ;  conse- 
quently, when  the  scale  is  lighted  by  the  candle  F,  the  rays  emitted  from  it 
leave  the  lens  e  in  parallel  pencils  ;  a  portion  of  these,  being  reflected  from 
a  face  of  the  prism,  passes  through  a 
lens  x%  and  forms  a  perfectly  distinct 
image  of  the  micrometer  at  /,  thereby 
furnishing  the  means  of  measuring 
exactly  the  relative  distances  of  the 
different  spectral  lines. 

The  micrometric  telescope  C  (fig. 
531)  is  furnished  with  several  adjusting 
screws,  /,  0,  r  ;  of  these,  /  adjusts  the 
focus  ;  o  displaces  the  micrometer  in 
the  direction  of  the  spectrum  laterally  ; 
r  raises  or  lowers  the  micrometer, 
which  it  does  by  giving  different  incli- 
nations to  the  telescope. 

The  opening  whereby  the  light  of  the  flame  G  enters  the  telescope  B 
consists  of  a  narrow  vertical  slit,  which  can  be  opened  more  or  less  by 
causing  the  movable  piece  a  to  advance  or  recede  by  means  of  the  screw  v 
(fig.  533).  When,  for  purposes  of  comparison,  the  spectra  of  two  flames 
are  to  be  examined  simultaneously,  a  small  prism,  whose  refracting  angle 
is  60°,  is  placed  over  the  upper  part  of  the  slit.  Rays  from  one  of  the 
flames,  H,  fall  at  right  angles  on  one  face  of  the  prism  ;  they  then  experience 
total  reflection  on  a  second  face,  and  leave  the  prism  by  the  third  face,  and 
in  a  direction  at  right  angles  to  that  face.  By  this  means  they  pass  into  the 
telescope  in  a  direction  parallel  to  its  axis,  without  in  any  degree  mixing  with 
the  rays  which  proceed  from  the  second  flame,  G.  Consequently  the  two 
pencils  of  rays  traverse  the  prism  P  (fig.  532),  and  form  two  horizontal  spectra, 
which  are  viewed  simultaneously  through  the  telescope  A.  In  the  flames  G 
and  H  are  platinum  wires,  e,  e'.  These  wires  have  been  dipped  beforehand 
into  solutions  of  the  salts  of  the  metals  on  which  experiment  is  to  be  made  ; 
and  by  the  vaporisation  of  these  salts  the  metals  modify  the  transmitted 
light,  and  give  rise  to  definite  lines. 

Each  of  the  flames  G  and  H  is  a  jet  of  ordinary  gas.  The  apparatus 
through  which  the  gas  is  supplied  is  known  as  a  Buf2se?i's  burner.  The  gas 
comes  through  the  hollow  stem  k  (fig.  531).  At  the  lower  part  of  this  there 
is  a  lateral  orifice  which  admits  air  to  support  the  combustion  of  the  gas. 
This  orifice  can  be  more  or  less  closed  by  a  small  diaphragm,  which  acts  as 
a  regulator.  If  we  allow  a  moderate  amount  of  air  to  enter,  the  gas  burns 
with  a  luminous  flame,  and  the  lines  are  obscured.  But  if  a  strong  and 
steady  current  of  air  enters,  the  carbon  is  rapidly  oxidised,  the  flame  loses  its 
brightness,  and  burns  with  a  pale  blue  light,  but  with  an  intense  heat.  In 
this  state  it  no  longer  yields  a  spectrum.  If,  however,  a  metallic  salt  is  in- 
troduced either  in  a  solid  state  or  in  a  state  of  solution,  the  spectrum  of  the 
metal  makes  its  appearance,  and  in  a  fit  state  for  observation. 

There  are  three  chief  types  of  spectra  :  the  continuous  spectra,  or 
those  furnished  by  ignited  solids  and   liquids   (fig.   i,  Plate  I.)  ;  X\i&  band 

N  N  2 


S48 


On  LicrJit. 


[576- 


or  litic  spectrum,  consisting  of  a  number  of  bright  lines,  and  produced  by- 
ignited  gases  or  vapours  ;  and  absorption  spectra,  or  those  furnished  by  the 
sun  or  fixed  stars.  For  an  explanation  of  these  see  art.  579.  Bodies  at  a 
red  heat  give  only  a  short  spectrum,  extending  at  most  to  the  orange  ;  as 
the  temperature  gradually  rises,  yellow,  green,  blue,  and  violet  successively 
appear,  while  the  intensity  of  the  lower  colours  increases. 

Instead  of  the  prism  very  pure  spectra  may  also  be  obtained  by  means  of 
a  grating  (647).    For  more  detailed  investigations  of  the  spectral  lines  a  train 

oj  prisms  is  used.  Fig.  534  repre- 
sents one  with  nine  prisms.  The 
light  issuing  from  the  collimeter  A 
passes  in  succession  through  each 
of  the  prisms.  As  the  successive 
deviations  add  themselves  the  dis- 
persion is  very  much  increased,  and 
a  spectrum  of  great  extent  is  ob- 
tained. It  is,  however,  feebly  lumi- 
nous, owing  partly  to  its  extension,. 
and  partly  to  the  loss  of  light  which 
is  observed  through  the  telescope  B, 
which  it  undergoes  in  traversing  all 
these  refracting  surfaces.  In  the 
case  of  ten  prisms  the  loss  of 
light  has  been  found  to  amount  to 
ninety-nine  per  cent. 

Christie  has  used  with  advan- 
tage a  semi-prism  obtained  by  cut- 
ting an  isosceles  prism  by  a  plane 
at  right  angles  to  the  base.  These 
semi-prisms  have  the  advantage  that  they  produce  as  much  dispersion  as 
with  several  prisms  without  any  appreciable  loss  in  the  sharpness  of  the 
images  ;  and  without  that  absorption  of  light  which  in  the  case  of  a  number 
of  prisms  is  so  very  considerable. 

577.  Direct  vision  spectroscope. — Prisms    may  oe  combined  so  as  to 
get  rid  of  the  dispersion  without  entirely  destroying  the  refraction  (584)  ; 

they  may,  conversely, 
be  combined  so  that 
tlie  light  is  not  re- 
fracted, but  is  decom- 
posed and  produces  a 
J,. spectrum.       Combina- 

tions of  prisms  of  this 
kind  are  used  in  what  are  called  direct  vision  spectroscopes.  Fig.  535  repre- 
sents the  section  of  such  an  instrument  in  about  \  the  natural  size.  A  system 
of  two  flint  and  three  crown-glass  prisms  is  placed  in  a  tube  which  moves  in 
a  second  one;  at  the  end  of  this  is  an  aperture  o,  and  inside  it  a  slit  the 
width  of  which  can  by  a  special  arrangement  be  regulated  by  simply  turning 
a  ring  r.  A  small  achromatic  lens  is  introduced  at  aa,  the  focus  of  which  is 
at  the  slit,  so  that  the  rays  pass  parallel  through  the  tram  of  prisms,  and  the 
spectrum  is  viewed  at  c. 


^'ig-  534- 


-578 J  Experiments  ivith  the  Spectroscope.  549 

The  reversion  spectroscope  contains  two  equal  systems  of  direct  vision 
prisms  arranged  close  to  each  other,  but  reversed,  so  that  two  spectra  are 
obtained  with  the  colours  in  opposite  order.  By  suitable  micrometric  move- 
ment of  a  split  lens,  the  position  of  the  two  spectra  may^be  moved  apart  or 
nearer  each  other.  Hence  it  is  possible  to  bring  any  two  identical  lines  so 
.that  they  are  in  the  same  vertical  line.  If  now  the  position  of  these  lines  in 
the  spectrum  is  altered,  the  displacement  will  take  place  in  the  opposite 
direction  in  the  two  spectra,  and  will  therefore  be  twice  as  distinct. 

578.  Experiments  with  the  spectroscope. — The  coloured  plate  at  the 
■beginning  shows  certain  spectra  observed  by  means  of  the  spectroscope. 
No.  I  represents  the  continuous  spectrum. 

No.  2  shows  the  spectrum  of  sodium.  The  spectrum  contains  neither 
red,  orange,  green,  blue,  nor  violet.  It  is  marked  by  a  very  brilliant  yellow 
ray  in  exactly  the  same  position  as  Fraunhofer's  dark  line  D.  Of  all  metals 
sodium  is  that  which  possesses  the  greatest  spectral  sensibility.  In  fact,  it 
has  been  ascertained  that  one  two-hundred-millionth  of  a  grain  of  sodium 
is  enough  to  cause  the  appearance  of  the  yellow  line.  Consequently  it  is  very 
difficult  to  avoid  the  appearance  of  this  line.  A  very  little  dust  produced  in 
the  apartment  is  enough  to  produce  it — a  circumstance  which  shows  how 
abundantly  sodium  is  distributed. 

No.  3  is  the  spectrum  of  lithium.  It  is  characterised  by  a  well-marked 
line  in  the  red  called  Lia,  and  by  the  feebler  orange  line  Li/:i. 

Nos.  4  and  5  show  the  spectra  of  ccesimn  and  ritbidiwn,  metals  discovered 
by  Bunsen  and  Kirchhofif  by  means  of  spectrum  analysis.  The  former  is 
distinguished  by  two  blue  lines,  Csa  and  Cs/3  ;  the  latter  by  two  very  brilliant 
dark  red  lines,  Rby  and  RbS,  and  by  two  less  intense  violet  lines,  Rba  and 
Bb/^.  A  third  metal,  thallium,  has  been  discovered  by  the  same  method 
by  Mr.  Crookes  in  England,  and  independently  by  M.  Lamy  in  France. 
Thallium  is  characterised  by  a  single  green  line.  Subsequently  to  this 
Richter  and  Reich  discovered  a  new  metal  associated  with  zinc,  and  which 
they  call  indium  from  a  couple  of  characteristic  lines  which  it  forms  in  the 
indigo ;  and  quite  recently  Boisbaudran  has  discovered  a  new  metal  which 
he  calls  gallium  existing  in  zinc  in  very  minute  quantities. 

The  extreme  delicacy  of  the  spectrum  reactions,  and  the  ease  with  v/hich 
they  are  produced,  constitute  them  a  most  valuable  help  in  the  qualitative 
analysis  of  the  alkalies  and  alkaline  earths.  It  is  sufficient  to  place  a  small 
portion  of  the  substance  under  examination  on  platinum  wire  as  represented 
in  fig.  533,  and  compare  the  spectrum  thus  obtained  either  directly  with  that 
■of  another  substance  or  with  the  charts  in  which  the  positions  of  the  lines 
produced  by  the  various  metals  are  laid  down. 

With  other  metals  the  production  of  their  spectra  is  more  difficult,  es- 
pecially in  the  case  of  some  of  their  compounds.  The  heat  of  a  Bunsen's 
burner  is  insufficient  to  vaporise  the  metals,  and  a  more  intense  tempera- 
ture must  be  used.  This  is  effected  by  taking  electric  sparks  between 
wires  consisting  of  the  metal  whose  spectrum  is  required,  and  the  electric 
sparks  are  most  conveniently  obtained  by  means  of  Ruhmkorff's  coil. 
Thus  all  the  metals  may  be  brought  within  the  sphere  of  spectrum  obser- 
•ivation. 

The  power  of  the  apparatus  has  great  influence  on  the  nature  of  the 


550  On  Light.  [578- 

spectrum  ;  while  an  apparatus  with  one  prism  only  gives  in  a  sodium  flame 
the  well-known  yellow  line,  an  apparatus  with  more  prisms  resolves  it  into 
two  or  three  lines. 

It  has  been  observed  that  the  character  of  the  spectrum  changes  with  the 
temperature  ;  thus  chloride  of  lithium  in  the  flame  of  a  Bunsen's  burner  gives 
a  single  intense  peach-coloured  line  ;  in  a  hotter  flame,  as  that  of  hydrogen, 
it  gives  an  additional  orange  line  ;  while  in  the  oxyhydrogen  jet  or  the 
voltaic  arc  a  broad  brilliant  blue  band  comes  out  in  addition.  The  sodium 
spectrum  produced  by  a  Bunsen's  burner  consists  of  a  single  yellow  line  ; 
if,  by  the  addition  of  oxygen,  the  heat  be  gradually  increased,  more  bright 
lines  appear  ;  and  with  the  aid  of  the  oxyhydrogen  flame  the  spectrum  is 
continuous.  Sometimes  also,  in  addition  to  the  appearance  of  new  lines,  an 
increase  in  temperature  resolves  those  bands  which  exist  into  a  number  of 
fine  lines,  which  in  some  cases  are  more  and  in  some  less  refrangible  than  the 
bands  from  which  they  are  formed.  It  may  be  supposed  that  the  glowing 
vapour  formed  at  the  low  temperature  consists  of  the  oxide  of  some  difficultly 
reducible  metal,  whereas  at  the  enormously  high  temperature  of  the  spark 
these  compounds  are  decomposed,  and  the  true  bright  lines  of  the  metal  are 
formed. 

The  delicacy  of  the  reaction  increases  very  considerably  with  the  tem- 
perature. With  the  exception  of  the  alkalies,  it  is  from  40  to  400  times 
greater  at  the  temperature  of  the  electric  spark  than  at  that  of  Bunsen's 
burner. 

The  spectra  of  the  permanent  gases  are  best  obtained  by  taking  the 
electric  spark  of  a  Ruhmkorff's  coil,  or  Holtz's  machine,  through  glass 
tubes  of  a  special  construction,  provided  with  electrodes  of  platinum  and 
filled  with  the  gas  in  question  in  a  state  of  great  attenuation,  known  as 
Geissler's  tubes  ;  if  the  spark  be  passed  through  hydrogen,  the  light  emitted 
is  bright  red,  and  its  spectrum  consists  of  one  red,  two  blue  lines,  >io.  7,  the 
first  two  of  which  appear  to  coincide  with  Fraunhofer's  lines  C  and  F,  and 
the  third  with  a  line  between  F  and  G.  No.  6  represents  the  spectrum  of 
oxygen.  No.  8  is  the  spectrum  of  nitrogen.  The  light  of  this  gas  in  a 
Geissler's  tube  is  purple,  and  the  spectrum  very  complicated. 

If  the  electric  discharge  takes  place  through  a  compound  gas  or  vapour, 
the  spectra  are  those  of  the  elementary  constituents  of  the  gas.  It  seems  as 
if,  at  very  intense  temperatures,  chemical  combination  were  impossible,  and 
oxygen  and  hydrogen,  chlorine  and  the  metals,  could  coexist  in  a  separate 
form,  as  though  mechanically  mixed  with  each  other. 

The  nature  of  the  spectra  of  the  elementary  gases  is  very  materially  in- 
fluenced by  alterations  of  temperature  and  pressure.  \Vi.iH,ner  made  a  series 
of  very  accurate  observations  on  the  gases  oxygen,  hydrogen,  and  nitrogen. 
He  not  only  used  gases  in  closed  tubes,  which  by  various  electrical  means 
he  raised  to  different  temperatures  ;  but  in  one  and  the  same  series  of  ex- 
periments, in  which  a  small  inductorium  was  used,  he  employed  pressures 
varying  from  100  millimetres  to  a  fraction  of  a  millimetre  ;  while  in  another 
series  in  which  a  larger  apparatus  was  used,  he  extended  the  pressure  to 
2,000  millimetres.  At  the  lowest  pressure  of  less  than  one  millimetre,  the 
spectrum  of  hydrogcii  was  found  to  be  green,  and  consisting  of  six  splendid 
groups  of  lines,  whu  h  at  a  higher  pressure  than   i   millimetre  changed  to 


-579]  Explanation  of  the  Dark  Lines  of  the  Soiar  Spectrum.   551 

continuous  bands  ;  at  2  to  3  millimetres  the  spectrum  consisted  of  the  often- 
mentioned  three  lines,  which  did  not  disappear  under  a  higher  pressure,  but 
gradually  became  less  brilliant  as  the  continuous  spectrum  increased  in  extent 
and  lustre.  From  this  point  the  light,  and  therefore  the  spectrum,  became 
feebler.  Using  the  larger  apparatus,  the  band  spectrum  appeared  only  under 
a  higher  pressure  ;  at  the  highest  pressure  of  2,000  millimetres  it  gave  place 
to  the  continuous  spectrum,  since  the  bright  lines  continually  extended  and 
ultimately  merged  into  each  other. 

579.  Explanation  of  tbe  dark  lines  of  the  solar  spectrum. — It  has 
been  already  seen  that  incandescent  sodium  vapour  gives  a  bright  yellow 
line  corresponding  to  the  dark  line  D  of  the  solar  spectrum.  Kirchhoft' 
found  that,  when  the  brilliant  light  produced  by  incandescent  lime  passes 
through  a  flame  coloured  by  sodium  in  the  usual  manner,  a  spectrum  is  pro- 
duced in  which  is  a  dark  line  coinciding  with  the  dark  line  D  of  the  solar 
spectrum  ;  what  would  have  been  a  bright  yellow  line  becomes  a  dark  line 
when  formed  on  the  background  of  the  limelight.  By  allowing  in  a  similar 
manner  the  limelight  to  traverse  vapours  of  potassium,  barium,  strontium, 
&c.,  the  bright  lines  which  they  would  have  formed  were  found  to  be  con- 
verted into  dark  lines  :  such  spectra  are  called  absorption  spectra. 

It  appears,  then,  that  the  vapour  of  sodium  has  the  power  of  absorbing 
rays  of  the  same  refrangibility  as  that  which  it  emits.  And  the  same  is  true 
of  the  vapours  of  potassium,  barium,  strontium,  &c.  This  absorptive  power 
is  by  no  means  an  isolated  phenomenon.  These  substances  share  it,  for  ex- 
ample, with  the  vapour  of  nitrous  acid,  which  Brewster  found  to  possess  the 
following  property : — when  a  tube  filled  with  this  vapour  is  placed  in  the  path 
of  the  light  either  of  the  sun  or  of  a  gas  flame,  and  the  light  is  subsequently 
decomposed  by  a  prism,  a  spectrum  is  produced  which  is  full  of  dark  lines 
(No.  9,  Plate  I.)  ;  and  Miller  showed  that  iodine  and  bromine  vapour  pro- 
duced analogous  effects. 

Hence  the  origin  of  the  above  phenomenon  is,  doubtless,  the  absorption 
by  the  sodium  vapour  of  rays  of  the  same  kind — that  is,  having  the  same 
refrangibility — as  those  which  it  has  itself  the  power  of  emitting.  Other  rays 
it  allows  to  pass  unchanged,  but  these  it  either  totally  or  in  great  part  sup- 
presses. Thus  the  particular  lines  in  the  spectrum  to  which  these  rays 
would  converge  are  illuminated  only  by  the  feebly  luminous  sodium  flame, 
and  accordingly  appear  dark  by  contrast  with  the  other  portions  of  the 
spectrum  which  receive  light  from  the  powerful  flame  behind. 

By  replacing  one  of  the  flames  G  and  H  (fig.  533)  by  a  pencil  of  solar  light 
reflected  from  a  heliostat,  Kirchhoft"  ascertained  by  direct  comparison  that 
the  bright  lines  which  characterise  iron  correspond  to  dark  lines  m  tlie  solar 
spectrum.  He  also  found  the  same  to  be  the  case  with  sodium,  magnesium, 
calcium,  nickel,  and  some  other  metals. 

This  reversal  of  the  sodium  light  may  be  produced  even  without  a  prism 
by  an  apparatus  devised  by  Bunsen,  and  shown  in  fig.  536.  It  consists  of  a 
Woolfs  bottle  in  which  a  small  quantity  of  zinc,  dilute  sulphuric  acid,  and 
common  salt  are  placed  so  that  hydrogen  is  slowly  liberated,  charged  with 
particles  of  sodium  chloride.  Through  the  india-rubber  tube  L  ordinarj' 
coal  gas  is  admitted,  and  issues  through  the  tubes  R  and  R'.  On  each  of 
these  tubes  is  a  metal  burner.    The  gas  burns  at  the  top  A  with  a  broad  flat 


552  On  Light.  [579- 

flame,  C  ;  the  burner  B  is  cylindrical,  and  over  it  is  placed  a  conical  mantle 
closed  at  the  top  with  wire  gauze.  In  this  way  a  small  yellow  flame  is  pro- 
duced. On  looking  through  this  against  the  wide  flame,  the  former  appears 
dark,  as  if  smoky  on  a  light  background.  The  light  of  the  posterior  and  far 
brighter  flame  is  absorbed  by  the  front  and 
cooler  one,  and  replaced  by  light  of  lesser  in- 
tensity, which  thus  appears  dark  by  contrast. 

From  such  observations  we  may  draw  im- 
portant conclusions  with  respect  to  the  consti- 
tution of  the  sun.  Since  the  solar  spectrum  has 
dark  lines  where  sodium,  iron,  &c.,  give  bright 
ones  (No.  ii,  Plate  I.),  it  is  probable  that 
around  the  solid,  or  more  probably  liquid,  body 
of  the  sun  which  throws  out  the  light,  there 
exists  a  vaporous  envelope  which,  like  the 
sodium  flame  in  the  experiment  described  above, 
absorbs  certain  rays  ;  namely,  those  which  the 
envelope  itself  emits.  Hence  those  parts  of  the 
spectrum  which,  but  for  this  absorption,  would 
have  been  illuminated  by  these  particular  rays, 
appear  feebly  luminous  in  comparison  with  the 
other  parts,  since  they  are  illuminated  only  by 
the  light  emitted  by  the  envelope,  and  not  by 
the  solar  nucleus  ;  and  we  are  at  the  same  time 
led  to  conclude  that  in  this  vapour  there  exist 
the  metals  sodium,  iron,  &c. 

Huggins  and  Miller  applied  spectrum  ana- 
lysis to  the  investigation  of  the  heavenly  bodies. 
The  spectra  of  the  moon  and  planets,  whose 
light  is  reflected  from  the  sun,  give  the  same 
lines  as  those  of  the  sun.  Uranus  proves  an 
exception  to  this,  and  is  probably  still  in  a  self- 
luminous  condition.  The  spectra  of  the  fixed 
stars  contain,  however,  dark  lines  differing  from  the  solar  lines,  and  from 
one  another.  Four  distinct  types  of  spectra  were  distinguished  by  Secchi. 
The  first  embraces  the  white  stars,  and  includes  the  well-known  Sirius  and 
a  Lyra.'.  Their  spectra  (No.  12,  Plate  I.)  usually  contain  a  number  of  very 
fine  lines,  and  always  contain  four  broad  dark  lines  which  coincide  with 
the  bright  lines  of  hydrogen.  Out  of  346  stars  164  were  found  to  belong  to 
this  group.  The  second  group  embraces  those  having  spectra  intersected 
by  numerous  fine  lines  like  those  of  our  sun.  About  140  stars,  among  them 
Pollux,  Capclla,  (\)  Aquil.i?,  belong  to  this  group.  The  third  group  embraces 
the  red  and  orange  stars,  such  as  a  Orionis,  ii  Pegasi  ;  the  spectra  of  these 
(Nos.  13,  14,  Plate  I.)  are  divided  into  eight  or  ten  parallel  columnar  clusters 
of  dark  and  bright  bands  increasing  in  intensity  to  the  red.  (".roup  four  is 
made  up  of  small  red  stars  with  spectra,  and  is  constructed  of  three  bright 
zones  increasing  in  intensity  towards  the  violet.  It  would  thus  appear  that 
these  fixed  stars,  while  differing  from  one  another  in  the  matter  of  which 
they  are  composed,  are  constructed  on  the  same  general  plan  as  our  sun. 


-579J  Explanaiion  of  the  Dark  Lines  of  the  Solar  Spectrum.    553 

Huggins  has  observed  a  striking  difference  in  the  spectra  of  the  nebulas  ; 
where  they  can  at  all  be  observed  they  are  found  to  consist  generally  of 
bright  lines,  like  the  spectra  of  the  ignited  gases,  instead  of,  like  the  spectra 
of  the  sun  and  stars,  consisting  of  a  bright  ground  intersected  by  dark  lines. 
It  is  hence  probable  that  the  nebuk^  are 'masses  of  glowing  gas,  and  do  not 
consist,  like  the  sun  and  stars,  of  a  photosphere  surrounded  by  a  gaseous 
atmosphere. 

We  can  apply  the  reasoning  of  Doppler's  principle  (233)  to  the  case  of 
light,  and  assume  provisionally  that  the  motion  of  light  is  analogous  to  that 
of  sound.  When  a  source  of  light  is  approaching  the  earth,  the  eye  receives 
a  greater  number  of  waves  in  a  given  time,  the  waves  are  shorter  ;  as  it 
moves  away  the  opposite  is  the  case,  the  waves  are  longer.  Hence,  on  the 
approach  of  yellow  light,  for  instance,  the  bright  band  D  will  seem  displaced 
towards  the  violet  end  of  the  spectrum,  and  in  receding,  towards  the  red 
end.  This  will  also  be  the  case  with  the  corresponding  dark  line,  proving 
that  the  whole  medium  is  moved  at  the  same  time.  Accordingly,  by  observ- 
ing the  displacement  of  particular  lines,  conclusions  may  be  drawn  as  to  the 
relative  motions  of  what  are  called  the  fixed  stars.  Thus,  from  careful  ob- 
servation of  the  displacement  of  the  F  line  in  Sirius,  Huggins  has  inferred 
that  it  is  moving  away  from  the  earth  with  a  velocity  of  42  miles  per  second. 

One  of  the  most  interesting  triumphs  of  spectrum  analysis  has  been  the 
discovery  of  the  true  nature  of  the  proticberances,  which  appear  during  a 
solar  eclipse  as  mountains  or  cloud-shaped  luminous  objects  varying  in  size, 
and  surrounding  the  moon's  disc. 

During  the  eclipse  of  1868  it  had  been  ascertained  by  Jannsen  that  pro- 
tuberances emitted  certain  bright  lines  coinciding  with  those  of  hydrogen. 
They  have,  however,  been  fully  understood  only  since  Lockyer  and  Jannsen 
have  discovered  a  method  of  investigating  them  at  any  time.  The  principle 
of  this  method  is  as  follows  :— When  a  line  of  light  admitted  through  a  slit 
is  decomposed  by  a  prism,  the  length  of  the  spectrum  may  be  increased  by 
passing  it  through  two  or  more  prisms  ;  as  the  quantity  of  light  is  the  same, 
it  is  clear  that  the  intensity  of  the  spectrum  will  be  diminished.  This  is  the 
case  with  the  ordinary  sources  of  light,  such  as  the  sun  ;  if  the  light  be 
homogeneous,  it  will  be  merely  deviated,  and  not  reduced  in  intensity,  by 
dispersion.  And  if  the  source  of  light  emit  light  of  both  kinds,  the  image 
of  the  slit  of  light  of  a  definite  refrangibility,  which  the  mixture  maycontam, 
will  stand  out,  by  its  superior  intensity,  on  the  weaker  ground  of  the  con- 
tinuous spectrum.  This  is  the  case  with  the  spectrum  of  the  protuberances. 
Viewed  through  an  ordinary  spectroscope,  the  light  they  emit  is  overshadowed 
by  that  of  the  sun  ;  but  by  using  prisms  of  great  dispersive  power  the  sun's 
light  becomes  weakened,  and  the  spectrum  of  the  protuberances  may  be 
observed.  Lockyer's  researches  leave  no  doubt  that  they  are  ignited  gas 
masses,  principally  of  hydrogen.  By  altering  the  position  of  the  slit  a  series 
of  sections  of  the  prominences  is  obtained,  by  collating  which  the  form  of 
the  prominence  may  be  inferred.  They  are  thus  found  to  enclose  the  sun 
usually  to  a  depth  of  about  5,000  miles,  but  sometimes  in  enormous  local 
accumulations,  which  reach  the  height  of  70,000  miles.  Lockyer  has  not 
merely  examined  these  phenomena  right  on  the  edge  of  the  sun,  but  he  has 
been  able  to  observe  them  on  the  disc  itself.     He  has  shown  that  some  of 


554  On  Light.  [579- 

these  protuberances  are  the  results  of  sudden  outbursts  or  storms,  which 
move  with  the  enormous  velocity  of  120  miles  in  a  second  ;  and,  by  reasoning 
as  above,  the  direction  of  this  motion  has  been  determined. 

For  a  fuller  account  of  this  branch  of  physics,  which  is  incompatible  with 
the  limits  of  this  work,  the  reader  is  referred  to  Sir  H.  Roscoe's  '  Lectures  on 
Spectrum  Analysis,'  and  to  the  same  writers  articles,  and  those  of  Schuster, 
in  Watts's  '  Dictionary  of  Chemistry,'  or  to  Schellen's  '  Spectrum  Analysis,' 
translated  by  Lassell,  or  to  Lockyer  '  On  the  Spectroscope.' 

580.  Vses  of  the  spectroscope. — When  a  liquid  placed  in  a  glass  tube 
or  m  a  suitable  glass  cell  is  interposed  between  a  source  of  light  and  the 
slit  of  the  spectroscope,  the  spectrum  observed  on  looking  through  the 
telescope  will  in  many  cases  be  found  to  be  traversed  by  dark  bands. 
No.  10,  Plate  I.,  represents  the  appearance  of  the  spectrum  when  a  solution 
oi  chlorophyl,  the  green  colouring  matter  of  plants,  is  thus  interposed.  In 
the  red,  the  yellow,  and  the  violet  parts,  dark  bands  are  formed,  and  the 
blue  gives  way  to  a  reddish  shimmer.  If,  instead  of  chlorophyl,  arterial 
blood  greatly  diluted  be  used,  the  red  of  the  spectrum  appears  brighter,  but 
green  and  violet  are  nearly  extinguished.  As  these  bands  thus  differ  in 
different  liquids  as  regards  position,  breadth,  and  intensity,  in  many  cases 
they  afford  the  most  suitable  means  of  identifying  bodies.  Sorby  and 
Browning  have  devised  a  combination  of  the  microscope  and  spectroscope 
called  the  microspectroscope^  which  renders  it  possible  to  examine  even  very 
minute  traces  of  substances. 

This  application  of  the  spectroscope  has  been  very  useful  in  investigating 
substances  which  have  special  importance  in  physiology  and  pathology  ; 
thus  in  examining  normal  and  diseased  blood,  and  in  ascertaining  the  rate 
at  which  certain  substances  pass  into  the  various  fluids  of  the  system.  The 
characteristic  absorption  bands  with  certain  liquids,  such  as  wine,  beer,  &c., 
present  in  their  normal  state,  compared  with  those  yielded  by  adulterated 
substances,  furnish  a  delicate  and  certain  means  of  detecting  the  latter. 

Thus  the  adulteration  of  claret  with  the  juice  of  elderberries  is  detected 
by  the  appearance  of  faint  bands  near  line  D ,  which  are  not  seen  with  pure 
red  wine.  The  colouring  matter  of  malt  and  'hops  is  quite  distinct  from 
that  of  many  other  substances  with  which  it  is 
alleged  to  be  adulterated.  An  alkaline  solution 
of  blood  to  which  ammonium  sulphide  is  added> 
_  gives  two  very  powerful  absorption  bands  between 

.  ra  f  ,7j  D  and  E,  and  between  K  and  b  ;    this  is  the  most 

I^W  "I  \aluable  test  for  toxicological  cases.    Blood  charged 

with  carbonic  oxide  is  unchanged  on  the  addition 
Kig.  537.  of  ammonium  sulphide,   and   thus   the  poisoning 

by  carbonic  oxide  can  be  detected.  So,  too,  the 
appearance  of  the  characteristic  bands  of  gall  in  blood,  and  of  albumen  in 
urine,  arc  indications  of  jaundice  and  of  Bright's  disease  respectively. 

Suppose  the  slit  of  the  spectroscope  be  divided  into  two  halves,  s,  and  s,_. 
(fig.  537),  the  aperture  of  each  of  which  can  be  varied  to  any  measured  extent 
by  means  of  micromclric  screws.  If  then  a  layer  of  a  substance  of  known 
thickness  be  placed  in  front  of  the  slit  .s,,  for  instance,  and  the  spectrum  of 
a  particular  portion  be  observed,    there   will  be  a  difference  between  the 


-582J  Fluorescence.  555 

luminosity  of  the  two  parts  of  the  spectrum  ;  but  by  regulating  the  width 
of  the  slit  they  may  be  made  the  same;  The  luminosities  will  then  be  in- 
versely as  the  width  of  the  slit.  Thus,  if  the  widths  of  each  were  originally  i, 
and  the  uncovered  slit  had  to  be  narrowed  to  0-4,  the  intensity  of  the  light 
transmitted  through  the  screen  would  only  be  0-4  of  the  incident.  Vierordt 
has  based  on  this  a  method  of  quantitative  spectrum  analysis  ;  thus  if  the 
absorption  produced  by  a  definite  thickness  of  known  strength  be  known, 
the  relative  concentration  of  any  other  solution  of  the  same  substance  for 
the  same  thickness  may  be  determined. 

581.  Abnormal  dispersion. — A  remarkable  exception  to  the  ordinarj^ 
law  of  dispersion  was  discovered  by  Christiansen,  and  subsequently  confirmed 
and  extended  by  Soret  and  Kundt — that  the  solutions  of  certain  substances, 
such  as  indigo  and  permanganate  of  potassium,  give  spectra  in  which  the 
07-der  of  the  colours  is  not  the  same  as  in  the  prismatic  spectrum.  Thus,  when 
a  hollow  glass  prism  is  filled  with  an  alcoholic  solution  of  fuchsine,  the  order 
of  the  colours  in  the  spectrum  which  it  yields  is  as  follows.  Violet  is  least 
refracted,  then  red,  and  then  yellow,  which  is  most  refracted.  If  we  imagine 
that  the  central  green  of  an  ordinary  spectrum  is  removed,  and  then  the 
position  of  the  rest  is  interchanged,  we  get  an  idea  of  the  abnormal  spectrum 
of  fuchsine.  Kundt  examined  a  great  number  of  substances  in  this  direc- 
tion, mostly  the  colours  derived  from  aniline,  and  found  that  the  abnormal 
dispersion  is  exhibited  by  all  substances  with  surface  colour.  These  bodies 
have  the  peculiarity  that  when  viewed  in  diffused  light  they  exhibit  a  different 
colour  from  that  which  they  transmit.  Thus  a  thin  flake  of  fuchsine  appears 
green  in  diffused,  but  red  in  transmitted  light. 

The  substances  in  solution  are  examined  by  placing  them  in  hollow  glass 
prisms  ;  if  the  solutions  are  weak,  the  abnormal  dispersion  of  the  substance 
is  concealed  by  that  of  the  solvent,  while  stronger  solutions  absorb  so  much 
light  as  to  be  almost  opaque,  and  prisms  of  veiy  small  refracting  angle  have 
to  be  used.  Soret  gets  rid  of  this  difficulty  by  immersing  the  prism  contain- 
ing the  solution  in  glass  vessels  with  parallel  sides  filled  with  the  solvent. 
The  dispersion  due  to  the  solvent  is  thereby  eliminated,  and  only  that  of  the 
substance  comes  into  play.  Cyanine  gives  a  well-marked  abnormal  spec- 
trum, the  order  of  the  colours  being  the  following  :  green,  light  blue,  dark 
blue,  a  dark  space,  red,  and  traces  of  orange,  the  green  being  the  colour 
which  is  least  diffused. 

The  same  explanation  cannot  be  given  of  this  as  of  the  ordinaiy  colour 
of  bodies  (569),  but  must  be  ascribed  to  the  fact  that  the  bodies  in  question 
totally  reflect  light  of  certain  wave-lengths  (637)  at  almost  all  incidences, 
and  that  these  colours  are  reflected  on  the  surface.  Hence  it  follows  that 
the  colour  of  these  bodies  in  diffused  light  must  be  almost  complementary 
to  the  transmitted  light— a  prevision  which  experiment  confirms. 

582.  Fluorescence. — Stokes  made  the  remarkable  discoveiy  that  under 
certain  circumstances  the  rays  of  light  are  capable  of  undergoing  a  change 
of  refrangibility.  The  discovery  originated  in  the  study  of  a  phenomenon 
observed  by  Brewster,  and  by  Herschel,  that  some  varieties  of  fluorspar, 
and  also  the  solutions  of  certain  substances,  when  looked  at  by  trans- 
mitted light  appear  colourless,  but  when  viewed  in  reflected  light  present  a 
bluish  appearance.      Stokes  has  found  that   this  property,  which  he  calls 


556 


On  Light. 
been  obscned  in  fluorspar, 


[582- 

is  characteristic  of  a 


fluorescence  from  havinj 

large  number  of  bodies. 

If  by  means  of  a  lens  of  long  focus,  preferably  of  quartz,  a  line  of  the 

sun's  rays  be  focussed  on  a  solution  of  sulphate  of  quinine  contained  in  a 

glass  trough,  a  beautiful  cerulean  blue  cone  of  light  (fig.  538)  is  formed,  which 

is  much  the  brightest  on  the  surface  and  the  intensity  of  which  rapidly 

diminishes  as  it  penetrates  in  the  licjuid. 

It  thus  appears  that  fluorescence  is  due  to  an  absorption  of  certain  rays; 

rays  of  light  which  have  passed  through  a  sufficient  thickness  of  a  fluorescent 
substance  lose  thereby  the  power  of  exciting 
fluorescence  when  they  are  passed  through  a 
second  layer  of  the  same  substance  ;  thus  a  test 
tube  containing  a  fluorescent  liquid  is  brightly 
luminous  when  exposed  to  the  sun's  rays,  but 
loses  this  lustre  at  once  when  it  is  dipped  in  a 
trough  of  the  same  liquid,  on  the  front  of  which 
the  sun's  rays  fall.  This  also  results  from  a 
c(nnparison  of  the  absorption  spectrum  of  a 
flut>rescent  substance  with  the  appearance  pre- 
sented by  this  substance  when  the  spectrum 
falls  on  it.  When  the  fluorescence  begins  there 
also  begins  the  absorption,  and  to  a  maximum 
of  absorption  corresponds  a  maximum  of  fluor- 
escence. 

The  phenomenon  is  seen  when  a  solution  of 
ined  in  a  trough  with  parallel  sides,  is  placed  in 
solar  spectrum.     No  change  is  observed    in  the 


sulphate  of  (.[uinine,  conta 
ditibrcnt  positions  in  the 
upper  part  of  the  spectrum,  but  from  about  the  middle  of  the  lines  G  and  H 
(coloured  Plate)  to  some  distance  beyond  the  extreme  range  of  the  violet, 
rays  of  a  beautiful  sky-blue  colour  are  seen  to  proceed.  These  invisible 
ultra-violet  rays  also  become  visible  when  the  spectrum  is  allowed  to  fall  on 
paper  impregnated  with  a  solution  of  icsculinc  (a  substance  extracted  from 
horse-chestnut),  an  alcoholic  solution  of  stramonium,  or  a  plate  of  canary 
glass  (which  is  coloured  by  means  of  uranium).  If  light  be  allowed  to  fall 
on  paper  impregnated  with  platmanganideof  barium,  a  beautiful  green  fluor- 
escence is  observed. 

If  a  few  drops  of  a  strong  solution  of  fluorcsceine  in  soila  tall  into  a  large 
beaker  of  water  on  the  front  of  which  the  sun's  rays  fall,  beautiful  fluorescent 
clouds  are  first  produced,  and  on  shaking  the  "liquid  the  whole  vessel 
fluoresces  with  a  bright  green  light. 

This  change  arises  from  a  diminution  in  the  refrangibility  of  those  rays 
outside  the  violet,  which  are  ordinarily  too  refrangible  to  aftect  the  eye. 

Cilass  appears  to  absorb  many  of  these  more  refrangible  rays,  which  is 
not  the  case  nearly  to  the  same  extent  with  tjuartz.  When  a  prism  and 
trough  formed  of  plates  of  quartz  are  used,  and  the  spectrum  is  received 
on  a  sheet  of  paper  on  which  a  wash  of  solution  of  sulphate  of  cpiinine  has 
been  made,  two  juxtaposed  spectra  can  be  obtained.  That  which  is  on 
ihe  part  coated  with  sulphate  of  quinine  extends  beyond  the  line  H 
to  an  extent  eipial  to  that  of  the  visible  spectrum.     In  the  spectrum,  thus 


-683]  Chromatic  Aberration.  557 

made  visiI)lo,  dark  lines  may  be  seen  analogous  to  those  in  the  ordinary 
spectrum. 

The  phenomena  may  be  (observed  without  the  use  of  a  prism.  When  an 
aperture  in  a  dark  room  is  closed  l)y  means  of  a  piece  of  bhie  glass,  and  the 
light  is  allowed  to  fall  upon  a  piece  of  canary  glass,  it  instantly  aj)pcars  self- 
luminous  from  the  emission  of  the  altered  rays.  If  a  test  tube  be  half  filled 
with  a  solution  of  sulphate  of  quinine,  and  on  it  be  poured  a  freshly  prepared 
solution  of  chlorophyl  in  ether,  the  respective  layers  appear  colourless  and 
green  in  transmitted,  and  sky-blue  and  blood-red  in  reflected  light. 

In  most  cases  it  is  the  violet  and  ultra-violet  rays  which  undergo  an 
alteration  of  refrangibility,  but  the  phenomenon  is  not  confined  to  them.  A 
decoction  of  madder  in  alum  gives  yellow  and  violet  light  from  about  the 
line  I)  to  beyond  the  violet  ;  an  alcoholic  solution  of  chlorophyl  gives  red 
light  from  the  line  B  to  the  limit  of  the  spectrum.  In  these  cases  the 
yellow,  the  green,  and  the  blue  rays  experience  diminution  of  refrangibility  ; 
the  change  produces  more  highly  refrangible  rays.  An  exception  to  this  rule 
is  met  with  in  the  case  of  Magdala  red.  If  on  a  solution  of  this  substance 
contained  in  a  rectangular  glass  vessel  a  solar  spectrum  be  allowed  to  fall,, 
an  orange-yellow  fluorescence  is  found  even  in  the  red  part  of  the  spectrum. 

The  electric  light  gives  a  very  remarkable  spectrum.  With  quartz 
apparatus  Stokes  obtained  a  spectrum  six  or  eight  times  as  long  as  the 
ordinary  one.  Several  flames  of  no  great  illuminating  power  emit  very 
peculiar  light.  Characters  traced  on  paper  with  solution  of  stramonium,, 
which  are  almost  invisible  in  daylight,  appear  instantaneously  when  illu- 
minated by  the  flame  of  burning  sulphur  or  of  bisulphide  of  carbon. 
Robinson  has  found  that  the  light  of  the  aurora  is  peculiarly  rich  in  rays  of 
high  refrangibility. 

583.  Cbromatic  aberration.  —The  various  lenses  hitherto  described 
(551)  possess  the  inconvenience  that,  when  at  a  certain  distance  from  the 
eye,  they  give  images  with 
coloured  edges.  This  defect, 
which  is  most  observable  in 
condensing  lenses,  is  due  to 
the  unequal  refrangibilty  of  the 
simple  colours  (564),  and  is 
called  chromatic  aberration. 

Vox,  since  a  lens  may  be 
compared  to  a  series  of  prisms 
with  infinitely  small  faces,  and 

united  at  their  bases  (551),  it  not  only  refracts  light,  but  also  decomposes  it 
like  a  prism.  On  account  of  this  dispersion,  therefore,  lenses  have  really  a 
distinct  focus  for  each  colour.  In  condensing  lenses,  for  example,  the  red 
rays,  which  are  the  least  refrangible,  form  their  focus  at  a  point  R  on  the 
axis  of  the  lens  (fig.  539)  ;  while  the  violet  rays,  which  are  most  refrangible, 
coincide  in  the  nearer  point  V.  The  foci  of  the  orange,  yellow,  green,  blue, 
and  indigo  are  between  these  points.  The  chromatic  aberration  is  more 
perceptible  in  proportion  as  the  lenses  are  more  convex,  and  as  the  point 
at  which  the  rays  are  incident  is  farther  from  the  axis  ;  for  then  the  devia- 
tion, and  therefore  the  dispersion,  are  increased. 


558 


On  Light. 


[583- 


Fig.  540. 


If  a  pencil  of  rays  which  has  passed  through  a  condensing  lens  be 
received  on  a  screen  placed  at  mm  within  the  focal  distance,  a  bright  spot  is 
seen  with  a  red  border  ;  if  it  is  placed  at  i-j,  the  bright  spot  has  a  violet 
border. 

The  inequality  in  the  refraction  of  the  blue  and  red  rays  may  be  demon- 
strated by  closing  a  small  aperture,  half  with  red  and  half  with  blue  glass 
(fig.  540)  ;  on  each  half  a  black  arrow  is  painted,  and 
a  lamp  is  placed  behind  it.  By  means  of  a  lens  of 
60  cm.  focus  an  image  is  formed  on  a  screen  at  a  dis- 
tance of  about  2  metres.  If  the  screen  be  placed  so 
that  a  sharp  image  is  obtained  of  the  black  object  on  the 
blue  ground,  the  outlines  of  the  other  are  confused.  To 
get  a  sharp  image  of  the  arrow  on  the  red  ground  the 
screen  must  be  moved  farther  away. 

584.  Acbromatism By    combining    prisms    which 

have  different  refracting  angles  (544),  and  are  formed  of  substances  of  un- 
equal dispersive  powers  (564),  white  light  may  be  refracted  without  being 
dispersed.  The  same  result  is  obtained  by  combining  lenses  of  different 
substances,  the  curvatures  of  which  are  suitably  combined.  The  images  of 
objects  viewed  through  such  lenses  do  not  appear  coloured,  and  they  are 
accordingly  called  achromatic  lenses  ;  achromatisi?i  being  the  term  applied 
to  the  phenomenon  of  the  refractipn  of  light  without  decomposition. 

By  observing  the  phenomenon  of  the  dispersion  of  colours  in  prisms  ot 
water,  of  oil  of  turpentine,  and  of  crown  glass,  Newton  was  led  to  suppose 
that  dispersion  was  proportional  to  refraction.  He  concluded  that  there 
could  be  no  refraction  without  dispersion,  and,  therefore,  that  achromatism 
was  impossible.  Almost  half  a  century  elapsed  before  this  was  found  to  be 
incorrect.  Hall,  an  English  philosopher,  in  1733,  was  the  first  to  construct 
achromatic  lenses,  but  he  did  not  publish  his  discovery.  It  is  to  Dollond, 
an  optician  in  London,  that  we  owe  the  greatest  improvement  which  has 
been  made  in  optical  instruments.  He  showed  in  1757  that  by  combining 
two  lenses — one  a  double  convex  crown  glass  lens,  the  other  a  concavo- 
convex  lens  of  flint  glass  (fig.  542) — a  lens  is 
obtained  which  is  virtually  achromatic. 

To  explain  this  result,  let  two  prisms,  BFC 
and  CDF,  be  joined  and  turned  in  a  contrary 
direction,  as  shown  in  fig.  541.  Let  us  suppose  in 
the  first  case,  that  both  prisms  are  of  the  same 
material,  but  that  the  refracting  angle  of  the 
second,  CDF",  is  less  than  the  refracting  angle 
of  the  first ;  the  two  prisms  will  produce  the 
'  "''  '''''  same  effect  as  a  single  prism,  BAF  ;  that  is  to 

say,  that  white  light  which  traverses  it  will  not  only  be  refracted,  but  also 
decomposed.  If,  on  the  contrary',  the  first  prism  BCF  were  of  crown  glass, 
and  the  other  CKD  of  flint  glass,  the  dispersion  might  be  destroyed  without 
destroying  the  refraction.  For,  as  flint  glass  is  more  dispersive  than  crown, 
and  as  the  dispersion  produced  by  a  prism  diminishes  with  its  refracting 
angle  (564),  it  follows  that  by  suitably  lessening  the  refracting  angle  of  the 
Hint  glass  prism  CFD,  as  compared  with  the  refracting  angle  of  the  crown 


-584] 


Achromatisui. 


559 


glass  prism  BCP',  the  dispersive  power  of  these  prisms  may  be  equahscd  ; 
and  as,  from  their  position,  the  dispersion  takes  place  in  a  contrary  direc- 
tion, it  is  neutralised  ;  that  is,  the  emergent  rays  EO  are  parallel,  and 
therefore  give  white  light.  Nevertheless,  the  ratio  of  the  angles  BCF  and 
CFD,  which  is  suitable  for  the  parallelism  of  the  red  rays  and  violet 
rays,  is  not  so  for  the  intermediate  rays,  and,  consequently,  only  two  of 
the  rays  of  the  spectrum  can  be  exactly  combined,  and  the  achromatism  is 
not  quite  perfect.  To  obtain  perfect  achromatism,  several  prisms  would  be 
necessary,  of  unequally  dispersive  materials,  and  the  angles  of  which  were 
suitably  combined. 

The  refraction  is  not  destroyed  at  the  same  time  as  the  dispersion ;  that 
could  only  happen  if  the  refracting  power  of  a  body  varied  in  the  same  ratio 
as  its  dispersive  power,  which  is  not  the  case.     Consequently, 
the  emergent  ray  EO  is  not  exactly  parallel  to  the  incident  ray, 
and  there  is  a  refraction  without  appreciable  decomposition. 

Achromatic  lenses  are  made  of  two  lenses  of  unequal  dis- 
persive materials  :  one,  A,  of  flint  glass,  is  a  diverging  concavo- 
convex  (fig.  542) ;  the  other,  B,  of  crown  glass,  is  double  convex, 
and  one  of  its  faces  may  exactly  coincide  with  the  concave  face 
of  the  first.  As  with  prisms,  several  lenses  would  be  necessary 
to  obtain  perfect  achromatism  ;  but  for  optical  instruments  two 
are  sufficient,  their  curvatures  being  such  as  to  combine  not  the 
extreme  red  and  violet,  but  the  blue  and  orange  rays,  while  at  the  same  time 
regard  is  had  to  the  correction  for  spherical  aberration. 


V\%.  542- 


S6o 


On    Li  I' hi. 


.OSft 


CKAI'IKK    V. 
Ol'l  ((A  I,    INSIKl/MKNT-.. 


^K^.  TtiM  dittorent.  klndM  ol  optical  IniitruinuntR.  liy  the  U\\\\\  f>/>/i( nf 
itislriiiiinit  y.  inr-anl  ;iriy  <  omNin.ilidti  of  lfii',c-%,  or  of  lenses  and  niirrorn. 
(^plie.il  in;tiiiiiH-nt'.  may  he  divided  inl')  llirro  f  lasses,  arcordinji;  to  the 
ends  lliey  arc;  inlended  to  answer,  viz.  :  i.  Microscopes,  whir  h  arc  de-signcd 
to  obtain  a  inajniifKul  iina^'e  of  any  ohjcrl  whf)He  real  diniensionH  arc  too 
small  to  admit  of  its  bein^  seen  distinf  lly  by  the  naked  eye,  ii.  TclescopeSy 
by  whidi  very  distant  objects,  whether  (celestial  or  terrestrial,  may  be 
oljserved.  iii.  [nstrtniicnts  desi^nied  to  projec  I  on  a  sf  reen  a  maj^iified  or 
diminished  ima)MM)f  any  objctr  I  which  can  tlnrrc-by  b(!  eillic-r  clcpic  tc-d  oi 
rendered  visible  to  a  crowd  c»f  spcv  lalor',  ;  mic  h  as  the  (ttiiu'ni  Itiiida, 
the  catnmi  oliscurd,  piiotof^ropliii  nfi/inni/m,  the  iiuiyji  lantern,  the  solar 
microsco/ie,  ihc.  plioloelerlrii  vticrosrope^i^i.  i'lic-  two  former  (lasses  yield 
virtual  ima^jcts  ;  the  la', I,  widi  the  cxc  ciilion  of  Ihc  niinrni  Imiiln,  yield  real 
imajjes. 

MIC  I'O.c  C)M    .. 

5X/).   Th«  Hlinplo   tnloroNoopn.       The-    \iiiifilr   iiiii  ros,  <<fic,  or  in<ij^tn'/yini; 
^liis.s,  is  merely  a  (c>nvex  lens  cif  short  focal  len>;tli,  by  means  of  which  we 
betweiMi   the  lens  and   its   princ  ijjal   foe  ns.      I.el  Ali 
I     lo   I)c     oil  , CI  veil,    |.l;i.  cd    be!  ween    the    lens   and    its 
|»iiMc  i|)al    focus,    I''. 
i»iaw    the   sccond- 
.11  y   axes   AO   and 


look   at  objects   place 


I'.o, 

A  .11 


rcfcrenc  e  toihc-  .ci  c 
axes  in  A'  and  I'/  re 
I',  respr-c  lively.  The 
virlnal  ima^;e  of  the 


..la. y  axe-,, 
•  pc-c  lively. 
Icic,  the.e-f( 
ob)e-.  I    A  I'.. 


mcllhciel. 
■|hc-,c-    p.. 


Il',     ,iic-    III 

■•.al  A'lr 


and  also  from 

d  I',  raysparal 

I.  I    lu    ll.c-    axis    of 

llie-  lens  I'O.     Now 

ilie-.e-  lays, on  puHH- 

ii.;;      out     of      the 

lens,   lend    to  pass 

Ihroiif^di  the  second 

pi  inc  ipal  fociiN  V  ; 

I  c(iise(|iiently    they 

.lie   diverKent    with 

iidiic  ed,  will  e  lit  those 

viiliial  foe  i  of  A   and 

II  crec  I  and  ma)',iiili(-cl 


AH7J  (  onih'fions  of  nistini tth'ss  of  the    Inuiiys  Sf.i 

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olt|r<  I  Imm  llir  lot  u-t.  riiii's  il  AH  is  inovrd  lo  .//',  nciiici  llir  Itir.,  ilic 
SOtoiul;ny  aM">  will  (oul;iiii  a  j^UMln  iiiij^'.li',  iiiitl  llu"  iiiiii^c  will  lie  liiiiiicti  at 
<r/'',  anil  will  l»r  mm  li  Mn.illci,  ami  m<aicr  \\w  f-yr.  On  llii'  tillici  hand,  il 
llic'dlijril  i'l  mnvnl  lailln  I  (i..in  (lie  Irn-t,  llir  an^lr  lirlwrrn  llir  M'lnmlaiy 
a\i''i  i'.  ilimini'iliril,  aiiil  llun  inter. (<i  lion  willi  llie  |nolon}',alion  of  llir  ir 
lia.  In!  I. IV.  (.iKni):  |>la.  v  l.rson.l  ,\  H,  lln-  ini.i|;e  f.  loiiiir.l  l.nilin  Imiii  llir 
Icii'..  .iml  ih  l.iiK'i 

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I, nil    in,  KMM-  vMih  III,    .1.  :;i..    ,,|  iii,i|MiilM  ..lioii       W.-  Ii.nc  .,li,.,,l\    •..  .  n   ili.ii 
III,-  loiinn   ,.in    l..-    ..u,.,  i.,| 
I.V    liMiiK    .i.liiniiMli,     i.n,,-,      ^gpp^     '      -V 

^:''''""i"l"' ';;""' Ir"''""  ^^1^" .^      ^^s^  .^ 

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•u^-r  olMi.  Il  ...V.  onlv.r.  .11.-  Hm  .IfeJi'C 

nr.iily    paiallrl    I.,    llir    .im..  "" 

iIk-    splini.  al    al.ni.ilion   .,|  '"^'  '"'' 

llic'.r  ray.  Itniij;  nciiU'  iii.ippic,  i.ililc,  .'.plici  h  al  alirnalion  nia\  lir  •lill 
liiillirr  <  onn  led  liy  iisinj.;  two  pl.ino  ,  on\«  '.  li  iim ••,,  nr. I r, id  ol  onr  \  «i  \  ,  mi 
v.iUCMil  Irir,.  Wlini  llii'.  i'.  dour,  tli.'  pl.iiir  I.n.'  ol  .Mill  i-ir.  r.  linn.,! 
I.Mvai.l.  III.'  nl,|.-,  I  (liK.  MP.  .\lllioii,;li  ,-.1,  h  I.  ir,  r,  I,-,',  ,,.in.'s  lli.m  ill.- 
•.inipl.-  l.ir.  win.  li  l..y;.l  li.'l  lli.\  i.'pl.i.r,  \,l  lli,ii  |,uiil  iii.i);  iiil\  iii);  pou.'i  n. 
.r.  ^Mcal.  .111.1  Willi  a  I.-.',  .inioiinl  ..I  '.pli.'ii.  .d  al.i'i  lalioii,  mik  .■  iIm'  lir.l  l.ir, 
divril'.  lowaid'i  llic  a\r.  ill.'  i.iy.  win,  li 
l.dl  on  111."..'.  ..ml  l.'ir..  •I'lii'i .  ..iiilmi.ilion 
..I  l.iiM".  r.  Km.wn  a-.  Wof/./sfon's di'uNrf. 
rii.'n-  .11.-  inanv  {.iinn.  .>f  llir  '.iiiipl.' 
nil,  1..'..  .ip.'  (  Ml.'  ,.l  111.'  Im'.i  v.  Ili.il  I.' 
pi.-,.'nl.',l    III    II):     M',.       •  'II    a    li,.ii/oiil.d 


nppoK      I',     uln.li 


in 


,1       ..II. I 


I'.    .1    M.ii  K    ,yi/>ii;r   ///,    in    lli.'    >  .iiIk' 

vvlii,  h  I',  lilird  a  !\miill  <  (in\  .'s  Ln.,     I',.!..vv 

tin.  I,  111.'  i7,/,/.v/'.  wlii.  Il  r,   lis.',!,  ami   ..ii 

will,  Il  111.    ..l.j.',  I  r,  pi. I,.', I    Iwiw.'cn   Hiif.'. 

pl.il.    .        In    ..i.i.'i    h.  illnniin.il.'  llic  olijc  | 

p..w.'iliillv..lillM'..  d  li):lil   r.  i.'ll.',  I.'. I  In. Ill 

.1    .on.  ,n.'    ;:l.r.-.    iiiiii.h.    M,    ■,,.    lli.il     ih.- 

i,'ll.'<  I.'. I    I. IV'.    I.dl    upon    111.'    ,,l.|.,  I         In 

n'.nin    llir.    ini.  i.i'..  .ipc    llif    <'\.'    i.    pla,  <  .1 

M'tV   n.'.ii    111.'   l.'ii'..    wimli    I-,   l..w.i.',!    ,n  "■    •'' 

lai'.f.l  null!  llir  poitilinn  ii  l.iiin.l  ,il   win.  Ii  lli.'  ..I.l.'.  I  .ipprai't    m    il'i  ciralr.l 

',M/.  OiiiMlllloiiN  Of  (llRlliinliinHii  of  ilin  iiiiMK<i«.  In  .ml.  i  lli.il  nli|.'.  I  . 
Inol.i  .1  al  lliioii):li  a  mi.  i.i'<.  .ipr  '.lioiit.l  lie  '...'n  Willi  dr, Inn  In.  ,  .,  llif\  niii'.l 
liavr  a  t.lioii^;  IihIiI  iIiiowii  iip.iii  lliriii,  liiil  lliii  i'.  Ity  mi  iiiramt  rn.Mi|;li,  Il 
Il  iirtr'i'taiy  lli.il  llw  im.i).;r  lir  I.n  mr.l  :il  a  drirrminillr  di'.lain  r  lioiii  llir 
ryr  In  la,  t,  lliiir  it  l.ii  cin  li  piTLni  a  iil\fiiHii'  of  itii'st  ih\fiihf  riMoti  a 
dr. I. III.  r,  lli.il  I  .  lo  '.ay,  al  wlm  li  .m  t,l,|i',  i  mini  he  pla.  cl  liom  .m  ,.lr..  i\.  r>, 


5^2 


On  Li ^ J  it. 


[587- 


eye  in  order  to  be  seen  with  greatest  distinctness.  This  distance  is  different 
for  different  observers,  but  ordinarily  is  between  lo  and  12  inches.  It  is, 
therefore,  at  this  distance  from  the  eye  that  the  image  ought  to  be  formed. 
Moreover,  this  is  why  each  observer  has  io  focus  the  instrument  ;  that  is,  to 
adapt  the  microscope  to  his  own  distance  of  most  distinct  vision.  This  is 
effected  by  slightly  vaiying  the  distance  from  the  lens  to  the  object,  for  we 
have  seen  above  that  a  slight  displacement  of  the  object  causes  a  great  dis- 
placement of  the  image.  With  a  common  magnifying  glass,  such  as  is  held 
in  the  hand,  the  adjustment  is  effected  by  merely  moving  it  nearer  to  or 
farther  from  the  object.  In  the  microscope  the  adjustment  is  effected  by 
means  of  a  rack  and  pinion,  which  in  the  case  of  the  instrument  shown  in 
fig.  544  moves  the  eyepiece,  but  moves  the  object  in  the  case  of  the 
instrument  depicted  in  fig.  545.  What  has  been  said  about  focussing  the 
microscope  applies  equally  to  telescopes.  In  the  latter  instrument  the  eye- 
piece is  generally  adjusted  with  respect  to  the  image  formed  in  the  focus  of 
the  object-glass. 

In  respect  of  the  distinctness  of  the  miage  the  general  rules  for  convex 
lenses  apply 

In  order  to  lessen  dispersion,  lenses  have  been  constructed  of  diamond, 
of  ruby,  and  of  other  precious  stones,  which  for  a  small  amount  of  dispersion 
have  a  great  degree  of  refrangibility.  A  drop  of  water  or  of  Canada  balsam 
in  a  small  hole  in  a  thin  piece  of  wood  or  of  metal,  acts  as  a  microscope. 

588.  Apparent  mag-nitude  of  an  object. — The  apparent  magnitude 
or  apparent  diameter  of  a  body  is  the  angle  it  subtends  at  the  eye  of  the 


Fig.  547- 


observer.  Thus,  if  AB  is  the  object,  and  O  the  observer's  eye  (figs.  546,  547), 
the  apparent  magnitude  of  the  object  is  the  angle  AOB  contained  by  two 
visual  rays  drawn  from  the  centre  of  the  pupil  to  the  extremities  of  the  object. 
In  the  case  of  objects  seen  through  optical  instruments,  the  angles 
which  they  subtend  are  so  small  that  the  arcs  which  measure  the  angles  do 
not  differ  sensiljly  from  their  tangents.  The  ratio  of  two  such  angles  is 
therefore  the  same  as  that  of  their  tangents.  Hence  we  deduce  the  two 
following  principles  : 


-589]  Measure  of  Magnification.  563 

i.  IVJien  the  same  object ts  seen  at  tmeqiial  distances,  the  apparent  diatneter 
varies  inversely  as  the  distance  from  the  observer's  eye. 

ii.  In  the  case  of  two  objects  seen  at  the  sa?ne  distance,  the  ratio  oj  the 
apparent  diameters  is  the  same  as  that  of  their  absolute  magnitudes. 

These  principles  may  be  proved  as  follows  : — i.  In  fig.  546^  let  AB  be  the 
object  in  its  first  position,  and  ab  the  same  object  in  its  second  position. 
For  the  sake  of  distinctness  these  are  represented  in  such  positions  that  the 
line  OC  passes  at  right  angles  through  their  middle  points  C  and  c  respec- 
tively. It  is,  however,  sufficient  that  ab  and  AB  should  be  the  bases  of 
isosceles  triangles  having  a  common  verte.x  at  O.  Now,  by  what  has  been 
said  above,  AB  is  virtually  an  arc  of  a  circle  described  with  centre  O  and 
radius  OC  ;  likewise  ab  is  virtually  an  arc  of  a  circle  whose  centre  is  O  and 
radius  Oc.     Therefore, 

A0B:.^0^  =  ^5:/;^=   L  :  _l. 
OC     Oc    OC     Oc 

Therefore,  AOB  varies  inversely  as  OC. 

ii.  Let  AB  and  A'B'  be  two  objects  placed  at  the  same  perpendicular 
distance,  OC,  from  the  eye,  O,  of  the  observer  (fig.  547).  Then  they  are 
virtually  arcs  of  a  circle  whose  centre  is  O  and  radius  OC.     Therefore, 

AOB  :A'OB'  =  ^^  :^'  =  AB:  A'B'. 

a  proportion  which  expresses  the  second  principle. 

589.  Measure  of  magnification. — In  the  simple  microscope  the  measure 
of  the  magnification  produced  is  the  ratio  of  the  apparent  diameter  of  the 

image   to   that  of  the    

object,  both  being  at 
the  distance  of  most 
distinct  vision.  The 
same  rule  holds  good 
for  other  microscopes. 
It  is,  however,  impor- 
tant to  obtain  an  ex- 
pression for  the  magni- 
fication depending  on 
data  that  are  of  easier 
determination. 

In  fig.  548  let  AB  ^-ig.  ^^g. 

be  the  object,  and  A'B' 

its  image  formed  at  the  distance  of  most  distinct  vision.     Let  a'b'  be  the 

projection  of  AB  on  A'B'.     Then,  since  the  eye  is  very  near  the  glass,  the 

A'OB'        A'B'  A'B' 

magnification  equals  ^-,  or     -  -  ;  that  is,   -  „.    But  since  the  triangles 

a  Oo  a  b  AB  ° 

A'OB'  and  AOB  are  similar,  A'B' :  AB  =  DO  :  CO.  Now  DO  is  the  dis- 
tance of  most  distinct  vision,  and  CO  is  very  nearly  equal  to  FO,  the  focal 
length  of  the  lens.  Therefore,  the  magnification  equals  the  ratio  of  the  dis- 
tance of  most  distinct  vision  to  the  focal  length  of  the  lens.  Hence  we  con- 
clude that  the  magnification  is  greater,  ist,  as  the  focal  length  of  the  lens  is 

002 


564  On  Light.  [589- 

smaller — in  other  words,  as  the  lens  is  more  convergent ;  2ndly,  as  the 
observer's  distance  of  most  distinct  vision  is  greater. 

A  simpler  and  more  general  definition  of  the  measure  of  magnification 
may  be  stated  thus  : — Let  a  be  the  angular  magnitude  of  the  object  as  seen 
by  the  naked  eye,  /S  the  angular  magnitude  of  the  image,  whether  real  or 
virtual,  actually  present  to  the  eye,  then  the  magnification  is/3-=-a.  T^is 
rule  applies  to  telescopes. 

By  changing  the  lens  the  magnification  can  be  increased,  but  only  within 
certain  limits  if  we  wish  to  obtain  a  distinct  image.  By  means  of  a  simple 
microscope  distinct  magnification  may  be  obtained  up  to  120  diameters. 

The  magnification  we  have  here  considered  is  linear  magnification. 
Superficial  magnification  equals  the  square  of  the  linear  magnification  ;  for 
instance,  the  former  will  be  1,600  when  the  latter  is  40. 

590.  Principle  of  the  compound  microscope.^ — The  compound  micro- 
scope in  its  simplest  form  consists  of  two  condensing  lenses  :  one,  with  a 
short  focus,  is  called  the  object-glass,  or  obJcctive,he.ca.nse.  it  is  turned  towards 
the  object ;  the  other  is  less  condensing,  and  is  called  the  eyepiece,  ox  power, 
because  it  is  close  to  the  observer's  eye. 

Fig.  549  represents  the  path  of  the  luminous  rays  and  the  formation  of 
the  image  in  the  simplest  form  of  a  compound  microscope.     An  object  AB 

being  placed  very 
^^  ~^;»^^^^^i^  near  the  principal 
VB  W^^^^^H  focus  of  the  object- 
'■  ^^  ^^^BfiH  glass  M,  but  a  little 
farther  from  the 
glass,  a  real  image 
ab,  inverted  and 
somewhat  magni- 
fied, is  formed  on  the  other  side  of  the  object-glass  (556).  Now  the  distance 
of  the  two  lenses  M  and  N  is  such  that  the  position  of  the  image  ab  is 
between  the  eyepiece  N  and  its  focus  F.  From  this  it  follows  that  for  the 
eye  at  E,  looking  at  the  image  through  the  eyepiece,  this  glass  produces  the 
same  effect  as  a  simple  microscope,  and  instead  of  this  image  ab,  another 
image,  a'b',  is  seen,  which  is  virtual,  and  still  more  magnified.  This  second 
image,  although  erect  as  regards  the  first,  is  inverted  in  reference  to  the 
object.  It  may  thus  be  said  that  the  compound  microscope  is  in  effect  a 
simple  microscope  applied  not  to  the  object  but  to  its  image  already  magni- 
fied by  the  first  lens. 

591.  Compound  microscope. — The  princi]ilc  of  the  compound  micro- 
scope has  been  already  (590)  explained  ;  the  ))rincipal  accessories  to  the 
instrument  remain  to  be  described. 

Fig.  550  represents  a  perspective  view,  and  fig.  551a  section  of  a  com- 
pound microsco])c.  The  body  of  the  microscope  consists  of  a  series  of  brass 
tubes,  1)D',  H,  and  I  ;  in  H  is  fitted  the  cyciMcce  D,  and  in  the  lower  part 
of  DD'  the  object-glass  0.  The  tube  I  moves  with  gentle  friction  in  the  tube 
DD',  which  in  turn  can  also  be  uioved  in  a  larger  tube  fixed  in  the  ring  E. 
This  latter  is  fixed  to  a  piece  BB',  which,  by  means  of  a  very  fine  screw 
worked  by  the  milled  head  'i',  can  be  moved  up  and  down  an  inner  rod,  c, 
not  represented  in  the  figure.     The  whole  body  of  the  microscope  is  raised 


-591] 


Compound  Microscope. 


565 


and  lowered  with  the  piece  BB',  so  that  it  can  be  placed  near  or  far 
from  the  object  to  be  examined.  Moreover,  the  rod  c,  and  all  the  other 
pieces  of  the  apparatus,  rest  on  a  horizontal  axis  A,  with  which  they  turn 
under  so  much  friction  as  to  remain  fixed  in  any  position  in  which  they  may 
be  placed. 

The  object  to  be  observed  is  placed  between  two  glass  plates,  V,  on  a 
stagc^  R.  This  is  perforated  in  the  centre,  so  that  light  can  be  reflected  upon 
the  object  by  a  concave  reflecting  glass  mirror,  M.     The  mirror  is  mounted 


Fig.  550. 

on  a  jointed  support  so  that  it  can  be  placed  in  any  position  whatever,  so 
as  to  reflect  to  the  object  either  the  diffused  light  of  the  atmosphere,  or  that 
from  a  candle  or  lamp.  Between  the  reflector  and  the  stage  is  a  diaphragm 
or  stop,  K,  perforated  by  four  holes  of  different  sizes,  any  one  of  which  can 
be  placed  over  the  perforation  in  the  stage,  and  thus  the  light  falling  on  the 
object  may  be  regulated  ;  the  light  can,  moreover,  be  regulated  by  raising, 
by  a  lever  n,  the  diaphragm  K,  which  is  movable  in  a  slide.  Above  the 
diaphragm  is  a  piece,  w,  to  which  can  be  attached  either  a  very  small  stop, 
so  that  only  very  little  light  can  reach  the  object,  or  a  condensing  lens, 


566  On  Light.  [591- 

which  illuminates  it  strongly,  or  an  oblique  prism,  represented  at  X.  The 
rays  from  the  reflector  undergo  two  total  reflections  in  this  prism,  and 
emerge  by  a  lenticular  face  that  concentrates  them  on  the  object,  but  in  an 
oblique  direction,  which  in  some  microscopic  observations  is  an  advantage. 
Objects  are  generally  so  transparent  that  they  can  be  lighted  from  below  ; 
but  where,  owing  to  their  opacity,  this  is  not  possible,  they  are  lighted  from 
above  by  means  of  a  condensing  lens  mounted  on  a  jointed  support,  and  so 
placed  that  they  receive  the  diffused  light  of  the  atmosphere. 

Fig.  551  shows  the  arrangement  of  the  lenses  and  the  path  of  the  rays 
in  the  microscope.  At  0  is  the  object-glass,  consisting  of  three  small  con- 
densing lenses,  represented  on  a  larger  scale  at  L,  on  the  right  of  the  figure. 
The  effect  of  these  lenses  being  added  to  each  other  is  that  they  act  like  a 
single  very  powerful  condensing  lens.  The  object  being  placed  at  /,  a  very 
little  beyond  the  principal  focus  of  the  system,  the  emerging  rays  fall  upon  a 
fourth  condensing  lens,  n,  the  use  of  which  will  be  seen  presently  (592,  593). 
Having  become  more  convergent,  owing  to  their  passage  through  the  lens 
«,  the  rays  form  at  aa'  a  real  and  amplified  image  of  the  object  /.  This 
image  is  between  a  fifth  condensing  lens,  O,  and  the  principal  focus  of  this 
lens.  Hence,  on  looking  through  this,  it  acts  as  a  magnifier  (556),  and  gives 
at  AA'  a  virtual  and  highly  magnified  image  of  aa\  and  therefore  of  the 
object.  The  two  glasses  71  and  O  constitute  the  eyepiece,  in  the  same 
manner  as  the  three  glasses  0  constitute  the  object-glass. 

The  first  image,  aa',  must  not  merely  be  formed  between  the  glass  O 
and  its  principal  focus,  but  at  such  a  distance  from  this  glass  that  the  second 
image,  AA',  is  formed  at  the  observer's  distance  of  distinct  vision.  This 
result  is  obtained  in  moving,  by  the  hand,  the  body  DH  of  the  microscope 
in  the  larger  tube  fixed  to  the  ring  E,  until  a  tolerably  distinct  image  is 
obtained  ;  then  turning  the  milled  head  T  in  one  direction  or  the  other, 
the  piece  BB',  and  with  it  the  whole  microscope,  are  moved  until  the  image 
AA'  attains  its  greatest  distinctness,  which  is  the  case  when  the  image  aa' 
is  formed  at  the  distance  of  distinct  vision :  a  distance  which  can  always  be 
ultimately  obtained,  for  as  the  object-glass  approaches  or  recedes  from  the 
object,  the  image  aa'  recedes  from  or  approaches  the  eyepiece,  and  at  the 
same  time  the  image  AA'. 

This  operation  is  called  the  focussitig.  In  the  microscope,  where  the 
distance  from  the  object-glass  to  the  eyepiece  is  constant,  it  is  effected  by 
altering  their  distance  from  the  object.  In  telescopes,  where  the  objects 
are  inaccessible,  the  focussing  is  effected  by  varying  the  distance  of  the  eye- 
piece and  the  object-glass. 

The  microscope  possesses  numerous  eyepieces  and  object-glasses,  by 
means  of  which  a  great  variety  of  magnifying  power  is  obtained.  A  small 
magnifying  power  is  also  obtained  by  removing  one  or  two  of  the  lenses  of 
the  object-glass. 

The  above  contains  the  essential  features  of  the  microscope  ;  it  is  made 
in  a  great  variety  of  forms,  which  differ  mainly  in  the  construction  of  the 
stand,  the  arrangement  of  the  lenses,  and  in  the  illumination.  For  descrip- 
tions of  these  the  student  is  referred  to  special  works  on  the  microscope. 

592.  Acbromatlsiu  of  tbe  microscope.  Campanl's  eyepiece. — When 
a  compound  microscope  consists  of  two  single  lenses,  as  in  fig.  549,  not  only 


-592]  AcJirouiatisni  of  the  Microscope.  567 

is  the  spherical  aberration  uncorrected,  but  also  the  chromatic  aberration, 
the  latter  defect  causing  the  images  to  be  surrounded  by  fringes  of  the 
prismatic  colours,  these  fringes  being  larger  as  the  magnification  is  greater. 
It  is  with  a  view  to  correcting  these  aberrations  that  the  object-glass  (see 
fig-  550  is  composed  of  three  achromatic  lenses,  and  the  eyepiece  of  two 
lenses,  n  and  O  ;for  the  first  of  these, «,  would  be  enough  to  produce  colour 
unless  the  magnifying  power  were  low. 

The  efifect  of  this  eyepiece  in  correcting  the  colour  may  be  explained 
as  follows  : — It  will  be  borne  in  mind  that  with  respect  to  red  rays  the  focal 
length  of  a  lens  is  greater  than  the  focal  length  of  the  same  lens  with  refer- 
ence to  the  violet  rays. 

■D 

In  fact,  if  in  the  equation  (4)  (559)  we  write  R'  =  oo,  we  obtain  /=  . 

n—  I 

which  gives  the  focal  length  of  a  plano-convex  lens  whose  refractive  index 

is  n.     Now,  in  flint  glass,  and  for  the  red  ray,  n  -  1  equals  0-63,  and  for  the 

violet  ray  n  —  1  equals  o'Gj. 

Let  ai  be  the  object,  O  the  object-glass,  which  is  corrected  for  colour. 

Consequently,  a  pencil  (fig.  552)  of  rays  falling  from  a  on  O  would  converge 


Fig.  552. 
to  the  focus  A  without  any  separation  of  colours  ;  but  falling  on  the  fietd- 
glass  C,  the  red  rays  would  converge  to  r,  the  violet  rays  to  v,  and  inter- 
mediate colours  to  intermediate  points.  In  like  manner  the  rays  from  b, 
after  passing  through  the  field-glass,  would  converge  to  r',  or  v',  and  inter- 
mediate points.  So  that  on  the  whole  there  would  be  formed  a  succession 
of  coloured  images  oi  ab  ;  viz.  a  red  image  at  rr',  a  violet  image  at  vv\  and 
between  them  images  of  intermediate  colours.  Let  d  be  the  point  of  the 
object  which  is  situated  on  the  axis.  The  rays  from  d  will  converge  to  R, 
V,  and  intermediate  points.  Now  suppose  the  eye-glass  O'  to  be  placed  in 
such  a  manner  that  R  is  the  principal  focus  of  O'  for  the  red  rays,  then  V 
will  be  its  principal  focus  for  the  violet  rays.  Consequently,  the  red  rays, 
after  emerging  from  O,  will  be  parallel  to  the  axis,  and  so  will  the  violet 
rays  coming  from  V,  and  so  of  any  other  colour.  Accordingly,  the  colours 
of  d,  which  are  separated  by  C,  are  again  combined  by  O'.  The  same  is 
very  nearly  true  of  r  and  v,  and  of  r'  and  v'  Hence  a  combination  of  lenses 
C  and  O'  corrects  the  chromatic  aberration  that  would  be  produced  by  the 
use  of  a  single  eye-glass.  Moreover,  by  drawing  the  rays  towards  the  axis, 
it  diminishes  the  spherical  aberration,  and,  as  we  shall  see  in  the  next  article, 
enlarges  the  field  of  view. 

In  all  eyepieces  consisting  of  two  lenses  the  lens  to  which  the  eye  is 
applied  is  called  the  eye-lens  ;  the  one  towards  the  object-glass  is  called  the 
field-lens.  The  eyepiece  above  described  was  invented  by  Huyghens,  who 
was  not,  however,  aware  of  its  property  of  achromatism.  He  designed  it 
for  use  with  the  telescope.     It  was  applied  to  the  microscope  by  Campani. 


568 


On  Li^ht. 


[592- 


The  relation  between  the  focal  length  of  the  lenses  is  as  follows :— The  focal 
length  of  the  field-glass  is  three  times  that  of  the  eye-lens,  and  the  distance 
between  their  centres  is  half  the  sum  of  the  focal  length.  It  easily  follows 
from  this  that  the  image  of  the  point  d  would,  but  for  the  interposition  of 
the  field-lens,  be  formed  at  D,  which  is  so  situated  that  CD  is  three  times 
DO';  then  the  mean  of  the  coloured  images  would  be  formed  midway 
between  C  and  O'. 

593.  Field  of  view. — By  the  field  of  view  of  an  optical  instrument  is 
meant  all  those  points  which  are  visible  through  the  eyepiece.  The  advan- 
tage obtained  by  the  use  of  an  eyepiece  in  enlarging  the  field  of  view  will  be 
readily  understood  by  an  inspection  of  the  accompanying  figure.  As  before 
(fig.  553),  O  is  the  object-glass,  C  the  field-lens,  O'  the  eye-lens,  and  E  the 
eye  placed  on  the  axis  of  the  instrument.  Let  a  be  a  point  of  the  object ;  if 
we   suppose  the  field-lens  removed,  the  pencil   of  rays  from  a  would  be 

A       


Fig.  553. 

brought  to  a  focus  at  A,  and  none  of  them  would  fall  on  the  eye-lens  O', 
nor  pass  into  the  eye  E.  Consequently,  a  is  beyond  the  field  of  view.  But 
when  the  field-glass  C  is  interposed,  the  pencil  of  rays  is  brought  to  a  focus 
at  A',  and  emerges  from  O'  into  the  eye.  Consequently,  a  is  now  within 
the  field  of  view.  It  is  in  this  manner  that  the  substitution  of  an  eyepiece 
for  a  single  eye-lens  enlarges  the  field  of  view. 

594.  IMCag-nifyingr  power.  Micrometer. — The  magnifying  power  of  any 
optical  instrument  is  the  ratio  of  the  magnitude  of  the  image  to  the  mag- 
nitude of  the  object.  The  magnifying  power  in  a 
compound  microscope  is  the  product  of  the  respec- 
tive magnifying  powers  of  the  object-glass  and  of 
the  eyepiece  ;  that  is,  if  the  first  of  these  magnifies 
20  times,  and  the  other  10,  the  total  magnifying 
power  is  200.  The  magnifying  power  depends  on 
the  greater  or  less  convexity  of  the  object-glass 
and  of  the  eyepiece,  as  well  as  on  the  distance  be- 
tween these  two  glasses,  together  with  the  distance 
of  the  object  from  the  object-glass.  A  magnifying 
power  of  1,500  and  even  upwards  has  been  ob- 
tained ;  but  the  image  then  loses  in  sharpness 
what  it  gains  in  extent.  To  obtain  precise  and 
well-illuminated  images,  the  magnifying  power  ought  not  to  exceed  500  to 
600  diameters,  which  gives  a  superficial  enlargement  250,000  to  360,000  times 
that  of  the  object. 

The  magnifying  power  is  determined  experimentally  by  means  of  the 
glass  tnicroinctcr  :  this  is  a  small  glass  plate,  on  which,  by  means  of  a 
diamond,  a  scries  of  lines  is  drawn  at  a  distance  from  each  other  of  y^  or  yi,, 
of  a  millimetre.     The  mi(  rometcr  is  placed  in  front  of  the  object-glass,  and 


Fig-  554- 


-595]  Astronomical  Telescope.  569 

then,  instead  of  viewing-  directly  the  rays  emerging  from  the  eyepiece  O, 
they  are  received  on  a  piece  of  glass  A  (fig.  554),  inclined  at  an  angle  of  45°, 
and  the  eye  is  placed  above  so  as  to  see  the  image  of  the  micrometer  lines, 
which  is  formed  b)'  reflection  on  a  screen  E,  on  which  is  a  scale  divided  into 
millimetres.  By  counting  the  number  of  divisions  of  this  scale  correspond- 
ing to  a  certain  number  of  lines  of  the  image,  the  magnifying  power  may  be 
deduced.  Thus,  if  the  image  occupies  a  space  of  45  millimetres  on  the  scale 
and  contains  1 5  lines  of  the  micrometer,  the  distance  between  each  of  which 
shall  be  assumed  at  jj^  millimetre,  the  absolute  magnitude  of  the  object  will 
be  i"y  millimetre  ;  and  as  the  image  occupies  a  space  of  45  millimetres,  the 
magnification  will  be  the  quotient  of  45  by  y*,,";,,  or  300.  The  eye  in  this 
experiment  ought  to  be  at  such  a  distance  from  the  screen  E  that  the  screen 
is  distinctly  visible  :  this  distance  varies  with  different  observers,  but  is 
usually  10  to  12  inches.  The  magnifying  power  of  the  microscope  can  also 
be  determined  by  means  of  the  camera  hccida  ;  it  is  increased  at  the  expense 
ot  brightness,  definition,  and  field.  Hence  it  is  usual  to  have  several  eye- 
pieces with  each  microscope  so  as  to  obtain  greater  definition  of  higher 
magnification. 

Noberfs  Hires  are  frequently  used  as  test  objects  ;  these  are  lines  ruled 
on  glass  in  series  ;  in  the  first  group  the  lines  are  at  a  distance  of  jgi-^^  of  an 
inch  from  the  middle  of  one  line  to  the  middle  of  the  next  ;  in  the  finest  the 
lines  are  at  a  distance  of  ^-^^^-^  of  a  line.  Other  test  objects  are  the  scales 
of  certain  butterflies,  and  various  kinds  of  diatoms. 

When  once  the  magnifying  power  is  known,  the  absolute  magnitude  of 
objects  placed  under  the  microscope  is  easily  deduced.  For,  as  the  magni- 
fying power  is  the  cjuotient  of  the  size  of  the  image  by  the  size  of  the  object, 
it  follows  that  the  size  of  the  image  divided  by  the  magnifying  power  gives 
the  size  of  the  object :  in  this  manner  the  diameters  of  all  microscopic  objects 
are  determined. 

TELESCOPES. 

595.  Astronomical  telescope. — The  astVo7iomical  telescope  is  used  for 
obser\-ing  the  heavenly  bodies  ;  like  the  microscope,  it  consists  of  a  con- 
densing eye- 
piece and  I 
object-glass,  j 
The  object- 
glass,  M  (fig. 
555),  forms 
between  the 
eyepiece,  X, 
and  its  prin- 
cipal      focus  lig-  555- 

an  inverted  image  of  the  heavenly  body  ;  and  this  eyepiece,  which  acts  as 
a  magnifying  glass,  then  gives  a  virtual  and  highly  magnified  image,  a'b\  of 
the  image  ab.  The  astronomical  telescope  appears,  therefore,  analogous  to 
the  microscope  :  but  the  two  instruments  differ  in  this  respect,  that  in  the 
microscope,  the  object  being  very  near  the  object-glass,  the  image  is  formed 
much  beyond  the  principal  focus,  and  is  greatly  magnified,  so  that  both  the 


570 


Oti  Light. 


[595- 


object-glass  and  the  eyepiece  magnify  ;  while  in  the  astronomical  telescope, 
the  heavenly  body  being  at  a  great  distance,  the  incident  rays  are  parallel, 
and  the  image  formed  in  the  principal  focus  of  the  object-glass  is  much 
smaller  than  the  object.  There  is,  therefore,  no  magnification  except  by  the 
eyepiece,  and  this  ought,  therefore,  to  be  of  very  short  focal  length. 

Fig.  556  shows  an  astronomical  telescope  mounted  on  its  stand.  Above 
it  there  is  a  small  telescope  which  is  called  the  fi?idcr.  Telescopes  with  a 
large  magnifying  power  are  not  convenient  for  finding  a  star,  as  they  have 
but  a  small  field  of  view  :  the  position  of  the  star  is,  accordingly,  first  sought 
by  the  finder,  which  has  a  much  larger  field  of  view — that  is,  takes  in  a  far 
greater  extent  of  the  heavens  ;  it  is  then  viewed  by  means  of  the  telescope. 

that  is,  it  equals 


APR 

The  magnification  (589)  equals     ^^v,  (fig.  555) 
a  \J0 


and  therefore  is  approximately  equal  to 


CF 

OF' 


bOC 

F  being  the  focus  of  the  object- 
glass  M,  and 
being  supposed 
very    nearly 


to 
coincide  with 
the  focus  of  the 
eyepiece  N  ;  it 
may,  therefore, 
be  concluded 
that  the  magni- 
fying power  is 
greater  in  pro- 
portion as  the 
object-glass  is 
less  convex,  and 
the  eyepiece 
more  so. 

When      the 
telescope  is 

used  to  make 
an  accurate  ob- 
servation of  the 
stars  —  for  ex- 
ample, the  zenith  distance,  or  their  passage  over  the  meridian — a  cross  wire 
is  added.  This  consists  of  two  very  fine  metal  wires  or  spider  threads 
stretched  across  a  circular  aperture  in  a  small  metal  plate  (fig.  557).  The 
wires  ought  to  be  placed  in  the  position  where  the  inverted  image  is  pro- 
duced by  the  object-glass,  and  the  point  where  the  wires  cross  ought  to  be 
on  the  optical  axis  of  the  telescope,  which  thus  becomes  the  litie  of  sight  or 
collimation. 

596.  Terrestrial  telescope. — The  terrestrial  telescope  differs  from  the 
astronomical  telescope  in  producing  images  in  their  right  positions.  This  is 
effected  by  means  of  two  condensing  glasses,  P  and  Q  (fig.  558),  placed 
between  the  object-glass  M  and  the  eyepiece  R.  The  object  being  sup- 
posed to  be  at  Al$,  at  a  greater  distance  than  can  he  shown  in  the  drawing, 


Fig.  556. 


596] 


Terrestrial  Telescope. 


571 


an  inverted  and  much  smaller  image  is  formed  at  ba  on  the  other  side  of 
the  object-glass.  But  the  second  lens,  P,  is  at  such  a  distance  that  its 
principal  focus  coincides  with  the  image  ab  ;  from  which  it  follows  that  the 
luminous  rays  which  pass  through  b,  for  example,  after  traversing  the  lens 
P,  take  a  direc- 
tion parallel  to 
the  secondar\ 
axis  ^O  (552). 
Similarly,  the 
rays  passing  by 
a  take  a  direc-  Fig.  558. 

tion   parallel  to 

the  axis  aO.  After  crossing  in  H,  these  various  rays  traverse  a  third  lens  Q, 
whose  principal  focus  coincides  with  the  point  H.  The  pencil  B^H  con- 
verges towards  b\  on  a  secondary  axis  O'b',  parallel  to  its  direction  ;  the 
pencil  AizH  converging  in  the  same  manner  at  a',  an  erect  image  of  the 
object  AB  is  produced  at  a'b'.  This  image  is  viewed,  as  in  the  astrono- 
mical telescope,  through  a  condensing  eyepiece  R,  so  placed  that  it  acts  as 
a  magnifying  glass  ;  that  is,  its  distance  from  the  image  a'b'  is  less  than  the 
principal  focal  distance  ;  hence  there  is  formed,  at  a"b",  a  virtual  image  of 
a'b'^  erect  and  much  magnified.  The  lenses  P  and  Q,  which  only  serve  to 
rectify  the  position  of  the  image,  are  fixed  in  a  brass  tube,  at  a  constant 
distance,  which  is  equal  to  the  sum  of  their  principal  focal  distances.  The 
object-glass  M  moves  in  a  tube,  and  can  be  moved  to  or  from  the  lens  P, 
so  that  the  image  ab  is  always  formed  in  the  focus  of  the  lens,  whatever  be 
the  distance  of  the  object.  The  distance  of  the  lens  R  may  also  be  varied 
so  that  the  image  a"b"  may  be  formed  at  the  distance  of  distinct  vision. 

This  instrument  may  also  be  used  as  an  astronomical  telescope  by  using 
a  different  eyepiece  :  this  must  have  a  much  greater  magnifying  power  than 
in  the  former  case. 

In  the  terrestrial  telescope  the  magnifying  power  is  the  same  as  in  the 
astronomical  telescope,  provided  always  that  the  correcting  glasses,  P  and 
Q,  have  the  same  convexity. 

In  order  to  determine  directly  the  magnifying  power  of  a  telescope  when 
this  is  not  great,  a  divided  scale  at  a  distance,  or  the  tiles  of  a  house  may 
be  viewed  through  the  telescope  with  one  eye  and  directly  with  the  other. 
This  with  a  little  practice  is  not  difficult.  It  is  thus  ob- 
served how  many  unmagnified  divisions  correspond  to  a 
single  magnified  one.  Thus,  if  two  seen  through  the 
telescope  appear  like  seven,  the  magnifying  power  is  3^. 
Reading  ordinary  printing  from  a  distance  is  an  excellent 
means  of  testing  and  comparing  telescopes. 

The  excellence  of  a  telescope  depends  also  on  the 
sharpness  of  the  images.  To  test  this,  various  circular 
and  angular  figures  are  painted   in   black   on  a  white  '^'  ^^'* 

ground,  as  shown  in  fig.  559,  in  about  ^^j  the  full  size.  When  these  are 
looked  at  through  the  telescope  at  a  distance  of  80  or  100  paces,  they  should 
appear  sharply  defined,  perfectly  black,  without  distortion,  and  without 
coloured  edges.     The  penetration  or  penet7atjt7g  power  of  a  telescope  by 


572  On  Light.  [596- 

which  stars  are  seen  which  are  not  visible  to  the  naked  eye  depends  mainly 
on  the  aperture  of  the  object-glass.  Even  with  the  strongest  magnification 
the  fixed  stars  appear  as  luminous  points  without  apparent  diameter. 

597.  Galileo's  telescope. — Galileo's  telescope  is  the  simplest  of  all  tele- 
scopes, for  it  only  consists  of  two  lenses  ;  namely,  an  object-glass,  M,  and  a 

diverging  or  double  concave 
eyepiece,  R  (fig.  560),  and 
it  gives  at  once  an  erect 
image.  Opera-glasses  are 
constructed  on  this  prin- 
ciple. 

Fig.  360  If  the   object   be  repre- 

sented by  the  right  line  AB, 
a  real  but  inverted  and  smaller  image  would  be  formed  at  ba  ;  but  in 
traversing  the  eyepiece  R,  the  rays  emitted  from  the  points  A  and  B  are 
refracted  and  diverge  from  the  secondary  axis  bO'  and  aO'  which  coire- 
spond  to  the  points  b  and  a  of  the  image.  Hence,  these  rays  produced 
backward  meet  their  axes  in  a'  and  b' ;  the  eye  which  receives  them  sees 
accordingly  an  erect  and  magnified  image  in  a'b\  which  appears  nearer 
because  it  is  seen  under  an  angle,  a'0'b\  greater  than  the  angle,  AOB, 
under  which  the  object  is  seen. 

The  magnifying  power  is  equal  to  the  ratio  of  the  angle  a'O'b'  to  the 
angle  AOB,  and  is  usually  from  2  to  4. 

The  distance  of  the  eyepiece  R  from  the  image  ab  is  pretty  nearly  equal 
to  the  principal  focal  distance  of  this  eyepiece  ;  it  follows,  therefore,  that  the 
distance  between  the  two  lenses  is  the  distance  between  their  respective 
focal  distances  ;  hence  Galileo's  telescope  is  very  short  and  portable.  It 
has  the  advantage  of  showing  objects  in  their  right  position  ;  and,  further,, 
as  it  has  only  two  lenses,  it  absorbs  very  little  light  :  in  consequence,  how- 
ever, of  the  divergence  of  the  emergent  rays,  it  has  only  a  small  field  of  view, 
and  in  using  it  the  eye  must  be  placed  very  near  the  eyepiece.  The  eye- 
piece can  be  moved  to  or  from  the  object-glass,  so  that  the  image  a'b'  \s 
always  formed  at  the  distance  of  distinct  vision. 

The  opera-glass  is  usually  double,  so  as  to  produce  an  image  in  each  eye, 
by  which  greater  brightness  is  attained. 

The  time  at  which  telescopes  were  invented  is  not  known.  Some  attri- 
bute their  invention  to  Roger  Bacon  in  the  thirteenth  century  ;  others  to  J.  B. 
Porta  at  the  end  of  the  sixteenth  ;  others,  again,  to  a  Dutchman,  Jacques 
Metius,  who,  in  1609,  accidentally  found  that  by  combining  two  glasses,  one 
concave  and  the  other  convex,  distant  objects  appeared  nearer  and  much 
larger.  Galileo's  was  the  first  telescope  directed  towards  the  heavens.  By 
its  means  Galileo  discovered  the  mountains  of  the  moon,  Jupiter's  satellites, 
and  the  s])ots  on  the  sun. 

598.  Keflectlng-  telescope*. — The  telescopes  previously  described  are 
refractiftg  or  dioptric  telescopes.  It  is,  however,  only  in  recent  times  that  it 
has  been  possible  to  construct  achromatic  lenses  of  large  size  ;  before  this  a 
concave  metallic  mirror  was  used  instead  of  the  object-glass.  Telescopes 
of  this  kind  are  called  reflecting  or  catoptnc  telescopes.  The  principal  forms 
are  those  devised  by  Gregory,  Newton,  Hcrschel,  and  Cassegrain. 


-589]  The  Gregorian   Telescope.  573 

599.  The  Greg-orlan  telescope. — Fig.  561  is  a  representation  of  Gre- 
gory's telescope  ;  it  is  mounted  on  a  stand,  about  which  it  is  movable,  and 
can  be  inclined  at  any  angle.  This  mode  of  mounting  is  optional  ;  it  may 
be  equatorially  mounted.     Fig.  562  ^ 

gives  a  longitudinal  section.  It 
consists  of  a  long  brass  tube  closed 
at  one  end  by  a  concave  metallic 
mirror,  M,  which  is  perforated  in 
the  centre  by  a  round  aperture 
through  which  rays  reach  the  eye. 
There  is  a  second  concave  metal 
mirror,  N,  near  the  end  of  the  ' 
tube:  it  is  somewhat  larger  than 
the  central  aperture  in  the  large 
mirror,  and  its  radius  of  curvature 
is  much  smaller  than  that  of  the 
large  mirror.  The  axes  of  both 
mirrors  coincide  with  the  axis  of 
the  tube.  As  the  centre  of  curva- 
ture of  the  large  mirror  is  at  O, 
and  its  focus  at  ab,  rays  such  as  SA 
emitted  from  a  heavenly  body  are 
reflected  from  the  mirror  M,  and 
form  at  ab  an  inverted  and  very 
small  image  of  the  heavenly  body. 


Fig.  56 


The  distance  of  the  mirrors  and  their  curvatures  is  so  arranged  that  the 
position  of  this  image  is  between  the  centre,  0,  and  the  focus  _/j  of  the  small 
mirror  ;  hence  the  rays,  after  being  reflected  a  second  time  from  the  mirror 
N,  form  at  a'b'  a  magnified  and  inverted  image  of  ab,  and  therefore  in  the 
true  position  of  the  heavenly  body.  This  image  is  viewed  through  an  eye- 
piece, P,  which  may  either  be  simple  or  compound,  its  object  being  to 
magnify  it  again,  so  that  it  is  seen  at  a"b". 


Fig.  562. 

As  the  objects  viewed  are  not  always  at  the  same  distance,  ihe  focus  of 
the  large  mirror,  and  therefore  that  of  the  small  one,  vary  in  position. 

And  as  the  distance  of  distinct  vision  is  not  the  same  with  all  eyes,  the 
image  a"b''  ought  to  be  formed  at  different  distances.  The  required  adjust- 
ments may  be  obtained  by  bringing  the  small  mirror  nearer  to  or  farther  from 
the  larger  one  ;  this  is  effected  by  means  of  a  milled  head,  A  (fig.  561), 
which  turns  a  rod,  and  this  by  a  screw  moves  a  piece  to  which  the  mirror  is 
fixed. 


574 


On  Lio'ht. 


[600- 


600.  The  xrewtonian  telescope. — This  instrument  does  not  differ  much 
from  that  of  Gregory  ;  the  large  mirror  is  not  perforated,  and  there  is  a 
small  plane  mirror  inclined  at  an  angle  of  45°  towards  an  eyepiece  placed 
in  the  side  of  the  telescope. 

The  difficulty  of  constructing  metallic  mirrors  caused  telescopes  of 
Gregorian  and  Newtonian  construction  to  fall  into  disuse.  Of  late,  how- 
ever, the  process  of  silvering  glass  mirrors  has  been  carried  to  a  high  state 
of  perfection,  and  Foucault  applied  these  mirrors  to  Newtonian  telescopes 
with  great  success.  His  first  mirror  was  only  four  inches  in  diameter,  but 
he  has  successively  constructed  mirrors  of  8,  12,  and  13  inches,  and  at  the 
time  of  his  death  had  completed  one  of  32  inches  in  diameter. 

Fig.  564  represents  a  Newtonian  telescope  mounted  on  an  equatorial 
stand,  and  fig.  563  gives  a  horizontal  section  of  it.  This  section  shows  how 
the  luminous  rays  reflected  from  the  parabolic  mirror  M  meet  a  small  rect- 
angular prism,  w,  which  replaces  the  inclined  plane  mirror  used  in  the  old 
form  of  Newtonian  telescope.  After  undergoing  a  total  reflection  from  ;«, 
the  rays  form  at  a'b'  a  very  small  image  of  the  heavenly  body.  This  image 
is  viewed   through   an   eyepiece  with   four   lenses  placed  on   the  side  of 


the  telescope,  and  magnifying  from  50  to  800  times  according  to  the  size  of 
the  silvered  mirror. 

In  reflectors  the  mirror  acts  as  object-glass,  but  there  is,  of  course,  no 
chromatic  aberration.  The  spherical  aberration  is  corrected  by  the  form 
given  to  the  reflector,  which  is  paraboloid,  but  slightly  modified  by  trial  to 
suit  the  eyepiece  fitted  to  the  telescope. 

The  mirror  when  once  polished  is  immersed  in  a  silvenng  liquid,  which 
consists  essentially  of  ammoniacal  solution  of  nitrate  of  silver,  to  which  some 
reducing  agent  is  added.  When  a  polished  glass  surface  is  immersed  in 
this  solution,  silver  is  deposited  on  the  surface  in  the  form  of  a  brilliant 
metallic  layer,  which  adheres  so  firmly  that  it  can  be  polished  with  rouge  in 
the  usual  manner.  These  new  telescopes  with  glass  mirrors  have  the  ad- 
vantage over  the  old  ones  that  they  give  purer  images,  they  weigh  less,  and 
are  much  shorter,  their  focal  distance  being  only  about  six  times  the  diameter 
of  the  mirror. 

These  details  known,  the  whole  apparatus  remains  to  be  described.  The 
body  of  the  telescope  (fig.  564)  consists  of  an  octagonal  wooden  tube.  The  end 
G  is  open  ;  the  mirror  is  at  the  other  end.  At  a  certain  distance  from  this 
end  two  axles  are  fixed,  which  rest  on  bearings  supported  by  two  wooden 
uprights,  A  and  15.  These  are  themselves  fi.xed  to  a  table,  PQ,  which  turns 
on  a  fixed  plate,  R.S,  placed  e.xactly  parallel  to  the  equator.  On  the  circum- 
ference of  the  turning-table  there  is  a  brass  circle  divided  into  360  degrees  ; 


-600] 


TJic  Neivtonian   Telescope. 


575 


and  beneath  it,  but  also  fixed  to  the  turning-table,  there  is  a  circular  toothed 
wheel,  in  which  an  endless  screw,  V,  works.  By  moving  this  in  either 
direction  by  means  of  the  handle  m,  the  table  PQ,  and  with  it  the  telescope, 
can  be  turned.  A  vernier,  x,  fixed  to  the  plate  RS,  gives  fractions  of  a 
degree.  On  the  axis  of  the  motion  of  the  telescope  there  is  a  graduated 
circle,  O,  which  serves  to  measure  the  declination  of  the  star — that  is,  its 


Fig.  564. 

angular  distance  from  the  equator ;  while  the  degrees  traced  round  the  table 
RS  ser\^e  to  measure  the  right  ascension— that  is,  the  angle  which  the  de- 
clination circle  of  the  star  makes  with  the  declination  circle  passing  through 
the  first  point  of  Aries. 

In  order  to  fix  the  telescope  in  declination,  there  is  a  brass  plate,  E,  fixed 
to  the  upright ;  it  is  provided  with  a  clamp,  in  which  the  limb  O  works,  and 


576 


On  Light. 


[600- 


which  can  be  screwed  tight  by  means  of  a  screw  with  a  milled  head  r.  On 
the  side  of  the  apparatus  there  is  the  eyepiece  fl,  which  is  mounted  on  a 
shding  copper  plate,  on  which  there  is  also  the  small  prism  w,  represented 
in  section  in  fig.  562.  To  bring  the  image  to  the  right  place,  this  plate  may 
be  moved  by  means  of  a  rack  and  a  milled  head  a.  The  handle  n  serves  to 
clamp  or  unclavip  the  screw  V.  The  drawing  was  one  taken  from  a  tele- 
scope the  mirror  of  which  is  only  6i  inches  in  diameter,  and  which  gives  a 
magnifying  power  of  150  to  200. 

6or.  The  Herschellan  telescope. —  Sir  W.  Herschel's  telescope,  which 
until  recently  was  the  most  celebrated  instrument  of  modern  times,  was  con- 
structed on  a  method  differing  from  those  described.  The  mirror  was  so  in- 
clined that  the  image  of  the  star  was  formed  at  ab  on  the  side  of  the  telescope 
near  the  eyepiece  0 :  hence  it  is  termed  the  front-view  telescope.  As  the 
rays  in  this  telescope  only  undergo  a  single  reflection,  the  loss  of  light  is  less 
than  in  either  of  the  preceding  cases,  and  the  image  is  therefore  brighter. 
The  magnifying  power  is  the  quotient  of  the  principal  focal  distance  of  the 
mirror  by  the  focal  distance  of  the  eyepiece. 

Herschel's  great  telescope  was  constructed  in  1789;  it  was  40  feet  in 
length,  the  great  mirror  was  50  inches  in  diameter.     The  quantity  of  light 

obtained  by  this  instru- 
ment was  so  great  as 
to  enable  its  inventor  to 
use  magnifying  powers 
far  higher  than  anything 
which  had  hitherto  been 
attempted. 

Herschel's  telescope 
has  been  exceeded  by 
one  constructed  by  the 
late  Earl  of  Rosse.  This  magnificent  instrument  has  a  focal  distance  of  53 
feet,  the  diameter  of  the  spec^um  being  six  feet.  It  is  at  present  used  as 
a  Newtonian  telescope,  but  it  can  also  be  arranged  as  a  front-view  tele- 
scope. 

INSTRUMENTS    FOR    FORMING   l'ICTURi:S   OF   OBJECTS. 

602.  Camera  obacura. — The  camera  obsciira  (dark  chamber)  is,  as  its 
name  implies,  a  closed  space  impervious  to  light.     The  principle  of  this 

apparatus  is  illus- 
trated by  fig.  566. 
The  rays  proceed- 
ing from  an  external 
object  AI),  and  en- 
tering by  the  aper- 
ture O,  form  on  the 
opi)osite  side  an 
image  of  the  ob- 
ject ba  in  its  natural 
colours,  but  of  reduced  dimensions,  and  in  an  inverted  position. 

Porta,  a  Neapolitan  physician,  the  inventor  of  this  instrument,  found  that 


Fig-  565. 


604] 


Camera  Liicida. 


577 

the  im.'i"c  on  a 


by  tixiny  a  double  convex  lens  in  the  aperture,  and  receiving 
white  screen,  it  was  much  brighter  and  more  definite. 

603.  Camera  luclda. — The  camera  liicida  is  a  small  instrument  depend- 
ing on  internal  reflection,  and  serves  for  taking  an  outline  of  any  object.  It 
was  invented  by  Wollaston  in  1804.  It  consists  of  a  small  four-sided  glass 
prism,  of  which  fig.  567  gives  a  section  perpendicular  to  the  edges.  A  is  a 
right  angle,  and  C  an  angle  of  135°  ;  the  other  angles,  15  and  D,  are  67.}°. 
The  prism  rests  on  a  stand,  on  which  it  can  be  raised  or  lowered,  and  turned 
more  or  less  about  an  axis  parallel  to  the  prismatic  edges.  When  the  face 
AB  is  turned  towards  the  object,  the  rays  from  the  object  fall  nearly  per- 
pendicular on  this  face,  pass  into  the  prism  without  any  appreciable  refrac- 
tion, and  are  totally  reflected  from  BC  ;  for  as  the  line  ab  is  perpendicular  ta 
BC,  and  «L  to  A15,  the  angle  anV,  will  equal  the  angle  B  :  that  is,  it  will 
contain  671°,  and  this  being  greater  than  the  critical  angle  of  glass  (540), 
the  ray  L«  will  undergo  total  reflection.  The  rays  are  again  totally  reflected 
from  (?,  and  emerge  near  the  summit,  D,  in  a  direction  almost  perpendicular 
to  the  face  DA,  so  that  the  eye  which  receives  the  rays  sees  at  L'  an  image 
of  the  object  L.  If  the  outlines  of  the  image  are  traced  with  a  pencil,  a 
very  correct  design  is  obtained  ;  but  unfortunately  there  is  a  great  diffi- 
culty in  seeing  both  the  image  and  the  point  of  the  pencil,  for  the  rays 
from  the  object  give  an  image  which  is  farther  from  the  eye  than  the  pencil. 
This  is  corrected  by  placing  between  the  eye  and  prism  a  lens,  I,  which 
gives  to  the  rays  from  the  pencil  and  those  from  the  object  the  same 
divergence.  In  this  case,  however,  it  is  necessary  to  place  the  eye  very 
near  the  edge  of  the  prism,  so  that  the  aperture  of  the  pupil  is  divided 
into  two  parts,  one  of  which  sees  the  image  and  the  other  the  pencil. 

Amici's  camera  lucida,  represented  in  fig.  567,  is  preferable  to  that  of 
Wollaston,  inasmuch  as  it  allows  the  eye  to  change  its  position  to  a  con- 
siderable extent  without  ceasing  to  sec  the  image  and  the  pencil  at  the 
same  time.  It  con- 
sists of  a  rectangular 
glass  prism  ABC, 
having  one  of  its 
perpendicular  faces 
turned  towards  the 
object  to  be  depicted, 
while  the  other  is  at 
right  angles  to  an  in- 
clined plate  of  glass, 
7nn.  The  rays  LI, 
proceeding  from  the  ^'«-  5^^-  tis-  568. 

object,  and  entering  the  prism,  are  totally  reflected  from  its  base  at  D,  and 
emerge  in  the  direction  KH.  They  are  then  partially  reflected  from  the 
glass  plate  inn  at  H,  and  form  a  vertical  image  of  the  object  L,  which  is  seen 
by  the  eye  in  the  direction  OL'.  The  eye  at  the  same  time  sees  through 
the  glass  the  point  of  the  pencil  applied  to  the  paper,  and  thus  the  outline 
of  the  picture  may  be  traced  with  great  exactness. 

604.  Maeric  lantern. -This  is  an  apparatus  by  which  a  magnified  image 
of  small  objects  may  be  projected  on  a  white  screen  in  a  dark  room.    A  typical 

P  P 


578 


On  Light. 


[604- 


form  is  the  sciopiicon,  fig.  569.  The  box  C,  the  side  of  which  is  shown  re- 
moved, is  constructed  of  sheet  iron  ;  e  is  the  flame  of  a  lamp  V,  with  two 
long  flat  wicks,  fed  by  petroleum  from  the  reservoir  B.  The  box  is  airtight, 
and  the  chimney  F  producing  a  good  draught,  the  air  is  compelled  to  pass 
through  the  wicks,  by  which  smoke  and  smell  are  avoided,  and  a  flame  of 
high  illuminating  power  is  produced. 

The  ends  of  the  box  are  closed  by  glass  plates  z  and  i^.  G  is  a  hinged 
door,  and  on  its  inside  is  a  concave  mirror  ;  o  and  0^  are  two  plano-convex 
lenses  ;  p  a  spring  clamp,  in  which  is  placed  the  transparent  picture.  The 
sliding  piece  supports  the  lens  tube,  in  which  are  two  achromatic  lenses 
a  and  b,  the  fine  adjustment  of  which  is  effected  by  the  screw  S. 

The  rays  from  the  flame  e,  reinforced  by  the  reflection  from  G,  falling 
upon  the  lenses  0,  0^,  are  made  parallel,  or,  at  all  events,  very  slightly  diver- 
gent ;  these  lenses  are  accordingly  called  the  co?ide?isitig  lenses.     Passing 

_^_  through     the     object 

^^^^^^  which  is  depicted  on 

'     ,,       '       ^     the  slide  placed  in  /, 
they  are  concentrated 
to  an  image  which  is 
received  on  a  screen. 
The     image     is     in- 
verted, and  hence,  if 
objects  are  to  be  seen 
in  their  erect  position, 
they  must  be  drawn 
inverted.       But  ordi- 
nary    drawings     are 
easily     adjusted     by 
fixing   an  equilateral 
rectangular  prism,  P  (fig.  570),  in  front  of 
the  lens  tube,  so  that  the  hypotenuse  sur- 
face   is   horizontal.      The    parallel    rays 
falling  on  the  prism  are  inverted  in  con- 
sequence of  refraction  at  the  sides  and 
total  reflection  from  the  hypotenuse  sur- 
face, so  that  an  upright  position  is  ob- 
tained  instead   of  a   reverse   one.     The 
dotted   lines   abcde  and  fg/iik  gi\e   the 
path  of  two  rays. 

The  apparatus  can  be  used  for  projecting  on  a  screen  not  only  flat 
images,  but  also  simple  physical  experiments,  such  as  the  expansion  of  a 
liquid  in  a  thermometer,  the  divergence  of  the  gold  leaves  of  an  electroscope, 
and  so  forth. 

Dissolving  7'ic7i>s  are  obtained  by  arranging  two  magic  lanterns,  which 
are  quite  alike,  with  different  pictures,  in  such  a  manner  that  both  pictures 
are  produced  on  exactly  the  same  part  of  a  screen.  The  object-glasses  of 
both  lanterns  arc  closccl  by  shades,  which  are  so  arranged  that  according  as 
one  is  raised  the  other  is  lowered,  and  7'itc  7'crsit  In  this  way  one  picture 
is  gradually  seen  to  change  into  the  other. 


Fig.  570. 


-605] 


Solar  Microscope. 


579 


The  magnifying  power  of  the  magic  lantern  is  obtained  by  dividing  the 
•distance  of  the  lens  from  the  image  by  its  distance  from  the  object.  If  the 
image  is  loo  or  i,ooo  times  farther  from  the  lens  than  the  object,  the  image 
will  be  loo  or  i,ooo  times  as  large.  Hence  a  lens  with  a  very  short  focus 
can  produce  a  very  large  image,  provided  the  screen  is  sufficiently  large. 

605.  Solar  microscope. — The  solar  microscope  is  in  reality  a  magic 
lantern  illuminated  by  the  sun's  rays  ;  it  serves  to  produce  highly  magnified 
images  of  very  small  objects.  It  is  worked  in  a  dark  room  :  fig.  571  repre- 
sents it  fitted  in  the  shutter  of  a  room,  and  fig.  572  gives  the  internal  details. 

The  sun's  rays  fall  on  a  plane  mirror,  M,  placed  outside  the  room,  and 
arc  reflected  towards  a  condensing  lens,  /,  and  thence  to  a  second  lens,  o 


rn 


Fig.  571. 

(fig.  572),  by  which  they  are  concentrated  at  its  focus.  The  object  to  be 
magnified  is  at  this  point ;  it  is  placed  between  two  glass  plates,  which,  by 
means  of  a  spring,  n,  are  kept  in  a  firm  position  between  two  metal  plates, 
in.  The  object  thus  strongly  illuminated  is  very  near  the  focus  of  a  system 
of  three  condensing  lenses,  a-,  which  forms  upon  a  screen  at  a  suitable  distance 
an  inverted  and  greatly  magnified  image,  ab.  The  distance  of  the  lenses  o 
and  X  from  the  object  is  regulated  by  means  of  screws,  C  and  D. 

As  the  direction  of  the  sun's  light  is  continually  varying,  the  position  of 
the  mirror  outside  the  shutter  must  also  be  changed,  so  that  the  reflection  is 
always  in  the  direction  of  the  axis  of  the  microscope.  The  most  exact 
apparatus  for  this  purpose  is  the  heliostat  (534)  ;  but  as  this  instrument  is 
very  expensive,  the  object  is  usually  attained  by  inclining  the  mirror  to  a 
greater  or  less  extent  by  means  of  an  endless  screw  B,  and  at  the  same  time 
turning  the  mirror  itself  round  the  lens  /  by  a  knob  A,  which  moves  in  a 
fixed  slide. 

The  solar  microscope  labours  under  the  objection  of  concentrating  great 
heat  on  the  object,  which  soon  alters  it.  This  is  partially  obviated  by 
interposing  a  layer  of  a  saturated  solution  of  alum,  which,  being''  a  power- 
fully athe'rmanous  substance  (434),  cuts  off  a  considerable  portion  of  the 
heat. 


58o 


Oyi  Light, 


[605- 


The  magnifying  power  of  the  solar  microscope  may  be  deduced  experi- 
mentally by  substituting  for  the  object  a  glass  plate  marked  with  lines  at  a 
distance  of  }^  or  ji^  of  a  millimetre.  Knowing  the  distance  of  these  lines  on 
the  image,  the  magnifying  power  may  be  calculated.  The  same  method  is 
used  with  the  electric  light.  According  to  the  magnifying  power  which  it  is 
desired  to  obtain,  the  objective  x  is  formed  of  one,  two,  or  three  lenses, 
which  are  all  achromatic. 

The  solar  microscope  furnishes  the  means  of  exhibiting'to  a  large  audience 


Fig.  572 


many  curious  phenomena,  such,  for  instance,  as  the  circulation  of  blood  in 
the  smaller  animals,  the  crystallisation  of  salts,  the  occurrence  of  minute 
organisms  in  water,  vinegar,  (S:c.  &c. 

606.  Photo-electric  microscope. — This  is  in  effect  a  solar  microscope 
which  is  illuminated  by  the  electric  light  instead  of  by  the  sun's  rays.  The 
electric  light,  by  its  intensity,  its  steadiness,  and  the  readiness  with  which 
it  can  be  produced  at  any  time  of  the  day,  is  far  preferable  to  the  solar  light. 
The  microscope  alone  will  be  described  here  :  the  production  of  the  electric 
light  will  be  considered  under  the  head  of  Galvanism. 

Fig.  573  represents  the  arrangement  devised  by  Duboscq.  A  solar 
microscope,  ABD,  identical  with  that  already  described,  is  fi.xed  on  the 
outside  of  a  brass  box.  In  the  interior  are  two  charcoal  points  which  do 
not  quite  touch,  the  space  between  them  being  exactly  on  the  axis  of  the 
lenses.  The  electricity  of  one  end  of  a  powerful  battery  reaches  the  charcoal 
a  by  means  of  a  copper  wire  K  ;  while  the  electricity  from  the  opposite  end 
of  the  battery  reaches  c  by  a  second  copper  wire  H. 

During  the  passage  of  the  electricity  a  luminous  arc  is  formed  between 
the  two  ends  of  the  carbons,  which  gives  a  most  brilliant  light,  and  power- 
fully illuminates  the  microscope.  This  is  effected  by  placing  at  D  in  the 
inside  of  the  tube  a  condensing  lens,  whose  principal  focus  corresponds  to 
the  space  between  the  two  charcoals.  In  this  manner  the  luminous  rays 
which  enter  the  tubes  U  and  B  are  parallel  to  their  axis,  and  the  same 
effects  are  produced  as  with  the  ordinary  solar  microscope  ;  a  magnified 
image  of  the  object  placed  between  two  plates  of  glass  is  produced  on  the 
screen. 

In  continuing  the  experiment  the  two  carbons  become  consunTed,  and  to 
an  unequal  extent,  a  more  quickly  than  c.     Hence,  their  distance  increasing, 


607J 


IJcJithojisc  Lenses. 


581 


the  light  becomes  weaker,  and  is  ultimately  extinguished.  In  speaking 
afterwards  of  the  electric  light,  the  working  of  the  apparatus  P,  which  keeps 
these  charcoals  at  a  constant  distance,  and  thus  ensures  a  constant  light, 
will  be  explained. 

The  part  of  the  apparatus  MN  may  be  considered  as  a  .universal  photo- 
genic apparatus.  The  microscope  can  be  replaced  by  the  headpieces  of  the 
phantasmagoria,  the  polyorama,  the  megascope,  by  polarising  apparatus,  &c., 
and  in  this  manner  is  admirably  adapted  for  exhibiting  optical  phenomena 
to  a  large  auditory  Instead  of  the  electric  light,  we  may  use  with  this 
apparatus  the  oxyhydrogett  or  Driimmond's  light,  which  is  obtained  by  heat- 


Fig.  573. 
ing  a  cylinder  of  lime  in  the  flame  produced  by  the  combustion  of  a  mixture 
of  hydrogen  or  of  coal  gas  with  oxygen  gas. 

607.  Iiighthouse  lenses. — Lenses  of  large  dimensions  are  very  difficult 
of  construction  ;  they  further  produce  a  considerable  spherical  aberration, 
and  their  thickness  causes  the  loss  of  much  light.  In  order  to  avoid  these 
inconveniences,  echelo7i  lenses  have  been  constructed.  They  consist  of  a 
plano-convex  lens,  C  (figs.  574  and  575),  surrounded  by  a  series  of  annular 
and  concentric  segments,  A,  B,  each  of  which  has  a  plane  face  on  the  same 
side  as  the  plane  face  of  the  central  lens,  while  the  faces  on  the  other  side 
have  such  a  curvature  that  the  foci  of  the  different  segments  coincide  in  the 


582 


On  Light. 


[607- 


same  point.  These  rings  form,  together  with  the  central  lens,  a  single  lens, 
a  section  of  which  is  represented  in  fig.  575.  The  drawing  was  made  from 
a  lens  of  about  2  feet  in  diameter,  the  segments  of  which  are  formed  of  a 
single  piece  of  glass  ;  but,  with  larger  lenses,  each  segment  is  likewise  formed 
of  several  pieces. 

Behind  the  lens  there  is  a  support  fixed  b)-  three  rods,  on  which  a  body 
can  be  placed  and  submitted  to  the  sun's  rays.    As  the  centre  of  the  support 

coincides  with  the 
focus  of  the  lens, 
the  substances 
placed  there  are 
melted  and  vola- 
tilised by  the  high 
temperature  pro- 
duced. Gold,  pla- 
tinum, and  quartz 
are  melted.  The 
experiment  proves 
that  heat  is  re- 
fracted in  the  same 
way  as  light ;  for 
the  position  of  the 
calorific  focus  is 
identical  with  that 
of  the  luminous 
focus. 

Formerly  para- 
bolic mirrors  were 
used  in  sending 
the  light  of  bea- 
cons and  light- 
houses to  great 
distances,  but  they 
have  been  sup- 
planted by  the  use 
of  lenses  of  the 
above  construc- 
tion.        In     most 

cases  oil  is  used  in  a  lamp  of  peculiar  construction,  which  gives  as  much 
light  as  20  moderators.  The  light  is  placed  in  the  principal  focus  of  the 
lens,  so  that  the  emergent  rays  form  a  parallel  beam  (fig.  503),  which  loses 
intensity  only  by  absorption  in  the  atmosphere,  and  can  be  seen  at  a  dis- 
tance of  above  40  miles.  In  order  that  all  points  of  the  horizon  may  be 
successively  illuminated,  the  lens  is  continually  moved  round  the  lamp  by 
a  clockwork  motion,  the  rate  of  which  varies  with  different  lighthouses. 
Hence,  in  different  parts  the  light  alternately  appears  and  disappears  after 
equal  intervals  of  time.  These  alternations  serve  to  distinguish  lighthouses 
from  an  accidental  fire  or  a  star.  By  means,  too,  of  the  number  of  times  the 
light  disappears  in  a  given  time,  and  by  the  colour  of  the  light,  sailors  are 


-608J  PJiotography.  583 

enabled  to  distinguish  the  lighthouses  from  one  another,  and  hence  to  know 
their  position. 

Of  late  years  the  use  of  the  electric  light  has  been  substituted  for  that 
of  oil  lamps.  A  description  of  the  apparatus  will  be  given  in  a  subsequent 
chapter. 

PHOTOGRAPHY. 

60S.  Pbotograptay  is  the  art  of  fixing  the  images  of  the  camera  obscura 
on  substances  sensitive  to  light.  The  various  photographic  processes  may 
be  classed  under  three  heads  :  photography  on  metal,  photography  on 
paper,  and  photography  on  glass. 

Wedgwood  was  the  first  to  suggest  the  use  of  chloride  of  silver  in  fixing 
the  image,  and  Davy,  by  means  of  the  solar  microscope,  obtained  images  of 
small  objects  on  paper  impregnated  with  chloride  of  silver  ;  but  no  method 
was  known  of  preserving  the  images  thus  obtained,  by  preventing  the  further 
action  of  light.  Niepce,  in  18 14,  obtained  permanent  images  of  the  camera 
by  coating  glass  plates  with  a  layer  of  a  varnish  composed  of  bitumen  dis- 
solved in  oil  of  lavender.  This  process  was  tedious  and  inefficient,  and  it 
was  not  until  1839  that  the  problem  was  solved.  In  that  year  Daguerre 
described  a  method  of  fixing  the  images  of  the  camera  which,  with  the  sub- 
sequent improvements  of  Talbot  and  Archer,  has  rendered  the  art  of  photo- 
graphy one  of  the  most  marvellous  discoveries  ever  made,  whether  as  to  the 
beauty  and  perfection  of  the  results,  or  as  to  the  celerity  with  which  they  are 
produced. 

In  Daguerre's  process,  the  Dagiierrotypc,  the  picture  is  produced  on  a 
plate  of  copper  coated  with  silver.  This  is  first  very  carefully  polished — an 
operation  on  which  much  of  the  success  of  the  subsequent  processes  depends. 
It  is  then  rendered  sejisitive  by  exposing  it  to  the  action  of  iodine  vapour, 
which  forms  a  thin  layer  of  iodide  of  silver  on  the  surface.  The  plate  is  now 
fit  to  be  exposed  in  the  camera  ;  it  is  sensitive  enough  for  views  which  re- 
quire an  exposure  of  ten  minutes  in  the  camera,  but  when  greater  rapidity  is 
required,  as  for  portraits,  &c.,  it  is  further  exposed  to  the  action  of  an  accele- 
rator^ such  as  bromine  or  hypobromite  of  calcium.  All  the  operations  must 
be  performed  in  a  room  lighted  by  a  candle,  or  by  the  daylight  admitted 
through  yellow  glass,  which  cuts  off  all  chemical  rays.  The  plate  is  preserved 
from  the  action  of  light  by  placing  it  in  a  small  wooden  case  provided  with 
a  slide  on  the  sensitive  side. 

The  third  operation  consists  in  exposing  the  sensitive  plate  to  the  action 
of  light,  placing  it  in  that  position  in  the  camera  where  the  image  is  pro- 
duced with  greatest  delicacy.  For  photographic  purposes  a  camera  obscura 
of  peculiar  construction  is  used.  The  brass  tube  A  (figs.  576  and  577)  con- 
tains an  achromatic  condensing  lens,  which  can  be  moved  by  means  of  a  rack- 
work  motion,  to  which  is  fitted  a  milled  head  D.  At  the  opposite  end  of  the 
box  is  a  ground-glass  plate,  E,  which  slides  in  a  groove,  B,  in  which  the  case 
containing  the  plate  also  fits.  The  camera  being  placed  in  a  proper  position 
before  the  object,  the  sliding  part  of  the  box  is  adjusted  until  the  image  is 
produced  on  the  glass  with  the  utmost  sharpness  ;  this  is  the  case  when  the 
glass  slide  is  exactly  in  the  focus.  The  final  adjustment  is  made  by  means 
of  the  milled  head  D. 


584 


On  Light. 


[608- 


The  glass   slide   is   then  replaced  by  the  case  containing  the  sensitive 
plate ;  the  slide  which  protects  it  is  raised,  and  the  plate  exposed  for  a  time, 

J> 


the  duration  of  which  varies 
in  dififerent  cases,  and  can 
only  be  hit  exactly  by  great 
practice.  The  plate  is  then 
removed  to  a  dark  room. 
No  change  is  perceptible  to 
the  eye,  but  those  parts  on 
which  the  light  has  acted 
have  acquired  the  property 
of  condensing  mercuiy  ;  the 
plate  is  next  placed  in  a  box 
and  exposed  to  the  action  of 
mercurial  vapour  at  60  or  70 
degrees. 

The  mercury  is  deposited 
on  the  parts  affected,  in  the 
form  of  globules  imperceptible  to  the  naked  eye.  The  shadows,  or  those 
parts  on  which  the  light  has  not  acted,  remain  covered  with  the  layer  of 
iodide  of  silver.  This  is  removed  by  treatment  with  hyposulphite  of  sodium, 
which  dissolves  iodide  of  silver  without  affecting  the  rest  of  the  plate.  The 
plate  is  next  immersed  in  a  solution  of  chloride  of  gold  in  hyposulphite  of 
sodium,  which  dissolves  the   silver,  while   some   gold  combines   with  the 


Fig.  576. 


mercury  and  silver  of  the  parts  attacked,  and  greatly  increases  the  intensity 
of  the  lustre. 

Hence  the  light  parts  of  the  image  arc  those  on  which  the  mcrcur>'  has 
been  deposited,  and  the  shaded  those  on  which  ihc  metal  has  retained  its 
reflecting  lustre. 

Fig.  577  represents  a  section  of  the  camera  and  the  object-glass.  At  first 
it  consisted  of  a  double  convex  lens,  but  now  double  achromatic  lenses,  LL', 
are  used  as  object-glasses.  They  act  more  quickly  than  objectives  with  a 
.single  lens,  have  a  shorter  focus,  and  can  be  more  easily  focusscd  liy  moving 
the  lens  L'  by  means  of  the  rack  and  pinion  D. 

609.  PliotoffrapliH  on  paper. —  In  Daguerrc's  process,  which  has  just 
liecn  described,  the  images  are  jiroduced  •directly  on  metal  plates.     With 


-609]  Photograplis  on  Paper.  585 

paper  and  glass,  photographs  of  two  kinds  may  be  obtained  :  those  in  which 
an  image  is  obtained  with  reversed  tints,  so  that  the  hghtest  parts  have  be- 
come the  darkest  on  paper,  and  vice  versa  ;  and  those  in  which  the  hghts 
and  shades  are  in  their  natural  position.  The  former  are  called  ticgative 
and  the  \dX\.&x  positive  pictures. 

A  negative  may  be  taken  either  on  glass  or  on  paper  ;  it  serves  to  produce 
a  positive  picture. 

Negatives  on  glass. — A  glass  plate  of  the  proper  size  is  carefully  cleaned 
and  coated  with  a  uniformly  thick  layer  of  collodion  impregnated  with  iodide 
of  potassium.  The  plate  is  then  immersed  for  about  a  minute  in  a  bath  of 
nitrate  of  silver  containing  30  grains  of  the  salt  in  an  ounce  of  water.  This 
operation  must  be  performed  in  a  dark  room.  The  plate  is  then  removed, 
allowed  to  drain,  and,  when  somewhat  dry,  placed  in  a  closed  flame,  and 
afterwards  exposed  in  the  camera,  for  a  shorter  time  than  in  the  case  of  a 
Daguerrotype.  On  removing  the  plate  to  a  dark  room  no  change  is  visible ; 
but  on  pouring  over  it  a  solution  called  the  developer.,  an  image  gradually 
appears.  The  principal  substances  used  for  developing  are  protosulphate 
of  iron  and  pyrogallic  acid.  The  action  of  light  on  iodide  of  silver  appears 
to  produce  some  molecular  change,  or  else  some  actual  chemical  decom- 
position, in  virtue  of  which  the  developers  have  the  property  of  reducing 
to  the  metallic  state  those  parts  of  the  iodide  of  silver  which  have  been  most 
acted  upon  by  the  light.  When  the  picture  is  sufficiently  brought  out,  water 
is  poured  over  the  plate,  in  order  to  prevent  the  further  action  of  the 
developer.  The  parts  on  which  light  has  not  acted  are  still  covered  with 
iodide  of  silver,  which  would  be  aff'ected  if  the  plate  were  now  exposed  to 
the  light.  It  is,  accordingly,  washed  with  solution  of  hyposulphite  of  sodium, 
which  dissolves  the  iodide  of  silver  and  leaves  the  image  unaltered.  The 
picture  is  then  coated  with  a  thin  layer  of  spirit  varnish,  to  protect  it  from 
mechanical  injury. 

When  once  the  negative  is  obtained,  it  may  be  used  for  printing  an  in- 
definite number  of  positive  pictures.  For  this  purpose  paper  is  coated  with 
a  layer  of  egg-albumen  containing  a  certain  proportion  of  chloride  of 
ammonium,  and  then  left  to  dry.  The  paper  is  then  made  sensitive  by  float- 
ing it  on  a  bath  containing  30  to  40  grains  to  the  ounce  of  nitrate  of  silver. 
Chloride  of  silver  is  formed  by  the  double  decomposition  of  the  two  salts, 
and  this  again  acting  on  the  albumen  forms  an  obscure  compound  containing 
chloride  and  albuminate  of  silver.  The  negative  is  placed  on  a  sheet  of 
this  paper  in  a  copying  frame,  and  exposed  to  the  action  of  light  for  a 
certain  time.  The  chloride  of  silver  becomes  acted  upon— the  light  parts  of 
the  negative  being  most  affected,  and  the  dark  parts  least  so.  A  copy  is 
thus  obtained,  on  which  the  lights  of  the  negative  are  replaced  by  shades, 
and  inversely.  The  picture  is  then  immersed  in  a  bath  of  chloride  of  gold, 
which  gives  it  tone,  and  preserves  it  from  fading.  In  order  to  fix  the  picture 
it  is  now  immersed  in  a  solution  of  hyposulphite  of  sodium,  which  dissolves 
the  unaltered  chloride  of  silver.  The  print  must  now  be  washed  in  a  stream 
of  water  for  several  hours  in  order  to  get  rid  of  all  traces  of  the  hyposulphite, 
^vhich  if  left  in  would  ruin  the  picture. 

Of  late  years  permanent  and  very  beautiful  prints  have  been  obtained 
from  negatives  by  making  use  of  the  chemical  change  produced  by  light  on 


586  On  Light.  [609- 

a  mixture  of  bichromate  of  potass  and  gelatine.  On  this  reaction  are  based 
the  various  carbon  processes,  and  those  for  mechanical  printing.  Very 
beautiful  prints,  with  an  effect  resembling  that  of  steel  engravings,  are  pro- 
duced by  what  is  known  as  the.  platinum  process.  This  consists  in  exposing 
paper  charged  with  ferric  oxalate  to  light  and  then  developing  the  prmts  thus 
produced  by  platinum  salt ;  the  ferric  salt  by  exposure  to  light  is  reduced  to 
a  ferrous  oxalate,  which  in  turn  reduces  the  platinum  salt  to  black  metallic 
platinum. 

6 ID.  iregatlves  on  g-elatine  emulsions.  Dry  plates. — In  1 87 1  Dr. 
Maddox  demonstrated  that  the  sensitiveness  of  the  salts  of  silver  is  enor- 
mously increased  by  employing  gelatine  instead  of  collodion  as  the  basis  ot 
an  emulsion,  and  also  that  such  gelatine  emulsions  could  be  dried  and  kept 
for  an  almost  indefinite  time  without  losing  its  value.  Bennet  showed  in 
1878  that  the  sensitiveness  of  such  emulsions  is  still  further  increased  by 
heating  the  emulsion  to  32°  C.  for  several  days. 

Glass  plates  coated  with  gelatine  emulsion  containing  bromide  or  other 
haloid  salts  of  silver  are  made  commercially  in  vast  quantities  and  sold  under 
the  name  of  diy  plates. 

In  1 88 1  Dr.  Eder  showed  that  a  bromiodide  emulsion  could  be  made 
sensitive  to  a  far  greater  range  of  the  spectrum  by  adding  a  minute  propor- 
tion of  eosin,  or  other  aniline  dye.  These  ortJiochromatic  plates,  as  they  are 
called,  are  not  merely  sensitive  to  the  ultra-violet  rays,  but  are  highly  sensi- 
tive to  the  D  line  of  the  spectrum,  and  thus  yellow  objects,  instead  of 
appearing  black,  or  dark-blue  objects  appearing  white,  as  in  photographic 
prints  from  ordinary  plates,  appear  in  their  true  visible  relation  of  brightness 
to  one  another. 

611.  Positives  on  griass. — Very  beautiful  positives  are  obtained  by  pre- 
paring the  plates  by  the  '  wet  process  '  (§  609) ;  the  exposure  in  the  camera, 
however,  is  not  nearly  so  long  as  for  the  negatives.  The  picture  is  then 
developed  by  pouring  over  it  a  solution  of  protosulphate  of  iron,  which 
produces  a  negative  image  ;  and  by  afterwards  pouring  a  solution  of  cyanide 
of  potassium  over  the  plate,  this  negative  is  rapidly  converted  into  a 
positive.  It  IS  then  washed  and  dried,  and  a  coating  of  varnish  poured 
over  the  picture.  Positives  may  also  be  obtained  by  placing  a  gelatine  '  dry 
plate '  in  direct  contact  with  a  negative  in  a  printing  frame,  and  exposing  it 
to  an  artificial  light  for  a  few  seconds ;  the  time  of  exposure  depending  upon 
the  density  of  the  negative  and  the  intensity  of  illumination.  The  exposed 
plate  is  then  developed  in  the  ordinary  way,  except  that  the  process  must  be 
prolonged  in  order  to  get  greater  density  than  is  rcciuired  for  ordinaiy  print- 
ing purposes. 


-612] 


Structure  of  the  Human  Eye. 


587 


CHAPTER   VI. 

THE   EYE  CONSIDERED   AS   AN   OPTICAL   INSTRUMENT. 

612.  Structure  of  tbe  human  eye. — The  eye  is  placed  in  a  bony  cavity 
called  the  orbit ;  it  is  maintained  in  its  position  by  the  muscles  which  serve 
to  move  it,  by  the  optic  nerve,  the  conjunctiva,  and  the  eyelids. 

Fig.  578  represents  a  transverse  section  of  the  eye  from  back  to  front. 
The  general  shape  is  that  of  a  sphere,  or  more  strictly  speaking  it  consists 
of  the  segments  of  two  spheres  of  unequal  size,  of  which  the  anterior  is  much 
the  smaller  and  constitutes  the  cornea,  while  the  posterior,  forming  the  chief 
envelope  of  the  eyeball,  receives 
the  name  of  the  sclerotica.  The 
eye  is  composed  of  the  following 
parts :  the  cornea,  the  sclerotic, 
the  iris,  the  pupil,  the  aqueous 
htwtour,  the  crystalline,  the  vi- 
treous body,  the  hyaloid  mem- 
brane, the  choroid,  the  reti?ta, 
and  the  optic  nerve. 

Cornea. — The  cornea,  a,  is  a 
transparent  circular  tunic  form- 
ing the  anterior  segment  of  the 
eye.  It  is  nothing  more  than 
a  continuation  of  the  sclerotic 
forwards,  and  is  formed  by  the 
fibres  of  the  latter  becoming 
more  systematically  arranged  and  rendered  quite  transparent.  Its  front 
surface  is  lined  throughout  by  the  conjttnctiva.  This  is  a  soft  membrane 
which  not  only  covers  the  cornea  but,  passing  in  a  loose  fold  to  the  circum- 
ference of  the  orbit,  is  reflected  over  the  under  surface  of  the  lids,  thus  com- 
pletely closing-in  the  cavity  of  the  eyeball,  and  yet  being  so  loose  that  the 
eye  can  roll  freely  in  its  socket.  The  two  surfaces  of  the  cornea  are  so 
nearly  parallel  that  optically  they  may  be  considered  as  a  single  surface. 

Sclerotic. — This  (fig.  578,  /)  is  a  strong  tough  tunic  enveloping  the  whole 
of  the  eye  behind  the  cornea.  At  its  back  part  it  is  reflected  over  the  optic 
nerve,  forming  a  sheath  for  it  as  far  as  the  apex  of  the  orbit.  The  chief  func- 
tions of  the  sclerotic  are  to  maintain  the  shape  of  the  organ,  and  to  protect 
it  from  injur}'  and  pressure. 

Iris. — The  iris,  d,  is  an  annular,  opaque  diaphragm,  placed  between  the 
cornea  and  the  crystalline  lens.  It  constitutes  the  coloured  part  of  the  eye, 
and  is  perforated  by  an  aperture  called  the  pupil,  which  in  man  is  circular 


588  On  Light.  [612- 

In  some  animals,  especially  those  belonging  to  the  genus  Fclis,  it  is  narrow 
and  elongated  in  a  vertical  direction  ;  in  the  ruminants  it  is  elongated  in  a 
transverse  direction.  It  contains  a  large  number  of  muscular  fibres,  which 
are  disposed  partly  as  a  narrow  ring  close  to  the  pupil,  called  the  sphincter 
zridis,  and  partly  in  the  form  of  fibres  radiating  from  the  circumference  to 
the  sphincter,  called  the  dilator  iridis.  Thus,  as  the  one  or  the  other  set 
of  fibres  are  stimulated,  the  pupil  is  able  to  contract  or  dilate.  The  diameter 
of  the  pupil  is  constantly  varying,  the  variation  ranging  from  |  to  ^V  of  an 
inch,  but  these  limits  may  be  -exceeded.  In  total  darkness  the  pupil  is  en- 
larged to  its  utmost  limits,  but  it  contracts  instantly  in  a  bright  light.  The 
movements  of  the  iris  are  involuntary. 

It  appears  from  this  description  that  the  iris  is  a  screen  with  a  variable 
aperture,  whose  function  is  to  regulate  the  quantity  of  light  which  penetrates 
into  the  eye  ;  for  the  size  of  the  pupil  diminishes  as  the  intensity  of  light 
increases.  The  iris  serves  also  to  correct  the  spherical  aberration,  as  it 
prevents  the  marginal  rays  from  passing  through  the  edges  of  the  crystalline 
lens.  It  thus  plays  the  same  part  with  reference  to  the  eye  that  a  stop  does 
in  optical  instruments  (558). 

Aqueous  huinoiir. — Between  the  posterior  part  of  the  cornea  and  the 
front  of  the  crystalline  there  is  a  transparent  liquid  called  the  aqueous 
humour.  The  space,  ^,  occupied  by  this  humour  is  called  the  anterior 
in  contradistinction  to  the  posterior  chamber.,  a  space  which  the  older  ana- 
tomists imagined  to  exist  between  the  iris  and  the  capsule  of  the  lens.  But 
inasmuch  as  later  observations  have  shown  that  the  iris  lies  in  contact  with 
the  lens  in  its  capsule  throughout  the  greater  part  of  its  length  this  space 
has  no  practical  existence. 

Crystalline  lens. — This  is  a  double  convex  transparent  body  placed  im- 
mediately behind  the  iris,  which  it  supports,  though  not  attached  to  it.  The 
lens  is  enclosed  in  a  transparent  membrane,  called  \is  capsule.  The  structure 
of  the  lens  can  be  best  seen  by  boiling  it  in  water,  which  converts  it  into  a 
hard  opaque  mass.  A  succession  of  concentric  lamini^,  like  the  coats  of  an 
onion,  may  be  stripped  off,  leaving  a  hard  central  spherical  nucleus  of  the 
same  material.  These  lamina:  increase  in  density  and  refracting  power  from 
the  circumference  to  the  centre.  They  consist  entirely  of  long  ribbon-shaped 
fibres,  which  overlap  one  another  concentrically,  and  are  united  together 
by  a  kind  of  cement.  Optically,  the  lens  may  be  considered  as  a  system 
made  up  of  a  biconvex  lens  of  high  refracting  power  and  short  focal  length. 
Opticians  have  constructed  achromatic  lenses  on  the  same  Imes  for  photo- 
graphic purposes  by  cementing  two  meniscus  lenses  to  an  intermediate  flint 
lens. 

To  the  anterior  surface  of  the  capsule,  near  its  margin,  is  fixed  a  firm 
transparent  membrane,  and  known  as  the  suspensory  ligament  or  zonule  oj 
Zinn,  which  is  attached  behind  to  the  front  of  the  hyaloid  membrane,  and 
indirectly  to  the  ciliary  muscle.  This  ligament  exerts  attraction,  all  round, 
on  the  front  surface  of  the  lens,  and  renders  it  loss  convex  than  it  would 
otherwise  be,  and  its  relaxation  plays  an  important  ])art  in  the  adaptation  of 
the  eye  for  sight  at  different  distances. 

Vitreous  body.  Hyaloid  membrane. — The  vitreous  body,  or  vitreous 
humour,  is  a  transparent  gelatinous  mass  resembling  the  white  of  an  ^g^^ 


-612]  Structure  of  the  Human  Eye.  5  89 

which  occupies  all  the  part  of  the  ball  of  the  eye,  h,  behind  the  lens.  The 
vitreous  humour  is  surrounded  by  the  hyaloid  membrane^  /,  which  lines  the 
posterior  face  of  the  crystalline  capsule,  and  also  the  inner  face  of  another 
membrane  called  the  retina. 

Retina.  Optic  7ten'e. — The  retina,  w,  is  the  name  given  to  a  layer  of 
specially  modified  cells  which  receives  the  impression  of  light.  It  is  really 
nothing  more  than  the  terminal  fibres  of  the  optic  nerve,  altered  in  such  a 
way  as  to  be  sensitive  to  the  waves  of  light.  Each  optic  nerve  which 
conveys  to  the  mind  the  impression  produced  by  light  arises  from  three 
centres  in  the  brain,  and  the  fibres,  after  being  collected  into  a  thick  cord, 
pass  forward  along  the  base  of  the  brain.  Here  each  cord  after  forming  a 
junction  with  its  fellow  of  the  opposite  side  again  separates,  and,  passing 
through  a  hole  at  the  back  of  each  socket,  reaches  and  enters  the  eyeball,  in- 
side which  it  expands  into  a  cup-shaped  network  of  nerves  called  the  retitta. 
The  nerve  fibres  themselves  are  not  sensitive  to  light,  but  are  only  stimu- 
lated by  it  indirectly  through  the  intervention  of  certain  specially  adapted  cells. 
The  fibres  of  the  optic  nerve,  when  they  spread  out  to  form  the  inner  layer  of 
the  retina,  after  running  a  shorter  or  longer  distance  turn  abruptly  outward, 
and  each  fibre  becomes  connected  with  a  larger  ganglion  cell,  which  again  is 
connected  by  other  processes  with  smaller  cells  ;  and  each  group  of  these 
finally  ends  in  either  a  peculiarly  shaped  cylinder  called  a  rod,  or  a  thicker 
flask-shaped  structure  called  a  cone.  All  are  ranged  perpendicular  to  the 
surface  of  the  retina,  closely  packed  together,  so  as  to  form  a  regular  mosaic 
layer  when  viewed  from  the  outside.  In  the  retina  is  a  remarkable  spot 
which  is  situated  in  the  axis  of  vision  a  little  to  the  outside  of  the  place 
where  the  optic  nerve  enters  the  eyeball.  From  its  colour  it  is  called  the 
macula  littea  or  yellow  spot.  The  retina  is  here  somewhat  thick,  but  in  the 
middle  of  the  yellow  spot  is  found  a  depression,  the  fovea  centralis,  where 
the  retina  is  reduced  to  those  elements  alone  which  are  absolutely  necessary 
for  exact  vision.  Thxs  fovea,  or  pit  of  the  retina,  is  of  great  importance  for 
vision,  since  it  is  the  spot  where  the  most  exact  discrimination  of  distance 
is  made.  Only  those  parts  of  the  retinal  image  which  fall  on  the  yellow 
spot  are  sharp,  all  the  rest  are  more  inaccurate  the  nearer  they  fall  to  the 
limits  of  the  retina.  The  field  of  view  of  the  eye  is  like  a  drawing,  the 
centre  of  which  is  done  with  great  accuracy  and  delicacy  while  the  sur- 
rounding part  is  only  roughly  sketched.  Where  the  optic  nerve  enters  there 
are  no  rods  or  cones  ;  this  part  of  the  retina,  therefore,  is  insensitive  to 
light,  and  is  called  the  pimctuni  ccccuni  or  bli7id  spot.  When  examined  in 
the  living  subject  by  means  of  the  ophthalmoscope  it  appears  as  a  slightly 
oval  pinkish  disc  crossed  by  numerous  blood-vessels. 

The  only  property  of  the  retina  and  optic  nerve  is  that  of  receiving  and 
transmitting  to  the  brain  the  impression  of  objects.  These  organs  have 
been  cut  and  pricked  without  causing  any  pain  to  the  animals  submitted  to 
these  experiments  ;  but  there  is  reason  to  believe  that  irritation  of  the  optic 
nerve  causes  the  sensation  of  a  flash  of  light. 

Choroid. — The  choroid,  k,  is  a  membrane  between  the  retina  and  the 
sclerotic.  It  is  highly  vascular,  and  supplies  the  nourishment  necessary  for 
the  chemical  and  physiological  processes  concerned  in  vision.  On  its  inner 
surface,  and  in  close  contact  with  the  ends  of  the  rods  and  cones,  is  a  layer 


590  On  Light.  [612- 

of  densely  black  pigment  cells,  which  secrete  a  peculiar  yellowish  purple 
pigment  called  the  visual  purple^  and  which  is  rapidly  bleached  by  light.  It 
is  evidently  connected  with  the  act  of  vision,  but  its  precise  use  is  uncertain. 

The  choroid  forms  a  series  of  convoluted  folds  in  front,  called  ciliary 
'Processes,  which  penetrate  between  the  iris  and  the  lens  capsule,  forming 
round  the  latter  a  disc  resembling  a  radiated  flower.  The  ciliary  pro- 
cesses secrete  the  colourless  fluid  necessary  for  the  nourishment  of  the 
transparent  parts  of  the  eye,  which,  being  transparent  for  visual  purposes, 
cannot  be  nourished  by  means  of  blood-vessels. 

613.  Refractive  indices  of  the  transparent  media  of  the  eye. — The 
refractive  indices  from  air  into  the  transparent  parts  of  the  eye  were  deter- 
mined by  Brewster,  and  have  since  been  carefully  examined  by  Von  Helm- 
holtz.  Their  results  are  contained  in  the  following  table,  compared  with 
water  as  a  standard  : — 


Brewster 

Helmholtz 

1-3358      . 

•       1-3358 

1-3366      . 

•     1-33(^5 

1-3394     • 

■     1-3365 

•     1-3365 

1-3767     . 

•     1-3930 

1-3990    . 

•     1-4541 

1-3839     . 

•     I -4371 

Water 

Aqueous  humour  .... 
Vitreous  humour  .... 
Cornea 

External  coating  of  the  lens 

Centre  of  the  lens       .... 

Mean  refraction  of  the  lens 

From  this  it  will  be  noticed  that  the  refractive  index  of  all  the  media  ex- 
cepting the  lens  is  the  same. 

614.  Curvatures    and   dimensions    of  various   parts    of  the  human 

eye.— According  to  the  latest  tables  of  Von  Helmholtz  (1888),  these  are  :— 

Radius  of  curvature  of  the  cornea 7-83 

„                 „                      anterior  surface  of  the  crj'^stalline       .         .  10-00 

„                 „                      posterior  surface       „           „       .         .         .  6-oo 

Distance  from  apex  of  the  cornea  to  the  anterior  surface  of  the  lens  .  3-60 

„                     „                      „                  posterior       „               „            .  7-20 

Thickness  of  the  crystalline  lens 3-60 

615.  Path  of  rays  In  the  eye. — From  what  has  been  said  as  to  the 
structure  of  the  eye,  it  may  be  compared  to  a  camera  obscura  (602),  of  which 
the  i)upil  is  the  aperture,  the  crystalline  is  the  condensing  lens,  and  the 


Fifi.  579- 

retina  is  the  screen  on  which  the  image  is  formed.  Hence,  the  eftect  is  the 
same  as  when  the  image  of  an  object  placed  in  front  of  a  double  convex  lens 
is  formed  at  its  conjugate  focus.  Let  AB  (fig.  579)  be  an  object  placed 
before  the  eye,  and  let  us  consider  the  rays  emitted  from  any  point  of  the 


-617 j  Optic  Axis,  Optic  Angle,    Visual  Angle.  591 

object  A.  Of  all  these  rays,  those  which  are  directed  towards  the  pupil  are 
the  only  ones  which  penetrate  the  eye,  and  are  operative  in  producing  vision. 
These  rays,  on  passing  into  the  aqueous  humour,  experience  a  first  refraction 
which  brings  them  near  the  secondary  axis  ha  drawn  through  the  optic 
centre  of  the  crystalline  ;  they  then  traverse  the  crj'stalline,  which  again 
refracts  them  like  a  double  convex  lens,  and,  having  experienced  a  final 
refraction  by  the  vitreous  humour,  they  meet  in  a  point  <z,  and  form  the 
image  of  the  point  A.  The  rays  issuing  from  the  point  B  form  in  like  manner 
an  image  of  it  at  the  point  ^,  so  that  a  very  small,  real,  and  inverted  image  is 
formed  exactly  on  the  retina,  provided  the  eye  is  in  its  normal  condition. 

616.  Inversion  of  images. — In  order  to  show  that  the  images  formed 
on  the  retina  arc  really  inverted,  the  eye  of  an  albino  or  any  animal  with 
pink  eyes  may  be  taken  ;  this  has  the  advantage  that,  as  the  choroid  is 
destitute  of  pigment,  light  can  traverse  it  without  loss.  This  is  then  deprived 
at  its  posterior  part  of  the  cellular  tissue  surrounding  it,  and  fixed  in  a  hole 
in  the  shutter  of  a  dark  room  ;  by  means  of  a  lens  it  may  be  seen  that  the 
inverted  images  of  external  objects  are  depicted  on  the  retina. 

The  inversion  of  images  in  the  eye  has  greatly  occupied  both  physicists 
and  physiologists,  and  many  theories  have  been  proposed  to  explain  how  it 
is  that  we  do  not  see  inverted  images  of  objects.  The  chief  difficulty  seems 
to  have  arisen  from  the  conception  of  the  mind  or  brain  as  something 
behind  the  eye,  looking  into  it,  and  seeing  the  image  upon  the  retina  ; 
whereas  really  this  image  simply  causes  a  stimulation  of  the  optic  nerve, 
which  produces  some  molecular  change  in  some  part  of  the  brain  ;  and  it  is 
only  of  this  change,  and  not  of  the  image  as  such,  that  we  have  any  conscious- 
ness. The  mind  has  thus  no  direct  cognisance  of  the  image  upon  the  retina, 
nor  of  the  relative  positions  of  its  parts,  and,  sight  being  supplemented  by 
touch  in  innumerable  cases,  it  learns  from  the  first  to  associate  the  sensations 
brought  about  by  the  stimulation  of  the  retina  (although  due  to  an  inverted 
image)  with  the  correct  position  of  the  object  as  taught  by  touch. 

617.  Optic  axis,  optic  angle,  visual  angle. — 'Y\v&  principal  optic  axis 
of  an  eye  is  the  axis  of  its  figure ;  that  is  to  say,  the  straight  line  in  reference 
to  which  it  is  symmetrical.    In  a  well-shaped  eye  it  is  the  straight  line  passing 


Fig.  580. 


through  the  centre  of  the  pupil  and  of  the  crystalline.  The  lines  A«,  ^b, 
(fig.  581)  are  secondary  axes.  The  eye  sees  objects  most  distinctly  in  the 
direction  of  the  principal  optic  axis. 

The  optic  angle  is  the  angle  BAC  (fig.  5S0),  formed  between  the  principal 
optic  axes  of  the  two  eyes  when  they  are  directed  towards  the  same  point. 
This  angle  is  smaller  in  proportion  as  the  objects  are  more  distant. 


592  On  Light.  [617- 

The  visual  angle  is  the  angle  AOB  (fig.  581),  under  which  an  object  is  seen  ; 
that  is  to  say,  the  angle  formed  by  the  secondary  axes  drawn  from  the  optic 
centre  of  the  crystalline  to  the  opposite  extremities  of  the  object.  P^or  the 
same  distance,  this  angle  increases  with  the  magnitude  of  the  object,  and  for 
the  same  object  it  decreases  as  the  distance  increases,  as  is  the  case  when 
the  object  passes  from  AB  to  A'B'.    It  follows,  therefore,  that  objects  appear 


Fig.  53 


smaller  in  proportion  as  they  are  more  distant ;  for  as  the  secondaiy  axes, 
AO,  BO,  cross  in  the  centre  of  the  crystalline,  the  size  of  the  image  projected 
on  the  retina  depends  on  the  size  of  the  visual  angle  AOB. 

618.  Estimation  of  the  distance  and  size  of  objects. — The  estimation 
of  distance  and  of  size  depends  on  numerous  circumstances  ;  these  are — the 
visual  angle,  the  optic  angle,  the  comparison  with  objects  whose  size  is 
familiar  to  us  ;  to  these  must  be  added  the  effect  of  what  is  called  aerial 
perspective ;  that  is,  a  more  or  less  vaporous  medium  which  enshrouds  the 
distant  objects,  and  thereby  diminishes  not  only  the  sharpness  of  the  out- 
lines, but  also  softens  the  contrast  between  light  and  shade,  which  close  at 
hand  are  marked. 

When  the  size  of  an  object  is  known,  as  the  figure  of  a  man,  the  height 
of  a  tree  or  of  a  house,  the  distance  is  estimated  by  the  magnitude  of  the 
visual  angle  under  which  it  is  seen.  If  its  size  is  unknown,  it  is  judged 
relatively  to  that  of  objects  which  surround  it. 

A  colonnade,  an  avenue  of  trees,  the  gas-lights  on  the  side  of  a  road, 
appear  to  diminish  in  size  in  proportion  as  their  distance  increases,  because 
the  visual  angle  decreases  ;  but  the  habit  of  seeing  the  columns,  trees,  &c., 
in  their  proper  height,  leads  our  judgment  to  rectify  the  impression  produced 
by  vision.  Similarly,  although  distant  mountains  are  seen  under  a  veiy 
small  angle,  and  occupy  but  a  small  space  in  the  field  of  view,  our  familiarity 
with  the  effects  of  aerial  perspective  enables  us  to  form  a  correct  idea  of 
their  real  magnitude. 

The  optic  angle  is  also  an  essential  element  in  appreciating  distance. 
Since  this  angle  increases  or  diminishes  according  as  objects  approach  or 
recede,  we  move  our  eyes  so  as  to  make  their  optic  axes  converge  towards 
the  object  which  we  are  looking  at,  and  thus  obtain  an  idea  of  its  distance. 
Nevertheless,  it  is  only  by  long  custom  that  we  can  establish  a  relation 
between  our  distance  from  the  objects,  and  the  corresponding  motion  of  the 
eyes.  It  is  a  curious  fact  that  persons  born  blind,  and  whose  sight  has  been 
restored  by  the  operation  for  cataract,  imagine  at  first  that  all  objects  are  at 
the  same  distance. 

Vertical  distances  are  estimated  too  low  compared  with  horizontal  ones  ; 
on  high  mountains  and  over  large  surfaces  of  water,  distances  are  estimated 
too  low  owing  to  the  want  of  intervening  objects.  Practice  and  experience 
have  great  infiuence  on  our  correct  estimation  of  magnitude  and  distance. 


-618a]  Scheifiers  Experiment.  593 

As  \vc  ascend  mountains  much  less  frequently  than  \vc  walk  on  the  level,  we 
err  more  easily  in  estimating  a  height  than  in  judging  a  horizontal  distance. 
A  room  filled  with  furniture  appears  larger  than  an  empty  room  of  the  same 


We  cannot  recognise  the  true  form  of  an  object  if,  with  moderate  illu- 
mination, the  visual  angle  is  less  than  half  a  minute.  A  white  square,  a 
metre  in  the  side,  appears  at  a  distance  of  about  5  miles  under  this  angle  as 
a  bright  spot  which  can  scarcely  be  distinguished  from  a  circle  of  the  same 
size. 

A  very  bright  object,  however,  such  as  an  incandescent  platinum  wire, 
is  seen  in  a  dark  ground  under  an  angle  of  2  seconds.  So  too  a  small  dark 
object  is  seen  against  a  bright  ground  ;  thus  a  hair  held  against  the  sky  can 
be  seen  at  a  distance  of  i  or  2  metres. 

b\Za.  Sclieiner's  experiment. — If  we  look  at  a  small  object  placed 
either  within  or  beyond  the  point  on  which  the  eye  is  focussed,  through  a 
number  of  minute  openings  in  a  diaphragm,  arranged  so  close  together  that 
they  fall  within  the  circumference  of  the  pupil,  the  object  appears  multiple, 
each  object  furnishing  a  separate  retinal  image.  This  forms  what  is  known 
as  Scheincr's  expcjivient.  This  may  be  made  as  follows  :  By  means  of  a 
sewing  needle,  two  small  holes  are  pricked  in  a  piece  of  cardboard,  not  more 
than  Y^,.;  of  an  inch  apart,  i.e.  less  than  the  diameter  of  the  pupil.  The  card 
is  held  before  one  eye  with  the  holes  horizontally  in  front  of  the  pupil,  and 
with  the  other  hand  a  needle  is  held  at  ordinary  reading  distance  in  the  line 
of  vision.  If  the  eye  be  fixed  on  the  needle  itself,  it  appears  single  and 
clearly  defined  ;  as  soon,  however,  as  we  look  at  a  more  distant  object,  the 
needle  appears  double,  and  at  the  same  time  blurred.  If  we  block  out  the 
right-hand  hole,  the  left-hand  image  disappears,  and  vice  versa. 

If  we  now  fix  the  eye  on  an  object  nearer  than  the  needle,  the  latter 
again  appears  double  and  blurred,  and  blocking  either  hole  causes  the  image 
on  the  same  side  to  vanish.  The  explanation  of  these  phenomena  may  be 
simplified  by  the  following  diagram. 

C 


Fig.  382. 

Let  AB  (fig.  582)  be  the  two  holes  in  the  card  CC,  O  a  luminous  point  in 
the  needle,  OA,  OB  the  pencils  of  rays  passing  through  the  apertures  in  the 
card.  Let  H,  E,  M  represent  the  position  of  a  hypermetropic,  normal,  and 
myopic  eye  respecti\-ely.  When  the  normal  eye  E  is  accommodated  for  O 
the  rays  OA,  OB   meet  at  the  point  E,  and  the  needle  appears  sharply 


594  Oti  Light.  [618a- 

defined  and  single.  If  the  eye  is  fixed  on  a  point  beyond,  or,  what  amounts 
to  the  same  thing,  if  the  eye  be  hypermetropic,  the  retina  may  be  considered 
to  he  no  longer  at  E,  but  in  front  at  H,  and  the  rays  0\p  not  only  do  not 
meet  in  a  focus  at  p,  but  do  not  meet  the  rays  OV>p'  ;  hence  the  luminous 
spot  O  will  be  seen  at  two  points,  and  the  points  themselves  being  out  of 
focus  will  appear  blurred.  Moreover,  the  rays  passing  through  the  right- 
hand  hole  A  will  cut  the  retina  at  p,  and  will  appear  to  the  mind  on  the 
reverse  side,  i.e.  on  the  left ;  therefore  blocking  the  right-hand  hole  A 
causes  a  disappearance  of  the  left-hand  image,  and  vice  versa. 

For  similar  reasons,  if  the  eye  be  accommodated  for  a  point  nearer  the 
eye  than  O,  or,  what  amounts  to  the  same  thing,  if  the  eye  be  myopic,  the 
retina  may  be  considered  to  lie  behind  E  at  M,  and  the  image  will  again  be 
seen  doubled  and  blurred  ;  only  in  this  case  blocking  out  the  right-hand 
hole  A  will  cause  the  right-hand  image  to  disappear.  Stampfer  constructed 
an  optometer  based  on  this  principle.  He  employed  a  tube  containing  two 
diaphragms,  one  furnished  with  two  slits  i'"™  apart,  the  other  with  a  single 
slit  covered  with  ground  glass.  The  diaphragm  is  moved  to  or  from  the 
eye  until  the  slit  is  seen  single.  This  distance  from  the  eye  is  the  measure 
of  distinct  vision. 

619.  Distance  of  distinct  vision. — The  dista?tce  oj  distinct  vision.,  as 
already  stated  (587),  is  the  distance  at  which  objects  must  be  placed  so  as  to 
be  seen  with  the  greatest  distinctness.  It  varies  in  different  individuals,  and 
in  the  same  individual  it  is  often  different  in  the  two  eyes.  For  small  objects, 
such  as  print,  it  is  from  10  to  12  inches  in  normal  cases. 

Persons  who  see  objects  distinctly  only  at  a  very  short  distance  away  are 
called  myopic^  or  short-sighted,  and  those  who  require  a  convex  glass  to  see 
objects  distinctly  at  a  long  distance  are  hypermetropic,  or  long-sighted  (629). 

Sharpftess  of  sight  may  be  compared  by  reference  to  that  of  a  normal  eye 
taken  as  a  unit.  Such  a  standard  eye,  according  to  Snellen,  recognises 
quadrangular  letters  when  they  are  seen  under  an  angle  of  6' ;  if,  for  instance, 
such  letters  are  lo"""  high  at  a  distance  of  6  metres.  The  sharpness 
of  vision  of  one  who  recognises  these  letters  at  a  distance  of  6  metres  is 

then  -. 
6 

620.  Accommodation. —  By  this  term  is  meant  the  changes  which  occur 
in  the  eye  to  fit  it  for  seeing  distinctly  objects  at  different  distances  from  it. 

If  the  eye  be  supposed  fixed  and  its  parts  immovable,  it  is  evident  that 
there  could  only  be  one  surface  whose  image  would  fall  exactly  upon  the 
retina  ;  the  distance  of  this  surface  from  the  eye  being  dependent  on  the 
refractive  indices  of  the  media  and  the  curvatures  of  the  refractive  surfaces 
of  the  eye.  The  image  of  any  point  nearer  the  eye  than  this  distinctly  seen 
surface  would  fall  behind  the  retina  ;  the  image  of  any  more  distant  point 
would  be  formed  in  front  of  it  ;  in  each  case  the  section  of  a  luminous  cone 
would  be  perceived  instead  of  the  image  of  the  point,  and  the  latter  would 
appear  diffused  and  indistinct. 

Experience,  however,  shows  us  that  a  normal  eye  can  see  distinct  images 
of  objects  at  very  different  distances.  We  can,  for  example,  see  a  distant 
tree  through  a  window,  and  also  a  scratch  on  the  pane,  though  not  both  dis- 
tinctly at  the  same  moment  ;  for  when  the  eye  is  arranged  to  see  one  clearly, 


-621]  Binocular   Vision.  595 

the  image  of  the  other  does  not  fall  accurately  upon  the  retina.  An  eye 
completely  at  rest  seems  adapted  for  seeing  distant  objects ;  the  sense  of 
effort  is  greater  in  a  normal  eye  when  a  near  object  is  looked  at,  after  a 
distant  one,  than  in  the  reverse  case  ;  and  in  paralysis  of  the  nerves  govern- 
ing the  accommodating  apparatus,  the  eye  is  persistently  adapted  for  distant 
sight.  There  must,  therefore,  be  some  mechanism  in  the  eye  by  which  it 
can  be  voluntarily  altered,  so  that  the  more  divergent  rays  proceeding  from 
near  objects  shall  come  to  a  focus  upon  the  retina.  There  are  several  con- 
ceivable methods  by  which  this  might  be  effected  ;  it  is  actually  brought 
about  by  a  drawing  forwards  of  the  crystalline  lens  and  a  greater  convexity  of 
its  front  surface. 

This  is  shown  by  the  foUowmg  experiment  : — If  a  candle  be  placed  on 
one  side  of  the  eye  of  a  person  looking  at  a  distant  object,  and  his  eye  be 
observed  from  the  other  side,  three  distinct  images  of  the  flame  will  be 
seen  ;  the  first,  virtual  and  erect,  is  reflected  from  the  anterior  surface  of 
the  cornea  ;  the  next,  erect  and  less  bright,  is  reflected  from .  the  anterior 
surface  of  the  lens  ;  the  third,  inverted  and  brilliant,  is  formed  on  the 
posterior  surface  of  the  lens.  If  now  the  person  look  at  a  near  object,  no 
change  is  observed  in  the  first  and  third  images,  but  the  second  image 
becomes  smaller  and  approaches  the  first  ;  which  shows  that  the  anterior 
surface  of  the  crystalline  lens  becomes  more  convex  and  approaches  the 
cornea.  In  place  of  the  candle.  Von  Helmholtz  throws  light  through  two  holes 
in  the  screen  upon  the  eye,  and  observes  the  distance  on  the  eye  between 
the  two  shining  points,  instead  of  the  size  of  the  flame  of  the  candle. 

This  change  in  the  lens  is  effected  chiefly  by  means  of  a  circular  muscle 
(ciliary  muscle),  the  contraction  of  which  relaxes  the  suspensory  ligament, 
and  so  allows  the  front  surface  of  the  lens  to  assume  more  or  less  of  that 
greater  convexity  which  it  would  normally  exhibit  were  it  not  for  the  drag 
exercised  upon  it  by  the  ligament.  Certain  other  less  important  changes 
occur,  tending  to  make  the  lens  more  convex  and  to  push  it  forwards,  which 
cannot,  however,  be  explained  without  entering  into  minute  anatomical 
details.  When  the  eye  is  accommodated  for  near  vision,  the  pupil  contracts 
and  so  partially  remedies  the  greater  spherical  aberration. 

The  r(^;z^i?(?/(^£r^tf'w;;z£'^<:?/'/<?«,  called  by  Bonders     ,  is  measured  by  first 

of  all  determining  the  greatest  distance,  R,  at  which  a  person  can  read  with- 
out spectacles,  and  then  the  smallest,  P,  at  which  he  can  so  read  ;  then 

I  _  I  _  I 
A~P     R' 

621.  Binocular  vision. — A  single  eye  sees  most  distinctly  any  point 
situated  on  its  optical  axis,  and  less  distinctly  other  points  also,  towards 
which  it  is  not  directly  looking,  but  which  are  still  within  its  circle  of  vision. 

It  is  able  to  judge  of  the  directio7t  of  any  such  point,  but  unable  by  itself 
to  estimate  its  distance.  Of  the  distance  of  an  object  it  may,  indeed,  learn 
to  judge  by  such  criteria  as  loss  of  colour,  indistinctness  of  outline,  decrease 
in  magnitude,  &c.  ;  but  if  the  object  is  near,  the  single  eye  is  not  infallible, 
even  with  these  aids. 

When  the  two  eyes  are  directed  upon  a  single  point,  we  then  gain  the 

'.'  <.)  2 


596 


On  Light. 


[621- 


\ 

/ 

\ 

• 


power  of  judging  of  its  distance  as  compared  with  that  of  any  other  point, 
and  this  we  seem  to  gain  by  the  sense  of  greater  or  less  effort  required  in 
causing  the  optical  axes  to  converge  upon  the  one  point  or  upon  the  other. 
Now  a  solid  object  may  be  regarded  as  composed  of  points  which  are  at 
different  distances  from  the  eye.  Hence,  in  looking  at  such  an  object,  the 
axes  of  the  two  eyes  are  rapidly  and  insensibly  varying  their  angle  of  con- 
vergence, and  we  as  rapidly  are  gaining  experience  of  the  difference  in 
distance  of  the  various  points  of  which  the  object  is  composed,  or,  in  other 
words,  an  asurance  of  its  solidity.  Such  kind  of  assurance  is  necessarily 
unattainable  in  monocular  vision. 

622.  The  principle  of  tbe  stereoscope. — Let  any  solid  object,  such  as 
a  small  box,  be  supposed  to  be  held  at  some  short  distance  in  front  of  the 

two  eyes.  On  what- 
ever point  of  it  they 
are  fixed,  they  will 
see  that  point  the 
most  distinctly,  and 
other  points  more  or 
less  clearly.  But  it 
is  evident  that,  as  the 
two  eyes  see  from 
different  points  of 
/  '•  view,    there    will    be 

^'"-  5-3-  formed    in    the    right 

eye  a  picture  of  the  object  different  from  that  formed  in  the  left ;  and  it  is  by 
the  apparent  union  of  these  two  dissimilar  pictures  that  we  see  the  object 
in  relief.  If,  therefore,  we  delineate  the  object,  first  as  seen  by  the  right 
eye,  and  then  as  seen  by  the  left,  and  afterwards  present  these  dissimilar 
pictures  again  to  the  eyes,  taking  care  to  present  to  each  eye  that  picture 
which  was  drawn  from  its  point  of  view,  there  would  seem  to  be  no  reason 
why  we  should  not  see  a  representation  of  the  object,  as  we  saw  the  object 
itself,  in  relief.  Experiment  confirms  the  supposi- 
tion. If  the  object  held  before  the  eyes  were  a 
truncated  pyramid,  r  and  /,  fig.  583,  would  repre- 
sent its  principal  lines,  as  seen  by  the  right  and  left 
eyes  respectively.  If  a  card  is  held  between  the 
figures,  and  they  are  steadily  looked  at,  r  by  the 
right  eye,  and  /  simultaneously  by  the  left,  for  a 
few  seconds,  there  will  be  seen  a  single  picture 
having  the  unmistakable  appearance  of  relief.  Even 
without  a  card  interposed,  the  eye,  by  a  little  prac- 
tice, may  soon  be  taught  so  to  combine  the  two  as 
to  form  this  solid  picture.  Three  pictures  will  in 
that  case  be  seen,  the  central  one  being  solid,  and 
the  two  outside  ones  plane.  Kig.  584  will  explain 
this.  Let  r  and  /  be  any  two  corresponding  points, 
say  the  points  markctl  by  a  large  dot  in  the  figures 
drawn  above  ;  R  ami  L  the  positions  of  the  right  and  left  eyes  ;  then  the 
right  eye  sees  the  point  r  in  the  direction  R^,  and  the  left  eye  the  point  /  in 


-624] 


TJie  Refractmg  Stereoscope 


597 


the  direction  Lf,  and  accordingly  each  by  itself  judging  only  by  the  direc- 
tion, they  together  see  these  two  points  as  one,  and  imagine  it  to  be  situated 
at  o.  But  the  right  eye,  though  looking  in  the  direction  Rr,  also  receives 
an  image  of  /  on  another  part  of  the  retina,  and  the  left  eye  in  the  same  way 
an  image  of  r,  and  thus  three  images  arc  seen.  A  card,  however,  placed 
in  the  position  marked  by  the  dotted  line  will,  of  course,  cut  off  the  two  side 
pictures.  To  assist  the  eye  in  combining  such  pairs  of  dissimilar  pictures, 
both  mirrors  and  lenses  have  been  made  use  of,  and  the  instruments  in 
which  either  of  these  are  adapted  to  this  end  are  called  stereoscopes. 

623.  The  reflecting-  stereoscope. — In  the  reflecting  stereoscope  plane 
mirrors  are  used  to  change  the  apparent  position  of  the  pictures,  so  that  they 
are  both  seen  in  the  same  direction,  and  their  combination  by  the  eye  is 
thus  rendered  easy  and  almost  inevitable.  If  ab.,  ab  (fig.  585)  are  two  plane 
mirrors  inclined  to  one  another  at  an  angle  of  90°,  the  two  arrows,  x,  j',  would 
both  be  seen  by  the  eyes  situated  at  R  and  L  in  the  position  marked  by  the 
dotted  arrow.  If,  instead  of  the  arrows,  we  now  substitute  such  a  pair  of 
dissimilar  pictures  as  we  have  spoken  of  above,  of  the  same  solid  object,  it 
is  evident  that,  if  the  margins  of  the  pictures  coincide,  other  corresponding 


<:- 


■4  ^T- 


points  of  the  pictures  will  not.  The  eyes,  however,  almost  without  effort, 
soon  bring  such  points  into  coincidence,  and  in  so  doing  make  them  appear 
to  recede  or  advance,  as  they  are  farther  apart  or  nearer  together  than  any 
two  corresponding  points  (the  right-hand  corner,  for  instance)  of  the  margins 
when  the  pictures  are  placed  side  by  side,  as  in  the  diagram,  fig.  585.  It  will 
be  plain,  also,  on  considering  the  position  for  the  arrows  in  fig.  585,  that  to 
adapt  such  figures  as  those  in  fig.  584  for  use  in  a  reflecting  stereoscope  one 
of  them  must  be  reversed,  or  drawn  as  it  would  be  seen  through  the  paper 
if  held  up  to  the  light. 

624.  The  refracting-  stereoscope. — Since  the  rays  passing  through  a 
convex  lens  are  bent  always  towards  the  thicker  part  of  the  lens,  any  seg- 
ment of  such  a  lens  may  be  readily  adapted  to  change  the  apparent  position 
of  any  object  seen  through  it.  Thus,  if  (fig.  586)  two  segments  be  cut  from 
a  double  convex  lens,  and  placed  with  their  edges  together,  the  arrows,  :r,^, 
would  both  be  seen  in  the  position  of  the  dotted  arrow  by  the  eyes  at  R 
and  L. 

If  we  substitute  for  the  arrows  two  dissimilar  pictures  of  the  same  solid 


598  On  Light.  [624- 

object,  or  the  same  landscape,  we  shall  then,  if  a  diaphragm,  ab.,  be  placed 
between  the  lenses  to  prevent  the  pictures  being  seen  crosswise  by  the  eyes, 
see  but  one  picture,  and  that  apparently  in  the  centre,  and  magnified.  As 
before,  if  the  margins  are  brought  by  the  power  of  the  lenses  to  coincide, 
other  corresponding  points  will  not  be  coincident  until  combined  by  an 
almost  insensible  effort  of  the  eyes.  Any  pair  of  corresponding  points  which 
are  farther  apart  than  any  other  pair  will  then  be  seen  farther  back  in  the 
picture,  just  as  any  point  in  the  background  of  a  landscape  would  be  found 
(if  we  came  to  compare  two  pictures  of  the  landscape,  one  drawn  by  the 
right  eye,  and  the  other  by  the  left)  to  be  represented  by  two  points  farther 
apart  from  one  another  than  two  others  which  repre- 
£  r        sented  a  point  in  the  foreground. 

I\  /I  It  will  be  instructive  to  notice  that  there  is  also  a 

\  /    I       second  point  on  tJiis  side  of  the  paper,  at  which,  if  a 

\         /       1       person   look   steadily,   the   diagrams    in   fig.    587   will 
\o/  I       combine,  and  form  quite  a  different  stereoscopic  pic- 

"7^'  Y""  ture.     Instead  of  a  solid  pyramid,  a  hollow  pyramidal 

/   \  1      box  will  then  be  seen.     The  point  may  easily  be  found 

/  \       1     ^y  experiment.     Here  again  two  external  images  will 

/  \     1     also  be  seen.     If  we  wish  to  shut  these  out,  and  see 

\  I     only  their  central  stereoscopic  combination,  we  must 
\|    use  a  diaphragm  of  paper  held  parallel  to  the  plane  of 
Ji  ,.  B  the  picture  with  a  square  hole  in  it.    This  paper  screen 

'^'  ^"'^'  must  be  so  adjusted  that  it  may  conceal  the  right-hand 

figure  from  the  left  eye,  and  the  left-hand  figure  from  the  right  eye,  while 
the  central  stereoscopic  picture  may  be  seen  through  the  hole.  It  will  be 
plain  from  the  diagram  that  o  is  the  point  to  which  the  eyes  must  be 
directed,  and  at  which  they  will  imagine  the  point  to  be  situated,  which 
is  formed  by  the  combination  of  the  two  points  r  and  /.  The  dotted  line 
shows  the  position  of  the  screen.  A  stereoscope  with  or  without  lenses 
may  easily  be  constructed,  which  will  thus  give  us,  with  the  ordinary  stereo- 
scopic slides,  a  reversed  picture  ;  for  instance,  if  the  subject  be  a  landscape, 
the  foreground  will  retire  and  the  background  come  forward. 

\Mien  the  two  retinas  view  simultaneously  two  different  colours,  the  im- 
pression produced  is  that  of  a  single  mixed  tint.  The  power,  however,  of 
combining  the  two  tints  into  a  single  one  varies  in  different  individuals, 
and  in  some  is  extremely  weak.  If  two  white  discs  at  the  base  of  the  stereo- 
scope be  illuminated  by  two  pencils  of  complementary  colours,  and  if  each 
coloured  disc  be  looked  at  with  one  eye,  a  single  white  one  is  seen,  showing 
that  the  sensation  of  white  light  may  arise  from  two  complementary  and 
simultaneous  chromatic  impressions  on  each  of  the  two  retinas. 

Dove  found  that  if  a  piece  of  printing  and  a  copy  are  viewed  in  the  stereo- 
scope, a  difference  in  the  distance  of  the  words,  which  is  not  apparent  to  the 
naked  eye,  causes  them  to  stand  out  from  the  plane  of  the  paper. 

625.  Persistence  of  impressions  on  the  retina. — When  an  ignited 
l)iccc  of  charcoal  is  rapidly  rolatcil,  wc  cannot  distinguish  it;  the  appearance 
of  a  circle  of  fire  is  ])roduccd  ;  similarly,  rain,  in  falling  drops,  appears  m 
the  air  like  a  scries  of  liquid  threads.  In  a  rapidly  rotating  toothed  wheel 
the  individual  teeth  cannot  be  seen.     But  if,  during  darkness,  the  wheel  be 


-626]  Accidental  IiiKigcs.  599 

suddenly  illuminated,  as  by  the  electric  spark,  the  individual  parts  may  be 
clearly  made  out.  The  following  experiment  is  a  further  illustration  of  this 
property  : — A  series  of  equal  sectors  are  traced  on  a  disc  of  glass,  and  they 
are  alternately  blackened  ;  in  the  centre  there  is  a  pivot,  on  which  a  second 
disc  is  fixed  of  the  same  dimensions  as  the  first,  but  completely  blackened 
with  the  exception  of  a  single  sector  ;  then  placing  the  apparatus  between  a 
window  and  the  eye,  the  second  disc  is  made  to  rotate.  If  the  movement 
is  slow,  all  the  transparent  sectors  are  seen,  but  only  one  at  a  time  ;  by  a 
more  rapid  rotation  we  see  simultaneously  two,  three,  or  a  greater  number. 
These  various  appearances  are  due  to  the  fact  that  the  impression  of  these 
images  on  the  retina  remains  for  some  time  after  the  object  which  has  pro- 
duced them  has  disappeared  or  become  displaced.  The  duration  of  the  per- 
sistence varies  with  the  sensitiveness  of  the  retina  and  the  intensity  of  light. 

Plateau  investigated  the  duration  of  the  impression  by  numerous  similar 
methods,  and  has  found  that  it  is,  on  the  average,  half  a  second.  Among 
many  curious  instances  of  these  phenomena,  the  following  is  one  of  the  most 
remarkable.  If,  after  having  looked  at  a  brightly  illuminated  window,  the 
eyes  are  suddenly  closed,  the  image  remains  for  a  few  instants — that  is,  a 
sashwork  is  seen  consisting  of  luminous  panes  surrounded  by  dark  frames  ; 
after  a  few  seconds  the  colours  become  interchanged,  the  same  framework 
is  now  seen,  but  the  frames  are  now  bright,  and  the  glasses  are  perfectly 
black  ;  this  new  appearance  may  again  revert  to  its  original  appearance. 

The  impression  of  colours  remains  as  well  as  that  of  the  form  of  objects  ; 
for  if  circles  divided  into  sectors  are  painted  in  different  colours,  they  become 
confounded,  and  give  the  sensation  of  the  colour  which  would  result  from 
their  mixture.  Yellow  and  red  give  orange  ;  blue  and  red  violet  ;  the  seven 
colours  of  the  spectrum  give  white,  as  shown  in  Newton's  disc  (fig.  524). 
This  is  a  convenient  method  of  studying  the  tints  produced  by  mi.xed 
colouis. 

A  great  number  of  pieces  of  apparatus  are  founded  on  the  persistence 
of  sensation  on  the  retina ;  such  are  the  thauiiiatrope,  the  phettakistoscopc, 
Faraday's  wheel,  the  kaleidophone,  and  the  zoetrope. 

The  zoetrope  1  or  luheel  of  life,  is  very  convenient  for  representing  a  number 
of  optical,  acoustical,  and  other  vibratory  motions.  It  consists  of  an  open 
cylinder  which  can  be  rotated  about  its  vertical  axis.  At  the  top  are  a 
number  of  vertical  slips.  If  now  the  various  positions  of  a  vibrating  pendu- 
lum, for  instance,  are  drawn  on  a  narrow  strip  of  paper,  the  length  of  which 
is  equal  to  the  circumference,  and  this  is  placed  inside  the  cylinder,  when 
the  wheel  is  rapidly  rotated,  on  looking  through  the  slits  the  pendulum 
seems  as  if  it  were  steadily  vibrating. 

626.  Accidental  Imagres. — When  a  coloured  object  placed  upon  a  black 
ground  is  steadily  looked  at  for  some  time,  the  eye  is  soon  tired,  and  the 
intensity  of  the  colour  is  enfeebled  ;  if  now  the  eyes  are  directed  towards  a 
white  sheet,  or  to  the  ceiling,  an  image  will  be  seen  of  the  same  shape  as 
the  object,  but  of  the  complementary  colour  (570) ;  that  is,  such  a  one  as 
united  to  that  of  the  object  would  form  white.  For  a  green  object  the  image 
will  be  red  ;  if  the  object  is  yellow,  the  image  will  be  violet. 

Accidental  colours  are  of  longer  duration  in  proportion  as  the  object  has 
been  more  brilliantly  illuminated,  and  has  been  longer  looked  at.     When  a 


6oo  On  Light.  [626- 

lighted  candle  has  been  looked  at  for  some  time,  and  the  eyes  are  turned 
towards  a  dark  part  of  the  room,  the  appearance  of  the  flame  remains,  but  it 
gradually  changes  colour  ;  it  is  first  yellow,  then  it  passes  through  orange 
to  red,  from  red  through  violet  to  greenish  blue,  which  is  gradually  feebler 
until  it  disappears.  If  the  eye  which  has  been  looking  at  the  light  be  turned 
towards  a  white  wall,  the  colours  follow  almost  the  opposite  direction  :  there 
is  first  a  dark  picture  on  a  white  ground,  which  gi-adually  changes  into  blue, 
is  then  successively  green  and  yellow,  and  ultimately  cannot  be  distinguished 
from  a  white  ground. 

The  reason  of  this  phenomenon  is,  doubtless,  to  be  sought  in  the  fact 
that  the  subsecjuent  action  of  light  on  the  retina  is  not  of  equal  duration  for 
all  colours,  and  that  the  decrease  in  the  intensity  of  the  subsequent  action 
docs  not  follow  the  same  law  for  all  colours.  According  to  Kiilp,  the  dura- 
tions of  the  after-image  with  moderate  illumination  are  for  white,  yellow, 
red,  and  blue,  o-i,  0-09,  o-o8,  and  o-o66  of  a  second  respectively. 

627.  Irradiation. — This  is  a  phenomenon  in  virtue  of  which  white  objects, 
or  those  of  a  very  bright  colour,  when  seen  on  a  dark  ground,  appear  larger 
than  they  really  are.  Thus  a  white  square  upon  a  black  ground  seems 
larger  than  an  exactly  equal  black  square  upon  a  white  ground  (fig.  588). 
Irradiation  arises  from  the  fact  that  the  impression  produced  on  the  retina 
extends  beyond  the  outline  of  the  image.  It  bears  the  same  relation  to  the 
space  occupied  by  the  image,  that  the  duration  of  the  impression  does  to  the 
time  during  which  the  image  is  seen. 

The  effect  of  irradiation  is  very  perceptible  in  the  apparent  magnitude  of 

stars,  which  may  thus  appear  much  larger  than  they  really  are  ;  also  in  the 

appearance  of  the  moon  when  two  or  three  days  old,  the 

H^mgM|        brightly  illuminated  crescent  seeming  to  extend  beyond 

^^^^^^1        the  darker  portion  of  the  disc,  and  hold  it  in  its  grasp. 

■    |HH     ■  Plateau  found  that  irradiation  difters  ^•ery  much    in 

n     ^H|     I        different  people,  and  even  in  the  same  person  it  differs 

I  I        on    different    days.     He  also  found  that  irradiation  in- 

nH^^HBp        creases  with  the  lustre  of  the  object,  and  the  length  of 

^^^^^B  time  during  which  it  is  viewed.      It  manifests  itself  at 

■  H  all  distances ;  diverging  lenses  increase  and  condensing 

Hhh^I  lenses  diminish  it. 

_^^^^_J  Accidental  haloes  are  the  colours  which,  instead  of 

Fig.  5S8.  succeeding  the  impression  of  an  object  like  accidental 

colours,  appear  round  the  object  itself  when  it  is  looked 

at  fixedly.     The  impression  of  the  halo  is  the  opposite  to  that  of  the  object  : 

if  the  object  is  bright  the  halo  is  dark,  and  7-ice  versa.     These  appearances 

are  best  produced  in  the  following  manner :— A  white  surface,  such  as  a 

sheet  of  paper,  is  illuminated  by  coloured  light,  and  a  narrow  opaque  body 

held  so  as  to  cut  off  some  of  the  coloured  rays.     In  this  manner  a  narrow 

shadow  is  obtained  which  is  illuminated  by  the  surrounding  white  daylight, 

and  appears  complementary  to  the  coloured  ground.     If  red  glass  is  used, 

the  shadow  appears  green,  and  blue  when  a  yellow  glass  is  used. 

The  contrast  of  colours  is  a  reciprocal  action  exerted  between  two  adja- 
cent colours,  and  in  virtue  of  which  to  each  one  is  added  the  complementary 
colour  of  the  other.     Chevrcul  found  that  when  red  and  yellow  colours  are 


-628]  Tlie  Eye  is  not  Achromatic.  60 1 

adjacent,  red  acquires  a  violet  and  yellow  an  orange  tint.  If  the  experiment 
is  made  with  red  and  blue,  the  former  acquires  a  yellow,  and  the  latter  a 
green  tint  ;  with  yellow  and  blue,  yellow  passes  to  orange,  and  blue  towards 
indigo  ;  if  a  narrow  strip  of  grey  paper  be  laid  on  a  sheet  of  light  green 
paper,  it  appears  reddish,  if  laid  on  blue  paper  it  seems  yellow,  and  so  on 
for  a  vast  number  of  combinations ;  in  all  cases  the  colour  is  complementary 
to  the  colour  of  the  base.  The  importance  of  this  phenomenon  in  its  appli- 
cation to  the  manufacture  of  coloured  cloths,  carpets,  curtains,  &c.,  may  be 
readily  conceived. 

The  contrast  may  be  conveniently  ex- 
amined by  means  of  the  apparatus  shown 
in  fig.  589  in  about  ^  scale.  It  consists 
of  a  thin  vertical  board,  AB,  painted 
white,  and  the  base,  DC,  painted  black, 
on  which  are  painted  circles  about  %  of 
an  inch  in  diameter,  black  and  white 
respectively.  A  sheet  of  coloured  glass 
is  inclined  at  an  angle  of  45°  ;  if  now  the 
eye  be  so  held  that  the  image  of  the 
white    circle   on  DC  reflected  from    the  Fig.  5S9. 

under  surface  of  the  glass  plate  is  looked 

at  in  front  of  the  circle  on  AB,  the  image  appears  of  a  colour  complementary 
to  that  of  the  glass.  Thus  with  a  green  plate  a  red  spot  is  seen  on  a  green 
ground. 

62S.  The  eye  Is  not  achromatic- — It  had  long  been  supposed  that  the 
human  eye  was  perfectly  achromatic  ;  but  this  is  clearly  impossible,  as  all 
the  refractions  are  made  the  same  way,  viz.  towards  the  axis  ;  moreover,  the 
experiments  of  Wollaston,  of  Young,  of  Fraunhofer,  and  of  Miiller  have 
shown  that  it  was  not  true  in  any  absolute  sense. 

Fraunhofer  showed  that  in  a  telescope  with  two  lenses,  a  very  fine  wire 
placed  inside  the  instrument  in  the  focus  of  the  object-glass  is  seen  distinctly 
through  the  eyepiece,  when  the  telescope  is  illuminated  with  red  light  ;  but 
it  is  invisible  by  violet  light  even  when  the  eyepiece  is  in  the  same  position. 
In  order  to  see  the  wire  again,  the  distance  of  the  lenses  must  be  diminished 
to  a  far  greater  extent  than  would  correspond  to  the  degree  of  refrangibility 
of  violet  light  in  glass.  In  this  case,  therefore,  the  effect  must  be  due  to  a 
chromatic  aberration  in  the  eye. 

^^liiller,  on  looking  at  a  white  disc  on  a  dark  ground,  found  that  the  image 
is  sharp  when  the  eye  is  accommodated  to  the  distance  of  the  disc — that  is, 
when  the  image  forms  on  the  retina  ;  but  he  found  that,  if  the  image  is 
formed  in  front  of  or  behind  the  retina,  the  disc  appears  surrounded  by  a 
very  narrow  blue  edge.  If  a  finger  be  held  up  in  front  of  one  eye  (the  other 
being  closed)  in  such  a  manner  as  to  allow  the  light  to  enter  only  one  half 
of  the  pupil,  and,  of  course,  obliquely,  and  the  eye  be  then  directed  to  any 
well-defined  line  of  light,  such  as  a  slit  in  the  shutter  of  a  darkened  room, 
or  a  strip  of  white  paper  on  a  black  ground,  this  line  of  light  will  appear  as  a 
complete  spectrum. 

Miiller  concluded  from  these  experiments  that  the  eye  is  sensibly  achro- 
matic as  long  as  the  image  is  received  at  the  focal  distance,  or  when  it  is 


6o2  On  Light.  [628- 

accommodated  to  the  distance  of  the  object.  The  cause  of  this  apparent 
achromatism  cannot  be  exactly  stated.  It  has  generally  been  attributed  to 
the  tenuity  of  the  luminous  beams  which  pass  through  the  pupillary'  aperture, 
and  that  these  unequally  refrangible  rays,  meeting  the  surfaces  of  the  media 
of  the  eye  almost  at  the  normal  incidence,  are  ver}'  little  refracted,  from 
which  it  follows  that  the  chromatic  aberration  is  imperceptible  (584). 

Spherical  aberration,  as  we  have  already  seen,  is  corrected  by  the  iris 
(612).  The  iris  is,  in  point  of  fact,  a  diaphragm,  which  stops  the  marginal 
rays  and  only  allows  those  to  pass  which  are  near  the  axis. 

629.  Short  siiTht  and  long  sig:bt.  IVXyopia  and  Iiypermetropia. 
Astigmatism.  Presbyopia. — The  most  usual  affections  of  the  eye  are 
myopia,  Jiyper})ictropia,  pfcsbyopia,  and  astigmatism.  Myopia,  or  short  sight, 
is  the  inability  to  see  objects  clearly  defined  beyond  a  variable  but  always 
limited  distance.  The  usual  cause  of  myopia  is  an  abnormal  increase  in 
length  of  the  eyeball  along  the  axis  of  vision,  so  that  the  retina  lies  behind 
the  focus  of  the  dioptric  systems  of  the  eye  for  parallel  rays,  thereby  render- 
ing objects  on  the  retina  indistinct.  It  may  be  remedied  by  means  of 
diverging  concave  glasses,  which,  in  making  the  rays  deviate  from  their 
common  axis,  throw  the  focus  farther  back,  and  cause  the  image  to  be 
formed  on  the  retina. 

The  habitual  contemplation  of  small  objects,  sedentary  occupations,  a 
stooping  position  while  studying,  in  fact  anything  which  tends  to  congest 
the  eyes,  and  cause  an  unequal  strain  on  the  muscles  of  convergence,  may 
produce  short  sight.  It  is  common  in  the  case  of  young  people,  and,  when 
once  acquired,  tends  to  become  hereditary  ;  hence  the  percentage  of  myopes 
is  continually  on  the  increase. 

Hypermetropia,  or  long  sight,  is  the  contrary  of  short  sight.  The  eye  is 
abnormally  short  along  the  axis  of  vision,  so  that  the  retina  lies  in  front  of 
the  dioptric  system  of  the  eye  for  parallel  rays,  thereby  rendering  objects  on 
the  retina  indistinct  unless  the  rays  be  rendered  more  convergent  by  exerting 
the  muscles  of  accommodation.  Hence  the  ciliary'  muscle  can  never  be 
relaxed  without  the  image  becoming  blurred,  even  when  looking  at  distant 
objects.  When  regarding  near  objects,  however,  the  accommodator  has  to 
be  brought  into  play,  not  from  a  position  of  rest,  but  from  the  state  of  con- 
traction of  the  ciliary  muscle,  which  was  necessary-  to  see  distant  objects 
clearly.  Hence,  owing  to  this  increased  strain  of  accommodation,  the  eye 
becomes  easily  fatigued  when  regarding  near  objects,  which  thus  become 
blurred.  Hypermetropia  is  corrected  by  means  of  converging  (convex)  lenses* 
These  glasses  converge  the  rays  before  their  entrance  into  the  eye,  and, 
therefore,  if  the  converging  power  is  properly  chosen,  the  image  will  be 
formed  exactly  on  the  retina. 

Presbyopia. — As  we  grow  older  the  range  of  accommodation,  in  other 
words,  the  power  of  focussing  near  objects,  decreases.  Now  there  comes  a 
time  with  everyone  who  is  not  myopic  when  an  object  cannot  be  distmctly 
seen  nearer  than  eight  inches  (the  distance  arbitrarily  chosen  by  Bonders)- 
This  occurs  in  a  normal  or  emmetropic  eye  at  40  years  of  age.  Hence 
presbyopia,  as  it  is  called,  may  be  defined  as  the  contraction  of  the  visual 
range  due  to  physiological  weakening  of  the  accommodating  mechanism.  It 
IS  clear,  according  to  the  standard  of  Donders,  that  it  can  never  occur  in  very 


-630]  Eye-glasses.     Spectacles.  603 

short-sighted  persons,  as  their  near  point  is  always  much  less  than  8  inches 
to  begin  with,  whereas  in  hypermetropes,  on  the  other  hand,  it  may  become 
evident  at  a  much  earlier  age.  Presbyopia  is  corrected  by  suitable  convex 
glasses,  which,  by  converging  the  rays,  bring  the  point  of  near  vision  to  eight 
inches. 

Astigmatism. — We  have  hitherto  considered  the  dioptric  surfaces  as 
portions  of  true  spheres.  Should,  however,  one  of  the  surfaces  have  a  curve 
of  shorter  radius  in  one  of  its  meridians,  all  the  rays  from  a  luminous  point 
cannot  be  focussed  on  the  same  plane,  but  will  possess  two  linear  foci,  one 
anterior  corresponding  to  the  curvature  of  shorter  radius,  and  the  other 
behind  corresponding  to  the  curve  of  greater  radius.  This  defect  is  called 
astigtnatism ;  it  is  usually  most  marked  in  the  cornea,  and  sometimes  causes 
serious  impairment  of  vision.  It  may  be  corrected  by  applying  a  lens  ground 
on  a  cylindrical  surface  in  which  one  of  the  axes  only  is  a  plane  ;  a  curve  of 
such  a  radius  being  chosen  as  will  enable  the  two  linear  foci  to  unite  on  the 
same  plane. 

630.  Eye-glasses.  Spectacles. — The  glasses  commonly  used  by  short- 
or  long-sighted  persons  are  known  under  the  general  name  of  eye-glasses  or 
spectacles.  Generally  speaking,  numbers  are  engraved  on  the  trial  glasses 
which  express  their  focal  length  in  inches  or  diopters.  This  latter  term  is 
applied  to  the  standard  focal  length  of  all  spectacle  glasses  adopted  by  the 
Ophthalmological  Congress  at  Heidelberg,  and  now  the  only  standard 
officially  recognised  thx'oughout  Europe  and  America.  This  standard  is  the 
refractive  power  of  a  lens  having  a  focal  length  of  a  metre  (39"37  inches), 
and  is  represented  by  the  letter  D.    Here  the  refractive  power  is  the  inverse 

of  the  focal  distance,  i.e.  D  =  —  and  F  =  ^.     Hence  to  find   the  number  of 
F  D 

diopters  which  represent  the  focal  length  m  inches,  we  must  divide  39"37  by 
that  focal  distance,  and,  conversely,  to  find  the  number  of  inches  correspond- 
ing to  a  given  number  of  diopters,  we  have  only  to  divide  39-37  by  this 
latter. 

The  spectacles  must  be  so  chosen  that  they  are  close  to  the  eye,  and 
that  they  make  the  distance  of  most  distinct  vision  10  or  12  inches. 

The  number  which  a  short-  or  long-sighted  person  ought  to  use  may  be 
calculated,  knowing  the  distance  of  most  distinct  vision.     The  formula 

/^i4     w 

ser\-es  for  long-sighted  persons,  where  /"being  the  '  number '  of  the  spectacles 
which  ought  to  be  taken — that  is,  the  number  expressing  the  focal  length 
—p  is  the  distance  of  distinct  vision  in  ordinary  cases  (about  12  inches),  and 
d  the  distance  of  distinct  vision  for  the  person  affected  by  long  sight. 

The  above  formula  is  obtained  from  the  equation =  -  by  substi- 

p  p'  f 
tuting  d  for  p'.  In  this  case  the  formula  (6)  of  article  5  59  is  used,  and  not 
formula  (5),  because  the  image  seen  by  spectacles  being  on  the  same  side 
of  the  object  in  reference  to  the  lens,  the  sign^'  ought  to  be  the  opposite 
of  that  of  p,  as  in  the  case  of  virtual  images  from  the  paragraph  already 
cited. 


604  On  Light.  [630- 

For  short-sighted  persons,  /  is  calculated  by  the  formula  -  -    ,   =  - 
(559),  which  refers  to  concave  lenses,  and  which,  replacing/'  by  d,  gives 

f'f',      ■     ■    ■     ■     ■     <=> 

To  calculate,  for  instance,  the  number  of  a  glass  which  a  person  ought 
to  use  in  whom  the  distance  of  distinct  vision  is  36,  knowing  that  the  dis- 
tance of  ordinary  distinct  vision  is  12  inches  ;  making/ =  12  and  ^^'=36  in 

the  above  formula  (i),  we  get  /=^>^7^  =  18. 

631.  Diplopia. — Diplopia  is  an  affection  of  the  eye  which  causes  objects 
to  be  seen  double  ;  that  is,  that  two  images  a:re  seen  instead  of  one.  Usually 
the  two  images  are  almost  entirely  superposed,  and  one  of  them  is  much 
more  distinct  than  the  other.  Diplopia  is  usually  due  to  a  want  of  power  in 
one  or  more  of  the  ocular  muscles,  but  it  may  be  due  to  the  prismatic  action 
of  badly  centred  spectacles.  It  may  also  affect  a  single  eye.  The  latter 
case  is,  doubtless,  due  to  some  defect  of  conformation  in  the  crystalline  iris 
or  other  parts  of  the  eye  which  produces  a  bifurcation  of  the  luminous  ray, 
and  thus  two  images  are  formed  on  the  retina  instead  of  one. 

632.  Achromatopsy. — Achfoinatopsy.,  or  colour  blijtdncss,  is  a  curious 
affection  which  renders  us  incapable  of  distinguishing  colours,  or  at  any 
rate  certain  colours.  Persons  affected  in  this  manner  can  distinguish  the 
outlines  of  bodies  without  difficulty,  and  they  can  also  discriminate  between 
light  and  shade,  but  they  are  unable  to  distinguish  all  the  different  colours. 

The  commonest  case  is  that  of  red-blindness  ;  Dalton  had  it  in  a  pre- 
eminent degree,  and  from  the  fact  that  he  very  carefully  described  it,  the 
disease  has  been  sometimes  called  Daltonism.  To  a  person  so  affected  red 
appears  like  black,  and  the  brighter  shades  bluish-green  ;  bluish-green 
and  pink  seem  the  same,  or  at  all  events  only  different  in  shade.  Yellow 
appears  like  green,  but  he  distinguishes  between  them,  for  the  yellow 
appears  brighter. 

He  who  is  blind  for  green,  sees  that  colour  as  black,  and  its  lighter 
shades  red.  He  only  sees  red  and  blue  with  their  intermediate  stages  ; 
yellow  appears  bright  red  ;  white  and  pink  are  alike,  the  spectrum  is  only 
red  and  blue  ;  in  the  green  there  is  a  grey  band.  Violet  blindness  is  \'ery 
infrequent  and  not  well  known  ;  it  can  be  artificially  produced  by  taking 
santonine.  Colour  disease  is  often  congenital.  It  is  far  more  frequent 
with  males  than  with  females. 

Owing  to  the  difference  in  really  healthy  individuals  as  regards  their 
perception  of  different  shades  of  colour,  the  only  certain  means  of  discerning 
any  particular  tint  is  to  define  its  position  by  means  of  the  nearest  Fraun- 
hofcr's  line  (574).  Owing  to  the  danger  which  may  arise  from  the  observa- 
tion of  coloured  signals  on  railways  and  the  like,  numerous  methods  have 
l:)een  proposed  for  the  qualitative  and  quantitative  observation  of  the  colour 
sense. 

The  best  test  for  ordinary  use  is  to  give  the  patient  a  standard  skein  of 
wool  of  a  particular  tint,  green,  rose,  or  red,  and  to  require  him  to  match  it, 
with  others  which  appear  to  him  of  the  same  tint,  among  a  large  bundle  of 


-633] 


Oph  thalviascopc 


605 


skeins  of  many  colours.  In  order  to  detect  simulation  the  experiment  should 
be  repeated  within  a  few  weeks. 

633.  Ophthalmoscope. — This  instrument,  as  its  name  indicates,  is  de- 
signed for  the  examination  of  the  eye,  and  was  invented  in  185 1  by  Professor 
Helmholtz.  It  consists  :— r.  Of  a  concave  spherical  reflector  of  glass  or 
metal,  M  (figs.  590,  591),  in  the  middle  of  which  is  a  small  hole  about  a 
sixth  of  an  inch  in  diameter.  The  focal  length  of  the  reflector  is  from  8  to 
10  inches.  2.  Of  a  converging  lens,  0,  which  is  held  in  front  of  the  eye  of 
the  patient. 

To  make  use  of  the  ophthalmoscope,  the  patient  is  placed  in  a  room,  and 


Fig.  596. 

a  lamp  put  beside  him,  E.  The  screen  serves  to  shade  the  light  from  his 
head,  and  keep  it  in  darkness.  The  observer,  A,  holding  in  one  hand  the 
reflector,  employs  it  to  concentrate  the  light  of  the  lamp  near  the  eye,  B, 
of  the  patient,  and  with  his  other  hand  holds  the  achromatic  lens,  <?,  in  front 
of  the  eye.  By  this  arrangement  the  back  of  the  eye  is  lighted  up,  and  its 
structure  can  be  clearly  discerned. 

Fig.  591  shows  how  the  image  of  the  back  of  the  eye  is  produced,  which 
the  observer.  A,  sees  on  looking  through  the  hole  in  the  reflector.     Let  nh 


Fig.  591- 

be  the  part  of  the  retina  on  which  the  light  is  concentrated,  pencils  of  rays 
proceeding  from  ab  would  form  an  inverted  and  aerial  image  of  ah  at  ab'. 
These  pencils,  however,  on  leaving  the  eye,  pass  through  the  Jens  ^,  and 
thus  the  image  a"b"  is  in  fact  formed,  inverted,  but  distinct,  and  in  a  position 
fit  for  vision. 

Modern  ophthalmoscopes  are  now  usually  provided  with  either  one  or 


6o6  On  Light.  [633- 

more  discs  of  metal  carrying  a  complete  series  of  convex  and  concave  lenses, 
or  with  a  similar  series  of  lenses  forming  a  chain  of  discs  fitted  in  the  handle 
and  body  of  the  instrument.  These  lenses  are  so  arranged  that  the  observer 
by  rotating  a  small  wheel  can  bring  a  lens  of  any  focal  length  he  pleases 
behind  the  aperture  of  the  mirror.  This  mirror  is  usually  of  a  much  shorter 
focal  length  than  in  the  instrument  previously  described,  and  is  tilted  at  an 
angle  so  that  its  plane  is  not  parallel  to  the  lenses  behind  the  mirrors.  By 
this  means,  the  ophthalmoscope  can  be  held  almost  touching  the  patient's 
eye,  while  the  light  can  still  be  reflected  into  the  patient's  eye  from  the 
mirror.  In  this  form  of  ophthalmoscope  the  lens  o  is  dispensed  with,  and  by 
placing  behind  the  mirrors  the  lens  which  corrects  the  sum  (or  difference) 
of  the  refractive  errors  of  the  patient's  and  the  observer's  eye,  the  observer's 
eye  is  rendered  emmetropic  for  the  pencils  of  light  which  reach  it.  In  this  case 
the  rays  of  light  from  the  lamp  are  reflected  from  the  mirrors  directly  on  the 
back  of  the  patient's  eye,  and  proceeding  from  ab.,  are  converted  by  the  lens 
placed  behind  the  mirrors  in  such  a  manner  that  they  form  a  distinct  image 
on  the  retina  of  the  observer's  eye.  In  the  latter  case  the  image  is  erect  and 
enlarged  about  fourteen  times,  while  in  the  former  indirect  method  the  image 
is  inverted  and  enlarged  only  about  four  or  five  times.  By  a  simple  contrivance 
in  the  form  of  a  swivel  carrying  the  two  kinds  of  mirrors,  either  can  be  at 
once  rotated  in  front  of  the  aperture,  and  thus  the  same  instrument  can  be 
employed  for  both  methods  of  examination.  The  direct  method  just 
described  affords  a  ready  means  of  estimating  the  refraction  of  the  patient's 
eye,  or,  in  other  words,  of  ascertaining  at  once  the  focal  length  of  the  lens 
necessary  to  enable  the  patient  to  see  distant  objects.  To  find  this,  all  that 
is  necessary  is  that  the  observer  should  previously  ascertain  the  exact 
number  of  diopters  necessary  to  correct  his  eye  for  distant  vision,  and  to 
accustom  himself  to  relax  his  accommodation  to  the  full  when  using  the 
instrument.  On  the  patient's  part  this  relaxation  occurs  insensibly.  The 
eye  of  both  persons  being  adjusted  for  distant  objects,  the  observer  now 
looks  through  the  aperture  of  the  mirror,  holding  the  instrument  as  close  to 
the  patient's  eye  as  possible.  Should  both  eyes  be  emmetropic  (normal), 
the  rays  of  light  which  are  practically  parallel  would  be  focussed  on  the 
retinae  of  both  the  eyes,  and  no  correcting  lens  would  be  needed.  Should 
the  observer's  eye  be  at  fault,  the  lens  which  wull  correct  it  for  parallel  rays 
will  enable  him  to  see  the  details  of  the  patient's  retina.  Should  both  eyes 
want  correcting,  then  the  number  of  diopters  which  are  found  necessary  to 
add  to  or  subtract  from  the  number  which  correct  the  observer's  eye  will 
indicate  the  error  in  the  patient's  eye.  By  thus  correcting  for  the  vessels  in 
the  retina  which  run  in  every  direction,  both  the  ;ixis  and  the  amount  of 
astigmatism  present  may  be  readily  ascertained. 


-635j  Phosphorescence.  607 


CHAPTER  VII. 

SOURCES   OF   LIGHT.      PHOSPHORESCENCE. 

634.  Various  sources  of  llgrht. — The  various  sources  of  light  are  the 
sun,  the  stars,  heat,  chemical  combination,  phosphorescence,  electricity,  and 
meteoric  phenomena.  The  last  two  sources  will  be  treated  under  the  articles 
Electricity  and  Meteorology. 

The  origin  of  the  light  emitted  by  the  sun  and  by  the  stars  is  unknown  ;  the 
sun  is  the  chief  source  ;  its  temperature  is  estimated  at  hundreds  of  thousands 
of  degrees.  The  ignited  envelope  by  which  the  sun  is  surrounded  is  gaseous, 
because  the  light  of  the  sun,  like  that  emitted  from  all  gaseous  bodies,  gives 
no  trace  of  polarisation  in  the  polarising  telescope,  chap.  viii. 

Terrestrial  bodies  become  sources  of  heat  when  they  are  raised  to  a 
sufficiently  high  temperature  ;  according  to  Draper  all  bodies  begin  to  glow 
with  a  red  heat  at  525°  ;  the  light  is  brighter  as  the  temperature  is  higher, 
and  at  1,170°  it  is  a  white  heat. 

The  luminous  effects  witnessed  in  many  chemical  combinations  are  due 
to  the  high  temperatures  produced.  Ordinar)'  luminous  flames  are  nothing 
more  than  gases  containing  solids  heated  to  incandescence. 

635.  Pbosphorescence. — Certain  bodies  have  the  property  of  becoming 
luminous  in  the  dark  without  any  considerable  rise  of  temperature.  This 
phenomenon,  which  is  well  seen  in  phosphorus,  is  for  this  reason  known  as 
phosphorescence.  Here  it  is  undoubtedly  due  to  a  slow  oxidation,  for  it 
ceases  in  spaces  where  no  oxygen  is  present.  Phosphorus  is  also  exhibited 
under  certain  conditions  by  decaying  animal  and  vegetable  matter.  This  is 
also  due  to  slow  oxidation. 

Phosphorescence  is  observed  in  living  animals,  of  which  the  best  known 
case  is  that  of  the  glowworm  ;  here  it  is  very  intense,  and  the  brightness 
seems  to  depend  on  the  will.  Its  light  consists  of  a  continuous  spectrum 
from  C  to  near  b.,  and  is  particularly  rich  in  blue  and  green  rays.  In  tropical 
climates  the  sea  is  often  covered  with  a  bright  phosphorescent  light  due  to 
myriads  of  small  luminous  infusoria  {iioctiliica  milians). 

Phosphorescence  by  rise  of  temperature.  This  is  best  seen  in  certain 
species  of  diamonds,  and  particularly  in  chlorophafte,  a  variety  of  fluorspar, 
which,  when  heated  to  300°  or  400°,  suddenly  becomes  luminous,  emitting  a 
greenish-blue  light  which  lasts  for  several  days. 

Hagenbach  examined  the  spectrum  of  phosphorescent  fluorspar,  and 
found  that  it  consisted  of  only  nine  bands  :  four  blue,  two  green,  two  yellow, 
and  one  orange.  As  the  relative  intensities  of  these  bands  are  continually 
changing,  it  is  easy  to  understand  the  difl'ercnt  colours  presented  by  diftercnt 
specimens  of  this  mineral. 


6o8  On  Light.  [635- 

Phosphoresccnce  by  ineclianical effects^  such  as  friction,  percussion,  cleavage, 
&c.  ;  for  example,  when  two  crystals  of  quartz  are  rubbed  against  each  other 
in  darkness,  when  a  lump  of  sugar  is  broken,  or  when  a  plate  of  mica  is 
cleft.  To  this  category  belong  also  the  disengagement  of  light  when 
arsenious  acid  crystallises. 

Phosphorescence  by  electricity,  like  that  which  results  from  the  friction  of 
mercury  against  the  glass  in  a  barometric  tube. 

636.  Phosphorescence  by  insolation. — A  large  number  of  substances, 
after  having  been  exposed  to  the  direct  action  of  sunlight,  or  even  of  the 
diffused  light  of  the  atmosphere,  emit  in  darkness  a  phosphorescence  the 
colour  and  intensity  of  which  depend  on  the  nature  and  physical  condition 
of  these  substances. 

This  was  first  observed  in  1604  in  Bolognese  phosphorus  (sulphide  of 
barium),  but  it  also  exists  in  a  great  number  of  substances.  The  sulphides 
of  calcium  and  strontium  are  those  which  present  it  in  the  highest  degree. 
They  must  be  prepared  in  the  dry  way  and  at  high  temperatures.  \\'hen 
well  prepared,  after  being  exposed  to  the  light,  they  are  luminous  for  several 
hours  in  darkness.  But  as  this  phosphorescence  takes  place  in  a  vacuum  as 
well  as  in  a  gaseous  medium,  it  cannot  be  attributed  to  a  chemical  action,  but 
rather  to  a  temporary  modification  which  the  body  undergoes  from  the  action 
of  light.  A  phosphorescent  sulphide  of  calcium  is  prepared  for  industrial 
purposes,  and  is  known  as  Balmain's  luminous  paint. 

After  the  substances  above  named,  the  best  phosphorescents  are  the 
following,  in  the  order  in  which  they  are  placed  :  a  large  number  of  diamonds 
(especially  yellow  ones),  and  most  specimens  of  fluorspar  ;  then  arragonite, 
calcareous  concretions,  chalk,  apatite,  heavy  spar,  dried  nitrate  of  calcium, 
and  dried  chloride  of  calcium,  cyanide  of  calcium,  a  large  number  of  stron- 
tium or  barium  compounds,  magnesium  and  its  carbonate,  &c.  Besides 
these  a  large  number  of  organic  substances  also  become  phosphorescent  by 
insolation  ;  for  instance,  dry  paper,  silk,  cane-sugar,  milk-sugar,  amber,  the 
teeth,  &c. 

The  different  spectral  rays  are  not  ecjually  well  fitted  to  render  substances 
phosphorescent.  The  maximum  effect  takes  place  in  the  violet  rays,  or 
even  a  little  beyond  ;  while  the  light  emitted  by  phosphorescent  bodies 
generally  corresponds  to  rays  of  a  smaller  refrangibility,  that  is,  of  greater 
wave-length,  than  those  of  the  light  received  by  them  and  giving  rise  to  the 
action. 

The  tint  which  phosphorescent  bodies  assume  is  very  variable,  and  even 
in  the  same  body  it  changes  with  the  manner  in  which  it  is  prepared.  In 
strontium  compounds  green  and  blue  tints  predominate;  and  orange,  yellow, 
and  green  tints  in  the  sulphides  of  barium. 

The  duration  of  phosphorescence  varies  also  in  different  bodies.  In  the 
sulphides  of  calcium  and  strontium,  phosphorescence  lasts  as  long  as  thirty 
hours  ;  with  other  substances  it  does  not  exceed  a  few  seconds,  or  even  a 
fraction  of  a  second. 

The  colour  emitted  by  an  artificial  phosphorescent  alters  with  the  tem- 
perature during  insolation.  Thus  with  sulphide  of  strontium  the  light  is  dark 
violet  at  -20°  C,  Ijright  blue  at  +40°,  bluish-green  at  70°,  greenish-j^ellow 
at  100°,  and  reddish-yellow  of  feeble  luminosity  at  .200°  C. 


-636] 


Pliosplioroscopc. 


Gog 


When  a  phosphorescent  body  has  been  heated  the  Hght  emitted  is 
brighter,  but  the  greater  the  emission  of  Hght  the  shorter  is  the  duration  of 
the  phosphorescence.  Heat,  therefore,  produces  a  more  rapid  irradiation 
of  the  hght. 

PhospJioroscope.  In  experimenting  with  bodies  whose  phosphorescence 
lasts  a  few  minutes  or  even  a  few  seconds,  it  is  simply  necessary  to  expose 
them  to  solar  or  diffused  light  for  a  short  time,  and  then  place  them  in  dark- 
ness :  their  luminosity  is  very  apparent,  especially  if  care  has  been  taken  to 


close  the  eyes  previously  for  a  few  moments.  But  in  the  case  of  bodies  whose 
phosphorescence  lasts  only  a  very  short  time,  this  method  is  inadequate. 
Becquerel  invented  an  ingenious  apparatus,  the  phosphoroscope,  by  which 
bodies  can  be  viewed  immediately  after  being  exposed  to  light  :  the  interval 
which  separates  the  insolation  and  observation  can  be  made  as  small  as 
possible,  and  measured  with  great  precision. 

This  apparatus  consists  of  a  closed  cylindrical  box,  AB  (fig.  592),  of 
blackened  metal  ;  on  the  ends  are  two  apertures  opposite  each  other  which 
have  the  form  of  a  circular  sector.     One  only  of  these,  (?,  is  seen  in  the 

R  R 


6io  On  Light.  [636- 

figure.  The  box  is  fixed,  but  it  is  traversed  in  the  centre  by  a  movable  axis, 
to  which  are  fixed  two  circular  screens,  MM  and  PP,  of  blackened  metal 
(fig.  593).  Each  of  these  screens  is  perforated  by  four  apertures  of  the 
same  shape  as  those  in  the  box  ;  but  while  the  latter  correspond  to  each 
other,  the  apertures  of  the  screens  alternate,  so  that  the  open  parts  of  the 
one  correspond  to  the  closed  parts  of  the  other.  The  two  screens,  as 
already  mentioned,  are  placed  in  the  box,  and  fixed  to  the  axis,  which  by 
means  of  a  train  of  wheels,  worked  by  a  handle,  can  be  made  to  turn  with 
any  velocity. 

In  order  to  investigate  the  phosphorescence  of  any  body  by  means  of 
this  instrument,  the  body  is  placed  on  a  stirrup  interposed  between  the  two 
rotating  screens.  The  light  cannot  pass  at  the  same  time  through  the 
opposite  apertures  of  the  sides  A  and  B,  because  one  of  the  closed  parts  of 
the  screen  MM,  or  of  the  screen  PP,  is  always  between  them.  So  that  when 
a  body,  a,  is  illuminated  by  light  from  the  other  side  of  the  apparatus,  it 
could  not  be  seen  by  an  observer  looking  at  the  aperture,  o^  for  then  it  would 
be  masked  by  the  screen  PP.  Accordingly,  when  an  observer  saw  the  body 
(?,  it  would  not  be  illuminated,  as  the  light  would  be  intercepted  by  the  closed 
parts  of  a  screen  MM.  The  body  a  would  alternately  appear  and  disappear; 
it  would  disappear  during  the  time  of  its  being  illuminated,  and  appear  when 
it  was  no  longer  so.  The  time  which  elapses  between  the  appearance  and 
disappearance  depends  on  the  velocity  of  rotation  of  the  screens.  Suppose, 
for  instance,  that  they  made  150  turns  in  a  second  ;  as  one  revolution  of  the 
screens  is  effected  in  -^  of  a  second,  there  would  be  four  appearances  and 
four  disappearances  during  that  time.  Hence  the  length  of  time  elapsing 
between  the  time  of  illumination  and  of  observation  would  be  i  of  j',„  of  a 
second  or  o-ooo8  of  a  second. 

Observations  with  the  phosphoroscope  are  made  in  a  dark  chamber,  the 
observer  being  on  that  side  on  which  is  the  wheelwork.  A  ray  of  solar  or 
electric  light  is  allowed  to  fall  upon  the  substance  <?,  and,  the  screens  being 
made  to  rotate  more  or  less  rapidly,  the  body  a  appears  luminous  by  trans- 
parence in  a  continuous  manner,  when  the  interval  between  insolation  and 
observation  is  less  than  the  duration  of  the  phosphorescence  of  the  body. 
By  experiments  of  this  kind,  Becquerel  has  found  that  substances  which 
usually  are  not  phosphorescent  become  so  in  the  phosphoroscope  ;  such,  for 
instance,  is  Iceland  spar.  Uranium  compounds  present  the  most  brilliant 
appearance  in  this  apparatus  ;  they  emit  a  very  bright  luminosity  when  the 
observer  can  see  them  0-03  or  0-04  of  a  second  after  insolation.  But  a  large 
number  of  bodies  produce  no  effect  in  the  phosphoroscope  ;  for  instance, 
(juartz,  sulphur,  phosphorus,  metals,  and  licjuids. 


-637J  6ii 


CHAPTER  VIII. 

DOUBLE  REFRACTION.      INTERFERENCE.      POLARISATION. 

637.  Tbe  undulatory  tbeory  of  lig:ht. — It  has  been  already  stated  (499) 
that  the  phenomenon  of  Hght  is  ascribed  to  undulations  propagated  through 
an  exceedingly  rare  medium  called  the  luminiferous  ether,  which  is  supposed 
to  per\-ade  all  space,  and  to  exist  between  the  molecules  of  the  ordinary 
forms  of  matter.  In  short,  it  is  held  that  light  is  due  to  the  undulations  of 
the  ether,  just  as  sound  is  due  to  undulations  propagated  through  the  air. 
In  the  latter  case  the  undulations  cause  the  drum  of  the  ear  to  vibrate  and 
produce  the  sensation  of  sound.  In  the  former  case,  the  undulations  cause 
points  of  the  retina  to  vibrate  and  produce  the  sensation  of  light.  The  two 
cases  differ  in  this,  that  in  the  case  of  sound  there  is  independent  evidence 
of  the  existence  and  vibration  of  the  medium  (air)  which  propagates  the 
undulation  ;  whereas  in  the  case  of  light  the  existence  of  the  medium  and 
its  vibrations  is  assumed,  because  that  supposition  connects  and  explains  in 
the  most  complete  manner  a  long  series  of  very  various  phenomena.  There 
is,  however,  no  independent  evidence  of  the  existence  of  the  luminiferous 
ether. 

The  analogy  between  the  phenomena  of  sound  and  light  is  very  close  ; 
thus,  the  intensity  of  a  sound  is  greater  as  the  amplitude  of  the  vibration  of 
each  particle  of  the  air  is  greater,  and  the  intensity  of  light  is  greater  as  the 
amplitude  of  the  vibration  of  each  particle  of  the  ether  is  greater.  Again,  a 
sound  is  more  acute  as  the  length  of  each  undulation  producing  the  sound  is 
less,  or,  what  comes  to  the  same  thing,  according  as  the  number  of  vibrations 
per  second  is  greater.  In  like  manner,  the  colour  of  light  is  different  ac- 
cording to  the  length  of  the  undulation  producing  the  light :  a  red  light  is 
due  to  a  comparatively  long  undulation,  and  corresponds  to  a  deep  sound, 
while  a  violet  light  is  due  to  a  short  undulation,  and  corresponds  to  an  acute 
sound. 

Although  the  length  of  the  undulation  cannot  be  observed  directly,  yet 
it  can  be  inferred  from  certain  phenomena  with  great  exactness.  The 
following  table  gives  the  lengths,  in  inches  and  millimetres,  of  the  undulations 
corresponding  to  the  light  at  the  principal  dark  lines  of  the  spectrum  : — 

Length  of  Length  of 

Undul.-ition  Undulation- 

Dark  line  in  inches  in  millimetres 

B  . 0-0000271  00006874 

C 00000258  0-0006562 

D, 0-0000232  0-0005897 

E 0-0000207  0-0005271 

F 0000019 1  0-0004S62 

G  .    .    .    .    .    .    .  0-0000169  0-0004311 

H,  .    .    .    .    .    .    .  0-0000159  0-0003969 


6i2  On  Light.  [637- 

It  will  be  remarked  that  the  limits  are  very  narrow  within  which  the 
lengths  of  the  undulations  of  the  ether  must  be  comprised,  if  they  are  to 
be  capable  of  producing  the  sensation  of  light.  In  this  respect  light  is  in 
marked  contrast  to  sound.  For  the  limits  are  very  wide  within  which  the 
lenLjths  of  the  undulations  of  the  air  may  be  comprised  when  they  produce 
the  sensation  of  sound  (244). 

The  undulatory  theory  readily  explains  the  colours  of  different  bodies. 
According  to  that  theory,  certain  bodies  have  the  property  of  exciting  undula- 
tions of  different  lengths,  and  thus  producing  light  of  given  colours.  White 
light  or  daylight  results  from  the  coexistence  of  undulations  of  all  possible 
lengths. 

The  colour  of  a  body  is  due  to  the  power  it  has  of  extinguishing  certain 
vibrations,  and  of  reflecting  others  ;  and  the  body  appears  of  the  colour  pro- 
duced by  the  coexistence  of  the  reflected  vibrations.  A  body  appears  white 
when  it  reflects  all  different  vibrations  in  the  proportion  in  which  they  are 
present  in  the  spectrum  ;  it  appears  black  when  it  reflects  light  in  such 
small  quantities  as  not  to  affect  the  eye.  A  red  body  is  one  which  has  the 
property  of  reflecting  in  predominant  strength  those  vibrations  which  pro- 
duce the  sensation  of  red.  This  is  seen  in  the  fact  that,  when  a  piece  of  red 
paper  is  held  against  the  daylight,  and  the  reflected  light  is  caught  on  a 
white  wall,  this  also  appears  red.  A  piece  of  red  paper  in  the  red  part  of 
the  spectrum  appears  of  a  brighter  red,  and  a  piece  of  blue  paper  held  in 
the  blue  part  appears  a  brighter  blue  ;  while  a  red  paper  placed  in  the 
violet  or  lolue  part  appears  almost  black.  In  the  last  case  the  red  paper 
can  only  reflect  red  rays,  while  it  extinguishes  the  blue  rays,  and  as  the  blue 
of  the  spectrum  is  almost  free  from  red,  so  little  is  reflected  that  the  paper 
appears  black. 

The  undulatory  theory  likewise  explains  the  colours  of  transparent  bodies. 
Thus,  a  vibrating  motion  on  reaching  a  body  sets  it  in  vibration.  So  also  the 
vibrations  of  the  luminiferous  ether  are  communicated  to  the  ether  in  a  body, 
and,  setting  it  in  motion,  produce  light  of  different  colours.  When  this  motion 
is  transmitted  through  any  body,  it  is  said  to  be  transparent  or  translucent, 
according  to  the  different  degrees  of  strength  with  which  this  transmission  is 
effected.     In  the  opposite  case  it  is  said  to  be  opaque. 

When  light  falls  upon  a  transparent  body,  the  body  appears  colourless  if 
all  the  vibrations  are  transmitted  in  the  proportion  in  which  they  exist  in  the 
spectrum.  Hut  if  some  of  the  vibrations  are  checked  or  extinguished,  the 
emergent  light  will  be  of  the  colour  produced  by  the  coexistence  of  the  un- 
checked vibrations.  Thus,  when  a  piece  of  blue  glass  is  held  before  the  eye, 
the  vibrations  producing  red  and  yellow  are  extinguished,  and  the  colour  is 
due  to. the  emergent  vibrations  which  produce  blue  light. 

The  undulatory  theory  also  accounts  for  the  reflection  and  refraction  of 
light,  as  well  as  oilier  phenomena  which  arc  yet  to  be  described.  The  ex- 
planation of  the  refraction  of  light  is  of  so  much  importance  that  we  shall 
devote  to  it  the  following  article. 

638.  Physical  explanation  of  single  relVactlon. —  The  cxjilanation  of 
this  phenomenon  by  means  of  the  undulatory  theory  of  light  presupposes 
that  of  the  mode  of  propagation  of  a  plane  wave.  Now,  if  a  disturbance 
originated  at  any /fvV// of  the  ether,  it  would  be  propagated  as  a  spherical 


-639] 


Double  Refraction. 


613 


wave  in  all  directions  round  that  point  with  a  uniform  velocity.  If,  instead 
of  a  single  point,  we  consider  the  front  of  a  plane  wave,  it  is  evident  that 
disturbances  originate  simultaneously  at  all  points  of  the  front,  and  that 
spherical  waves  proceed  from  each  point  with  the  same  uniform  velocity. 
Consequently,  all  these  spheres  will  at  any  subsequent  instant  be  touched  by 
a  plane  parallel  to  the  original  plane.  The  disturbances  propagated  from 
the  points  in  the  first  position  of  the  wave  will  mutually  destroy  each  other, 
except  in  the  tangent  plane  ;  consequently  the  wave  advances  as  a  plane 
wave,  its  successive  positions  being  the  successive  positions  of  the  tangent 
plane.  If  the  wave  moves  in  any  medium  with  a  velocity  ?/,  it  will  describe 
a  space  vt  in  a  time  /,  in  a  direction  at  right  angles  to  the  wave-front. 

In  any  given  moment  let  tun  (fig.  594)  be  the  position  of  the  wave-front  of 
a  ray  of  light,  which,  moving  through  any  medium,  meets  the  plane  surface 
AB  of  any  denser  refract- 


ing medium.  In  the  same 
moment  in  which  the 
wa\e-front  reaches  «,  in 
becomes  the  centre  of  a 
spherical  wave  system 
which  moves  in  the  second 
medium  ;  and,  as  the  elas- 
ticity of  the  second  me- 
dium is  different  from 
that  of  the  first,  the  velo- 
city of  propagation  of  the 
wave  in  the  two  media  will  be  dififerent. 
71  to  K,  the  corresponding  wave  startin 


-^ 


Fig-  594- 


While  the  plane  wave  moves  from 
from  1)1  reaches  the  surface  of  a 
sphere  the  radius  of  which  is  less  than  «K,  if  the  second  medium  is  denser 
than  the  first.  The  incident  wave  in  like  manner  reaches  in'  and  ;/  simul- 
taneously, and  while  n'  moves  to  K,  m'  moves  to  o',  the  surface  of  a  sphere 
the  radius  of  which,  m'o\  is  to  mo  as  «'K  is  to  «K.  All  the  elementary 
waves  proceeding  from  points  intermediate  to  n  and  K  which  arise  from 
the  same  incident  wave,  touch  one  and  the  same  plane  Y.0'0,  and  the 
refracted  ray  proceeds  in  the  new  medium  perpendicular  to  this  tangent 
plane. 

Now  ;;K  and  nio  are  proportional  to  the  velocities  of  light  in  the  two 
media  respectively  :  let  ;«K  be  taken  as  unit  of  length,  then 
7zK  =  sin  «;//K  and  mo  =  sin  niKo. 

Now  fn?iK  is  the  angle  of  incidence  of  the  ray,  and  mKo  is  the  angle  of 
refraction,  and  nK  and  mo  are  proportional  to  the  velocities  of  light  in  the 
two  media  respectively  ;  hence  we  see  that  these  velocities  are  to  each 
other  in  the  same  ratio  as  the  sines  of  the  angles  of  incidence  and  refraction  ; 
a  conclusion  which  agrees  with  the  results  of  direct  observation  (506),  and 
forms  a  beautiful  confirmation  of  the  truth  of  the  undulatory  theory. 


DOUBLE    REFRACTION. 

6j9.  Double  refraction. — It  has  been  already  stated  (536)  that  a  large 
number  of  crystals  possess  the  property  of  double  refraction,  in  virtue  of 


6i4  On  Light. 

which  a  single  incident  ray  in  passing  through  any  one  of  them  is  divided 
into  two,  or  undergoes  bifurcation^  whence  it  follows  that,  when  an  object 
is  seen  through  one  of  these  crystals,  it  appears  double.  The  fact  of  the 
existence  of  double  refraction  in  Iceland  spar  was  first  stated  by  Bartholin 
in  1669,  but  the  law  of  double  refraction  was  first  enunciated  exactly  by 
Huyghens,  in  his  treatise  on  light,  written  in  1678  and  published  in  1690. 

Crystals  which  possess  this  peculiarity  are  said  to  be  double-refracting. 
It  is  found  to  a  greater  or  less  extent  in  all  crystals  which  do  not  belong  to 
the  cubical  system.  Bodies  which  crystallise  in  this  system,  and  those 
which,  like  glass,  are  destitute  of  crystallisation,  have  no  double  refraction. 
The  property  can,  however,  be  imparted  to  them  when  they  are  unequally 
compressed,  or  when  they  are  cooled  quickly  after  having  been  heated,  in 
which  state  glass  is  said  to  be  ujumnea/ed.  Of  all  substances,  that  which 
possesses  it  most  remarkably  is  Iceland  spar  or  crystallised  carbonate  of 
calcium.  In  many  substances,  the  power  of  double  refraction  can  hardly 
be  proved  to  exist  directly  by  the  bifurcation  of  an  incident  ray  ;  but  its 
existence  is  shown  indirectly  by  their  being  able  to  depolarise  light  (665). 

Fresnel  explained  double  refraction  by  assuming  that  the  ether  in  double- 
refracting  bodies  is  not  equally  elastic  in  all  directions  ;  from  which  it 
follows  that  the  vibrations,  in  certain  directions  at  right  angles  to  each 
other,  are  transmitted  with  unequal  velocities  ;  these  directions  being  depen- 
dent on  the  constitution  of  the  crystal.  This  hypothesis  is  confirmed  by 
the  property  which  glass  acquires  of  becoming  double-refracting  by  being 
unannealed  and  by  pressure. 

640.  Vniaxial  crystals. — In  all  double-refracting  crystals  there  is  one 
direction,  and  in  some  a  second  direction, possessing^  the  following  property : — 
When  a  point  is  looked  at  through  the  crystal  in  this  particular  direction,  it 
does  not  appear  double.  The  lines  fixing  these  directions  are  called  optic 
axes  ;  and  sometimes,  though  not  very  properly,  axes  of  double  refraction. 
A  crystal  is  called  u?iiaxial  when  it  has  otie  optic  axis  ;  that  is  to  say,  when 
there  is  one  direction  within  the  crystal  along 
which  a  ray  of  light  can  proceed  without 
bifurcation.  When  a  crystal  has  two  such 
axes,  it  is  called  a  biaxial  crystal. 

The  uniaxial  crystals  most  frequently 
used  in  optical  instruments  are  Iceland  spar, 
cjuartz,  and  tourmaline.  Iceland  spar  crystal- 
lises in  rhombohedra,  whose  faces  form  with 
each  other  angles  of  105°  5'  or  74°  55'.  It 
has  eiglit  solid  angles  (see  fig.  595).  Of  these,  two,  situated  at  the  extremi- 
ties of  one  of  the  diagonals,  are  severally  contained  by  three  obtuse  angles. 
A  line  drawn  within  one  of  these  two  angles  in  such  a  manner  as  to  be 
equally  inclined  to  the  three  edges  containing  the  angle  is  called  the  axis  of 
the  crystal.  If  all  the  edges  of  the  crystal  were  equal,  the  axis  of  the  crystal 
would  coincide  with  the  diagonal,  ab. 

Brewster  showed  that  in  all  uniaxial  crystals  the  optic  axis  coincides  with 
the  axis  of  crystallisation. 

The  principal  plane  with  reference  to  a  point  of  any  face  of  a  crystal, 
whether  natural  or  artificial,  is  a  plane  drawn  througli  that  point  at  right 


-642]      Laws  of  Double  Refraction  in  a  Uniaxial  Crystal.      615 

angles  to  the  face  and  parallel  to  the  optic  axis.  If  in  fig.  595  we  suppose 
the  edges  of  the  rhombohedron  to  be  equal,  the  diagonal  plane  abed  contains 
the  optic  axis  {ab),  and  is  at  right  angles  to  the  faces  aedf  ^\\A  chbg;  conse- 
quently it  is  parallel  to  the  principal  plane  at  any  point  of  either  of  those 
two  faces.  For  this  reason  abed  is  often  called  the  principal  plane  with 
I'espect  to  those  faces. 

641.  Ordinary  and  extraordinary  ray. — Of  the  two  rays  into  which 
an  incident  ray  is  divided  on  entering  a  uniaxial  crystal  one  is  called  the 
ordinary  and  the  other  the  extraordinary  ray.  The  ordinal  y  ray  follows 
the  laws  of  single  refraction  ;  that  is,  with  respect  to  that  ray  the  sine  of  the 
angle  of  incidence  bears  a  constant  ratio  to  the  sine  of  the  angle  of  refraction, 
and  the  plane  of  incidence  coincides  with  the  plane  of  refraction.  Except 
in  particular  positions,  the  extraordinary  ray  follows  neither  of  these  laws. 
The  images  corresponding  to  the  ordinary  and  extraordinary  rays  are  called 
the  ordinary  and  extraordinary  images  respectively. 

If  a  transparent  specimen  of  Iceland  spar  be  placed  over  a  dot  of  ink, 
on  a  sheet  of  white  paper,  two  images  will  be  seen.  One  of  them,  the 
ordinary  image,  will  seem  slightly  nearer  to  the  eye  than  the  other,  the  extra- 
ordinary image.  Suppose  the  spectator  to  view  the  dot  in  a  direction  at 
right  angles  to  the  paper,  then,  if  the  crystal,  with  the  face  still  on  the  paper, 
be  turned  round,  the  ordinary  image  will  continue  fixed,  and  the  extraordinary 
image  will  describe  a  circle  round  it,  the  line  joining  them  being  always  in 
the  direction  of  the  shorter  diagonal  of  the  face  of  the  crystal,  supposing  its 
edges  to  be  of  equal  length.  In  this  case  it  is  found  that  the  angle  between 
the  ordinary  and  extraordinary  ray  is  6°  12'. 

642.  The  laMTS  of  double  refraction  in  a  uniaxial  crystal. — These 
phenomena  are  found  to  obey  the  following  laws  : — 

i.  Whatever  be  the  plane  of  incidence,  the  ordinary  ray  always  obeys 
the  two  general  laws  of  single  refraction  (537).  The  refractive  index  for  the 
ordinary  ray  is  called  the  ordinary  refractive  index. 

ii.  In  every  section  perpendicular  to  the  optic  axis  the  extraordinary  ray  . 
also  follows  the  laws  of  single  refraction.     Consequently,  in  this  plane,  the 
extraordinary  ray  has  a  constant  refractive  index,  which  is  called  the  ordinary 
refractive  index. 

iii.  In  every  principal  section  the  e.xtraordinary  ray  follows  the  second 
law  only  of  single  refraction  ;  that  is,  the  planes  of  incidence  and  refraction 
coincide,  but  the  ratio  of  the  sines  of  the  angles  of  incidence  and  refraction 
is  not  constant. 

iv.  The  velocities  of  light  along  the  rays  are  unequal.  It  can  be  shown 
that  the  difference  between  the  squares  of  the  reciprocals  of  the  velocities 
along  the  ordinary  and  extraordinary  rays  is  proportional  to  the  square  of  the 
sine  of  the  angle  between  the  latter  ray  and  the  axis  of  the  crystal. 

There  is  an  important  difference  between  the  velocity  of  the  ray  and  the 
velocity  of  the  corresponding  plane  wave.  If  the  velocities  of  the  plane 
waves  corresponding  to  the  ordinary  and  extraordinary  rays  are  considered, 
the  difference  between  the  squares  of  these  velocities  is  proportional  to  the 
square  of  the  sine  of  the  angle  between  the  axis  of  the  crystal,  and  the  normal 
to  that  plane  wave  which  corresponds  to  the  extraordinary  ray.  The  normal 
and  the  ray  do  not  generally  coincide. 


6i6  On  Light.  [642- 

Huyghens  gave  a  very  simple  geometrical  construction,  by  means  of 
which  the  directions  of  the  refracted  rays  can  be  determined  when  the  direc- 
tions of  the  incident  ray  and  of  the  axis  are  known  relatively  to  the  face  of 
the  crystal.  This  construction  was  not  generally  accepted  by  physicists 
until  Wollaston,  and  subsequently  Malus,  showed  its  truth  by  numerous  exact 
measurements. 

643.  Positive  and  neg'ative  uniaxial  crystal. — The  term  extraordinary 
refractive  index  has  been  defined  in  the  last  article.  Yox  the  same  crystal 
its  magnitude  always  differs  from  that  of  the  ot'dinary  refractive  index  ;  for 
example,  in  Iceland  spar  the  ordinary  refractive  index  is  1-654,  while  the 
extraordinary  refractive  index  is  r483.  In  this  case  the  ordinary'  index 
exceeds  the  extraordinary  index.  When  this  is  the  case  the  crystal  is  said  to 
be  negative.  On  the  other  hand,  when  the  e.xtraordinary  index  exceeds  the 
ordinary  index,  the  crystal  is  said  to  be  positive.  The  following  list  gives  the 
names  of  some  of  the  principal  uniaxial  crystals  : — 

Negative  Uniaxial  Crystals. 
Iceland  spar  Ruby  Pyromorphite 

Tourmaline  Emerald  Ferrocyanide  of  potassium 

Sapphire  Apatite  Nitrate  of  sodium 

Positive  Uniaxial  Crystals. 
Zircon  Apophyllite  Titanite 

Quartz  Ice  Boracite 

644.  Double  refVactlon  In  biaxial  crystals. — A  large  number  of  crystals, 
including  all  those  belonging  to  the  tri/netric,  the  monoclinic,  and  the  triclinic 
systems,  possess  two  optic  axes  ;  in  other  words,  in  each  of  these  crystals 
there  are  two  directions  along  which  a  ray  of  light  passes  without  bifurcation. 
A  line  bisecting  the  acute  angle  between  the  optic  axes  is  called  the  medial 
line  ;  one  that  bisects  the  obtuse  angle  is  called  the  supplementary  line. 
It  has  been  found  that  the  medial  and  supplementary  lines  and  a  third  line 
at  right  angles  to  both  are  closely  related  to  the  fundamental  form  of  the 
crystal  to  which  the  optic  axes  belong.  The  acute  angle  between  the  optic 
axes  is  different  in  different  crystals.  The  following  table  gives  the  magnitude 
of  this  angle  in  the  case  of  certain  crystals  : — 


Xitre  . 

.       5°  20' 

Mica     . 

•     45° 

0' 

.Strontianite 

.       6    56 

.Sugar  . 

•     50 

0 

•A.rragonite  . 

.      18    iS 

Selenite 

.     60 

0 

Anhydrite    . 

.     28      7 

Epidote 

•     «4 

19 

Heavy  spar 

■     7>1    42 

Sul])hate 

of  iron   . 

.     90 

0 

When  a  ray  of  light  enters  a  biaxial  crystal,  and  passes  in  any  direction 
not  coinciding  with  an  optic  axis,  it  bifurcates  ;  in  this  case,  however, 
neither  ray  conforms  to  the  laws  of  single  refraction,  but  both  are  extra- 
ordinary rays.  To  this  general  statement  the  following  exception  must  be 
made  :  —  In  a  section  of  a  crystal  at  right  angles  to  the  medial  line  one  ray 
follows  the  laws  of  ordinary  refraction,  and  in  a  section  at  right  angles  to 
the  supplementary  line  the  other  ray  follows  the  laws  of  ordinary  refraction. 


-645] 


Intcrfcroicc  of  Light. 


617 


INTERFERKNCK   AMI    DIFKRACTIOX. 

645.  Interference  of  ligrbt. — The  name ////tvymv/t^^  is  given  to  the  re- 
ciprocal action  which  two  rays  of  light  exert  upon  each  other  when  they  are 
emitted  from  two  neighbouring  sources,  and  meet  each  other  under  a  very 
small  angle.  This  action  may  be  observed  by  means  of  the  following  ex- 
periment : — In  the  shutter  of  a  dark  room  two  very  small  apertures  of  the 
same  diameter  are  made  close  to  each  other.  The  apertures  are  closed 
by  pieces  of  coloured  glass— red,  for  example — by  which  two  pencils  of 
homogeneous  light  are  mtroduced.  These  two  pencils  form  two  divergent 
luminous  cones,  which  meet  at  a  certain  distance  ;  they  are  received  on  a 
white  screen  a  little  beyond  the  place  at  which  they  meet,  and  in  the  segment 
common  to  the  two  discs  which  form  upon  this  screen  some  very  well-defined 
alternations  of  red  and  black  bands  are  seen.  If  one  of  the  two  apertures 
be  closed,  the  fringes  disappear,  and  are  replaced  by  an  almost  uniform  red 
tint.  From  the  fact  that  the  dark  fringes  disappear  when  one  of  the  beams 
is  intercepted,  it  is  concluded  that  they  arise  from  the  interference  of  the  two 
pencils  which  cross  obliquely. 

This  experiment  was  first  made  by  Cirimaldi,  but  was  modified  by 
Young.    Grimaldi  had  drawn  from  it  the  conclusion  that  light  added  to  light 


Fig.  596. 

produced  darkness.  The  full  importance  of  this  principle  remained  for 
a  long  time  unrecognised,  until  these  inquiries  were  resumed  by  Young 
and  Fresnel,  of  whom  the  latter,  by  a  modification  of  Grimaldi's  experi- 
ment, rendered  it  an  experitneniuvi  crucis  of  the  truth  of  the  undulator\- 
hypothesis. 

In  Grimaldi's  experiment  diffraction  (646)  takes  place,  for  the  luminous 
rays  pass  by  the  edge  of  the  aperture.  In  the  following  experiment,  which 
is  due  to  Fresnel,  the  two  pencils  interfere  without  the  possibility  of  diffrac- 
tion. 

Two  plane  mirrors,  AB  and  BC  (fig.  596),  of  metal,  are  arranged  close  to 
each  other,  so  as  to  form  a  very  obtuse  angle,  ABC,  which  must  be  very  little 


6i8  On  Light.  [645- 

less  than  i8o°.  A  pencil  of  monochromatic  light — red,  for  instance — which 
passes  into  the  dark  chamber,  is  brought  to  a  focus,  F,  by  means  of  a  lens, 
L.  On  diverging  from  F  the  rays  fall  partly  on  AB,  and  partly  on  BC.  If 
BA  is  produced  to  P  and  FPFj  is  drawn  at  right  angles  to  AP,  and  if  PFj  is 
made  equal  to  PF,  then  the  rays  which  fall  on  AB  will,  after  reflection,  pro- 
ceed as  if  they  diverged  from  Fj.  If  a  similar  construction  is  made  for  the 
rays  falling  on  BC,  they  will  proceed  after  reflection  as  if  they  diverged  from 
F...  A  little  consideration  will  show  that  Fj  and  Fo  are  very  near  each  other. 
Suppose  the  reflected  rays  to  fall  on  a  screen  SSj  placed  nearly  at  right 
angles  to  their  directions.  Every  point  of  the  screen  which  receives  light 
from  both  pencils  is  illuminated  by  both  rays,  viz.,  one  from  F,,  the  other 

from  F„  :  thus  the 
jjoint  H  is  illuminated 
iDy  two  rays,  as  also 
are  K  and  I.  Now 
the  combined  action 
of  these  two  pencils  is 
to  form  a  series  of 
parallel  bands  alter- 
nately light  and  dark 
on  the  screen  at  right 
angles  to  the  plane  of 
the  paper  (fig.  597). 
They   are    distributed 


Fig   597. 


symmetrically  in  reference  to  one  of  them  cc,  which  is  more  brilliant  than 
the  others,  and  which  is  called  the  central  fringe.  This  is  the  fundamental 
phenomenon  of  interference  ;  and  that  it  results  from  \\\^  joint  action  of  the 
two  pencils  is  plain,  for  if  the  light  which  falls  upon  either  of  the  mirrors  is 
cut  off,  the  dark  bands  altogether  disappear. 

The  experiment  may  also  be  made  by  means  of  Ohm's  prism,  which  is  a 
prism  in  which  the  refracting  angle  is  very  nearly  180°. 

This  remarkable  experiment  is  explained  in  the  most  satisfactoiy  manner 
by  the  undulatory  theory  of  light.  The  explanation  exactly  resembles  that 
already  given  of  the  formation  of  nodes  and  loops  by  the  combined  action  of 
two  aerial  waves  (262)  ;  the  only  difference  being  that  in  that  case  the  vibrat- 
ing particles  were  supposed  to  be  particles  of  air,  whereas,  in  the  present 
case,  the  vibrating  particles  are  supposed  to  be  those  of  the  luminiferous 
ether.  Consider  any  point  K  on  the  screen,  and  first  let  us  suppose  the  dis- 
tance of  K  from  F,  and  F.^  to  be  equal.  Then  the  undulations  which  reach 
K  will  always  be  in  the  same  phase,  and  the  particle  of  ether  at  K  will  vibrate 
as  if  the  light  came  from  one  source  :  the  amplitude  of  the  vibration,  how- 
ever, will  be  increased  in  exactly  the  same  manner  as  happens  at  a  loop  or 
ventral  point  ;  c()nset|uently,  at  K  the  intensity  of  the  light  will  be  increased. 
And  the  same  will  Ije  true  for  all  parts  on  the  screen,  such  that  the  difference 
between  their  distances  from  the  two  images  equals  the  length  of  one,  two 
three,  &c.,  undulations.  If,  on  the  other  hand,  the  distances  of  K  from  F, 
and  v.,  differ  by  tlie  length  of  half  an  undulation,  then  the  two  waves  would 
reach  K  in  exactly  opposite  phases.  Consequently,  whatever  velocity  would 
be  communicated  at  any  instant  to  a  particle  of  ether  by  tlic  one  findulation, 


-646] 


Diffraction  and  Fringes. 


619 


an  exactly  equal  and  opposite  velocity  would  be  communicated  by  the  other 
undulation,  and  the  particle  would  he  pcnna/ioi/ly  at  rest,  or  there  would  be 
darkness  at  that  point  ;  this  result  being  produced  in  a  manner  precisely  re- 
sembling the  formation  of  a  ?iodal  point  already  explained.  The  same  will 
be  true  for  all  positions  of  K,  such  that  the  difference  between  its  distances 
from  Fj  and  F,_,  is  equal  to  three  halves,  or  five  halves,  or  seven  halves,  &:c., 
of  an  undulation.  Accordingly,  there  will  be  on  the  screen  a  succession  of 
alternations  of  light  and  dark  points,  or  rather  lines— for  what  is  true  of  points 
in  the  plane  of  the  paper  (fig.  597)  will  be  equally  true  of  other  points  on  the 
screen,  which  is  supposed  to  be  at  right  angles  to  the  plane  of  the  paper. 
Between  the  light  and  dark  lines  the  intensity  of  the  hght  will  vary,  increas- 
ing gradually  from  darkness  to  its  greatest  intensity,  and  then  decreasing 
to  the  second  dark  line,  and  so  on. 

If  instead  of  red  light  any  other  coloured  light  were  used — for  example, 
violet  light— an  exactly  similar  phenomenon  would  be  produced,  but  the  dis- 
tance from  one  dark  line  to  another  would  be  different.  If  white  light  were 
used,  each  separate  colour  tends  to  produce  a  different  set  of  dark  lines. 
Now  these  sets  being  superimposed  on  each  other,  and  not  coinciding,  the 
dark  lines  due  to  one  colour  are  illuminated  by  other  colours,  and  instead  of 
dark  lines  a  succession  of  coloured  bands  is  produced.  The  number  ot 
coloured  bands  produced  by  white  light  is  much  smaller  than  the  number  of 
dark  lines  produced  by  a  homogeneous  light  ;  since  at  a  small  distance  from 
the  middle  band  the  various  colours  are  completely  blended,  and  a  uniform 
white  light  produced. 

646.  Diffraction  and  frlngres. — Diffraction  is  a  modification  which  light 
undergoes  when  it  passes  the  edge  of  a  body,  or  when  it  traverses  a  small 
aperture — a  modification  in  virtue  of  which  the  luminous  rays  appear  to 
become  bent,  and  to  penetrate  into  the  shadow. 

This  phenomenon  may  be  observed  in  the  following  manner  : — A  beam  of 
sunlight  is  allowed  to  pass  through  a  very  small  aperture  in  the  shutter  of 


Fig.  59S. 

a  dark  room,  where  it  is  received  on  a  condensing  lens,  L  (fig.  59S),  with  a 
short  focal  length.  A  red  glass  is  placed  in  the  aperture  so  as  to  allow  only 
red  light  to  pass.  An  opaque  screen,  e,  with  a  sharp  edge  a — a  razor,  for 
instance — is  placed  behind  the  lens  beyond  its  focus,  and  intercepts  one  por- 
tion of  the  luminous  cone,  while  the  other  is  projected  on  the  screen  b,  of 
which  B  represents  a  front  view.  The  following  phenomena  are  now  seen  : — 
Within  the  geometrical  shadow,  the  limit  of  which  is  represented  by  the  line 
ab,  a  faint  light  is  seen,  which  gradually  fades  in  proportion  as  it  is  farther 
from  the  limits  of  the  shadow.  In  this  part  of  the  screen — which,  being  above 
the  line  ab,  might  be  expected  to  be  uniformly  illuminated— a  series  of 
alternate  dark  and  light  bands  or  fringes  is  seen  parallel  to  the  line  of  shadow, 
which  gradually  become  more  indistinct  and  ultimately  disappear.    The  limits 


620  On  Light.  [646- 

between  the  light  and  dark  fringes  are  not  quite  sharp  lines  :  there  are  parts 
of  maximum  and  minimum  intensity  which  gradually  fade  off  into  each  other. 
All  the  colours  of  the  spectrum  give  rise  to  the  same  phenomenon,  but 
the  fringes  are  broader  in  proportion  as  the  light  is  less  refrangible.  Thus 
with  red  light  they  are  broader  than  with  green,  and  with  green  than  with 
violet.  Hence,  with  white  light,  which  is  composed  of  different  colours,  the 
dark  spaces  of  one  tint  overlap  the  light  spaces  of  another,  and  thus  a  series 
of  prismatic  colours  will  be  produced. 

If,  instead  of  placing  the  edge  of  an  opaque  body  between  the  light  and 
the  screen,  a  very  narrow  body  be  interposed,  such  as  a  hair  or  a  fine  metallic 
wire,  the  phenomena  will  be  different.  Outside  the  space  corresponding  to 
the  geometrical  shadow,  there  is  a  series  of  fringes,  as  in  the  former  case. 
Hut  within  the  shadow  also  there  is  a  series  of  alternate  light  and  dark  bands. 
They  are  called  interior  fringes,  and  are  much  narrower  and  more  numerous 
than  the  external  fringes. 

When  a  small  opaque  circular  disc  is  interposed,  white  light  being  used, 
its  shadow  on  the  screen  shows  in  the  middle  a  bright  spot  surrounded  by  a 
series  of  coloured  concentric  rings  ;  the  bright  spot  is  of  various  colours 
according  to  the  relative  positions  of  the  disc  and  screen.  The  haloes  some- 
times seen  round  the  sun  and  moon  belong  to  this  class  of  phenomena.  They 
are  due,  as  Fraunhofer  showed,  to  the  diffraction  of  light  by  small  globules 
of  fogr  in  the  atmosphere.  Fraunhofer  even  gave  a  method  of  estimating 
the  mean  diameter  of  these  globules  from  the  dimensions  of  the  haloes. 

647.  Gratlng^s. — Phenomena  of  diffraction  of  another  class  are  produced 
by  allowing  the  pencil  of  light  from  the  luminous  point  to  traverse  an  aper- 
ture in  the  form  of  a  narrow  slit  in  an  opaque  screen.     The  diffracted  light 

may  be  received  on  a  sheet 

TirWninnriiBM      ofwhite  paper,  but  the  images 

are  much  better  seen  through 
a  small  telescope  placed  be- 
hind the  aperture.  If  the 
aperture  is  very  small,  the 
telescope  may  be  dispensed 
with,  and  the  figure  may  be 
viewed  by  placing  the  aper- 
ture before  the  eye.  If  now 
be  allowed  to  fall  through  such 


iistance(572)- 
rcd  light  is  seen,  and  right  and  left  of  it  a 
y  diminishing  in  brightness  and  separated  by 


monociiromatic  light — red,  for 
a  narrow  slit,  a  bright  band  ( 
series  of  similar  bands  gradiui 
dark  bands. 

The  brcatltii  of  these  bands  tliffcrs  wilii  liu-  nature  of  the  light,  being 
narrower  and  nearer  together  in  violet  than  in  green,  and  these  again  nar- 
rower and  nearer  than  in  red,  as  shown  in  fig.  599.  If  ordinary  white  light 
i)e  used,  then  the  i olours  are  not  exactly  superposed,  but  a  series  of  equi- 
distant spectra  is  fonned  on  each  side  of  tiie  bri-hl  line,  with  their  violet 
side  turned  inwards. 

In  order  to  explain  this,  let  us  refer  to  li;^.  600,  which  represents  the 
formation  of  the  first  daik  band.  When  light  is  incident  on  the  slit,  AB,  the 
particles  of  ether  there,  which  we  will  rejjresent   Ijy  the  dotted  lines,  will  be 


-647] 


Gnitiiios. 


621 


set  in  vil)iation,  and  each  point  w  ill  become  the  centre  of  a  new  series  of 
oscillations.  Consider  now  the  undulations  which  constitute  a  ray  proceed- 
ing at  riijht  angles  to  the  plane  of  the  slit  :  all  such  undulations  will  form  a 
band  of  light  on  the  screen  MN.  Those  which  are  not  parallel  but  proceed 
at  equal  inclinations,  and  meet  at  the  point  r,  will  be  in  the  same  phase  and 
will  reinforce  each  other,  and  the  line  of  maximum  brightness  will  be  at  r. 
Consider,  however,  a  pencil  of  rays  which  proceeds  from  the  slit  in  an 
oblique  direction  and  which  meets  the  screen,  or  the  retina,  in  the  point  s, 
and  let  us  suppose  that  the  difference  between  the  lengths  of  the  paths  of 
the  undulations  proceeding  from  the  edges  b  and  a — that  is,  bs  and  as — is 
equal  to  the  length  of  an  undulation.  Make  sc  =  sb  and  join  be;  then  ac  is 
the  length  of  the  undulation. 

Let  us  suppose  that  the  whole  set  of  undulations  which  proceeds  from 
the  slit  ab  is  divided  at  d  into  two  equal  groups  of  undulations.  Then  a 
little  consideration  will  show  that  at  any  part  of  the  path  there  will  be  a  dif- 
ference of  phase  of  half  an  undulation  l^etween  the  ray  from  the  margin  a, 
and  that  from  the  centre  d ;  and  to  each 
of  the  undulations  constituting  the  group 
on  the  left  there  will  be  a  corresponding  one 
among  the  groups  on  the  right,  which  just 
differs  from  it  by  half  an  undulation  ;  the 
general  effect  will  be  that  the  group  on 
the  left  will  be  half  an  undulation  behind 
the  group  on  the  right,  and  both  arriving 
at  the  screen  in  opposite  phases  neutralise 
each  other  and  produce  darkness. 

When  the  difference  between  the  paths 
of  the  marginal  undulations  is  equal  to 
half  a  wave-length,  a  partial  destruction 
of  light  takes  place  ;  the  luminous  inten- 
sity corresponding  to  this  obliquity  is  a 
little  less  than  half  that  of  the  undiffracted 
light.  If  the  marginal  distance  is  one 
and  a  half  undulations,  we  can,  as  before, 
conceive  the  whole  pencil  divided    into 

three  parts,  of  w-hich  two  will  neutralise  each  other,  and  the  third  only  will 
be  effective.  There  will  be  a  luminous  band,  but  one  of  less  intensity.  In 
like  manner  where  the  marginal  undulations  differ  by  two  whole  wave- 
lengths, they  will  again  extinguish  each  other,  and  a  dark  band  will  be  the 
result.  Thus  there  will  be  formed  a  series  of  alternate  dark  and  bright 
bands  of  rapidly  diminishing  intensity.  In  general,  when  the  difference  of 
path  of  the  rays  proceeding  from  the  margin  of  the  slit  amounts  to  n  wave- 
lengths, 71  being  any  whole  number,  we  have  a  dark  band,  and  when  it 
amounts  io  fi  +  ^  wave-lengths,  a  bright  band. 

The  phenomena  of  diffraction  produced  when  other  than  straight  lines  are 
used  are  often  of  great  beauty.  They  have  been  more  particularly  examined 
by  Schwerdt,  and  the  whole  of  the  phenomena  are  in  exact  accordance  with 
the  undulatory  theory,  though  the  explanation  is  in  many  cases  somewhat 
intricate.     The  theory  renders  it  possible  to  predict  the  appearance  which 


Fis.  600. 


622  On  Light.  [647- 

any  particular  aperture  will  produce,  just  as  astronomy  enables  us  to  foretell 
the  motions  of  the  heavenly  bodies.  Some  of  the  simpler  fonns — such  as 
straight  lines,  triangles,  squares — may  be  cut  out  of  tinfoil  pasted  on  glass, 
and  apertures  of  any  form  may  be  produced  with  great  accuracy  by  taking 
on  glass  a  collodion  photograph  of  a  sheet  of  paper  on  which  the  required 
shapes  are  drawn  in  black. 

Looking  through  any  of  these  apertures  at  a  luminous  point,  we  see  it  sur- 
rounded with  coloured  spectra  of  very  various  forms,  and  of  great  beauty. 
The  beautiful  colours  seen  on  looking  through  a  bird's  feather  at  a  distant 
source  of  light,  and  the  colours  of  striated  surfaces,  such  as  mother-of-pearl, 
are  due  to  a  similar  cause.  A  beautiful  phenomenon  of  the  same  kind  is  the 
aureole  observed  on  looking  at  a  candle  flame  through  lycopodium  powder 
strewn  on  glass.  Two  crossed  gratings  give  a  splendid  picture,  in  which  a 
bright  point  is  surrounded  in  all  directions  by  spectra. 

648.  Diffraction  spectra. — The  most  important  of  these  figures  are  the 
gratifigs  proper.,  which  may  be  produced  by  arranging  a  series  of  fine  wires 
parallel  to  each  other,  or  by  careful  ruling  on  a  piece  of  smoked  glass,  or  by 
photographic  reduction.  Nobert  has  made  such  gratings  by  ruling  lines  on 
glass  with  a  diamond,  in  which  there  are  no  less  than  12,000  lines  in  an  inch 
in  breadth.  Dr.  Stone  has  constructed  such  gratings  for  reflection,  by  ruling 
lines  on  plates  of  nickel ;  this  metal  has  the  advantage  of  hardness,  non- 
liability to  tarnish,  and  great  reflecting  power. 

If  a  grating  be  used  instead  of  a  single  slit,  as  above  described,  the 
phenomena  are  in  general  the  same,  though  of  greater  brilliancy.  With 
homogeneous  light  and  such  a  grating,  there  is  seen,  on  each  side  of  the 
central  bright  line,  a  series  of  sharply  defined  narrow  bands  and  lines  of 
light,  gradually  increasing  in  breadth  and  diminishing  in  intensity  as  their 
distance  from  the  central  line  increases.  If  white  light  be  used  the  white 
band  is  seen  in  the  centre,  and  on  each  side  of  it  a  sharply  defined  isolated 
spectrum  with  the  violet  edges  inwards.  Next  to  this,  and  separated  by  a 
dark  interval,  is  on  each  side  a  somewhat  broader  but  similar  spectrum, 
and  then  follow  others  which  become  fainter  and  broader  and  overlap  each 
other.  The  brightness  and  sharpness  of  these  spectra  depend  on  the  close- 
ness of  the  lines,  and  on  the  opacity  of  the  intemiediate  space.  In  those 
which  are  ruled  by  diamond  on  glass,  the  parts  scratched  represent  the 
opaque  parts. 

For  objective  representation  the  image  of  a  slit  in  a  dark  shutter,  through 
which  the  sunlight  enters,  is  focussed  by  means  of  a  convex  lens  on  a  screen 
at  a  distance,  and  then  a  grating  is  placed  in  the  path  of  the  rays. 

The  spectra  produced  by  means  of  a  grating  are  known  as  interference  or 
diffraction  spectra.  Very  accurate  gratings  can  now  be  easily  and  cheaply 
prepared  by  means  of  photography,  and  their  use  for  scientific  purposes  is 
extending. 

There  are  many  points  of  difference  between  these  spectra  and  those 
produced  by  the  prism,  and  for  scientific  work  the  former  are  preferable. 

A  diffraction  spectrum  is  the  purer  the  greater  the  number  of  lines  in  the 
grating,  provided  they  are  equidistant.  Tiie  spectra  arc,  however,  not  more 
than  ,'„  as  bright  as  prismatic  spectra  ;  and,  to  olnain  tlic  maximum  bright- 


-649] 


Determination  of  Wave-length. 


623 


ness,  the  opaque  intervals  should  be  as  opaque  and  the  transparent  ones  as 
transparent  as  possible. 

On  the  other  hand,  in  diffraction  spectra,  the  colours  are  uniformly  dis- 
tributed in  their  true  order  and  extent  according  to  the  difference  in  their 
wave-lengths,  and  according  therefore  to  a  property  which  is  inherent  in  the 
light  itself ;  while  in  prismatic  spectra  the  red  rays  are  concentrated,  and 
the  violet  ones  dispersed.  In  diffraction  spectra  the  centre  is  the  brightest 
part. 

Fig.  601  represents  a  grating  spectrum,  together  with  an  equally  long 
spectrum  produced  by  a  flint-glass  prism ;  the  upper  being  that  produced  by 
the  grating.  It  will  be  seen  that  D  in  the  one  spectrum  is  in  almost  exactly 
the  same  position  as  F  in  the  other. 

Diffraction  spectra  have,  moreover,  the  advantage  of  giving  a  far  larger 
number  of  dark  lines,  and  of  giving  them  in  their  exact  relative  positions. 
Thus,  in  a  particular  region  in  which  Angstrom  had  mapped    118   lines, 


Fig.  601. 

Draper,  by  means  of  a  diffraction  spectrum,  was  able  to  photograph  at  least 
293.  Diffraction  spectra  also  extend  farther  in  the  direction  of  the  ultra- 
violet, and  give  more  dark  lines  in  that  region. 

The  most  perfect  gratings  have  quite  recently  been  constructed  by 
Professor  Rowland,  of  Baltimore,  by  means  of  a  machine  specially  planned 
and  constructed  for  the  purpose,  and  the  chief  feature  in  which  is  a  practi- 
cally perfect  screw.  Using  this  machine,  he  has  been  able  to  rule  gratings 
with  as  many  as  43,000  lines  to  the  inch,  nor  does  this  represent  the  limit  of 
the  power  of  the  machine.  Gratings  with  14,000  or  28,000  lines  give,  however, 
the  best  definition.  Another  great  improvement  is  to  rule  the  gratings  on 
spherical  instead  of  on  flat  surfaces  ;  in  this  way  the  spectrum  can  be  formed 
without  a  telescope,  which  is  a  matter  of  great  importance,  as  telescopes 
interfere  with  a  great  many  experiments.  The  spectroscope  is  thus  reduced 
to  its  simplest  form,  so  that  an  instrument  of  very  high  power  may  be  con- 
structed at  a  small  cost. 

By  means  of  his  gratings  Professor  Rowland  has  been  able  to  resolve 
lines  in  the  spectrum  which  had  never  hitherto  been  separated. 

It  has  been  proposed  to  use  the  fine  quartz  threads  prepared  by  Mr. 
Boys  (89)  for  making  gratings. 

649.  Betermination  of  wave-lengrth. — The  relative  positions  of  these 
bright  and  dark   lines  furnish  a  means  of  calculating  the  wave-length  or 


624  On  U^ht.  [649- 

len"-th  of  undulation  of  any  particular  colour.  We  must  first  of  all  know  the 
distance  rs  of  the  first  dark  band  from  the  bright  one.  The  bands  are  not 
uniform  in  brightness  or  darkness,  but  there  is  in  each  case  a  position  of 
maximum  intensity,  and  it  is  from  these  that  the  distances  are  measured. 
If  the  bands  are  viewed  through  a  telescope,  the  angle  is  observed  through 
which  the  axis  must  be  turned  from  the  position  in  which  the  cross  wire 
coincides  with  the  centre  of  the  bright  band  to  that  in  which  it  coincides 
with  the  centre  of  the  dark  band.  From  this  angle,  which  can  be  very  ac- 
curately measured,  the  distance  is  easily  calculated.  When  the  diffraction 
bands  are  received  on  a  screen,  the  distance  may  be  directly  measured,  and 
most  accurately  by  taknig  half  the  distance  between  the  centres  of  the  first 
pair  of  dark  bands. 

We  have  thus  the  similar  triangles  abc,  and  rds,  in  which  ac  :bc  =  rs  :  rd 
(fig.  600).  Now  be  may  be  taken  equal  to  ab^  the  width  of  the  slit,  which  can 
be  measured  directly  with  great  accuracy  by  means  of  a  micrometric  screw 
(II),  and  rd  is  the  distance  of  the  screen.     Hence 

rs  X  ab 
"'^--Vd- 

Now  rtf,  the  difference  between  as  and  sc^  is  equal  to  the  length  of  an  undu- 
lation of  this  particular  colour.  In  one  experiment  with  red  light  the  width 
of  the  slit  ab  was  0-015  in.,  the  distance  rs  0-15  in.,  and  the  distance  of  the 

screenosin.,  which  gave  at- =  —^''°°' ^  =  0-000024  in.  as  the  wave-length 

93 
of  red  light.     Using  blue  light  the  distance  of  r.y  was  found  to  be  o-i,  which 
gives  o-ooooi6. 

Knowing  the  length  of  the  undulations,  we  can  easily  calculate  their 

number  in  a  second,  «,  from  the  formula  71  =  -^(232),  where  v  is  the  velocity 

of  light.  Taking  this  at  186,000  miles,  we  get  for  the  red  corresponding  to 
the  dark  line  B  434,420,000,000,000  as  the  number  of  oscillations  in  a  second, 
and  for  the  H  in  the  violet  758,840,000,000,000  undulations. 

If,  instead  of  a  single  slit,  gratings  be  used,  we  have  the  possibility  of 
more  accurate  results,  for  the  contrast  is  greater,  and  thus  the  distance  is 
more  easily  determined.  The  width  of  the  slit  is  easily  calculated  by  count- 
ing the  number  of  lines  in  a  given  s|)ace. 

650.  Colours  of  tliln  plates.  Newrton's  ring's. — All  transparent  bodies, 
solids,  liquids,  or  gases,  when  in  sufficiently  fine  laminit,  appear  coloured 
with  very  bright  tints,  especially  by  reflection.  Crystals  which  cleave  easily, 
and  can  be  obtained  m  very  thin  plates,  such  as  mica  and  selenite,  show  this 
l)henomenon,  which  is  also  well  seen  in  soap-bubbles  and  in  the  layers  of  air 
in  cracks  in  glass  and  in  crystals.  Steel  becoming  covered  with  a  thin  layer 
of  oxide  exhibits  the  colour  of  thin  plates,  which  change  during  heating  as 
the  oxide  changes  its  thickness.  A  drop  of  oil  spread  rapidly  over  a  large- 
sheet  of  water  exhibits  all  the  colours  of  the  spectrum  in  a  constant  order. 
A  soap-bubble  appears  white  at  first,  but,  in  proportion  as  it  is  blown  out, 
brilliant  iridescent  colours  appear,  especially  at  the  top,  where  it  is  thinnest. 
These  colours  arc  arranged  in  horizontal  zones  around  the  summit,  which 


-651]  Explanation  of  Neivton's  Rings.  625 

appears  black  when  there  is  not  thickness  enough  to  reflect  Hght,  and  the 
bubble  then  suddenly  bursts. 

Newton,  who  first  studied  the  phenomena  of  the  coloured  rings  in  soap- 
bubbles,  wishing  to  investigate  the  relation  between  the  thickness  of  the 
thin  plate,  the  colour  of 
the  rings,  and  their  extent, 
produced  them  by  means 
of  a  layer  of  air  interposed 
between  two  glasses,  one 
plane  and  the  other  con- 

J       .  ,  ,  Fig.  602. 

vex,  and  with  a  very  long 

focus  (fig.  602).  The  two  surfaces  being  cleaned  and  exposed  to  ordinary 
light  in  front  of  a  window,  so  as  to  reflect  light,  there  is  seen  at  the  point  of 
contact  a  black  spot  surrounded  by  six  or  seven  coloured  rings,  the  tints  of 
which  become  gradually  less  strong.  If  the  glasses  are  viewed  by  transmitted 
light,  the  centre  of  the  rings  is  white,  and  each  of  the  colours  is  exactly  com- 
plementary of  that  of  the  rings  by  reflection.  The  lens  and  the  glass  plate 
are  usually  arranged  in  a  brass  mount  which  by  means  of  three  screws  allows 
the  pressure  to  be  regulated. 

With  homogeneous  light,  red  for  example,  the  rings  are  successively 
black  and  red  ;  the  diameters  of  corresponding  rings  are  less  as  the  colour 
is  more  refrangible,  but  with  white  light  the  rings  are  of  the  different  colours 
of  the  spectrum,  which  arises  from  the  fact  that,  as  the  rings  of  the  different 
simple  colours  have  different  diameters,  they  are  not  exactly  superposed,  but 
are  more  or  less  separated. 

It  is  usual  to  speak  of  the  successive  rings  as  the  first,  second,  third,  &c. 
By  XhG.  first  ring  is  understood  that  of  least  diameter.  Knowing  the  radius 
of  any  particular  ring,  p,  and  the  radius  of  curvature,  R,  of  the  lens,  the  thick- 
ness, d^  of  the  corresponding  layer  of  air  is  given  approximately  by  the 
formula 

Newton  found  that  the  thicknesses  corresponding  to  the    successive  dark 

rings  are  proportional  to  the  numbers   o,  2,  4,  6 ,    while  for  the 

(^;7]§/// rings  the  thicknesses  were  proportional  to  I,  3,  5 He  found 

that  for  the  first  bright  ring  the  thickness  was  fyg^ojo  ,,  vc  „ 

of  an  inch,  when  the  light  used  was  the  brightest  part  \\ 

of  the  spectmm  ;  that  is,  the  part  on  the  confines  of  \\ 

the  orange  and  yellow  rays.  U  ,/ 

If  the  focal  length  of  the  lens  is  from  three  to  four ^   -'' — 


yards,  the  rings  can  be  seen  with  the  naked  eye  ;  but  1 
if  the  length  is  less,  the  rings  must  be  viewed  with  a  ts — 
lens. 

651.   Explanation  ot  N'ewton's  rings. — Newton's 
rings,  and  all   phenomena  of  thin  plates,  are  simple       ^•'  y 
cases  of  interference.  ^'S-  603. 

In  fig.  603,  let  MNOP  represent  a  thin  plate  of  a  transparent  body,  on 
which  a  pencil  of  parallel  rays  of  homogeneous  light,  ab,  impinges  ;  this 

SS 


626  On  Light.  [651- 

will  be  partially  reflected  in  the  direction  be,  and  partially  refracted  towards 
d.  But  the  refracted  ray  will  undergo  a  second  reflection  at  the  surface,  OP  ; 
the  reflected  ray  will  emerge  at  c  in  the  same  direction  as  the  pencil  of  light 
reflected  at  the  first  surface  ;  and  consequently  the  two  pencils  be  and  ef 
will  destroy  or  augment  each  other's  effect  according  as  they  are  in  the 
same  or  different  phases.  We  shall  thus  have  an  effect  produced  similar  to 
that  of  fringes  (646). 

POLARISATION    OF    LIGHT. 

652.  Polarisation  by  double  refraction. — It  has  been  already  seen  that 
when  a  ray  of  light  passes  through  a  crystal  of  Iceland  spar  (641),  it  becomes 
divided  into  two  rays  of  equal  intensity  ;  viz.  the  ordinary  ray,  and  the  ex- 
traordinary ray.  These  rays  are  found  to  possess  other  peculiarities,  which 
are  expressed  by  saying  they  are  polarised;  namely,  the  ordinary  ray  in  a 
principal  plane,  and  the  extraordinary  ray  in  a  plane  at  right  angles  to  a 
principal  plane.  The  phenomena  which  are  thus  designated  may  be  de- 
scribed as  follows  : — Suppose  a  ray  of  light  which  has  undergone  ordinary 
refraction  in  a  crystal  of  Iceland  spar,  to  be  allowed  to  pass  through  a  second 
crystal,  it  will  generally  be  divided  into  two  rays  ;  namely,  one  ordinary,  and 
the  other  extraordinary,  but  of  imeqiial  intensities.  If  the  second  crystal 
be  turned  round  until  the  two  principal  planes  coincide — that  is,  until  the 
crystals  are  in  similar  or  in  opposite  positions— then  the  extraordinaiy  ray 
disappears,  and  the  ordinary  ray  is  at  its  greatest  intensity  ;  if  the  second 
crystal  is  turned  farther  round,  the  extraordinary  ray  reappears,  and  increases 
in  intensity  as  the  angle  increases,  while  the  ordinary  ray  diminishes  in  in- 
tensity until  the  principal  planes  are  at  right  angles  to  each  other,  when  the 
extraorchnary  ray  is  at  its  greatest  intensity  and  the  ordinary  ray  vanishes. 
These  are  the  phenomena  produced  when  the  ray  which  experienced  ordi- 
nary refraction  in  the  first  crystal  passes  through  the  second.  If  the  ray 
which  has  experienced  extraordinary  refraction  in  the  first  crystal  is  allowed 
to  pass  through  the  second  crystal,  the  phenomena  are  similar  to  those  above 
described  ;  but  when  the  principal  planes  coincide,  an  extraordinary  ray  alone 
emerges  from  the  second  crystal,  and  when  the  planes  are  at  right  angles,  an 
ordinary  ray  alone  emerges. 

These  phenomena  may  also  be  thus  described: — Let  O  and  E  denote 
the  ordinary  and  extraordinary  rays  produced  by  the  first  crj'stal.  When 
O  enters  the  second  crystal,  it  generally  gives  rise  to  two  rays,  an  ordinary 
(0(?),  and  an  extraordinary  {Oe),  of  unecjual  intensities.  When  E  enters  the 
second  crystal,  it  likewise  gives  rise  to  two  rays,  viz.  an  ordinary  (Ef)  and 
an  extraordinary  (E^),  of  unecjual  intensities,  the  intensities  varying  with 
the  angle  between  the  principal  planes  of  the  crystals.  When  the  principal 
planes  coincide,  only  two  rays,  viz.  Oo  and  Er,  emerge  from  the  second 
crystal,  and  when  the  planes  are  at  right  angles,  only  two  rays,  viz.  Oe  and 
E<9,  enicrge  from  the  second  crystal.  Since  O  gives  rise  to  an  ordinary  ray 
when  the  jjrincijjal  planes  are  parallel,  and  E  gives  rise  to  an  ordinary  ray 
when  they  are  at  right  angles,  it  is  manifest  that  O  is  related  to  the  principal 
plane  in  the  same  manner  that  E  is  related  to  a  plane  at  right  angles  to  a 
|)rincipal  plane. 


-654]  Angle  of  Polafisation.  627 

This  phenomenon,  which  is  produced  by  all  double-refracting^  crystals, 
was  tlrst  observed  by  Huyghens  in  Iceland  spar,  and  in  consequence  of  a 
suggestion  of  Newton's  was  afterwards  called 
polarisation.  It  remained,  however,  an  isolated 
fact  until  the  discovery  of  polarisation  by  re- 
flection recalled  the  attention  of  physicists  to 
the  subject.  The  latter  discovery  was  made  by 
Mai  us  in  1808. 

653.  Polarisation  by  reflection. — When 
a  ray  of  light,  ab  (fig.  604),  falls  on  a  polarised 
unsilvered  glass  surface, ^/«,  inclined  to  it  at 
an  angle  of  35°  25',  it  is  reflected,  and  the 
reflected  ray  is  polarised  in  the  plane  of  re- 
flection. If  it  were  transmitted  through  a 
crystal  of  Iceland  spar,  it  would  pass  through 
without  bifurcation,  and  undergo  an  ordinary  jt 
refraction  ;  when  the  principal  plane  coincides 
with  the  plane  of  reflection,  it  would  also  be 
transmitted  without  bifurcation,  but  undergo 
extraordinary  refraction,  when  the  principal  plane  is  at  right  angles  to  the 
plane  of  reflection  ;  in  other  positions  of  the  crystal  it  would  give  rise  to  an 
ordinary  and  an  extraordinary  ray  of  different  intensities,  according  to  the 
angle  between  the  plane  of  reflection  and  the  principal  plane  of  the  crystal. 
The  peculiar  property  which  the  light  has  acquired  by  reflection  at  the  sur- 
face fghi  can  also  be  exhibited  as  follows  : — Let  the  polarised  ray  be  be 
received  at  r,  on  a  second  surface  of  unsilvered  glass,  at  the  same  angle,  viz. 
35°  25'.  If  the  surfaces  are  parallel,  the  ray  is  reflected;  but  if  the  second 
plate  is  caused  to  turn  round  cb,  the  intensity  of  the  reflected  ray  continually 
diminishes,  and  when  the  glass  surfaces  are  at  right  angles  to  each  other,  no 
light  is  reflected.  By  continuing  to  turn  the  upper  mirror  the  intensity  of 
the  reflected  ray  gradually  increases,  and  attains  a  maximum  value  when  the 
surfaces  are  again  parallel. 

The  above  statement  will  serve  to  describe  the  phenomenon  of  polarisa- 
tion by  reflection  so  far  as  the  principles  are  concerned  ;  the  apparatus  best 
adapted  for  exhibiting  the  phenomenon  will  be  described  farther  on. 

654.  Angrle  of  polarisation. — T\\&  polarising  afigle  of  a  substance  is  the 
angle  which  the  incident  ray  must  make  with  the  perpendicular  to  a  plane 
polished  surface  of  that  substance  in  order  that  the  polarisation  be  complete. 
For  glass  this  angle  is  54°  35',  and  if  in  the  preceding  e.xperiment  the  lower 
mirror  were  inclined  at  any  other  angle  than  this,  the  light  would  not  be 
completely  polarised  in  any  position  ;  this  would  be  shown  by  its  being 
partially  reflected  from  the  upper  surface  in  all  positions.  Such  light  is 
said  to  he.  partially  polarised.  The  polarising  angle  for  water  is  52°  45' ; 
for  quartz,  57°  32' ;  for  diamond,  68°  ;  and  it  is  56°  30'  for  obsidian,  a  kind 
of  volcanic  glass  which  is  often  used  in  these  experiments. 

Light  which  is  reflected  from  the  surface  of  water,  from  a  slate  roof,  from 
a  polished  table,  or  from  oil  paintings,  is  all  more  or  less  polarised.  The 
ordinary  light  of  the  atmosphere  is  frequently  polarised,  especially  in  the 
earlier  and  later  periods  of  the  day,  when  the  solar  rays  fall  obliquely  on 


628  On  Light.  [654- 

the  atmosphere.  Almost  all  reflecting  surfaces  may  be  used  as  polarising 
mirrors.     Metallic  surfaces  form,  however,  an  important  exception. 

Brewster  discovered  the  following  remarkably  simple  law  in  reference  to 
the  polarising  angle  : — 

The  polanstfig-  angle  of  a  substance  is  that  angle  of  ificidence  for  which 
the  reflected  polarised  ray  is  at  right  angles  to  the  refracted  ray. 

Thus,  in  fig.  605,  if  si  is  the  incident,  ir 
the  refracted,  and  if  the  reflected  ray,  the 
polarisation  is  most  complete  when  //  is  at 
right  angles  to  ir. 

The  plane  of  polarisation  is  the  plane  of 
reflection  in  which  the  light  becomes  polar- 
ised ;  it  coincides  with  the  plane  of  inci- 
dence, and  therefore  contains  the  polarising 
angle. 

A  simple  geometrical  consideration  will 
show  that  the   above   law   may  be  thus  ex- 
'^"  ^"^"  pressed  : — The  tangent  of  the  angle  of  polari- 

sation of  a  substance  is  equal  to  its  refractive  index.  As  the  refractive  index 
differs  with  the  different  colours,  it  follows  that  the  angle  of  polarisation  can- 
not be  the  same  for  all  colours.  This  explains  why  a  ray  of  white  light  is 
never  completely  polarised. 

655.  Polarisation  by  singrle  refraction. — When  an  unpolarised  lu- 
minous ray  falls  upon  a  glass  plate  placed  at  the  polarising  angle,  one  part 
is  reflected  ;  the  other  part  becomes  refracted  in  passing  through  the  glass, 
and  the  transmitted  light  is  now  found  to  be  partially  polarised.  If  the  light 
which  has  passed  through  one  plate,  and  whose  polarisation  is  very  feeble, 
be  transmitted  through  a  second  plate  parallel  to  the  first,  the  effects  become 
more  marked,  and  by  ten  or  tweh'e  plates  are  tolerably  complete.  A  bundle 
of  such  plates,  for  which  the  best  material  is  the  glass  used  for  covering 
microscopic  objects,  fitted  in  a  tube  at  the  polarising  angle,  is  frequently 
used  for  examining  or  producing  polarised  light. 

If  a  ray  of  light  fall  at  any  angle  on  a  transparent  medium,  the  same 
holds  good  with  a  slight  modification.  In  fact,  part  of  the  light  is  reflected 
and  part  refracted,  and  both  are  found  to  be  partially  polarised,  equal  quan- 
tities in  each  beifig polarised,  and  their  planes  of  polarisation  being  at  right 
angles  to  each  other.  It  is,  of  course,  to  be  understood  that  the  polarised 
portion  of  the  reflected  light  is  polarised  in  the  plane  of  reflection,  which  is 
likewise  the  plane  of  refraction. 

656.  Polarising'  Instruments. — Every  instrument  for  investigating  the 
properties  of  polarised  light  consists  essentially  of  two  parts — one  for  polaris- 
ing the  light,  the  other  for  ascertaining  or  exhibiting  the  fact  of  light  having 
undergone  polarisation.  The  former  part  is  called  the  polariser,  the  latter 
the  analyser.  Thus  in  art.  652  the  crystal  producing  the  first  refraction  is 
the  polariser,  that  producing  the  second  refraction  is  the  analyser.  In  art. 
653  the  mirror  at  which  the  first  reflection  takes  place  is  the  polariser,  that 
at  which  the  second  reflection  takes  place  is  the  analyser.  Some  of  the 
most  convenient  means  of  producing  polarised  light  will  now  be  described, 
and  it  will  be  remarked  that  any  instrument  that  can  be  used  as  a  polariser 


657] 


Norrcmberg's  Apparatus. 


629 


can  also  be  used  as  an  analyser.     The  experimenter  has  therefore  consider- 
able liberty  of  selection. 

657.  STorrembergr's  apparatus. — The  most  simple  but  complete  instru- 
ment for  polarising  light  is  that  invented  by  Norremberg.  It  may  be  used 
for  repeating  most  of  the  experiments  on  polarised  light. 

It  consists  of  two  brass  rods,  b  and  d  (fig.  606),  which  support  an  unsil- 
vered  mirror,  //,  of  ordinary  glass,  movable  about  a  horizontal  axis.  A  small 
graduated  circle  indicates  the  angle  of  inclination  of  the  mirror.  Between 
the  feet  of  the  two  columns  there  is  a  silvered  glass,/,  which  is  fixed  and 
horizontal.  At  the  upper  end  of  the  columns  is  a  graduated  plate,  z,  in 
which  a  circular  disc,  o,  rotates.  This  disc,  in  which  there  is  a  square 
aperture,  supports  a  mirror  of  black  glass,  w,  which  is  inclined  to  the  vertical 
at  the  polarising  angle.  An  annular  disc,  k,  can  be  fixed  at  different  heights 
on  the  columns  by  means  of  a  screw.  A  second  ring,  a^  may  be  moved 
around  the  axis.  It  supports  a  black  screen,  in  the  centre  of  which  there  is 
a  circular  aperture. 

When  the  mirror  n  makes  with  the  vertical  an  angle  of  35°  25',  which  is 
the  complement  of  the  polarising  angle  for  glass,  the  rays  of  light,  S«, 
which  meet  the  mirror  at  this 
angle,  become  polarised,  and 
are  reflected  in  the  direction  np 
towards  the  mirror  /,  which 
sends  them  in  the  direction  pnr. 
After  having  passed  through 
the  glass,  71^  the  polarised  ray 
falls  upon  the  blackened  glass 
m  under  an  angle  of  35°  25', 
because  the  mirror  makes  ex- 
actly the  same  angle  with  the 
vertical.  But  if  the  disc,  c,  to 
which  the  mirror,  m,  is  fixed, 
be  turned  horizontally,  the  in- 
tensity of  the  light  reflected 
from  the  upper  mirror  gradually 
diminishes,  and  totally  disap- 
pears when  it  has  been  moved 
through  90°.  The  position  is 
that  represented  in  the  diagram  : 
the  plane  of  incidence  on  the 
upper  mirror  is  then  perpendi- 
cular to  the  plane  of  incidence, 
S;?_/>,  on  the  mirror  71.  When  the 
upper  mirror  is  again  turned,  the 
intensity  of  the  light  increases 
until  it  has  passed  through  180°, 
when  it  again  reaches  a  maxi- 
mum. The  mirrors  w  and  71 
are  then  parallel.  The  same  phenomena  are  repeated  as  the  mirror  171  con- 
tinues to  be  turned  in  the  same  direction,  until  it  again  comes  into  its  original 


630  On  Light.  [667- 

position  ;  the  intensity  of  the  reflected  Hght  being  greatest  when  the  mirrors 
are  parallel,  and  being  reduced  to  zero  when  they  are  at  right  angles.  If  the 
mirror  m  is  at  a  greater  or  less  angle  than  35°  25',  a  certain  quantity  of 
light  is  reflected  in  all  positions  of  the  plane  of  incidence. 

658.  Tourmaline. — The  primary  form  of  this  crystal  is  a  regular  hex- 
agonal prism.  Tourmaline,  as  already  stated,  is  a  negative  uniaxial  crystal, 
and  its  optic  axis  coincides  with  the  axis  of  the  prism.  For  optical  purposes 
a  plate  is  cut  from  it  parallel  to  the  axis.  When  a  ray  of  light  passes 
through  such  a  plate,  an  ordinary  ray  and  an  extraordinary  ray  are  produced 
polarised  in  planes  at  right  angles  to  each  other  ;  viz.  the  former  in  a  plane 
at  right  angles  to  the  plate  parallel  to  the  axis,  and  the  latter  in  a  plane  at 
right  angles  to  the  axis.  The  crystal  possesses,  however,  the  remarkable 
property  of  rapidly  absorbing  the  ordinary  ray  ;  consequently,  when  a  plate 
of  a  certain  thickness  is  used,  the  extraordinary  ray  alone  emerges — in 
other  words,  a  beam  of  common  light  emerges  from  the  plate  of  tourmaline 
polarised  in  a  plane  at  right  angles  to  the  axis  of  the  crystal.  If  the  light 
thus  transmitted  be  viewed  through  another  similar  plate  held  in  a  parallel 
position,  little  change  will  be  observed,  excepting  that  the  intensity  of  the 
transmitted  light  will  be  about  equal  to  that  which  passes  through  a  plate  of 
double  the  thickness  ;  but  if  the  second  tourmaline  be  slowly  turned,  the 
light  will  become  feebler,  and  will  ultimately  disappear  when  the  axes  of  the 
two  plates  are  at  right  angles. 

The  objections  to  the  use  of  the  tourmaline  are  that  it  is  not  very  trans- 
parent, and  that  plates  of  considerable  thickness  must  be  used  if  the  polarisa- 
tion is  to  be  complete.  Yox  unless  the  ordinary  ray  is  completely  absorbed 
the  emergent  light  will  be  only  partially  polarised. 

Herapath  discovered  that  sulphate  of  iodoquinine  has  the  property  of 
polarising  light  in  a  remarkable  degree.  Unfortunately,  it  is  a  very  fragile 
salt,  and  difficult  to  obtain  m  large  crystals. 

659.  Bouble-refractingr  prism  of  Iceland  spar.— When  a  ray  of  light 
passes  through  an  ordinary  rhombohedron  of  Iceland  spar,  the  ordinary  and 
extraordinary  rays  emerge  parallel  to  the  original  ray,  consequently  the 
separation  of  the  rays  is  proportional  to  the  thickness  of  the  prism.  But  if 
the  crystal  is  cut  so  that  its  faces  are  inclined  to  each  other,  the  deviations 
of  the  ordinary  and  extraordinary  rays  will  be  different,  they  will  not  emerge 
parallel,   and    their  separation  will   be   greater   as  their  distance  from  the 

prism  increases.  The  light,  however,  becomes  decomposed  in 
passing  through  the  prism,  and  the  rays  will  be  coloured.  It 
is  tliercforc  necessary  to  acliroiiiatisc  (584)  the  prism,  which  is 
done  by  combining  it  with  a  prism  of  glass  with  its  refracting 
angle  turned  in  the  contrary  direction  (fig.  608).  In  order 
to  obtain  the  greatest  amount  of  divergence,  the  refracting 
edges  of  the  prism  should  be  cut  parallel  to  the  optic  axis, 
Fig.  608.  'ind  this  is  always  done. 

Let  us  suppose  that  a  ray  of  polarised  light  passes  along 
the  axis  of  the  cylinder  (fig.  608),  and  let  us  suppose  that  the  cylinder  is 
caused  to  turn  slowly  about  its  axis  ;  then  the  resulting  phenomena  are 
exactly  like  those  already  described  (643).  Generally  there  will  be  an  ordi- 
nary and  extraordinary  ray  produced,  whose  relative  intensities  will  vary  as 


-661]  riiysical  Theory  of  Polarised  Light.  631 

the  tube  is  turned.  But  in  two  opposite  positions  the  ordinaiy  ray  alone 
will  emerge,  and  in  two  others  at  right  angles  to  the  former  the  extraordinary 
ray  will  alone  emerge.  When  the  ordinaiy  ray  alone  emerges,  the  principal 
plane  of  the  ciystal— that  is,  a  plane  at  right  angles  to  its  face,  and  parallel 
to  its  refracting  edge — coincides  with  the  original  plane  of  polarisation  of  the 
ray.  Consequently,  by  means  of  the  prism,  it  can  be  ascertained  both  that 
the  ray  is  polarised,  and  likewise  the  plane  in  which  it  is  polarised. 

66a  sricol's  prism. — The  Nicol's  prism  is  one  of  the  most  valuable 
means  of  polarising  light,  for  it  is  perfectly  colourless,  it  polarises  light  com- 
pletely, and  it  transmits  only  one  beam  of  polarised  light,  the  other  being 
entirely  suppressed. 

It  is  constructed  from  a  rhombohedron  of  Iceland  spar,  about  an  inch 
in  height  and  \  of  an  inch  in  breadth.  This  is  bisected  in  the  plane  which 
passes  through  the  obtuse  angles  as  shown  in  fig.  611  ;  that  is,  along  the 
plane  acbd  (fig.  597).  The  two  halves  are  then  again  joined  in  the  same 
order  by  means  of  Canada  balsam. 

The  principle  of  the  Nicol's  prism  is  this  :— The  refractive  index  of 
Canada  balsam,  1-549,  is  less  than  the  ordinary  index  of  Iceland  spar  1-654, 


Fig.  609.  Fig.  610. 

but  greater  than  its  extraordinarj'  index  1-483.  Hence  when  a  luminous  ray 
SC  (fig.  610)  enters  the  prism,  the  ordinary  ray  is  totally  reflected  on  the  sur- 
face, ab.,  and  takes  the  direction!  C^O,  by  which  it  is  refracted  out  of  the 
cr)'Stal,  while  the  extraordinary  ray,  C^,  emerges  alone.  Since  the  Nicol's 
prism  allows  only  the  extraordinary  ray  to  pass,  it  may  be  used,  like  a  tour- 
maline, as  an  analyser  or  as  a  polariser. 

Foucault  replaced  the  layer  of  Canada  balsam  by  one  of  air,  the  two 
prisms  being  kept  together  by  the  mounting.  The  advantage  of  this  is  that 
the  section  ab  (fig.  610)  need  not  be  so  acute,  so  that  the  prism  becomes 
shorter,  and  therefore  cheaper. 

Nicol's  prism  is  the  most  important  feature  of  most  polarising  apparatus. 
It  is  better  than  the  polarising  mirror  on  account  of  its  more  complete  polar- 
isation, and  has  the  advantage  over  tourmaline  of  giving  a  colourless  field 
of  view. 

661.  Pbysical  theory  of  polarised  llgrbt. — The  explanation  of  the  dark 
bands  produced  by  the  interference  of  light  is  stated  in  art.  650  to  resemble 
exactly  that  of  the  formation  of  nodes  and  loops  given  in  art.  276. 

It  might  hence  be  supposed  that  the  vibrations  producing  light  are  quite 
similar  to  those  producing  sound.  But  this  is  by  no  means  the  case.  In 
fact,  no  assumption  is  made  in  art.  652  as  to  the  direction  in  which  the 
vibrating  particles  move,  and  accordingly  the  explanation  is  equally  true 
whether  the  particles  vibrate  in  the  direction  AB,  BA,  or  at  right  angles 
to  AB.     As  a  matter  of  fact,  the  former  is  the  case  with  the  vibrations  pro- 


632  071  Light.  '  [661- 

ducing  sound,  the  latter  with  the  vibrations  producing  hyht.  In  other  words, 
the  vibrations  producing  sound  take  place  in  the  direction  of  propagation,  the 
vibrations  producing  light  are  transvcfsal  to  the  direction  of  propagation. 

This  assumption  as  to  the  direction  of  the  vibration  of  the  particles  of 
ether  producing  light  is  rendered  necessary,  and  is  justified,  by  the  pheno- 
mena of  polarisation. 

When  a  ray  of  light  is  polarised,  all  the  particles  of  ether  in  that  ray 
vibrate  in  straight  lines  parallel  to  a  certain  direction  in  the  front  of  the 
wave  corresponding  to  the  ray. 

When  a  ray  of  light  enters  a  double-refracting  medium,  such  as  Iceland 
spar,  it  becomes  divided  into  two,  as  we  have  already  seen.  Now  it  can  be 
shown  to  be  in  strict  accordance  with  mechanical  principles  that,  if  a  medium 
possesses  unequal  elasticity  in  different  directions,  a  plane  wave  produced 
by  transversal  vibrations  entering  that  medium  will  give  rise  to  two  plane 
waves  moving  with  different  velocities  within  the  medium,  and  the  vibrations 
of  the  particles  in  front  of  these  waves  will  be  in  directions  parallel  respec- 
tively to  two  lines  at  right  angles  to  each  other.  If,  as  is  assumed  in  the 
undulatory  theory  of  light,  the  ether  exists  in  a  double-refracting  ciystal  in 
such  a  state  of  unequal  elasticity,  then  the  two  plane  waves  will  be  formed 
as  above  described,  and  these,  having  different  velocities,  will  give  rise  to 
two  rays  of  unequal  refrangibility  (638).  This  is  the  physical  account 
of  the  phenomenon  of  double  refraction.  It  will  be  remarked  that  the 
\ibrations  corresponding  to  the  two  rays  are  transversal,  rectilinear,  and 
in  directions  perpendicular  to  each  other  in  the  rays  respectively.  Accord- 
ingly the  same  theory  accounts  for  the  fact  that  the  t\\o  rays  are  both 
polarised,  and  in  planes  at  right  angles  to  each  other. 

It  is  a  point  still  unsettled  whether,  when  a  ray  of  light  is  polarised  with 
respect  to  a  given  plane,  the  vibrations  take  place  in  directions  within  or 
perpendicular  to  that  plane.  Fresnel  was  of  the  latter  opinion.  It  is,  how- 
ever, convenient  in  some  cases  to  regard  the  plane  of  polarisation  as  that 
plane  in  which  the  vibrations  take  place. 


COLOURS   PRODUCED   BY   THE   INTERFERENCE   OF   POLARISED    LIGHT, 

662.  I.aws  of  the  interference  of  polarised  rays. — After  the  discovery 
of  polarisation,  Fresnel  and  Arago  tried  whether  polarised  rays  presented 
the  same  phenomena  of  inteifcrencc  as  ordinary  rays.  They  were  thus  led 
to  the  discovery  of  the  following  laws  in  reference  to  the  interference  of 
polarised  light,  and,  at  the  same  time,  of  the  brilliant  phenomena  of  colora- 
tion, which  will  be  presently  described  :— 

I.  When  two  rays  polarised  in  the  same  plane  interfere  with  each  other, 
they  produce,  by  their  interference,  fringes  of  the  very  same  kind  as  if  they 
were  common  light. 

II.  When  two  rays  of  light  are  polarised  at  right  angles  to  each  other, 
tliey  produce  no  coloured  fringes  in  the  same  cirrumstances  in  which 
two  rays  of  common  light  would  produce  them.  When  the  rays  arc  po- 
larised in  planes  inclined  to  each  other  at  any  other  angles,  they  produce 
fringes  of  intermediate  brightness  :  and  if  the  angle  is  made  to  change,  the 


-664]     Ejfcct  produced  ivlicn  Plate  of  Crystal  is  very  Thin.     633 

fringes  gradually  decrease  in  brightness  from  0°  to  90°,  and  arc  totally 
obliterated  at  the  latter  angle. 

III.  Two  rays  originally  polarised  in  planes  at  light  angles  to  each  other 
may  be  subsequently  brought  into  the  same  plane  of  polarisation  without 
acquiring  the  power  of  forming  fringes  by  their  interference. 

I\'.  Two  rays  polarised  at  right  angles  to  each  other,  and  afterwards 
brought  into  the  same  plane  of  polarisation,  produce  fringes  by  their  inter- 
ference like  rays  of  common  light,  provided  they  originated  in  a  pencil  the 
whole  of  which  was  originally  polarised  in  any  one  plane. 

\.  In  the  phenomena  of  interference  produced  by  rays  that  ha\e  suffered 
double  refraction,  a  difference  of  half  an  undulation  must  be  allowed,  as  one 
of  the  pencils  is  retarded  by  that  tjuantity,  from  some  unknown  cause. 

663.  Effect  produced  by  causing:  a  pencil  of  polarised  rays  to  tra- 
verse a  double-refVactlng-  crystal.-  -The  following  important  experiment 
may  be  made  most  conveniently  by  Norremberg's  apparatus  (fig.  606).  At 
^((ig.  607)  there  is  a  Nicol's  prism.  A  plate  of  a  double-refracting  crystal 
cut  parallel  to  its  axis  is  placed  on  the  disc  at  e.  In  the  first  place,  however, 
suppose  the  plate  of  the  crystal  to  be  removed.  Then,  since  the  Nicol's 
prism  allows  only  the  extraordinary  ray  to  pass  when  it  is  turned  so  that  its 
principal  plane  coincides  with  the  plane  of  reflection,  no  light  will  be  trans- 
mitted (660).  Place  the  plate  of  doubly  refracting  crystal,  which  is  supposed 
to  be  of  moderate  thickness,  in  the  path  of  the  reflected  ray  at  c.  Light  is 
now  transmitted  through  the  Nicol's  prism.  On  turning  the  plate,  the 
intensity  of  the  transmitted  light  varies  ;  it  reaches  its  maximum  when  the 
principal  plane  of  the  plate  is  inclined  at  an  angle  of  45°  to  the  plane  of 
reflection,  and  disappears  when  these  planes  either  coincide  with  or  are  at 
right  angles  to  each  other.  The  light  in  this  case  is  white.  The  interposed 
plate  may  be  called  the  depolarising  plate.  The  same  or  equivalent  phe- 
nomena are  produced  when  any  other  analyser  is  used.  Thus,  assume  the 
double-refracting  prism  to  be  used  and  suppose  the  depolarising  plate  to  be 
removed.  Then,  generally,  two  rays  are  transmitted  ;  but  if  the  principal 
plane  of  the  analyser  is  turned  in  the  plane  of  primitive  polarisation,  the 
ordinary  ray  only  is  transmitted,  and  then,  when  turned  through  90°,  the 
extraordinary  ray  only  is  transmitted.  Let  the  analyser  be  turned  into 
the  former  position,  then,  when  the  depolarising  plate  is  interposed,  both 
ordinary  and  extraordinary  rays  are  seen,  and  when  the  depolarising  plate 
is  slowly  turned  round,  the  ordinary  and  extraordinary  rays  are  seen  to  vary 
in  intensity,  the  latter  vanishing  when  the  principal  plane  of  the  polarising 
plate  either  coincides  with,  or  is  at  right  angles  to,  the  plane  of  primitive 
polarisation. 

664.  Effect  produced  when  the  plate  of  crystal  Is  very  thin.— In 
order  to  exhibit  this,  take  a  thin  film  of  sclcnitc  or  mica  between  the  twen- 
tieth and  sixtieth  of  an  inch  thick,  and  interpose  it  as  in  the  last  article.  If 
the  thickness  of  the  film  is  uniform,  the  light  now  transmitted  through  the 
analyser  will  be  no  longer  white,  but  of  a  uniform  tint  ;  the  colour  of  the 
tint  being  different  for  different  thicknesses— for  instance,  red,  or  green,  or 
blue,  or  yellow,  according  to  the  thickness  ;  the  intensity  of  the  colour  de- 
pending on  the  inclination  of  the  principal  plane  of  the  film  to  the  plane  of 
reflection,  being  greatest  when  the  angle  of  inclination  is  45°.     Let  us  now 


634  On  Light.  [664- 

suppose  the  crystalline  film  to  be  fixed  in  that  position  in  which  the  light  is 
brightest,  and  suppose  its  colour  to  be  red.  Let  the  analyser  (the  Nicol's 
prism)  be  turned  round,  the  colour  will  grow  fainter,  and  when  it  has  been 
turned  through  45°,  the  colour  disappears,  and  no  light  is  transmitted  ;  on 
turning  it  further,  the  complementary  colour,  ^r^^;/,  makes  its  appearance, 
and  increases  in  intensity  until  the  analyser  has  been  turned  through  90°  ; 
after  which  the  intensity  diminishes  until  an  angle  of  135°  is  attained,  when 
the  light  again  vanishes,  and,  on  increasing  the  angle,  it  changes  again  into 
red.  Whatever  be  the  colour  proper  to  the  plate,  the  same  series  of  pheno- 
mena will  be  observed,  the  colour  passing  into  its  complementarj'  when  the 
analyser  is  turned.  That  the  colours  are  really  complementary  is  proved 
by  using  a  double-refracting  prism  as  analyser.  In  this  case  two  rays  are 
transmitted,  each  of  which  goes  through  the  same  changes  of  colour  and  in- 
tensity as  the  single  ray  described  above  ;  but  whatever  be  the  colour  and 
intensity  of  the  one  ray  in  a  given  position,  the  other  ray  will  have  the  same 
when  the  analyser  has  been  turned  through  an  angle  of  90°.  Consequently, 
these  two  rays  give  simultaneously  the  appearances  which  are  successively 
presented  in  the  above  case  by  the  same  ray  at  an  interval  of  90°.  If  now 
the  two  rays  are  allowed  to  overlap,  they  produce  white  light ;  thereby 
proving  their  colours  to  be  complementary. 

Instead  of  using  plates  of  different  thicknesses  to  produce  different  tints, 
the  same  plate  may  be  employed  inclined  at  different  angles  to  the  polarised 
ray.  This  causes  the  ray  to  traverse  the  film  obliquely,  and,  in  fact,  amounts 
to  an  alteration  in  its  thickness. 

With  the  same  substance,  but  with  plates  of  increasing  thickness,  the 
tints  follow  the  laws  of  the  colours  of  Newton's  rings  (660).  The  thickness 
of  the  depolarising  plate  must,  however,  be  different  from  that  of  the  layer 
of  air  in  the  case  of  Newton's  rings  to  produce  corresponding  colours.  Thus 
corresponding  colours  are  produced  by  a  plate  of  mica  and  a  layer  of  air 
when  the  thickness  of  the  former  is  about  400  times  that  of  the  latter.  In 
the  case  of  selenite  the  thickness  is  about  230  times,  and  in  the  case  of  Ice- 
land spar  about  13  times,  that  of  the  corresponding  layer  of  air. 

665.  Theory  of  the  phenomena  of  depolarisatlon. — The  phenomena 
described  in  the  last  articles  admit  of  complete  e.xplanation  by  the  undulatory 
theory,  but  not  without  the  aid  of  abstruse  mathematical  calculations.  What 
follows  will  show  the  nature  of  the  explanation.  Let  us  suppose,  for  con- 
venience, that  in  the  case  of  a  polarised  ray  the  particles  of  ether  vibrate 
in  the  plane  of  polarisation  (661),  and  that  the  analyser  is  a  double  refract- 
ing prism,  with  its  principal  plane  in  the  plane  of  primitive  polarisation  ; 
then  the  vibrations,  being  wholly  in  that  plane,  have  no  resolved  part 
in  a  plane  at  right  angles  to  it,  and,  consequently,  no  e.xtraordinary  ray  passes 
through  the  analyser ;  in  other  words,  only  an  ordinary  ray  passes.  Now 
take  the  depolarising  plane  cut  parallel  to  the  axis,  and  let  it  be  interposed 
in  such  a  manner  that  its  principal  plane  makes  any  angle  {6)  with  the  plane 
of  primitive  polarisation.  The  effect  of  this  will  be  to  cause  the  vibrations 
of  the  primitive  ray  to  be  resolved  in  the  principal  plane  and  at  right  angles 
to  the  principal  plane,  thereby  giving  rise  to  an  ordinary  ray  (O)  and  an  ex- 
traordinary ray  (E),  which,  however,  do  not  become  separated  on  account  of 
the  thinness  of  the  depolarising  plate.     They  will  not  form  a  single  plane 


666]  Coloured  Rings  produced  by  Polarised  Light.  635 

polarised  ray  on  leaving  the  plate,  since  they  are  unequally  retarded  in  pass- 
ing- through  it,  and  consequently  leave  it  in  different  phases.  Since  neither 
of  the  planes  of  polarisation  of  O  and  E  coincides  with  the  principal  plane 
of  the  analyser,  the  vibrations  composing  them  will  again  be  resolved — viz. 
O  gives  rise  to  Oo  and  O^,  and  E  gives  rise  to  E^  and  E^.  But  the  vibra- 
tions composing  Oo  and  E<7,  being  in  the  same  phase,  give  rise  to  a  single 
ordinary  ray,  I^,  and  in  like  manner  Oe  and  E^  give  rise  to  a  single  extra- 
ordinary ray,  \e.  Thus  the  interposition  of  the  depolarising  plate  restores 
the  extraordinary  ray. 

Suppose  the  angle  i^  to  be  either  0°  or  90°.  In  either  case  the  vibrations 
are  transmitted  through  the  depolarising  plate  without  resolution,  conse- 
quently they  remain  wholly  in  the  plane  of  primitive  polarisation,  and  on 
entering  the  analyser  cannot  give  rise  to  an  extraordinary  ray. 

If  the  Nicol's  prism  is  used  as  an  analyser,  the  ordinary  ray  is  suppressed 
by  mechanical  means.  Consequently  only  \e  will  pass  through  the  prism, 
and  that  for  all  values  of  6  except  0°  and  90°. 

A  little  consideration  will  show  that  the  joint  intensities  of  all  the  rays 
existing  at  any  stage  of  the  above  transformations  must  continue  constant, 
but  that  the  intensities  of  the  individual  rays  will  depend  on  the  magnitude 
of  ^;  and  when  this  circumstance  is  examined  in  detail,  it  explains  the  fact 
that  \e  increases  in  intensity  as  6  increases  from  0°  to  45°,  and  then  decreases 
in  intensity  as  6  increases  from  45°  to  90°. 

In  regard  to  the  colour  of  the  rays,  it  is  to  be  observed  that  the  formulae 
for  the  intensities  of  \o  and  \e  contain  a  term  depending  on  the  length  of  the 
wave  and  the  thickness  of  the  plate.  Consequently,  when  white  light  is  used 
the  relative  intensities  of  its  component  colours  are  changed,  and  therefore 
\o  and  \e  will  each  have  a  prevailing  tint,  which  will  be  different  for  different 
thicknesses  of  the  plate.  The  tints  will,  however,  be  complementary,  since 
the  joint  intensities  of  \o  and  \e  being  the  same  as  that  of  the  original  ray, 
they  will,  when  superimposed,  restore  all  the  components  of  that  ray  in  their 
original  intensities,  and  therefore  produce  white  light. 

666.  Coloured  rings  produced  by  polarised  ligrht  in  traversing- 
double  refracting:  films. — In  the  experiments  with  Norremberg's  apparatus 
Avhich  have  just  been  described  (663),  a  pencil  of  parallel  rays  traverses  the 
film  of  crystal  perpendicularly  to  its  faces,  and  as  all  parts  of  the  film  act  in 
the  same  manner,  there  is  everywhere  the  same  tmt.    But  when  the  incident 


rays  traverse  the  plate  under  different  obliquities,  which  comes  to  the  same 
thing  as  if  they  traversed  plates  differing  in  thickness,  coloured  rings  are 
formed  similar  to  Newton's  rings. 

The  best  method  of  observing  these  new  phenomena  is  by  means  of  the 
tourmaline  pi7icette  (fig.  611).  This  is  a  small  instrument  consisting  of  two 
tourmalines,  cut  parallel  to  the  axis,  each  of  them  being  fitted  in  a  copper 


636  On  Light.  [666- 

disc.  These  two  discs,  \vhich  are  perforated  in  the  centre,  and  blackened, 
are  mounted  in  two  rings  of  silvered  copper,  which  is  coiled,  as  shown  in 
the  figure,  so  as  to  form  a  spring,  and  press  together  the  tourmalines.  The 
tourmalines  turn  with  the  disc,  and  may  be  so  arranged  that  their  axes  are 
either  perpendicular  or  parallel. 

The  crystal  to  be  experimented  upon,  being  fixed  in  the  centre  of  a  cork 
disc,  is  placed  between  the  two  tourmalines,  and  the  pincette  is  held  before 
the  eye  so  as  to  view  diffused  light.  The  tourmaline  farthest  from  the  eye 
acts  as  polariser  and  the  other  as  analyser.  If  the  crystal  thus  viewed  is 
uniaxial,  and  cut  perpendicularly  to  the  axis,  and  a  homogeneous  light — 
red  for  instance — is  looked  at,  a  series  of  alternately  dark  and  red  rings 
is  seen.  With  another  simple  colour  similar  rings  are  obtained,  but  their 
diameter  decreases  with  the  refrangibility  of  the  colour.  On  the  other 
hand,  the  diametei^s  of  the  rings  diminish  when  the  thickness  of  the  plates 
increases,  and  beyond  a  certain  thickness  no  more  rings  are  produced. 
If,  instead  of  illuminating  the  rings  by  homogeneous  light,  white  light  be 
used,  then  since  the  rings  of  the  different  colours  produced  have  not  the 
same  diameter,  they  are  partially  superposed,  and  produce  very  brilliant 
variegated  colours. 

The  position  of  the  crystal  has  no  influence  on  the  rings,  but  this  is  not 
the  case  with  the  relative  position  of  the  two  tourmalines.  For  instance, 
in  experimenting  on  Iceland  spar  cut  perpendicular  to  the  axis,  and  from  i 
to  20  millimetres  in  thickness,  when  the  axes  of  the  tourmalines  are  perpen- 
dicular, a  beautiful  series  of  rings  is  seen,  brilliantly  coloured,  and  traversed 
by  a  black  cross,  as  shown  in  fig.  i,  Plate  II.  If  the  axes  of  the  tourmalines 
are  parallel,  the  rings  have  tints  complementary  to  those  they  had  at  first, 
and  there  is  a  white  cross  (fig.  2,  Plate  II.)  instead  of  a  black  one. 

In  order  to  understand  the  formation  of  these  rings  when  polarised  light 
traverses  double-refracting  films,  it  must  first  be  premised  that  these  films 
are  traversed  by  a  converging  conical  pencil,  whose  summit  is  the  eye  of  the 
observer.  Hence  it  follows  that  the  virtual  thickness  of  the  film  which  the 
rays  traverse  increases  with  their  divergence  ;  but  for  rays  of  the  same 
obliquity  this  thickness  is  the  same  ;  hence  there  result  different  degrees  of 
retardation  of  the  ordinary  with  respect  to  the  extraordinary  ray  at  different 
points  of  the  plate,  and  consequently  different  colours  are  produced  at 
different  distances  from  the  axis,  but  the  same  colours  will  be  produced  at 
the  same  distance  from  the  axis,  and  consequently  the  colours  are  arranged 
in  circles  round  the  axis.  The  arms  of  the  black  cross  are  parallel  to  the 
optic  axis  of  each  of  the  tourmalines,  and  are  due  to  an  absorption  of  the 
polarised  light  in  these  directions.  When  the  tourmalines  are  parallel  the 
vibrations  are  transmitted,  and  hence' the  white  cross. 

Analogous  effects  are  produced  with  all  uniaxial  crystals  ;  for  instance, 
tourmaline,  emerald,  sapjjhire,  beryl,  mica,  jiyromorphite,  and  ferrocyanide 
of  potassium. 

667.  Hln^s  In  biaxial  crystals. — ^In  biaxial  crystals,  coloured  rings  are 
also  produced,  liut  their  form  is  more  complicated.  The  coloured  bands, 
instead  of  being  circular  and  concentric,  have  the  form  of  curves,  with  two 
centres,  the  centre  of  each  system  corresponding  to  an  axis  of  the  crystal. 
Figs.  4,  5,  and  6,  Plate  II.,  represent  the  curves  seen  wIkmi  a  plate  of  either 


IV 


f*^**i 


\ 


'^^ 


M&N.Ka^^rt   litn 


-668]  Colours  produced  by  Compressed  or  Unanneakd  Glass.  637 

cerussite,  topaz,  or  nitre,  cut  perpendicularly  to  the  axis,  is  placed  between 
the  two  tourmalines,  the  plane  containing  the  axis  of  the  crystal  being  in  the 
plane  of  primitive  polarisation.  When  the  axes  of  the  two  tourmalines  are 
at  right  angles  to  each  other,  fig.  4,  Plate  II.,  is  obtained.  On  turning  the 
crj'stal  without  altering  the  tourmalines,  fig.  5,  Plate  II.,  is  seen,  which 
changes  into  fig.  6,  Plate  II.,  when  the  crystal  has  been  turned  through  45°. 
If  the  axes  of  the  tourmalines  are  parallel,  the  same  coloured  curves  are 
obtained,  but  the  colours  are  complementary,  and  the  black  cross  changes 
into  white.  The  angle  of  the  optic  axis  in  the  case  of  nitre  is  only  5°  20', 
and  hence  the  whole  system  can  be  seen  at  once.  But  when  the  angle  exceeds 
20°  to  25°,  the  two  systems  of  curves  cannot  be  simultaneously  seen.  There 
is  then  only  one  dark  bar  instead  of  the  cross,  and  the  bands  are  not  oval, 
but  circular.  Fig.  3,  Plate  II.,  represents  the  phenomenon  as  seen  with 
arragonite. 

Sir  John  Herschel,  who  carefully  measured  the  rings  produced  by  biaxial 
cr^'stals,  referred  them  to  the  kind  of  curve  known  in  geometry  as  the  lem- 
niscate,  in  strict  accordance  with  the  principles  of  the  undulatory  theory  of 
light. 

The  observation  of  the  system  of  rings  which  plates  of  cr>'stals  give  in 
polarised  light  presents  a  means  of  distinguishing  between  optical  uniaxial 
and  optical  biaxial  crystals,  even  in  cases  in  which  no  conclusion  can  be 
drawn  as  to  the  system  in  which  a  mineral  crystallises  from  mere  morpho- 
logical reasons.  In  this  way  the  optical  investigation  becomes  a  valuable 
aid  in  mineralogy  ;  as,  for  example,  in  the  case  of  mica,  of  which  there  are 
two  mineralogical  species,  the  uniaxial  and  the  biaxial. 

All  the  phenomenon  which  have  been  described  are  only  obtained  by 
means  of  polarised  light.  Hence,  a  double  refracting  film,  with  either  a 
Nicol's  prism  or  a  tourmaline  as  analyser,  may  be  used  to  distinguish  between 
polarised  and  unpolarised  light  ;  that  is  as  a  polariscope. 

668.  Colours  produced  by  compressed  or  by  unannealed  grlass. — 
Ordinary  glass  is  not  endowed  with  the  power  of  double  refraction.  It 
acquires  this  property,  however,  if  by  any  cause  its  elasticity  becomes 
more  modified  in  one  direction  than  in  another.  In  order  to  effect  this, 
it  may  be  strongly  compressed  in  a  given  direction,  or  it  may  be  curved, 
or  tempered  ;  that  is  to  say,  cooled  after  having  been  heated.  If  the 
glass  is  then  traversed  by  a  beam  of  polarised  light,  effects  of  colour  are 
obtained  which  are  entirely  analogous  to  those  described  in  the  case  of 
doubly  refracting  crystals.  They  are,  however,  susceptible  of  far  greater 
variety,  according  as  the  plates  of  glass  have  a  circular,  square,  rectangular, 
or  triangular  shape,  and  according  to  the  degree  of  tension  of  their  particles. 

When  the  polariser  is  a  mirror  of  black  glass,  on  which  the  light  of  the 
sky  is  incident,  and  the  analyser  is  a  Nicol's  prism,  through  which  the 
glass  plates  traversed  by  polarised  light  are  viewed,  figs.  612,  613,  615 
represent  the  appearances  presented  successively,  when  a  square  plate 
of  compressed  glass  is  turned  in  its  own  plane;  figs.  614  and  617  re- 
present the  appearances  produced  by  a  circular  plate  under  the  same 
circumstances  ;  and  fig.  617  that  produced  when  one  rectangular  plate  is 
supei-posed  on  another.  This  figure  also  varies  when  the  system  of  plates 
is  turned. 


638 


07t  Lio-ht. 


[668- 


In  consequence  of  being  rapidly  cooled,  glass  often  acquires  a  strained 
condition.  Hence,  when  the  masses  of  glass,  more  especially  the  larger  ones, 
from  which  lenses  are  made,  are  examined  by  polarised  light,  the  existence  of 

Fig.  612. 


Fig.  615. 


Fig.  616. 


Fig.  617. 


Strains  may  be  revealed  which  would  render  it  useless  to  go  to  the  trouble 
and  expense  of  working  such  masses,  as  they  would  probably  break  in  the 
operation. 


KLLIl'TICAL,    CIRCULAR,   AND    ROTATORY    POLARISATION. 

669.  Definition  of  elliptical  and  circular  polarisation.— In  the  cases 
hitherto  considered,  the  particles  of  ether  composing  a  polarised  ray  vibrate 
in  parallel  straight  lines  ;  to  distinguish  this  case  from  those  we  are  now  to 
consider,  such  light  is  frequently  called  plane polatised light.  It  sometimes 
happens  that  the  particles  of  ether  describe  ellipses  about  their  positions  of 
rest,  the  planes  of  the  ellipses  being  perpendicular  to  the  direction  of  the 
ray.  If  the  axes  of  these  ellipses  are  equal  and  parallel,  the  ray  is  said  to  be 
elliptically  polarised.  In  this  case  the  particles  which,  when  at  rest,  occu- 
pied a  straight  line,  are,  when  in  motion,  arranged  in  a  helix  round  the  hne 
of  their  original  position  as  an  axis,  the  helix  exchanging  from  instant  to 
instant.  If  the  axes  of  the  ellipses  are  equal,  they  become  circles,  and  the 
light  is  said  to  be  circularly  polarised.  If  the  minor  axes  become  zero,  the 
ellipses  coincide  with  their  major  axes,  and  the  light  becomes  plane  polarised. 
Consequently, /Ajz/r  ]K)lariscd  light  and  circularly  polarised  light  are  parti- 
cular cases  of  ellii)ti(:ally  polarised  light. 

670.  Theory  of  the  origin  of  elliptical  and  circular  polarisation. — 
Let  us  in  the  first  place  consider  a  simple  pendulum  (55)  vibrating  in  any 
plane,  the  arc  of  vibration  being  small.  Suppose  that,  when  in  its  lowest 
position,  it  received  a  blow  in  a  direction  at  right  angles  to  the  direction  ol 
its  motion,  such  as  would  make  it  vibrate  in  an  arc  at  right  angles  to  its 


-671]  FresneVs  R/iowb.  639 

arc  of  primitive  vibration,  it  follows  from  the  law  of  the  composition  of 
velocities  (52)  that  the  joint  effect  will  be  to  make  it  vibrate  in  an  arc  inclined 
at  a  certain  angle  to  the  arc  of  primitive  vibration,  the  magnitude  of  the 
angle  depending  on  the  magnitude  of  the  blow.  If  the  blow  communicated 
a  velocity  equal  to  that  with  which  the  body  is  already  moving,  the  angle 
would  be  45°.  Next  suppose  the  blow  to  communicate  an  equal  velocity, 
but  to  be  struck  when  the  body  .is  at  its  highest  point,  this  will  cause  the 
particle  to  describe  a  circle,  and  to  move  as  a  conical  pendulum.  If  the 
blow  is  struck  under  any  other  circumstances,  the  particle  will  describe  an 
ellipse.  Now  as  the  two  blows  would  produce  separately  two  simple  vibra- 
tions in  directions  at  right  angles  to  each  other,  we  may  state  the  result 
arrived  at  as  follows  : — If  two  rectilinear  vibrations  are  superinduced  on 
the  same  particle  in  directions  at  right  angles  to  each  other,  then  :  i.  If 
they  are  in  the  same  or  opposite  phases,  they  make  the  point  describe  a 
rectilinear  vibration  in  a  direction  inclined  at  a  certain  angle  to  either  of 
the  original  vibrations.  2.  But  if  their  phases  differ  by  90°  or  a  quarter 
of  a  vibration,  the  particle  will  describe  a  circle,  provided  the  vibrations 
are  equal.  3.  Under  other  circumstances  the  particle  will  describe  an 
ellipse. 

To  apply  this  to  the  case  of  polarised  light.  Suppose  two  rays  of  light 
polarised  in  perpendicular  planes  to  coincide,  each  would  separately  cause 
the  same  particles  to  vibrate  in  perpendicular  directions.  Consequently — 
r.  If  the  vibrations  are  in  the  same  or  opposite  phases,  the  light  resulting-  from 
the  two  rays  is  plane  polarised.  2.  If  the  rays  are  of  equal  intensity,  and 
their  phases  differ  by  90°,  the  resulting  light  is  circularly  polarised.  3.  Under 
other  circumstances  the  light  is  elliptically  polarised. 

As  an  example,  if  reference  is  made  to  arts.  665  and  666,  it  will  be  seen 
that  the  rays  denoted  by  O  and  E  are  superimposed  in  the  manner  above 
described.  Consequently,  the  light  which  leaves  the  depolarising  plate  is 
elliptically  polarised.  If,  however,  the  principal  plane  of  the  depolarising 
plate  is  turned  so  as  to  make  an  angle  of  45°  with  the  plane  of  primitive 
polarisation,  O  and  E  have  equal  intensities  ;  and  if,  further,  the  plate  is 
made  of  a  certain  thickness,  so  that  the  phases  of  O  and  E  may  differ  by 
90°,  or  by  a  quarter  of  a  vibration,  the  light  which  emerges  from  the  plate  is 
circularly  polarised.  This  method  may  be  employed  to  produce  circularly 
polarised  light. 

Circular  or  elliptical  polarisation  may  be  either  right-handed  or  left- 
handed^  or  what  is  sometimes  called  dextrogyrate  and  hevogyrate.  If  the  ob- 
server looks  along  the  ray  in  the  direction  of  propagation,  from  polariser 
to  analyser,  then,  if  the  particles  move  in  the  same  direction  as  the  hands 
of  a  watch  with  its  face  to  the  observer,  the  polarisation  is  right-handed. 

671.  Fresnel's  rhomb. — This  is  a  means  of  obtaining  circularly  polarised 
light.  We  have  just  seen  (670)  that,  to  obtain  a  ray  of  circularly  polarised 
light,  it  is  sufficient  to  decompose  a  ray  of  plane  polarised  light  in  such 
a  manner  as  to  produce  two  rays  of  light  of  equal  intensity  polarised 
in  planes  at  right  angles  to  each  other,  and  differing  in  their  paths  by  a 
quarter  of  an  undulation.  Fresnel  effected  this  by  means  of  a  rhomb  which 
has  received  his  name.  It  is  made  of  glass  ;  its  acute  angle  is  54',  and  its 
obtuse  126°.     If  a  ray  (a,  fig.  618)  of  pLiin  polarised  light  falls  perpendicu- 


640  0)1  Light.  [671- 

larly  on  the  face  of  AB,  it  will  undergo  two  total  internal  reflections  at  an  angle 
of  about  54°,  one  at  E,  and  the  other  at  F,  and  will  emerge  perpendicularly. 
If  the  plane  ABCD  be  inclined  at  an  angle  of 
45°  to  the  plane  of  polarisation,  the  polarised  ray 
will  be  divided  into  two  coincident  rays,  with  their 
planes  of  polarisation  at  right  angles  to  each  other, 
and  it  appears   that   one    of  them    loses    exactly   a 
quarter  of  an  undulation,  so  that  on  emerging  from 
the  rhomb  the  ray  is  circularly  polarised.     If  the  ray 
emerging   as    above   from    Fresnel's    rhomb    is    ex- 
amined, it  will  be  found  to  differ  from  plane  polarised 
light  in  this,  that,  when  it  passes  through  a  double 
refracting    prism,    the    ordinary   and    extraordinary 
*"!  rays  are  of  ec^ual    intensity  in  all  positions  of  the 

p.     g^g  prism.     Moreover,  it  differs  from  ordinary  light    in 

this,  that,  if  it  pass  through  a  second  rhomb  placed 
parallel  to  the  first,  a  second  quarter  of  an  undulation  will  be  lost,  so  that 
the  parts  of  the  original  plane  polarised  ray  will  differ  by  half  an  undulation, 
and  the  emergent  ray  will  be  plane  polarised  ;  moreover  the  plane  of  polar- 
isation will  be  inclined  at  an  angle  of  45°  to  ABCD,  but  on  the  other  side 
from  the  plane  of  primitive  polarisation. 

672.  Elliptical  polarisation. — In  addition  to  the  method  already  men- 
tioned (671),  elliptically  polarised  light  is  generally  obtained  whenever  plane 
polarised  light  sufTers  reflection.  Polarised  light  reflected  from  metals 
becomes  elliptically  polarised,  the  degree  of  ellipticity  depending  on  the  direc- 
tion of  the  incident  ray,  and  of  its  plane  of  polarisation,  as  well  as  on  the  nature 
of  the  reflecting  substance.  When  reflected  from  silver,  the  polarisation  is 
almost  circular,  and  from  galena  almost  plane.  If  elliptically  polarised  light  be 
analysed  by  the  Nicol's  prism,  it  never  vanishes,  though  at  alternate  positions 
it  becomes  fainter ;  it  is  thus  distinguished  from  plane  and  from  circular 
polarised  light.  If  analysed  by  Iceland  spar,  neither  image  disappears,  but 
they  undergo  changes  in  intensity. 

Light  can  also  be  polarised  elliptically  in  P'resnel's  rhomb.  If  the  angle 
between  the  planes  of  primitive  polarisation  and  of  incidence  be  any  other 
than  45°,  the  emergent  ray  is  elliptically  polarised. 

673.  Rotatory  polarisation. — Rock  crystal  or  quartz  possesses  a  re- 
markable property  which  was  long  regarded  as  peculiar  to  itself  among  all 
crystals,  though  it  has  been  since  found  to  be  shared  by  tartaric  acid  and  its 
salts,  together  with  some  other  crystallised  bodies.  This  property  is  called 
rotatory  polarisation,  and  may  be  described  as  follows  :  Let  a  ray  of 
homogeneous  light  be  polarised,  and  let  the  analyser,  say  a  Nicol's  prism,  be 
turned  till  the  light  does  not  pass  through  it.  Take  a  thin  section  of  a  quartz 
crystal  cut  at  right  angles  to  its  axis,  and  place  it  between  the  polariser  and 
the  analyser  with  its  plane  at  right  angles  to  the  rays.  The  light  will  now 
pass  through  the  analyser.  The  phenomenon  is  not  the  same  as  that  pre- 
viously described  (663),  for,  if  the  rock  crystal  is  turned  round  its  axis,  no 
effect  is  produced,  and  if  the  analyser  is  turned,  the  ray  is  found  to  ht  plane 
polarised  in  a  plane  inclined  at  a  certain  angle  to  the  plane  of  primitive 
polarisation.     If  the  light  is  red,  and  the  plate  i  millimetre  thick,  this  angle 


-675J         Coloration  produced  by  Rotary  Polarisation.  641 

is  about  17°.  In  some  specimens  of  quartz  the  plane  of  polarisation  is 
turned  to  the  right  hand,  in  others  to  the  left  hand.  Specimens  of  the 
former  kind  are  said  to  be  right-handed,  those  of  the  latter  kind  left-handed 
(670).  This  difference  corresponds  to  a  difference  in  crystallographic  struc- 
ture. The  property  possessed  by  rock  crystal  of  turning  the  plane  of  polari- 
sation through  a  certain  angle  was  thoroughly  investigated  by  Biot,  who, 
amongst  other  results,  arrived  at  this  : — For  a  given  colour,  the  angle, 
through  which  the  plane  of  polarisation  is  turned,  is  proportional  to  the 
thickness  of  the  quartz. 

674.  Pbysical  explanation  of  rotary  polarisation. — The  explanation 
of  the  phenomenon  described  in  the  last  article  is  as  follows  :  When  a  ray 
of  polarised  light  passes  along  the  axis  of  the  quartz  crystal,  it  is  divided  into 
two  rays  of  circularly  polarised  light  of  equal  intensity,  which  pass  through 
the  crystal  with  different  velocities.  In  one  the  circular  polarisation  is  right- 
handed,  in  the  other  left-handed  (670).  The  existence  of  these  rays  was 
proved  by  Fresnel,  who  succeeded  in  separating  them.  On  emerging  from 
the  crystal,  they  are  compounded  into  a  plane  polarised  ray  ;  but,  since  they 
move  with  unequal  velocities  within  the  crystal,  they  emerge  in  different 
phases,  and  consequently  the  plane  of  polarisation  will  not  coincide  with  the 
plane  of  primitive  polarisation.  This  can  be  readily  shown  by  reasoning 
similar  to  that  employed  in  art.  670.  The  same  reasoning  will  also  show 
that  the  plane  of  polarisation  will  be  turned  to  the  right  or  left,  according 
as  the  right-handed  or  left-handed  ray  moves  with  the  greater  velocity. 
Moreover,  the  amount  of  the  rotation  will  depend  on  the  amount  of  the 
retardation  of  the  ray  whose  velocity  is  least  ;  that  is  to  say,  it  will  depend 
on  the  thickness  of  the  plate  of  quartz.  In  this  manner  the  phenomena  of 
rotary  polarisation  can  be  completely  accounted  for. 

675.  Coloration  produced  by  rotary  polarisation. — The  rotation  is 
different  with  different  colours  ;  its  magnitude  depends  on  the  refrangibility, 
and  is  greatest  with  the  most  refrangible  rays.  In  the  case  of  red  light  a 
plate  I  millimetre  in  thickness  will  rotate  the  plane  17°,  while  a  plate  of  the 
same  thickness  will  rotate  it  44°  m  the  case  of  violet  light.  Hence  with 
white  light  there  will,  in  each  position  of  the  analysing  NicoFs  prism,  be  a 
greater  or  less  quantity  of  each  colour  transmitted.  In  the  case  of  a  right- 
handed  crystal,  when  the  Nicol's  prism  is  turned  to  the  right,  the  colours 
will  successively  appear  from  the  less  refrangible  to  the  more  so — that  is, 
in  the  order  of  the  spectrum,  from  red  to  violet ;  with 

a  left-handed  crystal  in  the  reverse  order.     Obviously    ^l|B^  .^-ifim^ 
in  turning  the  Nicol's  prism  to  the  left,  the  reverse  of  m^BB 
these  results  will  take  place.  ^E^^& 

When    a   quartz   plate   cut    perpendicularly    to    the   ^HS|F''fe;*isA<^ 
axis,    and    traversed   by   a   ray   of    polarised    light,    is 
looked    at    through    a    doubly    refracting    prism,    two  '^'    "^' 

brilliantly  coloured  images  are  seen,  of  which  the  tints  are  complementaiy  : 
for  their  images  are  partially  superposed,  and  in  this  position  there  is 
white  light  (fig.  619).  When  the  prism  is  turned  from  left  to  right,  the  two 
images  change  colour  and  assume  successively  all  the  colours  of  the 
spectrum. 

This  will   be  understood  from  what  has  been   said  about  the  different 


642  On  Light.  [675- 

rotation  for  dififeient  colours.  Quartz  rotates  the  plane  of  polarisation  for 
red  17°  for  each  millimetre,  and  for  violet  44°  ;  hence  from  the  great  difference 
of  these  two  angles,  when  the  polarised  light  which  has  traversed  the  quartz 
plate  emerges,  the  various  simple  colours  which  it  contains  are  polarised 
in  different  planes.  Consequently,  when  the  rays  thus  transmitted  by  the 
quartz  pass  through  a  double-refracting  prism,  they  are  each  decomposed 
into  two  others  polarised  at  right  angles  to  each  other  :  the  various  simple 
colours  are  not  divided  in  the  same  proportion  between  the  ordinary  and 
extraordinary  rays  furnished  by  the  prism  ;  the  two  images  are,  therefore, 
coloured  ;  but,  since  those  which  are  wanting  in  one  occur  in  the  other,  the 
colours  of  the  images  are  perfectly  complementary. 

These  phenomena  of  coloration  may  be  well  seen  by  means  of  Norrem- 
berg's  apparatus  (fig.  606).  A  quartz  plate,  J',  cut  at  right  angles  to  the  axis 
and  fixed  in  a  cork  disc,  is  placed  on  a  screen  e  ;  the  mirror  «  being  then 
so  inclined  that  a  ray  of  polarised  light  passes  through  the  c[uartz,  the  latter 
is  viewed  through  a  double-refracting  prism,  g  ;  when  this  tube  is  turned,  the 
complementary  images  furnished  by  the  passage  of  polarised  light  through 
the  quartz  are  seen. 

676.  Rotary  power  of  liquids. —Biot  found  that  a  great  number  of 
liquids  and  solutions  possess  the  property  of  rotary  polarisation.  He 
further  observed  that  the  deviation  of  the  plane  of  polarisation  can  reveal 
differences  in  the  composition  of  bodies  where  none  is  exhibited  by  chemical 
analysis.  For  instance,  the  two  sugars  obtained  by  the  action  of  dilute  acids 
on  cane-sugar  deflect  the  plane  of  polarisation,  the  one  to  the  right  and  the 
other  to  the  left,  although  the  chemical  composition  of  the  two  sugars  is  the 
same. 

The  rotary  power  of  licjuids  is  far  less  than  that  of  quartz.  In  con- 
centrated syrup  of  cane-sugar,  which  possesses  the  rotary  power  in  the 
highest  degree,  the  power  is  5^5  that  of  quartz,  so  that  it  is  necessary  to 
operate  upon  columns  of  liquids  of  considerable  length— 8  inches,  for 
example. 

Fig.  620  represents  an  apparatus  devised  by  Biot  for  measuring  the 
rotary  power  of  liquids.  On  a  metal  groove,^,  fixed  to  a  support,  r,  is  a 
brass  tube,^,  20  centimetres  long,  in  which  is  contained  the  liquid  experimented 
upon.  This  tube,  which  is  tinned  inside,  is  closed  at  each  end  by  glass 
plates  fastened  by  screw  collars.  At  ni  is  a  mirror  of  black  glass,  inclined 
at  the  polarising  angle  to  the  axis  of  the  tubes  bd  and  (X,  so  that  the  ray  re- 
flected by  the  mirror  m,  in  the  direction  bda,  is  polarised.  In  the  centre  of 
the  graduated  circle  //,  inside  the  tube  a,  and  at  right  angles  to  the  axis  bda., 
is  a  double-refracting  achromatic  prism,  which  can  be  turned  about  the  axis 
of  the  apparatus  by  means  of  a  button  n.  The  latter  is  fixed  to  a  limb  c,  on 
which  is  a  vernier,  to  indicate  the  number  of  degrees  turned  through.  Lasth', 
from  the  position  of  the  mirror  w,  the  plane  of  polarisation,  Sod^  of  the  le- 
llccted  ray  is  vertical,  and  the  zero  of  the  graduation  of  the  circle  //  is  on 
this  plane. 

Before  i)lacing  the  tube  d  in  the  groove  g,  the  extraordinary  image  fur- 
nished by  the  double-refracting  prism  disappears  whenever  the  limb  c  corre- 
sponds to  the  zero  of  the  graduation,  because  then  the  double-refracting  prism 
is  so  turned  that  its  principal  section  coincides  with  the  plane  of  polarisation 


-677]  Rotary  poiver  of  Liquids.  643 

(661).  This  is  the  case  also  when  the  tube  d  is  full  of  water  or  any  other 
inactive  Hquid,  hke  alcohol,  ether,  &c.,  which  shows  that  the  plane  of  polari- 
sation has  not  been  turned.  But  if  the  tube  be  filled  with  a  solution  of  cane- 
sugar  or  any  other  active  liquid,  the  extraordinary  image  reappears,  and  to 
extinguish  it,  the  limb  must  be  turned  to  a  certain  extent  either  to  the  right 
or  to  the  left  of  zero,  according  as  the  liquid  is  right-handed  or  left-handed, 
showing  that  the  polarising  plane  has  been  turned  by  the  same  angle.  With 
solution  of  cane-sugar  the  rotation  takes  place  to  the  right  ;  and  if  with  the 
same  solution  tubes  of  different  lengths  are  taken,  the  rotation  is  found  to 
increase  proportionally  to  the  length,  in  conformity  with  art.  673  ;  further, 


Fig.  620. 

with  the  same  tube,  but  with  solutions  of  various  strengths,  the  rotation 
increases  with  the  quantity  of  sugar  dissolved,  so  that  the  quantitative 
analysis  of  a  solution  may  be  made  by  means  of  its  angle  of  deviation. 

In  this  experiment  homogeneous  light  must  be  used  ;  for,  as  the  various 
tints  of  the  spectra  have  different  rotary  powers,  white  light  is  decomposed 
in  traversing  an  active  liquid,  and  the  extraordinary  image  does  not  disappear 
completely  in  any  position  of  the  double-refracting  prism — it  simply  changes 
the  tint.  The  transition  tint  (677)  may,  however,  be  observed.  To  avoid 
this  inconvenience,  a  piece  of  red  glass  is  placed  in  the  tube  between  the  eye 
and  the  double-refracting  prism,  which  only  allows  red  light  to  pass.  The 
extraordinary  image  disappears  in  that  case,  whenever  the  principal  section 
of  the  prism  coincides  with  the  plane  of  polarisation  of  the  red  ray. 

677.  Soleil's  Saccbarlmeter. — Soleil  constructed  an  apparatus,  based 
upon  the  rotary  power  of  liquids,  for  analysing-  saccharine  substances, 
to  which  the  name  saccJuiri meter  is  applied.     Fig.  621   represents  the  sac- 

T  T  2 


644 


On  Li<rht. 


[677- 


charimeter  fixed  horizontally  on  its  foot,  and  fig.  622  gives  a  longitudinal 
section. 

The  principle  of  this  instrument  is  not  that  of  observing  the  amplitude 
of  the  rotation  of  the  plane  of  polarisation,  as  in  Biot"s  apparatus,  but  that 
of  compensation ;  that  is  to  say,  a  second  active  substance  is  used  acting  in  the 
opposite  direction  to  that  analysed,  and  whose  thickness  can  be  altered  until 
the  contrary  actions  of  the  two  substances  completely  neutralise  each  other. 


Fig.  621 


Instead  of  measuring  the  deviation  of  the  plane  of  polarisation,  the  thick- 
ness is  measured  which  the  plate  of  quartz  must  have  in  order  to  obtain 
perfect  compensation. 

The  apparatus  consists  of  three  parts— a  tube  containing  the  lit|uid  to  be 
analysed,  a  polariser,  and  an  analyser. 

The  tube  m,  containing  the  licjuid,  is  made  of  copper,  tinned  on  the 
inside,  and  closed  at  both  ends  by  two  glass  plates.  It  rests  on  a  support, 
/',  terminated  at  both  ends  by  tubes,  r  and  a,  in  which  are  the  cr>'stals  used 
as  analysers  and  polarisers,  and  which  are  represented  in  section  (fig.  622). 

In  front  of  the  aperture  S  (fig.  622)  is  placed  an  ordinary  lamp. 
The  light  emitted  by  this  lamp  in  the  direction  of  the  axis  first  meets  a 
double-refracting  prism  r,  which  serves  as  polariser  (659).  The  ordinary 
image  alone  meets  the  eye,  the  extraordinary  image  being  projected  out  of 
the  field  of  vision  in  consec[uence  of  the  amplitude  of  the  angle  which  the 
ordinary  makes  with  the  extraordinary  ray.  The  double  refracting  prism  is 
in  such  a  position  that  the  plane  of  polarisation  is  vertical,  and  passes  through 
the  axis  of  the  apparatus. 

Emerging  from  the  double-refracting  prism,  the  polarised  ray  meets  a 
plate  of  quartz  with  double  rotation  ;    that  is,  this  plate  rotates  the  plane 


-677] 


Sfl/cil ' J  Saccharimetcr. 


645 


both  to  the  right  and  to  the  left.  This  is  effected  by  constructing  the  plate 
of  two  quartz  plates  of  opposite  rotation  placed  one  on  the  other,  as  shown 
in  fig.  623,  so  that  the  line  of  separation  is  vertical  and  in  the  same  plane  as 
the  axis  of  the  apparatus.  These  plates,  cut  perpendicularly  to  the  axis, 
have  a  thickness  of  3-65  millimetres,  corresponding  to  a  rotation  of  90°,  and 
gi\e  a  rose-violet  tint,  called  the  /////  of  passage,  or  transitiojt  tint.  As  the 
quartz,  whether  right-handed  or  left-handed,  turns  always  to  the  same  extent 
for  the  same  thickness,  it  follows  that  the  two  quartz  plates  a  and  b  turn 
the  plane  of  polarisation  equally,  one  to  the  right  and  the  other  to  the  left. 
Hence,  looked  at  through  a  double-refracting  prism,  they  present  e.xactly  the 
same  tint. 

Having  traversed  the  quartz,  q,  the  polarised  ray  passes  into  the  liquid 
in  the  tube  ;//,  and  then  meets  a  single  plate  of  quartz,  /,  of  any  thickness, 
the  use  of  which  will  be  seen  presently.  The  compensator, ;/,  which  destroys 
the  rotation  of  the  column  of  liquid,  w,  consists  of  two  quartz  plates,  with  the 
same  rotation  either  to  the  right  or  the  left,  but  opposite  to  that  of  the  plate 
/.     These  two  quartz  plates,  a  section  of  which  is  represented  in  fig.  623,  are 


Fig.  622. 


m%L 


wir 


Fig.  623. 


Fig.  624. 


Fig.  625. 


obtained  by  cutting  obliquely  a  quartz  plate  with  parallel  sides,  so  as  to  form 
two  prisms  of  the  same  angle,  N,  N',  which  is  called  a  biqiiartz  ;  super- 
posing, then,  these  two  prisms,  as  shown  in  the  figure,  a  single  plate  is 
obtained  with  parallel  faces,  which  can  be  varied  at  will.  This  is  effected 
by  fixing  each  prism  to  a  slide,  so  as  to  move  it  in  either  direction  without 
disturbing  the  parallelism.  This  motion  is  effected  by  means  of  a  double 
rackwork  and  pinion  motion  turned  by  a  milled  head,  b  (figs.  621,  622). 

When  these  plates  move  in  the  direction  indicated  by  the  arrows  (fig.  623), 
it  is  clear  that  the  sum  of  their  thicknesses  increases,  and  that  it  diminishes 
when  the  plates  are  moved  in  the  contrary  direction.  A  scale  and  a  vernier 
follow  the  plates  in  their  motion,  and  measure  the  thickness  of  the  compen- 
sator. This  scale,  represented  with  its  vernier  in  fig.  624,  has  two  divisions 
with  a  common  zero,  one  from  left  to  right  for  right-handed  liquids,  and 
another  from  right  to  left  for  left-handed. 

When  the  vernier  is  at  zero  of  the  scale,  the  sum  of  the  thicknesses  of 
the  plates  NN'  is  exactly  equal  to  that  of  the  plate  /,  and  as  the  rotation  of 
the  latter  is  opposed  to  that  of  the  compensator,  the  effect  is  zero.     But  by 


646  On  Light.  [677- 

moving  the  plates  of  the  compensator  in  one  or  the  other  direction  either 
the  compensator  or  the  quartz,  /,  preponderates,  and  there  is  a  rotation  from 
left  to  right. 

Behind  the  compensator  is  a  double-refracting  prism,  c  (fig.  622),  serving 
as  analyser  to  observe  the  polarised  ray  which  has  traversed  the  liquid  and 
the  various  quartz  plates.  In  order  to  understand  more  easily  the  object  or 
the  prism  c^  we  will  neglect  for  a  moment  the  crystals  and  the  lenses  on  the 
left  of  the  drawing.  If  at  first  the  zero  of  the  vernier  v  coincides  with  that 
of  the  scale,  and  if  the  liquid  in  the  tube  is  inactive,  the  actions  of  the  com- 
pensator, and  of  the  plate  z,  neutralise  each  other  ;  and,  the  liquid  having  no 
action,  the  two  halves  of  the  plate  ^,  seen  through  the  prism  r,  give  exactly 
the  same  tint  as  has  been  observed  above.  But  if  the  tube  filled  with  inac- 
tive liquid  be  replaced  by  one  full  of  solution  of  sugar,  the  rotary  power  of 
this  solution  is  added  to  that  of  one  of  the  halves  {a  or  b)  of  the  plate  q  (viz. 
that  half  which  tends  to  turn  the  plane  of  polarisation  in  the  same  direction 
as  the  solution),  and  subtracted  from  that  of  the  other.  Hence  the  two 
halves  of  the  plate  q  no  longer  show  the  same  tint  ;  the  half  <■;,  for  instance, 
is  red,  while  the  half  b  is  blue.  The  prisms  of  the  compensator  are  then 
moved  by  turning  the  milled  head  b,  either  to  the  right  or  to  the  left,  until 
the  difference  of  action  of  the  compensator  and  of  the  plate  i  compensates 
the  rotary  power  of  the  solution,  which  takes  place  when  the  two  halves 
of  the  plate  ^,  with  double  rotation,  revert  to  their  original  tint. 

The  direction  of  the  deviation  and  the  thickness  of  the  compensator  are 
measured  by  the  relative  displacement  of  the  scale  r,  and  of  the  vernier  v. 
Ten  of  the  divisions  on  the  scale  correspond  to  a  difference  of  i  millimetre 
in  the  thickness  of  the  compensator  ;  and  as  the  vernier  gives  itself  tenths 
of  these  divisions,  it  therefore  measures  differences  of  j^^  in  the  thickness  of 
the  compensator. 

When  once  the  tints  of  the  two  halves  of  the  plate  are  exactly  the  same, 
and  therefore  the  same  as  before  interposing  the  solution  of  sugar,  the 
division  on  the  scale  corresponding  to  the  vernier  is  read  off,  and  the  cor- 
responding number  gives  the  strength  of  the  solution.  This  depends  on  the 
experimental  fact  that  16-471  grains  of  pure  and  well-dried  sugar-candy  being- 
dissolved  in  water,  and  the  solution  diluted  to  the  volume  of  100  cubic  cen- 
timetres, and  obsei-ved  in  a  tube  of  20  centimetres  in  length,  the  deviation 
produced  is  the  same  as  that  effected  by  a  quartz  plate  a  millimetre  thick. 
In  making  the  analysis  of  raw  sugar,  a  weight  of  16-471  grains  of  sugar  is 
taken,  dissolved  in  water,  and  the  solution  made  up  to  100  cubic  centimetres, 
with  which  a  tube  20  centimetres  in  length  is  filled,  and  the  number  indicated 
by  the  vernier  read  off,  when  the  primitive  tint  has  l:)cen  obtained.  This 
number  being  42,  for  example,  it  is  concluded  that  the  amount  of  ciystallisable 
sugar  in  the  solution  is  42  per  cent,  of  that  which  the  solution  of  sugar-candy 
contained,  and,  therefore,  16-471  grains  >;  j'Ja,  or  6-91 8  grains.  This  result 
is  only  valid  when  the  sugar  is  not  mixed  with  uncrystallisable  sugar  or 
some  other  left-handed  substance.  In  that  case  the  crystallisable  sugar, 
which  is  right-hantlcil,  must  be,  by  means  of  hydrochloric  acid,  converted 
into  uncrystallisable  sugar,  which  is  left-handed  ;  and  a  new  determination 
is  made,  which,  together  with  the  first,  gives  tin-  quantity  of  crystallisable 
sugar. 


-679]  Polarisation  of  Heat.  647 

The  arrangement  of  crystals  and  lenses,  o,g,f,  and  a,  placed  behind  the 
prism  t-,  forms  what  Soleil  calls  the  producer  of  sensible  tints.  For  the 
most  delicate  tint — that  by  which  a  very  feeble  difference  in  the  coloration 
of  the  two  halves  of  the  rotation  plate  can  be  distinguished — is  not  the  same 
for  all  eyes  ;  for  most  people  it  is  of  a  vioIet-bluc  tint,  like  flax  blossom  ;  and 
it  is  important  either  to  produce  this  tint,  or  some  other  equally  sensible  to 
the  eye  of  the  observer.  This  is  effected  by  placing  in  front  of  the  prism,  c, 
at  tirst  a  quartz  plate,  0,  cut  perpendicular  to  the  axis,  then  a  small  Galileo's 
telescope  consisting  of  a  double  convex  glass,  ^,  and  a  double  concave  glass, 
f,  which  can  be  approximated  or  removed  from  each  other  according  to  the 
distance  of  distinct  vision  of  each  observer.  Lastly,  there  is  a  double- 
refracting  prism,  f,  acting  as  polariser  in  reference  to  the  quartz,  and  the  prism 
a  as  analyser  ;  and  hence,  when  the  latter  is  turned  either  right  or  left,  the 
light  which  has  traversed  the  prism  t,  and  the  plate  <?,  changes  its  tint,  and 
finally  gives  that  which  is  the  most  delicate  for  the  experimenter. 

678.  Analysis  of  diabetic  urine. — In  the  disease  diabetes,  the  urine 
contains  a  large  quantity  of  fermentable  sugar,  called  diabetic  sugar,  which 
in  the  natural  condition  of  the  urine  turns  the  plane  of  polarisation  to  the 
right.  To  estimate  the  quantity  of  this  sugar,  the  urine  is  first  clarified  by 
heating  it  with  acetate  of  lead  and  filtering  ;  the  tube  is  filled  with  the  clear 
liquid  thus  obtained  ;  and  the  milled  head  b  turned  until,  by  means  of  the 
double-rotating-  plate,  the  same  tint  is  obtained  as  before  the  interposition  of 
the  urine.  Experiment  has  shown  that  100  parts  of  the  saccharimetric  scale 
represent  the  displacement  which  the  quartz  compensators  must  have  when 
there  are  225"6  grains  of  sugar  in  a  litre  ;  hence  each  division  of  the  scale 
represents  2-256  of  sugar.  Accordingly,  to  obtain  the  quantity  of  sugar  in  a 
given  urine,  the  number  indicated  by  the  vernier,  at  the  moment  at  which 
the  primitive  tint  reappears,  must  be  multiplied  by  2-256. 

679.  Polarisation  of  beat. — The  rays  of  heat,  like  those  of  light,  may 
become  polarised  by  reflection  and  by  refraction.  The  experiments  on  this 
subject  are  difficult  of  execution  ;  they  were  first  made  by  Malus  and 
Berard,  in  1810  ;  after  the  death  of  Malus  they  were  continued  by  the  latter 
philosopher. 

In  his  experiments,  the  heat  rays  reflected  from  one  mirror  were  re- 
ceived upon  a  second,  just  as  in  Norremberg's  apparatus  ;  from  the  second 
they  fell  upon  a  small  metallic  reflector,  which  concentrated  them  upon  the 
bulb  of  a  differential  thermometer.  Berard  observed  that  heat  was  not 
reflected  when  the  plane  of  reflection  of  the  second  mirror  was  at  right  angles 
to  that  of  the  first.  As  this  phenomenon  is  the  same  as  that  presented  by 
light  under  the  same  circumstances,  Berard  concluded  that  heat  became 
polarised  in  being  reflected. 

The  double  refraction  of  heat  may  be  shown  by  concentrating  the  sun's 
rays  by  means  of  a  heliostat  on  a  prism  of  Iceland  spar,  and  investigating 
the  resultant  pencil  by  means  of  a  thermopile,  which  must  have  a  sharp 
narrow  edge.  In  this  case  also  there  is  an  ordinary  and  an  extraordinary 
ray,  which  follow  the  same  laws  as  those  of  light.  In  the  optic  axis  of  the 
calcspar,  heat  is  not  doubly  refracted.  A  Nicol's  prism  can  be  used  for  the 
polarisation  of  heat  as  well  as  for  that  of  light  :  a  polarised  ray  does  not 
traverse  the  second  Nicol  if  the  plane  of  its  principal  section  is  perpendicular 


648  On  Light.  [679- 

to  the  vibrations  of  the  ray.  The  phenomena  of  the  polarisation  of  heat 
may  also  be  studied  by  means  of  plates  of  tourmaline  and  of  mica.  The 
angle  of  polarisation  is  virtually  the  same  for  heat  as  fof  light.  In  all  these 
experiments  the  prisms  must  be  very  near  each  other. 

The  diffraction,  and  therefore  the  interference,  of  rays  of  heat  has  recently 
been  established  by  the  experiments  of  Knoblauch  and  others.  And  Forbes, 
who  has  repeated  Fresnel's  experiment  with  a  rhombohedron  of  rock  salt, 
has  found  that  by  two  total  internal  reflections,  heat  is  circularly  polarised, 
just  as  is  the  case  with  light. 


-681]  649 


BOOK    VIII. 
ON     MAGNETISM. 


CHAPTER    I. 
PROPERTIES   OF   MAGNETS, 

680.  STatural  and  artificial  magnets.— Afa£ne/s  are  substances  which 
have  the  property  of  attracting  iron,  and  the  term  inagnetisin  is  applied  to 
the  cause  of  this  attraction  and  to  the  resulting  phenomena. 

This  property  was  known  to  the  ancients  ;  it  exists  in  the  highest  degree 
in  an  ore  of  iron  which  is  known  in  chemistry  as  the  magnetic  oxide  of  iron. 
Its  composition  is  represented  by  the  formula  Fe.,04. 

This  magnetic  oxide  of  iron,  or  lodestone,  as  it  is  called,  was  first  found 
at  Magnesia,  in  Asia  Minor,  the  name  magnet  being  derived  from  this  cir- 
cumstance. The  name  lodestone,  which  is  applied  to  this  natural  magnet, 
was  given  on  account  of  its  being  used  when  suspended  as  a  guiding  or  lead- 
ing stone,  from  the  Saxon  ladan^  to  lead ;  so  also  the  word  lodestar.  Lode- 
stone is  very  abundant  in  nature  :  it  is  met  with  in  the  older  geological  forma- 
tions, especially  in  Sweden  and  Norway,  where  it  is  worked  as  an  iron  ore, 
and  furnishes  the  best  quality  of  iron. 

When  a  bar  or  needle  of  steel  is  rubbed  with  a  magnet,  it  acquires 
magnetic  properties  without  the  magnet  losing  anything  of  its  own  force. 
Such  bars  are  called  artificial  magnets  :  they  are  more  powerful  than  natural 
magnets,  and,  as  they  are  also  more  convenient,  they  will  be  exclusively 
referred  to  in  describing  the  phenomena  of  magnetism.  The  best  modes  of 
preparing  them  will  be  explained  in  a  subsequent  article. 

681.  Poles  and  neutral  lines. — When  a  small  piece  of  soft  iron  is  sus- 
pended by  a  thread  and  a  magnet  is  approached  to  it,  the  iron  is  attracted 
towards  the  magnet,  and  some  force  is  required  for  its  removal.  The  force 
of  the  attraction  varies  in  different  parts  of  the  magnet  ;  it  is  strongest  at  the 
two  ends,  and  is  totally  wanting  in  the  middle. 

This  variation  may  also  be  seen  very  clearly  when  a  bar  magnet  is 
placed  in  iron  filings  ;  these  become  arranged  round  the  ends  of  the  bar 
in  feathery  tufts,  which  decrease  towards  the  middle  of  the  bar,  where  there 
are  none.  That  part  of  the  surface  of  the  bar  where  there  is  no  visible 
magnetic  force  is  called  the  ticutral  line  ;  and  the  parts  near  the  ends  of  the 
bar  where  the  attraction  is  greatest  are  called  the  poles.     Every  magnet, 


650 


On  Magnetism. 


[681- 


whether  natural  or  artificial,  has  two  poles  and  a  neutral  line  :  sometimes, 
however,  in  magnetising  bars  and  needles,  poles  are  produced  lying  between 
the  extreme  points.  Such  magnets  are  abnormal,  and  these  points  are  called 
intermediate  or  consequent  poles.  The  shortest  line  joining  the  two  poles  is 
termed  the  axis  of  the  magnet  ;  in  a  horseshoe  magnet  the  axis  is  in  the 
direction  of  the  keeper.  The  plane  at  right  angles  to  the  axis  of  a  bar 
magnet  and  passing  through  the  neutral  line  is  sometimes  called  the  equator 
of  the  magnet,  and  the  length  of  a  magnet,  as  far  as  magnetic  actions  are 
concerned,  is  the  distance  of  the  poles. 

We  shall  presently  see  that  a  freely  suspended  magnet  always  sets  with 
one  pole  pointing  towards  the  north,  and  the  other  towards  the  south.     The 

end  pointing  towards  the 
ji^t^^Hj^  north  is  called  in  this 
country  the  north  pole., 
and  the  other  end  is 
the  south  pole.  The  end 
of  the  magnetic  needle 
pointing  to  the  north  is 


Pf71»' 


'|illl'fl'IPiillHill|iillillli|iiilllHilHMi 


Fig.  626. 

also  sometimes  called  the  marked  end  of  the  needle.  Sometimes  also  the 
end  pointing  to  the  north  is  called  the  red  pole,  and  that  to  the  south  the 
blue  pole  ;  the  corresponding  terms  red  and  blue  magnetisms  are  also  some- 
times used. 

682.  Reciprocal  action  of  two  poles. — The  two  poles  of  a  magnet  appear 
identical  when  they  are  brought  in  contact 
with  iron  filings  (fig.  626),  but  this  identity 
is  only  apparent,  for  when  a  small  mag- 
netic needle,  ab  (fig.  627),  is  suspended  by 
a  fine  thread,  and  the  north  pole,  A,  of 
another  needle  is  brought  near  its  north 
pole,  a,  a  repulsion  takes  place.  If,  on 
the  contrary,  A  is  brought  near  the  south 
pole,  (5,  of  the  movable  needle,  the  latter 
is  strongly  attracted.  Hence  these  two 
poles,  a  and  b.,  are  not  identical,  for  one 
is  repelled,  and  the  other  attracted,  by  the 
same  pole  of  the  magnet  A.  It  may  be 
shown  in  the  same  manner  that  the  two 
poles  of  the  latter  are  also  different,  by 
successively  presenting  them  to  the  same 
pole,  a,  of  the  movable  needle.  In  one 
in  the  other  attraction.     Hence  the  following  law 


Fig.  627. 


case  there  is  repulsion, 
may  be  enunciated  :— 

I^oles  of  tiic  same  name  repel,  and  poles  of  contrary  naiiie  attract,  one 
another. 

The  opposite  actions  of  the  north  and  south  polos  may  be  shown  by  the 
following  experiment  : — A  piece  of  iron,  a  key  for  example,  is  supported 
by  a  bar  magnet.  A  second  bar  magnet  of  the  same  dimensions  is  then 
moved  along  the  first,  so  that  their  poles  are  contrary  (fig.  628).  The  key 
remains  suspended  so  long  as  the  two  poles  are  at  some  distance,  but  when 


Fig.  628. 


-684]  Precise  Definition  of  Poles.  65  r 

they  are  sufficiently  near,  the  key  drops,  just  as  if  the  bar  which  supported 

it  had  lost  its  magnetism.     This,  however,  is  not  the  case,  for  the  key  would 

be   again   supported    if    the 

first  magnet  were  presented     \<>H. 

to   it   after  the   removal    of  ^^C/*""--^^ 

The  attraction  which  a  ■'■'■ii^^^^^^gj^^^^^^^^^^^^^^p> 
magnet  exerts  upon  iron  is  "  ^"^^^^  'i,"^^'^  '^ 

reciprocal,  which    is   indeed  ^^  ^ 

a  general  principle  of  all 
attractions.  It  is  easily  veri- 
fied by  presenting  a  mass  of 
iron  to  a  movable  magnet,  when  the  latter  is  attracted. 

683.  Hypothesis  of  two  mag-netic  fluids. — In  order  to  explain  the  phe- 
nomena of  magnetism,  the  existence  of  two  hypothetical  magnetic  fluids  has 
been  assumed,  each  of  which  acts  repulsively  on  itself,  but  attracts  the  other 
fluid.  The  fluid  whose  action  predominates  at  the  north  pole  of  the  magnet 
is  called  the  north  fluid  or  red  magnetism  ;  and  that  at  the  south  pole  the 
south  fluid,  or  bltie  magnetism.  It  is  usual  also  to  speak  of  north  magnetism 
as  positive  and  of  south  as  negative.,  or  +  and  —  respectively.  The  term 
'  fluid '  is  apt  to  puzzle  beginners,  from  its  ambiguity.  Ordinarily  the  idea 
o  a  liquid  is  associated  with  the  term  'a  fluid;'  hence  the  use  of  this  term 
to  explain  the  phenomena  of  magnetism  and  electricity  has  produced  a 
widely  prevailing  impression  of  the  material  nature  of  these  two  forces.  The 
word  'fluid,'  it  must  be  remembered,  embraces  gases  as  well  as  liquids,  and 
here  it  must  be  pictured  to  the  mind  as  representing  an  invisible,  elastic, 
gaseous  atmosphere  or  shell  surrounding  the  particles  of  all  magnetic  sub- 
stances. 

It  is  assumed  that,  before  magnetisation,  these  fluids  are  combined  round 
each  molecule,  and  mutually  neutralise  each  other  ;  they  can  be  separated 
by  the  influence  of  a  force  greater  than  that  of  their  mutual  attraction,  and 
can  arrange  themselves  round  the  molecules  to  which  they  are  attached,  but 
cannot  be  removed  from  them. 

The  hypothesis  of  the  two  fluids  is  convenient  in  explaining  magnetic 
phenomena,  and  will  be  adhered  to  in  what  follows.  But  it  must  not  be  re- 
garded as  anything  more  than  a  provisional  hypothesis,  and  it  will  afterwards 
be  shown  (879)  that  magnetic  phenomena  appear  to  result  from  electrical 
currents,  circulating  in  the  molecules  of  magnetic  bodies  ;  a  mode  of  view 
which  connects  the  theory  of  magnetism  with  that  of  electricity. 

684.  Precise  definition  of  poles. — By  aid  of  the  preceding  hypothesis 
we  are  enabled  to  obtain  a  clear  idea  of  the  distribution  of  the  magnetism 
in  a  magnetised  bar,  and  to  account  for  the  circumstance  that  there  is  no 
free  magnetism  in  the  middle  of  the  bar,  and  that  it  is  strongest  at  the  poles. 
If  AB  (fig.  629)  represent  a  magnet,  then  the  alternate  black  and  white 
spaces  may  be  taken  to  represent  the  position  of  the  magnetisms  in  a  series 
of  particles  after  magnetisation  :  the  black  spaces,  representing  the  south 
magnetism,  all  point  in  one  direction,  and  the  white  ones  the  north  in  the 
opposite  direction.  The  last  half  of  the  terminal  molecule  at  one  end  would 
have  north  polarity,  and  at  the  other  south  polarity.     Let  N  represent  the 


652  Ofi  Magnetism.  [684- 

north  pole  of  a  magnetic  needle  placed  near  the  magnet  AH  ;  then  the  south 
magnetism  s  in  the  terminal  molecule  would  tend  to  attract  N,  and  the 
north  magnetism  ;/  would  tend  to  repel  it  ;  but  as  the  molecule  of  south 
magnetism  s  is  nearer  N  than  the  molecule  of  the  north  magnetism  /?,  the 
attraction  between  s  and  N  would  be  greater  than  the  repulsion  between  n 
and  X.  Similarly  the  attraction  between  s'  and  N  would  be  greater  than 
the  repulsion  between  n'  and  N,  and  so  on  with  the  following  s"  and  //",  &c. 
And  all  these  forces  would  give  a  resultant  tending  to  attract   X,  whose 

//"  s"  >i'  s'  11  s 


CHO 


Fig.  629. 

point  of  application  would  have  a  certain  fixed  position,  which  would  be  the 
south  pole  of  AB.  In  like  manner  it  might  be  shown  that  the  resultant  of 
the  forces  acting  at  the  other  end  of  the  bar  would  form  a  north  pole,  and 
would  hence  repel  the  north  pole  of  the  needle,  but  would  attract  its  south 
pole. 

That  such  a  series  of  polarised  particles  really  acts  like  an  ordinary 
magnet  may  be  shown  by  partly  filling  a  glass  tube  with  steel  filings,  and 
passing  the  pole  of  a  strong  magnet  several  times  along  the  outside  in  one 
constant  direction,  taking  care  not  to  shake  the  tube.  The  individual  filings 
will  thus  be  magnetised,  and  the  whole  column  of  them  presented  to  a  mag- 
netic needle  will  attract  and  repel  its  poles  just  like  an  ordinary  bar  magnet, 
exhibiting  a  north  pole  at  one  end,  a  south  pole  at  the  other,  and  no  polarity 
in  the  middle  ;  but  on  shaking  the  tube,  or  turning  out  the  filings,  and  put- 
ting them  in  again  so  as  to  destroy  the  regularity,  every  trace  of  polarity  will 
disappear.  It  appears  hence  that  the  polarity  at  each  end  of  a  magnet  is 
caused  by  the  fact  that  the  resultant  action  on  a  magnetic  body  is  strongest 
near  the  ends,  and  does  not  arise  from  any  accumulation  of  magnetisms  at 
the  ends. 

The  same  point  may  be  illustrated  by  the  following  experiment,  which  is 
due  to  Sir  W.  Grove  : — In  a  glass  tube  with  flat  glass  ends  is  placed  water  in 
which  is  diffused  magnetic  oxide  of  iron.  Round  the  outside  of  the  tube  is 
coiled  some  insulated  wire.  On  looking  at  a  light  through  the  tube  the 
liquid  appears  dark  and  muddy,  but  on  passing  a  current  of  electricity  through 
the  wire  it  becomes  clearer  (879).  This  is  due  to  the  fact  that  by  the  mag- 
uftising  action  of  the  current,  the  particles,  becoming  magnetised,  set  with 
their  longest  dimension  parallel  to  the  axis  of  the  tube,  in  which  position 
they  obstruct  the  passage  of  light  to  a  less  extent. 

685.  Experiments  wltb  broken  magnets.— That  the  two  magnetisms 
arc  present  in  all  parts  of  the  bar,  and  arc  not  simply  accumulated  at  the 
ends,  is  also  evident  from  the  following  experiment  : — A  steel  knitting- 
needle  (fig.  630)  is  magnetised  by  rubbing  it  with  one  of  the  poles  of  a  mag- 
net, and  then,  the  existence  of  the  two  poles  .\l'>  and  of  the  neutral  line  \ 


-686]  Magnetic  Induction.  653 

having-  been  ascertained  by  means  of  iron  filings,  it  is  broken  in  the  middle. 
But  now,  on  presenting  successively  the  two  halves  to  a  magnet,  each  will  be 
found  to  possess  two  opposite  poles  AB'  and  A'B  with  a  neutral  line  N,  and 
in  fact  is  a  perfect  magnet.  If  these  new  magnets  are  broken  in  turn  into 
two  halves,  each  will  be  a  complete  magnet  AB"  and  A"B  with  its  two  poles 
and  neutral  line,  and  so  on,  as  far  as  the  division  can  be  continued.     It  is, 


therefore,  concluded  by  analogy  that  the  smallest  parts  of  a  magnet,  the 
ultimate  molecules,  contain  the  two  magnetisms ;  that  magnetism,  in  short, 
is  a  phenomenon  the  cause  of  which  resides  in  the  elementary  particle  or 
molecule  itself.  Each  molecule  is  a  magnet.  It  follows  also  from  this  ex- 
periment that  it  is  impossible  to  obtain  an  independent  positive  or  negative 
mass  of  magnetism  which  is  not  associated  with  an  equal  mass  of  the 
opposite  sign,  in  other  words  that  unipolar  magnets  have  no  existence. 

686.  Magnetic  induction. — When  a  magnetic  substance  is  placed  in 
contact  w  ith  a  magnet,  the  two  magnetisms  of  the  former  become  separated  ; 
and  so  long  as  the  contact  remains,  it  is  a  complete  magnet,  having  its  two 
poles  and  its  neutral  line.  For  instance,  if  a  small  cylinder  of  soft  iron,  ab 
(fig.  631),  be  placed  in  contact  with  one  of  the  poles  of  a  magnet,  the  cylinder 
can  in  turn  support  a  second  cylinder ;  this  in  turn  a  third,  and  so  on,  to  as 


many  as  seven  or  eight,  according  to  the  power  of  the  magnet.  Each  of  these 
little  cylinders  is  a  magnet  ;  if  it  be  the  north  pole  of  the  magnet  to  which 
the  cylinders  are  attached,  the  part  a  will  have  south,  and  b  north  magnetism  ; 
b  will  in  like  manner  develop  in  the  nearest  end  of  the  next  cylinder  south 
magnetism,  and  so  on.  But  these  cylinders  are  only  magnets  so  long  as  the 
influence  of  a  magnetised  bar  continues.  For,  if  the  first  cylinder  be  re- 
moved from  the  magnet,  the  other  cylinders  immediately  drop,  and  retain  no 
trace  of  magnetism.  The  separation  of  the  two  magnetisms  is  only  moment- 
ary, which  proves  that  the  magnet  yields  nothing  to  the  iron.  Hence  we 
may  have  temporary  magnets  as  well  as  permanent  magnets  ;  the  former  of 
iron  and  nickel,  the  latter  of  steel  and  cobalt  (688). 

This  action,  in  virtue  of  which  a  magnet  can  develop  magnetisation  in 


654  On  Magnetism.  [686- 

iron,  is  called  magnetic  induction  or  influence^  and  it  can  take  place  witliout 
actual  contact  between  the  magnet  and  the  iron,  as  is  seen  in  the  following 
experiment :— A  bar  of  soft  iron  is  held  with  one  end  near  a  magnetic  needle. 
If  now  the  north  pole  of  a  magnet  be  approached  to  the  iron  without  touch- 
ing it,  the  needle  will  be  attracted  or  repelled,  according  as  its  south  or 
north  pole  is  near  the  bar.  For  the  north  pole  of  the  magnet  will  develop 
south  magnetism  in  the  end  of  the  bar  nearest  it,  and  therefore  north  mag- 
netism at  the  other  end,  which  would  thus  attract  the  south,  but  repel  the 
north  end  of  the  needle.  Obviously,  if  the  other  end  of  the  magnet  were 
brought  near  the  iron,  the  opposite  effects  would  be  produced  on  the  needle; 
or  if  the  opposite  pole  of  a  second  magnet  of  equal  strength  simultaneously 
be  brought  near  the  iron,  the  needle  would  be  unaffected,  as  one  magnet 
would  undo  the  work  of  the  other. 

Among  other  things,  magnetic  induction  explains  the  formation  of  the 
tufts  of  iron  filings  which  become  attached  to  the  poles  of  magnets  (fig.  626). 
The  parts  in  contact  with  the  magnet  are  converted  into  magnets  ;  these 
act  inductively  on  the  adjacent  parts,  these  again  on  the  following  ones,  and 
so  on,  producing  a  filamentary  arrangement  of  the  filings.  The  bush-like 
appearance  of  these  filaments  is  due  to  the  repulsive  action  which  the 
free  poles  exert  upon  each  other.  Any  piece  of  soft  iron  while  being 
attracted  by  a  magnet  is  for  the  time  being  converted  into  a  magnet  ; 
hence  is  explained  the  paradoxical  statement  that  '  magnets  only  attract 
magnets.' 

6S7.  Coercive  force. — We  have  seen  from  the  above  experiments  that 
soft  iron  becomes  instantaneously  magnetised  under  the  influence  of  a 
magnet,  but  that  this  magnetism  is  not  permanent,  and  ceases  when  the 
magnet  is  removed.  Steel  likewise  becomes  magnetised  by  contact  with  a 
magnet  ;  but  the  operation  is  effected  with  difficulty,  and  in  general  the 
more  so  as  the  steel  is  more  highly  tempered.  Placed  in  contact  with  a 
magnet,  a  steel  bar  accjuires  magnetic  properties  very  slowly  ;  and,  to  make 
the  magnetism  complete,  the  steel  must  be  rubbed  with  one  of  the  poles. 
But  this  magnetism,  once  evoked  in  steel,  is  permanent,  and  does  not  dis- 
appear when  the  inducing  force  is  removed. 

These  different  effects  in  soft  iron  and  steel  arc  ascribed  to  a  kind  of 
resistance  analogous  to  friction  which  is  often  called  coercive  force,  and  which, 
in  a  magnetic  substance,  offers  a  hindrance  to  the  separation  of  the  two 
magnetisms,  but  which  also  prevents  their  recombination  w^hen  once  sepa- 
rated. In  steel  this  coercive  force  is  very  great  ;  in  soft  iron  it  is  very  small 
or  almost  absent.  By  oxidation,  stretching,  pressure,  torsion,  or  hammering, 
etc.,  a  certain  amount  of  coercive  force  may  be  imparted  to  soft  iron  ;  and 
by  heat  the  coercive  force  may  be  lessened,  as  will  be  afterwards  seen. 

688.  Difference  bet\ireen  magrnets  and  magnetic  substances. — JLn^- 
nctic  substatiics  arc  sul)slanccs  which,  like  iron,  steel,  and  nickel,  arc  attracted 
l)y  the  magnet,  'ihey  contain  the  two  magnetisms,  but  in  a  state  of  neu- 
tralisation. Compounds  containing  iron  are  usually  magnetic,  and  the  more 
so  in  proportion  as  they  contain  a  larger  quantity  of  iron.  Some,  however 
like  iron  pyrites,  are  not  attracted  by  the  magnet. 

A  magnetic  substance  is  readily  distinguished  from  a  magnet.  The 
former  has  no  poles  ;  if  successively  presented  to  the  two  ends  of  a  magnetic 


-688]  Difference  between  Magnets  and  Magnetic  Substances.   655 

needle,  ab  (fig.  627),  it  will  attract  both  ends  equally,  while  with  one  and  the 
same  end  a  ma^'^net  would  attract  the  one  end  of  the  needle,  but  repel  the 
other.  Magnetic  substances  also  have  no  action  on  each  other;  while  mag- 
nets attract  or  repel  each  other,  according  as  unlike  or  like  poles  are  pre- 
sented.    Attraction  is  no  proof  that  a  body  is  a  magnet  ;  repulsion  is. 

Iron  is  not  the  only  substance  which  possesses  magnetic  properties  ; 
nickel  has  considerable  magnetic  power,  but  far  less  than  that  of  iron  ;  cobalt 
is  less  magnetic  than  nickel  ;  while  to  even  a  slighter  extent  chromium  and 
manganese  are  magnetic.  Further,  we  shall  see  that  powerful  magnets  exert 
a  peculiar  influence  on  all  substances. 

In  the  magnetic  but  unmagnetised  condition  the  molecular  magnets  are 
arranged  quite  irregularly,  and  their  mutual  action  neutralises  one  another, 
so  that  there  is  no  action  on  an  external  body.  But  if  they  are  acted  on  by 
any  magnetising  power,  a  magnet,  for  example,  the  effect  is  to  give  the 
molecular  magnets  a  direction  parallel  to  those  of  the  magnet,  and  as  soon 
as  more  molecular  magnets  set  in  one  certain  direction  than  in  another,  the 
magnet  shows  polarity  ;  this  polarity  increases  the  more  any  one  direction 
preponderates,  and  reaches  a  maximum  when  all  the  molecular  magnets  set 
in  one  direction. 


656  On  Magnetism.  [689- 


CHAPTER    II. 

TERRESTRIAL    MAGNETISM.      COMPASSES. 

689.  Directive  action  of  the  earth  on  magnets.— When  a  magnetic 

needle  is  suspended  by  a  thread,  as  represented  in  fig.  628,  or  is  placed 

on  a  pivot  on  which  it  can  move  freely  (fig.  632),  it  ultimately  sets  in  a 

position    which    is   more    or   less   north  and 

.^     south.     If    removed    from    this    position    it 

always  returns  to  it  after   making  a  certain 

number  of  oscillations. 

Analogous  observations  have  been  made 
in  different  parts  of  the  globe,  from  which  the 
earth  has  been  compared  to  an  immense  mag- 
net, whose  poles  are  very  near  the  terrestrial 
poles,  and  whose  neutral  line  virtually  coin- 
cides with  the  equator. 

The  polarity  in  the  northern  hemisphere 
is  called  the  norf/tcrn  or  boreal  polarity,  and 
that  in  the  southern  hemisphere  the  southern 
'^'   ^^"  ox  austral  Yio\?ix\\.y.    In  French  works  the  end 

of  the  needle  pointing  north  is  called  the  austral  or  southern  pole,  and  that 
pointing  to  the  south  the  boreal  or  northern  pole  ;  a  designation  based  on 
this  hypothesis  of  a  terrestrial  magnet,  and  on  the  law  that  unlike  magnet- 
isms attract  each  other.  In  practice  it  will  be  found  more  convenient  to 
use  the  English  names,  and  call  that  end  of  the  magnet  which  points  to  the 
north  the  north  pole.,  and  that  which  points  to  the  south  the  south  pole  ;  the 
north  pole  of  a  magnet  is  a  7iorth-seeking  pole,  and  a  south  pole  a  south-seek- 
ing pole.  Tc  avoid  ambiguity,  that  end  of  the  needle  pointing  north  is  in 
England  sometimes  spoken  of  as  the  jnarked  end  of  the  needle  (68 1 ). 

690.  Terrestrial  mag-netlc  couple. — From  what  has  been  stated,  it  is 
clear  that  the  magnetic  action  of  the  earth  on  a  magnetised  needle  may  be 
compared  to  a  couple  ;  that  is,  to  a  system  of  two  c(|ual  forces,  parallel,  but 
acting  in  contrary  directions. 

For  let  ab  (fig.  633)  be  a  movable  magnetic  needle  making  an  angle  with 
the  magnetic  meridian  M'M  (6gi).  The  earth's  north  pole  acts  attractively 
on  the  marked  pole,  «,  and  repulsively  on  the  other  pole,  b.,  and  two  contrary 
forces  are  produced,  an  and  bn\  which  are  equal  and  parallel  :  for  the 
terrestrial  pole  is  so  distant,  and  the  needle  so  small,  as  to  justify  the  assump- 
tion tliat  the  two  directions  an  and  bn'  are  parallel,  and  that  the  two  poles 
arc  e(|uidistant  from  the  earth's  north  pole.  Ihit  the  earth's  south  pole  acts 
similarly  on  the  jjoles  of  the  needle,  and  produces  two  other  forces,  ^/j  and/'.y, 
whii  h  arc  also  e(|ual  and  parallel  ;  but  the  two  forces  an  and  as  may  be  re- 


Fig.  633. 


-691]  Magnetic  Eieinents.     Declination.  657 

duced  to  a  single  resultant  ^N  {t,^),  and  the  forces  bn'  and  bs'  to  a  resultant 
/'S  ;  the  two  forces  aN  and  bS  are  equal,  parallel,  and  act  in  opposite  direc- 
tions, and  they  constitute  the  terrestrial  magnetic  couple  ;  it  is  this  couple 
which        makes 

the    needle    set  „    _, ^  .  , 

ultimately        in 

the       magnetic  ^r!_ 

meridian— a  po-  ------.v.-^v^pg^— :.-;-;=..  j^ 

sition    in   which  ,.---- 

the    two    forces  -r- 

N  and  S  are  in 
equilibrium. 

The  force  which  determines  the  direction  of  the  needle  thus  is  neither 
attractive  nor  repulsive,  but  simply  directive.  It  has  no  horizontal  com- 
ponent. If  a  small  magnet  be  placed  on  a  cork  floating  in  water,  it  will  at 
first  oscillate,  and  then  gradually  set  in  a  line  which  is  virtually  north  and 
south.  But  if  the  surface  of  the  water  be  quite  smooth,  the  needle  will  not 
move  either  towards  the  north  or  towards  the  south. 

If,  however,  a  magnet  be  approached  to  a  floating  needle,  attraction  or 
repulsion  ensues,  according  as  one  or  the  other  of  the  poles  is  presented. 
The  reason  of  the  different  actions  exerted  by  the  earth  and  by  a  magnet  on 
a  floating  needle  is  as  follows  : — When  the  north  pole,  for  instance,  of  the 
magnet  is  presented  to  the  south  pole  of  the  needle,  the  latter  is  attracted  ; 
it  is,  however,  repelled  by  the  south  pole  of  the  magnet.  Now  the  force  of 
magnetic  attraction  or  repulsion  decreases  with  the  distance  ;  and,  as  the  dis- 
tance between  the  south  pole  of  the  needle  and  the  north  pole  of  the  magnet 
is  less  than  the  distance  Ijetween  the  south  pole  of  the  needle  and  the  south 
pole  of  the  magnet,  the  attraction  predominates  over  the  repulsion,  and  the 
needle  moves  towards  the  magnet.  But  the  earth's  magnetic  north  pole  is 
so  distant  from  the  floating  needle  that  its  length  may  be  considered  in- 
finitely small  in  comparison,  and  one  pole  of  the  needle  is  just  as  strongly 
repelled  as  the  other  is  attracted. 

The  action  of  the  earth  on  a  magnet  has  also  no  component  which  is 
directed  vertically  ;  for  if  a  steel  bar  be  carefully  equipoised  and  then 
magnetised  there  is  not  the  least  alteration  in  the  weight. 

691.  Magnetic  elements.  Declination, — In  order  to  obtain  a  full 
knowledge  of  the  earth's  magnetism  at  any  place,  three  essentials  are  re- 
quisite ;  these  are — i.  Declination  ;  ii.  Inclination  ;  iii.  Force  or  Intensity. 
These  three  are  termed  the  magnetic  elements  of  the  place  We  shall  explain 
them  in  the  order  in  which  they  stand. 

The  geographical  meridian  of  a  place  is  the  imaginary  plane  passing 
through  this  place  and  through  the  two  terrestrial  poles,  and  the  meridian 
is  the  outline  of  this  plane  upon  the  surface  of  the  globe.  Similarly  the 
magnetic  meridian  of  a  place  is  the  vertical  plane  passing  at  this  place 
through  the  two  poles  of  a  movable  magnetic  needle  in  equilibrium  about  its 
vertical  axis. 

In  general  the  magnetic  meridian  does  not  coincide  with  the  geogra- 
phical meridian,  and  the  angle  which  the  magnetic  makes  with  the  geogra- 
phical meridian— that  is  to  say,  the  angle  which  the  direction  of  the  needle 

U  U 


658 


On  Magnetism. 


[691- 


makes  with  the  meridian — is  called  the  declination  or  variation  of  the  mag- 
netic needle.  The  declination  is  said  to  be  east  or  ivest^  according  as  the 
north  pole  of  the  needle  is  to  the  east  or  west  of  the  geographical  meridian. 

692.  Variations  in  declination. — The  declination  of  the  magnetic 
needle,  which  varies  in  different  places,  is  at  present  west  in  Europe  and  in 
Africa,  but  east  in  Asia  and  in  the  greater  part  of  North  and  South  America. 
It  shows  further  considerable  variations  even  in  the  same  place.  These  varia- 
tions are  of  two  kinds  ;  some  are  regular,  and  are  either  secular,  annual, 
or  diurnal  ;  others,  which  are  irregular,  are  called  magnetic  storms  (694). 

Secular  variations. — In  the  same  place  the  declination  varies  in  the 
course  of  time,  and  the  needle  appears  to  make  oscillations  to  the  east  and 
west  of  the  meridian,  the  duration  of  which  extends  over  centuries.  The 
declination  has  been  known  at  Paris  since  1580,  and  the  following  table 
represents  the  variations  which  it  has  undergone  : — 


Year 

Declination 

Year 

Declination 

1580 

ii°3o'E. 

1835 

22°     4'W. 

1663 

0° 

1850 

20°  30'  W. 

1700 

8°  10'  W. 

1855 

19°  57'  W. 

1780 

i9°55'W. 

i860 

19°  32'  w. 

1785 

22°  00'  W. 

1865 

i8°44'W. 

1805 

22°    5'W. 

1875 

i7°2i'W.     . 

1814 

22°  34'  w. 

1880 

16°  53'  w. 

1825 

22°  22'  W. 

1883 

16°  zi>'  w. 

1830 

22°  12'  W. 

1888 

i5°58'W. 

This  table  shows  that  since  1580  the  declination  has  varied  at  Paris  as 
much  as  34°,  and  that  the  greatest  westerly  declination  was  attained  in  1814, 
since  which  time  the  needle  has  gradually  tended  towards  the  east. 

At  London  the  needle  showed  in  1580  an  easterly  declination  of  1 1°  36' ; 
in  1663  it  was  at  zero  ;  from  that  time  it  gradually  tended  towards  the  west, 
and  reached  its  maximum  declination  of  24°  41'  in  1818  ;  since  then  it  has 
steadily  diminished  ;  it  was  22°  30'  in  1850,  19°  32'  in  1873,  I9°  24'  in  1874, 
19°  16' in  1875,  19°  10'  in  1876,  19°  3' in  1877,  18°  52'  in  1878,  18°  40'in 
1881,  18^  15'  in  1883,  and  is  now  (1889)  17°  42'  W. 

At  Yarmouth  and  Dover  the  variation  is  about  40'  less  than  at  London  ; 
at  Hull  and  Southampton  about  20'  greater  ;  at  Newcastle  and  Swansea 
about  1'^  45,' and  at  Liverpool  2°  o',  at  Edinburgh  3°  o',  and  at  Glasgow  and 
Dublin  about  3°  50'  greater  than  at  London. 

The  following  are  the  observations  of  the  magnetic  elements  at  Kew 
extending  over  twenty  years  : — 


■   Year 

Declination 

Inclination 

Horizontal 
force 

1865 
1869 
1872 
1875 
1878 

20°  59' 

20°  32,' 
20°    0' 
19°  41' 
19°  14' 

68°    7' 
68°    2' 
67°  54' 
67°  48' 
67°  44' 

3-829 
3-848 
3-869 
3-885 

3-895        1 

693] 


A  nnual  Variations. 


659 


Year 

Declination 

Inclination 

HorizoBtal 
force 

1879 
1880 
1881 
1882 
1883 
1884 
1885 

19°    6' 
i8°  59' 

18°  50' 

18°  45' 
18°  41' 
18°  32' 
18°  26' 

67°  42' 
67"  42' 
67°  41' 
67°  41' 
67°  41' 

67°  39' 
67°  38' 

3-900 
3-899 
3-903 
3-904 
3-909 
3-916 
3-917 

In  certain  parts  of  the  earth  the  magnet  coincides  with  the  geographical 
meridian.  These  points  are  connected  by  an  irregularly  curved  imaginary 
line,  called  a  line  of  tio  vatiation  or  agofiic  line.  Such  a  line  cuts  the  east 
of  South  America,  and,  passing  east  of  the  West  Indies,  enters  North 
America  near  Philadelphia,  and  traverses  Hudson's  Bay  ;  thence  it  passes 
through  the  North  Pole,  entering  the  Old  World  east  of  the  White  Sea, 
traverses  the  Caspian,  cuts  the  east  of  Arabia,  turns  then  towards  Australia, 
and  passes  through  the  South  Pole,  to  join  itself  again. 

hogonic  lines  are  lines  connecting  those  places  on  the  earth's  surface  in 
which  the  declination  is  the  same.  The  first  of  the  kind  was  constructed  in 
1700  by  Halley  ;  as  the  elements  of  the  earth's  magnetism  are  continually 
changing,  the  course  of  such  a  line  can  only  be  determined  for  a  certain  time. 
Maps  on  which  such  isogenic  lines  are  depicted  are  called  declination 
or  variation  maps  \  and  a  comparison  of  these  in  various  years  is  well  fitted 
to  show  the  variation  which  this  magnetic  element  undergoes.  Plate  III. 
represents  a  map  on  Mercator's  projection  giving  these  lines  for  the  year  1882, 
It  will  be  seen  that  the  surface  of  the  globe  is  divided  by  these  lines  into  two 
regions  :  one,  the  smaller,  in  which  the  variation  is  westerly,  as  indicated  by 
the  continuous  lines  ;  the  other,  in  which  the  variation  is  easterly,  as  indicated 
by  the  dotted  lines.  This  chart  is  useful  to  the  mariner  as  not  only  giving 
him  the  declination  in  any  place,  but  also  as  showing  him  the  places  on  the 
globe  where  the  declination  changes  most  rapidly.  Of  these  the  most 
remarkable  are  the  coast  of  Newfoundland,  the  Gulf  of  St.  Lawrence,  the 
seaboard  of  North  America,  and  the  English  Channel  and  its  approaches. 

693.  Annual  variations. — Cassini  first  discovered  in  1780  that  the 
declination  is  subject  to  small  annual  variations.  At  Paris  and  London  it  is 
greatest  about  the  vernal  equinox,  diminishes  from  that  time  to  the  summer 
solstice,  and  increases  again  during  the  nine  following  months.  It  does  not 
exceed  from  15'  to  18',  and  it  varies  somewhat  at  different  epochs. 

The  diurnal  variatio7is  were  first  discovered  by  Graham  in  1722  ;  they 
can  only  be  observed  by  means  of  long  needles  or  delicate  indicators  such 
as  the  reflection  of  a  ray  of  light  (522)  and  very  sensitive  instruments  (702). 
In  this  country  the  north  pole  moves  ever)'  day  from  east  to  west  from  sun- 
rise until  one  or  two  o'clock  ;  it  then  tends  towards  the  east,  and  at  about 
ten  o'clock  regains  its  original  position.  During  the  night  the  needle  is 
almost  stationary.  Thus  the  westerly  declination  is  greatest  during  the 
warmest  part  of  the  day. 

At  Paris  the  mean   amplitude   of  the   diurnal  variation  from  April  to 

u  u  2 


66o 


0)1  Mao;netisni. 


[693 


September  is  from  13'  to  15',  and  for  the  other  months  from  8'  to  10'.  On 
some  days  it  amounts  to  25',  and  on  others  does  not  exceed  5'.  The  greatest 
variation  is  not  always  at  the  same  time.  The  ampHtude  of  the  daily  varia- 
tions decreases  from  the  poles  towards  the  equator,  where  it  is  very  feeble. 
Thus  in  the  island  of  Rewak  it  never  exceeds  3'  to  4'. 

694.  Accidental  variations  and  perturbations. — The  declination  is 
accidentally  disturbed  in  its  daily  variations  by  many  causes,  such  as  earth- 
quakes, the  aurora  borealzs,  and  volcanic  eruptions.  The  effect  of  the  aurora 
is  felt  at  great  distances.  Auroras,  which  are  only  visible  in  the  most  northerly 
parts  of  Europe,  act  on  the  needle  even  in  these  latitudes,  where  accidental 
variations  of  1°  or  2°  have  been  observed.  In  polar  regions  the  needle  fre- 
quently oscillates  several  degrees  ;  its  irregularity  on  the  day  before  the  aurora 
borealis  is  a  presage  of  the  occurrence  of  this  phenomenon. 

Another  remarkable  phenomenon  is  the  simultaneous  occurrence  of 
magnetic  perturbations  in  very  distant  countries.  Thus  Sabine  mentions 
a  magnetic  disturbance  which  was  felt  simultaneously  at  Toronto,  the  Cape, 
Prague,  and  Van  Diemen's  Land.  Such  simultaneous  perturbations  have 
received  the  name  of  magnetic  storms  (702). 

695.  Declination  compass. — The  declination  compass  is  an  instrument 
by  which  the  magnetic  declination  of  any  place  may  be  determined  when 

its  astronomical  meridian  is 
known.  The  form  repre- 
sented in  fig.  634  consists  of 
a  brass  box,  AB,  in  the  bot- 
tom of  which  is  a  graduated 
circle,  M.  In  the  centre  is  a 
pivot  on  which  oscillates  a 
very  light  lozenge-shaped 
magnetic  needle,  ah.  To  the 
box  are  attached  two  uprights 
supporting  a  horizontal  axis, 
X,  on  which  is  fixed  an 
astronomical  telescope,  L, 
movable  in  a  vertical  plane. 
The  box  rests  on  a  foot,  P, 
about  which  it  can  turn  in  a 
horizontal  plane,  taking  with 
it  the  telescope.  A  fixed 
circle,  QR,  which  is  called 
the    azimuthal  circle,   mea- 

T  sures  the  number  of  degrees 
through  which  the  telescope 
has  been  turned,  by  means 
of  a  vernier,  V,  fixed  to  the 
box.  The  inclination  of  the 
telescope,  in  reference  to  the 
horizon,  maybe  measured  liy 

ixis  of  the  telescope,  and  is  read 


^^^►:lv»  vt,r 


Fig.  634. 

another  vernier,  K,  which  moves 
off  on  a  fixed  graduated  arc,  jr. 


itii  the 


-697] 


Mariners  Compass. 


66 1 


The  first  thing  in  determining  the  declination  is  to  adjust  the  compass 
horizontally  by  means  of  the  screws  SS,  and  the  level  n.  The  astronomical 
meridian  is  then  foimd,  either  by  an  observation  of  the  sun  at  noon  exactly, 
or  by  any  of  the  ready  methods  known  to  astronomers.  The  box  AB  is 
then  turned  until  the  telescope  is  in  the  plane  of  the  astronomical  meridian. 
The  angle  made  by  the  magnetic  needle  with  the  diameter  N,  which  corre- 
sponds with  the  zero  of  the  scale,  and  is  exactly  in  the  plane  of  the  telescope, 
is  then  read  off  on  the  graduated  limb,  and  this  is  east  or  west,  according  as 
the  pole  a  of  the  needle  stops  at  the  east  or  west  of  the  diameter  N. 

696.  Correction  of  errors. — These  indications  of  the  compass  are  only 
correct  when  the  magnetic  axis  of  the  needle — that  is,  the  right  line  passing 
through  the  two  poles — coincides  with  its  axis  of  figure,  or  the  line  connect- 
ing its  two  ends.  This 
is  not  usually  the  case, 
and  a  correction  must 
therefore  be  made, 
which  is  done  by  the 
nietJiod  of  reversion. 
For  this  purpose  the 
needle  is  not  fixed  in 
the  cap,  but  merely 
rests  on  it,  so  that  it 
can  be  removed  and 
its  position  reversed  ; 
thus  what  was  before 
the  lower  is  now  the 
upper  face.  The  mean  between  the  observations  made  in  the  two  cases 
gives  the  true  declination. 

For,  let  NS  be  the  astronomical  meridian,  ab  the  axis  of  figure  of  the 
needle,  and  inn  its  magnetic  axis  (fig.  635).  The  true  declination  is  not  the 
arc  Nrt:,  but  the  arc  N;//,  which  is  greater.  If  now  the  needle  be  turned,  the 
line  inn  makes  the  same  angle  with  the  meridian  NS  ;  but  the  north  end  of 
the  needle,  which  was  on  the  right  of  w;?,  is  now  on  the  left  (fig.  636),  so  that 
the  declination,  which  was  previously  too  small  by  a  certain  amount,  is  now 
too  large  by  the  same  amount.  Hence  the  true  declination  is  given  by  the 
mean  of  these  two  observations. 

697.  Mariner's  compass.^ — The  magnetic  action  of  the  earth  has  received 
its  most  important  application  in  the  mariner's  compass.  This  is  a  declina- 
tion compass  used  in  guiding  the  course  of  a  ship.  Fig.  637  represents  a 
view  of  the  whole,  and  fig.  638  a  vertical  section.  It  consists  of  a  cylindrical 
case,  BB',  which  to  keep  the  compass  in  a  horizontal  position  in  spite  of  the 
rolling  of  the  vessel,  is  supported  on  gimbals.  These  are  two  concentric 
rings,  one  of  which,  attached  to  the  case  itself,  moves  about  the  axis  xd  which 
plays  m  the  outer  ring  AB,  and  this  moves  in  the  supports  PQ,  about  the 
axis  w;/,  at  right  angles  to  the  first. 

In  the  bottom  of  the  box  is  a  pivot,  on  which  is  placed  by  means  of  an 
agate  cap,  a  magnetic  bar,  ab,  which  is  the  needle  of  the  compass.  On  this 
is  fixed  a  disc  of  mica,  a  little  larger  than  the  length  of  the  needle,  on  which 
is  traced  a  star  or  7-ose.,  with  thirty-two  branches,  making  the  eight  points  or 


Fig.  636. 


66: 


On  Alagnetism. 


[697- 


rhiimbs  of  the  wind,  the  demi-rhumbs,  and  the  quarters.  The  branch  ending 
in  a  small  star,  and  called  N,  corresponds  to  the  bar  ab,  which  is  underneath 
the  disc. 

The  compass  is  placed  near  the  stem  of  the  vessel  in  the  binnacle. 
Knowing  the  direction  of  the  compass  in  which  the  ship  is  to  be  steered,  the 
pilot  has  the  rudder  turned  till  the  direction  coincides  with  the  sight-vane 


passing  through  a  line  d  marked  on  the  inside  of  the  box,  and  parallel  with 
the  keel  of  the  vessel. 

The prisniaiic  compass  is  greatly  used  for  surA'eying  and  more  especially 
for  military  purposes  ;  it  differs  from  the  mariner's  compass  mainly  in  its 
dimensions,  and  in  the  Avayin  which  observations  are  made.  It  consists  of  a 
shallow  metal  box  about  2h  inches  in  diameter  (fig.  639)  ;  the  needle,  which  is 
fixed  below  the  compass  card,  plays  on  a  pivot  much  as  in  fig.  638.  A  is  a  metal 
frame  across  which  is  stretched  a  horse-hair,  forming  a  sight-vane.  Exactly  op- 
posite this  is  a  right-angled  prism  P  enclosed  ^ 
in  a  metal  case,  with  an  eyehole  and  a  slit  as 
represented  at  the  side  of  the  figure  (fig.  639). 
In  order  to  make  an  observation  the 
compass    is   held    horizontally,  and  so  that 


•■■';;•  f'jS.  Kig.  639. 

the  slit  in  the  prism,  the  hair  of  the  sight-vanc,  antl  the  distant  object  are 
seen  to  be  in  the  same  line  ;  looking  through  the  eyehole,  the  angle  which 
the  needle  makes  is  then  noted  ;  a  similar  observation  is  made  with  another 
object,  and  thus  the  angle  between  them,  or  their  bearing,  is  given. 

The  sight-vane  is  connected  with  a  Itvcr,  and  can  l)c  turned  down  when 


-698]  hidiuation.     Magnetic  Eqitator.  663 

it  presses  the  magnet  on  the  pivot,  thus  keeping  it  rigid,  so  that  the  compass 
can  be  transported  in  any  position. 

As  the  image  is  seen  through  the  convex  face  of  the  prism  it  is  magnified, 
and  as  it  is  seen  by  reflection  it  is  reversed,  so  that  in  order  to  read  the  figures 
correctly  they  must  be  reversed  on  the  card ;  the  reflection  being  total  there 
is  little  loss  of  light. 

698.  Inclination.  Mag-netlc  equator. — It  might  be  supposed  from  the 
northerly  direction  which  the  magnet  needle  takes,  that  the  force  actin  ^ 
upon  it  is  situated  in  a  point  of  the  horizon.  This  is  not  the  case,  for  if  the 
needle  be  so  arranged  that  it  can  move  freely  in  a  vertical  plane  about  a  hori- 
zontal axis,  it  will  be  seen  that,  although  the  centre  of  gravity  of  the  needle 
coincides  with  the  centre  of  suspension,  the  north  pole  in  our  hemisphere  dips 
downwards.  In  the  other  hemisphere  the  south  pole  is  inclined  downwards. 
The  angle  which  the  magnetic  needle  makes  with  the  horizon,  when  the 
vertical  plane,  in  which  it  moves,  coincides  with  the  magnetic  meridian,  is 
called  the  inclination  or  dip  of  the  needle.  In  any  other  plane  than  the 
magnetic  meridian  the  inclination  increases^  and  is  90°  in  a  plane  at  right 
angles  to  the  magnetic  meridian.  For  the  magnetic  inclination  represents 
the  direction  of  the  total  magnetic  force,  and  may  be  resolved  into  two 
forces,  one  acting  in  a  horizontal  and  the  other  in  a  vertical  plane.  When 
the  needle  is  moved  so  that  it  is  at  right  angles  to  the  magnetic  meridian, 
the  horizontal  component  can  only  act  in  the  direction  of  the  axis  of  suspen- 
sion, and  therefore  cannot  affect  the  needle,  which  is  then  solely  influenced 
by  the  vertical  component,  and  stands  vertically.  The  following  considera- 
tions will  make  this  clearer  : — 

Let  NS  (fig.  640)  represent  a  magnetic  needle  capable  of  moving  in  a 
vertical  plane.  Let  NT  represent,  in  direction  and  intensity,  the  entire 
force  of  the  earth's  magnetism  acting 
on  the  pole  N.  Then  NT  can  be  re- 
solved into  the  forces  N/;  and  N  V  ;  TNA 
being^  the  angle  of  inclination  or  dip. 

NT  is  termed  the  total  force  M  ;  and 
its  components  are  N/;,  or  the  horizontal 
force  H,  and  NV,  or  the  vertical  force  Z.  Fig.  640. 

Now,  it  is  clear  that  the  greater  the  angle  of  dip,  TN/:,  the  less  becomes 
N//,  or  the  horizontal  force,  and  the  greater  NV,  or  the  vertical  force. 
Hence,  in  high  latitudes  the  directive  force  of  a  compass,  which  depends  on 
the  horizontal  force,  is  less  than  in  low  latitudes.  At  the  magnetic  poles  the 
horizontal  force  will  be  «//,  and  the  vertical  force  a  maximum  ;  here,  there- 
fore, the  needle  will  be  vertical.  At  the  magnetic  equator  the  reverse  is  the 
case,  and  the  needle  will  be  horizontal.  Hence,  the  oscillations  of  a  compass 
needle,  by  which,  as  will  presently  be  explained,  the  strength  of  the  earth's 
magnetism  is  measured,  become  fewer  and  fewer  in  a  given  time  as  the 
magnetic  poles  are  approached,  although  there  is  really  an  increase  in  the 
total  force  of  the  earth. 

Again,  the  reason  why  a  dip  needle  stands  vertical  when  placed  E. 
and  W.  is  clearly  because  in  those  positions  the  horizontal  force  now  acting 
at  right  angles  to  the  plane  of  motion  of  the  needle  is  ineffectual  to  move  it, 
and  therefore  merely  produces  a  pressure  on  the  pivot  which  supports  the 
needle.     But  the  vertical  component  of  the  total  force  remains  unaffected 


664 


On  Alairnetisni. 


[698 


by  the  new  position  of  the  needle.  Acting,  therefore,  entirely  alone  when 
the  dip  needle  is  exactly  E.  and  W.,  this  vertical  component  drags  the 
needle  into  a  line  with  itself ;  that  is,  90°  from  the  horizontal  plane. 

The  value  of  the  dip,  like  that  of  the  declination,  differs  in  different 
localities.  It  is  greatest  in  the  polar  regions,  and  decreases  with  the  latitude 
to  the  equator,  where  it  is  approximately  zero.  In  London  at  the  present  tmie 
(1889)  the  dip  is  67°  26',  reckoning  from  the  horizontal  line.  In  the  southern 
hemisphere  the  inclination  is  again  seen,  but  in  a  contrary  direction  ;  that  is, 
the  south  pole  of  the  needle  clips  below  the  horizontal  line. 

The  magnetic  poles  are  those  places  in  which  the  dipping-needle  stands 
vertical  ;  that  is,  where  the  inclination  is  90°.  In  1830  the  first  of  these,  the 
terrestrial  north  pole,  was  found  by  Sir  James  Ross  in  96°  43'  west  longitude 
of  70°  north  latitude.  The  same  observer  found  in  the  South  Sea,  in  76° 
south  latitude  and  168°  east  longitude,  that  the  inclmation  was  88°  2,1'-  From 
this  and  other  observations,  it  has  been  calculated  that  the  position  of  the 
magnetic  south  pole  was  at  that  time  in  about  1 54°  east  longitude  and  75^° 
south  latitude.  The  line  of  no  declination  passes  through  these  poles,  and 
the  lines  of  equal  declination  converge  towards  them. 

The  niagnetic  equator,  or  aclinic  line,  is  the  line  which  joins  all  those 
places  on  the  earth  where  there  is  no  dip  ;  that  is,  all  those  in  which  the 
dipping-needle  is  quite  horizontal.  It  is  a  somewhat  sinuous  line,  not  differ- 
ing much  from  a  great  circle  inclined  to  the  equator  at  an  angle  of  12°,  and 
cutting  it  on  two  points  almost  exactly  opposite  each  other — one  in  the 
Atlantic,  and  one  in  the  Pacific.  These  points  appear  to  be  gradually  moving 
their  position,  and  travelling  from  east  to  west. 

Lines  connecting  places  in  which  the  dipping-needle  makes  equal  angles 
are  called  isoclinic  lines.  They  have  a  certain  analogy  and  parallelism  with 
the  parallels  of  latitude,  and  the  term  niagnetic  latitude  is  sometimes  used  to 
denote  positions  on  the  earth  with  reference  to  the  magnetic  dip.  Plate  IV. 
is  an  inclination  map  for  the  year  1882,  the  construction  of  which  is  quite 
analogous  to  that  of  the  map  of  declination. 

The  inclination  is  subject  to  secular  variations,  like  the  declination,  as  is 
readily  seen  from  a  comparison  of  maps  of  inclination  for  different  epochs. 
At  Paris,  in  1671,  the  inclination  was  75°  ;  since  then  it  has  been  continually 
decreasing  :  in  1835  it  was  67°  24';  in  1849,  67°  ;  in  1859,  66°  16'  ;  in  1869, 
65°  43' ;  in  1879,  65°  32' ;  in  1883,  65°  17' ;  and  in  1888,  65°  14'. 

The  following  table  gives  the  alterations  in  the  inclination  at  London, 
from  which  it  will  be  seen  that  since  1723,  in  which  it  was  at  its  maximum,  it 
has  continually  diminished  by  something  more  than  two  minutes  in  each  year. 


Year 
1576 

Iiicliiiatioii 

Veiir 

Inclination 

7.°  50' 

1828 

69°  47'         , 

1600 

72° 

1838 

69°  17' 

1676 

If  30' 

1854 

68°  31' 

^T-l 

74°  42' 

1859 

68°  21' 

1773 

72°  19' 

IS74 

67°  43' 

1780 

72°    8' 

1876 

67°  39' 

1790 

71°  33' 

1878 

67°  36' 

1800 

70°  35' 

1880 

67'  35' 

1821 

70°  31' 

I88I 

67°  35' 

-699]  Inclhiatioft   CoDipass.  665 

699.  Inclination  compass. — An  inclination  compass,  or  dip  7iecdlc,  is  an 
instrument  for  measuring  the  magnetic  inclination  or  dip.  One  form,  repre- 
sented in  fig.  641,  though  not  best  adapted  for  the  most  accurate  measure- 
ments, is  well  suited  for  illustrating  the  principle.  It  consists  of  a  graduated 
horizontal  brass  circle  w,  supported  on  three  legs,  provided  with  levelling 
screws.  Above  this  circle  there  is  a  plate  A,  movable  about  a  vertical  axis, 
and  supporting,  by  means  of  two  columns,  a  second  graduated  circle  M,  which 
measures  the  inclination.  The  needle  rests  on  a  frame  r,  and  the  diameter 
passing  through  the  two  zeros  of  the  circle  N  can  be  ascertained  to  be 
perfectly  horizontal  by  means  of  the  spirit-level  /i. 

To  observe  the  inclination,  the  magnetic  meridian  must  first  be  deter- 
mined, which  is  effected  by  turning  the  plate  A  on  the  circle  ;«,  until  the 
needle  is  vertical,  which  is  the  case  when  it  is  in  a  plane  at  right  angles  to 
the  magnetic  meridian  (698).  The  plate  A  is  then  turned  90°  on  the  circle 
in,  by  which  the  ^•ertical  circle  M  is  brought  into  the  magnetic  meridian. 
The  angle  dca,  which  the  magnetic  needle  makes  with  the  horizontal  dia- 
meter, is  the  angle  of  inclination. 

There  are  here  several  sources  of  error,  which  must  be  allowed  for.  The 
most  important  are  these  : — i.  The  magnetic  a.xis  of  the  needle  may  not 
coincide  with  its  axis  of  figure  : 
hence  an  error  which  is  cor- 
rected by  a  method  of  reversion 
analogous  to  that  already  de- 
scribed (696).  ii.  The  centre  of 
gravity  of  the  needle,  may  not 
coincide  with  the  axis  of  suspen- 
sion, and  then  the  angle  dca  is 
too  great  or  too  small,  according 
as  the  centre  of  gravity  is  below 
or  above  the  centre  of  suspen- 
sion ;  for  in  the  first  case  the 
action  of  gravity  is  in  the  same 
direction  as  that  of  magnetism, 
and  in  the  second  it  is  in  the 
opposite  direction.  To  correct 
this  error,  the  poles  of  the 
needle  must  be  reversed  by  first 
demagnetising  it,  and  then  im- 
parting a  contrary  magnetism 
to  what  it  had  at  first.  The 
inclination  is  now  re-determined, 
and  the  mean  taken  of  the  re-  ^...^  ^  ^ 

suits  obtained  in  the  two  groups 

of  operations,  iii.  The  plane  of  the  ring  may  not  coincide  with  the  true  mag- 
netic meridian.  It  should  be  in  that  plane  when  the  needle  has  its  minimum 
deviation  ;  an  observation  of  this  kind  should  therefore  be  taken  along  with 
that  previously  described,  by  which  the  needle  is  moved  90°  from  its  maxi- 
mum deviation. 

The  dip  needle  may  be  used    to   determine  the  inclination  in  another 


666 


On  Magnetism. 


[699- 


way.  It  is  first  allowed  to  oscillate  in  the  magnetic  meridian,  and  then  in 
a  plane  at  right  angles  to  it.  If  the  number  of  oscillations  m  a  given  time 
in  the  first  position  be  7i,  and  in  the  second  position  «,,  then  in  the  first  position 
the  whole  force  of  the  earth's  magnetism  E  acts,  and  in  the  second  posi- 
tion only  the  vertical  component,  which  is  E  sin  x,  x  being  the  angle  of  dip. 
Now,  since  the  forces  acting  on  the  needle  are,  from  the  laws  of  the  pendulum 
(55),  as  the  squares  of  the  number  of  oscillations  in  a  given  time,  we  have 

■ ; =  —  .  from  which  sin  x=  -^. 

E  sm  X    n~  n- 

700.  Astatic  needle  and  astatic  system. — An  astatic  needle  is  one 
which  is  uninfluenced  by  the  earth's  magnetism.  A  needle  movable  about 
an  axis  in  the  plane  of  the  magnetic  meridian  and  parallel  to  the  inclination 
would  be  one  of  this  kind  ;  for  the  terrestrial  magnetic  couple,  acting  then 
in  the  direction  of  the  axis,  cannot  impart  to  the  needle  any  determinate 
direction. 

An  astatic  system  is  a  combination  of  two  needles  of  the  same  force 
joined  parallel  to  each  other  with  the  poles  in  contrary  directions,  as  shown 
in  fig.  642.  If  the  two  needles  have  exactly  the 
same  magnetic  force,  the  opposite  actions  of  the 
earth's  magnetism  on  the  poles  a'  and  b  and  on 
the  poles  a  and  b'  counterbalance  each  other  ;  the 
system  is  then  completely  astatic,  and  sets  at  right 
angles  to  the  magnetic  meridian. 

A  single  magnetic  needle  may  also  be  rendered 
astatic  by  placing  a  large  magnet  near  it.  By 
repeated  trials  a  certain  position  and  distance  can 
be  found  at  which  the  action  of  the  magnet  on  the 
needle  just  neutralises  that  of  the  earth's  magnetism, 
and  the  needle  is  free  to  obey  any  third  force  ;  in 
other  words,  the  field  due  to  the  magnet  just  neutralises  the  earth's  field. 

701.  Force  of  the  earth's  magnetism. — If  a  magnetic  needle  be 
moved  from  its  position  of  equilibrium,  it  will  revert  to  it  after  a  series  of 
oscillations,  which  follow  laws  analogous  to  those  of  the  pendulum  (80).  If 
the  magnet  be  removed  to  another  place,  and  caused  to  oscillate  during 
the  same  length  of  time  as  the  first,  a  different  number  of  oscillations 
will  be  observed.  And  the  earth's  magnetic  force  in  the  two  places  will  be 
respectively  proportional  to  the  squares  of  the  number  of  oscillations. 

If  at  M  the  number  of  oscillations  in  a  minute  had  been  35  =;;,  and  at 
another  place  M',  24  =  ;/',  we  should  have — 


Fig.  642. 


1-085. 


Force  of  the  earth's  magnetism  at  M  _  «^  _  625 
Force  of  the  earth's  magnetism  at  M'    »/     576 

That  is,  if  the  force  of  the  magnetism  at  the  second  place  is  taken  as  unity, 
that  of  the  first  is  1*085.  ^f  the  magnetic  condition  of  the  needle  had  not 
changed  in  the  inter\al  between  the  two  obscr\ations,  this  method  would 
give  the  relation  of  the  force  at  the  two  places. 

In  these  determinations  of  the  force,  it  would  be  necessary  to  have  the 
oscillations  of  the  dip-needle,  which  are  produced  by  the  total  force  of 
the    earth's    magnetism.      These,   however,   are   difiicult    to    obtain   with 


-702]  Magnetic  Observatories.  66y 

accuracy,  and  therefore  those  of  the  declination  needle  are  usually  taken. 
The  force  which  makes  the  declination  needle  oscillate  is  only  a  portion 
of  the  total  magnetic  force,  and  is  smaller  in  proportion  as  the  inclination 
is  greater.  If  a  line  nc=M  (fig.  643)  represent  the  total  force,  the  angle  i 
the  inclination,  then  the  horizontal  component  ab  =  H  is  M  cos  i.  Hence,  to 
express  the  total  force  in  the  two  places  by  the  oscillations  of  the  declina- 
tion needle,  we  must  substitute  the  values  M  cos  i  and  M'  cos  i'  for  M  and 
IVr  in  the  preceding  equation,  and  we  have —  t 


M   cos  t      n-      ■,  M      «^  cos  z  177 

TTTT •/=,-.;  hence        =_— . .  NX 

M'  cos  t      n-  M'     n~  cos  z  .  \. 

That   is 'to  say,  having   obsei-ved   in   two   different   places   the;       \ 

number  of  oscillations,  71  and  «',  that  the  same  needle  makes  in  I         \ 

the  same  time,  the  ratio  of  the  magnetic  force  in  the  two  places  j  \ 

will  be  found  by  multiplying  the    ratio  of  the   square   of  the  1 

number  of  oscillations  by  the  inverse  ratio  of  the  cosine  of  the  ~ 

angle  of  dip.  ^'^•^+3. 

Plate  V.  is  a  chart  representing  the  horizontal  component  of  the  earth's 
force.  Knowing  the  angle  of  dip  z,  the  total  force  M,  or  the  vertical  force  Z, 
in  any  place,  may  be  obtained  from  the  values  in  the  chart  by  the  formula 
M  =  H  sec  i  ;  and  Z  =  H  tan  z. 

The  total  force  is  least  near  the  magnetic  equator,  and,  increasing  with 
the  latitude,  is  greatest  near,  but  not  quite  at,  the  magnetic  poles  ;  the  places 
of  maximum  intensity  are  conveniently  named  the  magiietic  foci.  The  chart 
shows  that  the  horizontal  force  diminishes  as  we  go  towards  the  poles  :  this 
is  not  inconsistent  with  the  above  statement  if  we  take  the  dip  into  account 
(698). 

The  lines  connecting  places  of  equal  force  are  called  isodynamic  lines. 
They  are  not  parallel  to  the  magnetic  equator,  but  seem  to  have  about  the 
same  direction  as  the  isothermal  lines.  According  to  Kuppfer,  the  force 
appears  to  diminish  as  the  height  of  the  place  is  greater  ;  a  needle  which 
made  one  oscillation  in  24"  vibrated  more  slowly  by  o-oi"  at  a  height  of 
1,000  feet :  but,  according  to  Forbes,  the  force  is  only  ^~  less  at  a  height 
of  3,000  feet.  There  is,  however,  some  doubt  as  to  the  accuracy  of  these 
observations,  owing  to  the  uncertainty  of  the  correction  for  temperature. 

The  intensity  varies  in  the  same  place  with  the  time  of  day  :  it  attains  its 
maximum  between  4  and  5  in  the  afternoon,  and  is  at  its  minimum  between 
10  and  II  in  the  morning. 

According  to  Gauss,  the  total  magnetic  action  of  the  earth  is  the  same  as 
that  which  would  be  exerted  if  in  each  cubic  yard  there  were  eight  steel 
bar  magnets  each  weighing  a  pound. 

It  is  probable,  though  it  has  not  yet  been  ascertained  with  certainty,  that 
the  force  undergoes  secular  variations.  From  measurements  made  at  Kew, 
it  appears  that  on  the  whole,  the  total  force  experiences  a  very  slight  annual 
increase  (692). 

702.  ivxagrnetic  observatories.^ — During  the  last  few  years  great  atten- 
tion has  been  devoted  to  the  observation  of  the  magnetic  elements,  and  obser- 
vatories for  this  purpose  have  been  fitted  up  in  different  parts  of  the  globe. 
These  observations  have  led  to  the  discovery  that  the  magnetism  of  the  earth 
is  in  a  state  of  constant  fluctuation,  like  the  waves  of  the  sea.  And  in  study- 
ing the  variations  of  the  declination,  (S:c.,  the  mean  of  a  great  number  of 


668  On  Magnetism.  [702- 

observations  must  be  taken,  so  as  to  eliminate  the  irregular  disturbances, 
and  bring  out  the  general  laws. 

The  principle  on  which  magnetic  observations  are  automatically  recorded 
is  as  follows  : — Suppose  that  in  a  dark  room  a  bar  magnet  is  suspended 
horizontally,  and  at  its  centre  is  a  small  mirror  ;  suppose  further  that  a  lamp 
sends  a  ray  of  light  to  this  mirror,  the  inclination  of  which  is  such  that  the  ray 
is  reflected,  and  is  received  on  a  horizontal  drum  placed  underneath  the  lamp. 
The  axis  of  the  drum  is  at  right  angles  to  the  axis  of  the  magnet  ;  it  is  covered 
with  sensitive  photographic  paper,  and  is  rotated  uniformly  by  clockwork. 
If  now  the  magnet  is  quite  stationary,  and  the  drum  rotates,  the  reflected 
spot  of  light  will  trace  a  straight  line  on  the  paper  with  which  the  revolving 
drum  is  covered.  But  if,  as  is  always  the  case,  the  position  of  the  magnet 
varies  during  the  twenty-four  hours,  the  effect  will  be  to  trace  a  sinuous  line 
on  the  paper.  These  lines  can  afterwards  be  fixed  by  ordinary  photographic 
methods.  Knowing  the  distance  of  the  mirror  from  the  drum,  and  the  length 
of  the  paper  band  which  comes  under  the  influence  of  the  spot  of  light  in  a 
given  time — twenty-four  hours,  for  instance — the  angular  deflection  at  any 
given  moment  may  be  deduced  by  a  simple  calculation  (522). 

The  observations  made  in  the  English  magnetic  observatories  were 
reduced  by  Sabine,  and  revealed  some  curious  facts  in  reference  to  mag- 
netic storms  (694).  He  found  that  there  is  a  certain  periodicity  in  their 
appearance,  and  that  they  attain  their  greatest  frequency  about  every  ten 
years.  Independently  of  this,  Schwabe,  who  for  many  years  studied  the- sub- 
ject, found  that  the  spots  on  the  sun,  seen  on  looking  at  it  through  a 
coloured  glass,  vary  in  their  number,  size,  and  frequency,  but  attain  their 
maximum  about  every  ten  or  eleven  years.  Now  Sabine  established  the 
interesting  fact  that  the  period  of  their  greatest  frequency  coincides  with  the 
period  of  greatest  magnetic  disturbance.  Other  remarkable  connections 
between  the  sun  and  terrestrial  magnetism  have  been  observed  ;  one, 
especially,  of  recent  occurrence  has  attracted  considerable  attention.  It  was 
the  flight  of  a  large  luminous  mass  across  a  vast  sun-spot,  while  a  simul- 
taneous perturbation  of  the  magnetic  needle  was  observed  in  the  observatory 
at  Kew  :  subsequent  examination  of  magnetic  observations  in  various  parts 
of  the  world  showed  that  within  a  few  hours  one  of  the  most  violent  magnetic 
storms  ever  known  had  prevailed. 

It  seems,  however,  that  these  accidental  variations  in  the  declination  can- 
not be  due  to  changes  in  any  direct  action  of  a  possible  magnetic  condition 
of  either  the  sun  or  the  moon.  For  it  can  be  shown  that  if  the  magneti- 
sation of  the  latter  were  as  powerful  as  that  of  the  earth,  the  deflection 
which  it  could  produce  would  not  amount  to  the  ?,^\\\  of  a  second,  a  quantity 
which  cannot  be  measured.  In  order  to  produce  a  variation  of  10',  such 
as  is  frequently  met  with,  the  magnetisation  of  the  sun  or  of  the  moon 
must  be  12,000  times  that  of  the  earth  ;  in  other  words,  a  more  powerful  de- 
gree of  magnetisation  than  that  of  powerfully  magnetised  steel  bars. 

Magnetic  storms  are  nearly  always  accompanied  by  the  exhibition  of  the 
aurora  borealis  in  high  latitudes  ;  that  this  is  not  universal  may  be  due  to 
the  fact  that  many  auroras  escape  notice.  The  converse  of  this  is  true,  that 
no  great  display  of  the  aurora  takes  place  without  a  violent  magnetic  storm. 
The  centre  or  focus  towards  which  the  rays  of  the  aurora  converge  lies 
approximately  in  tlic  prolongation  of  the  direction  of  the  dipping-needle. 


704] 


669 


CHAPTER    III. 

LAWS   OF   MAGNETIC  ATTRACTION   AND   REPULSION. 


703.  law  of  decrease  witb  distance. — Coulomb  discovered  the  remark- 
able law  in  reference  to  magnetism,  t]iat  magnetic  attractions  and  repulsions 
are  inversely  as  the  squares  of  the  distances.  He  proved  this  by  means  of 
two  methods  : — (i.)  that  of  the  torsion  balance,  and  (ii.)  that  of  oscillations. 

704.  i.  The  torsion  balance. — This  apparatus  depends  on  the  principle 
that,  when  a  wire  is  twisted  through  a  certain  space,  the  angle  of  torsion  is 
proportional  to  the  force  of  torsion 
(89).  It  consists  (fig.  644)  of  a 
glass  case  closed  by  a  glass  top, 
with  an  aperture  near  the  edge, 
to  allow  the  introduction  of  a  mag- 
net, A.  In  another  aperture  in  the 
centre  of  the  top  a  glass  tube  fits, 
provided  at  its  upper  extremity 
with  a  micrometer.  This  consists 
of  two  circular  pieces  :  f?,  which  is 
fixed,  is  divided  on  the  edge  into 
360^,  while  on  one  ^,  which  is  mov- 
able, there  is  a  mark,  ^,  to  indicate 
its  rotation.  D  and  E  represent 
the  two  pieces  of  the  micrometer 
on  a  larger  scale.  On  E  there 
are  two  uprights  connected  by  a 
horizontal  axis,  on  which  is  a  very 
fine  silver  wire  supporting  a  mag- 
netic  needle,  ab.     On   the  side  of 


Fig.  644. 


the  case  there  is  a  graduated  scale,  which  indicates  the  angle  of  the  needle 
rt/5,  and  hence  the  torsion  of  the  wire. 

When  the  mark  c  of  the  disc  E  is  at  zero  of  the  scale  D,  the  case  is  so 
arranged  that  the  wire  supporting  the  needle  and  the  zero  of  the  scale  in  the 
case  are  in  the  magnetic  meridian.  The  needle  is  then  removed  from  its 
stirrup,  and  replaced  by  an  exactly  similar  one  of  copper,  or  any  unmagnetic 
substance  ;  the  tube,  and  with  it  the  pieces  D  and  E,are  then  turned  so  that 
the  needle  stops  at  zero  of  the  graduation.  The  magnetic  needle  ab.,  being 
now  replaced,  is  exactly  in  the  magnetic  meridian,  and  the  wire  e.xerts  no 
torsion. 

Before  introducing  the  magnet  A,  it  is  necessary  to  investigate  the  action 
of  the  earth's  magnetism  on  the  needle  ab.  when  the  latter  is  removed  out  of 


6/0  On  Magnetism.  [704- 

the  magnetic  meridian.  This  will  vary  with  the  dimensions  and  force  of  the 
needle,  with  the  dimensions  and  nature  of  the  particular  wire  used,  and  with 
the  intensity  of  the  earth's  magnetism  in  the  place  of  observation.  Accord- 
ingly, the  piece  E  is  turned  until  ab  makes  a  certain  angle  with  the  magnetic 
meridian.  Coulomb  found  in  his  experiments  that  E  had  to  be  turned  36° 
in  order  to  move  the  needle  through  1°  ;  that  is,  the  earth's  magnetism  was 
equal  to  a  torsion  of  the  wire  corresponding  to  35°.  As  the  force  of  torsion 
is  proportional  to  the  angle  of  torsion,  when  the  needle  is  deflected  from  the 
meridian  by  2,  3  .  .  .  degrees,  the  directive  action  of  the  earth's  magnetism 
is  equal  to  2,  3  .  .  .  times  35°. 

The  action  of  the  earth's  magnetism  having  been  determined,  the  magnet 
A  is  placed  in  the  case  so  that  similar  poles  are  opposite  each  other.  In  one 
experiment  Coulomb  found  that  the  pole  a  was  repelled  through  24°.  Now 
the  force  which  tended  to  bring  the  needle  into  the  magnetic  meridian 
was  represented  by  24°  +  24  x  35  =  864,  of  which  the  part  24°  was  due  to  the 
torsion  of  the  wire,  and  24  x  35°  was  the  equivalent  in  torsion  of  the  directive 
force  of  the  earth's  magnetism.  As  the  needle  was  in  equilibrium,  it  is  clear 
that  the  repulsive  force  which  counterbalanced  those  forces  must  be  equal 
to  864°.  The  disc  was  then  turned  until  ab  made  an  angle  of  1 2°.  To  effect 
this,  eight  complete  rotations  of  the  disc  were  necessary.  The  total  force 
which  now  tended  to  bring  the  needle  into  the  magnetic  meridian  was  com- 
posed of: — 1st,  the  12°  of  torsion  by  which  the  needle  was  distant  from  its 
starting  point ;  2nd,  of  8  x  360°  =  2880,  the  torsion  of  the  wire  ;  and  3rd,  the 
force  of  the  earth's  magnetism,  represented  by  a  torsion  of  12  x  35°.  Hence 
the  forces  of  torsion  which  balance  the  repulsive  forces  exerted^at  a  distance 
of  24°  and  of  1 2°  are — 

24°        ...         .  864 

12°        ...         .         3312 

Now,  3312  is  very  nearly  four  times  864  ;  hence  for  half  the  distance  the 
repulsive  force  is  four  times  as  great. 

705.  ii,  Metbod  of  oscillations. — A  magnetic  needle  oscillating  under 
the  influence  of  the  earth's  magnetism  may  be  considered  as  a  pendulum, 
and  the  laws  of  pendulum  motion  apply  to  it  (55).  The  method  of  oscilla- 
tions consists  in  causing  a  magnetic  needle  to 
oscillate  first  under  the  influence  of  the  earth's 
magnetism  alone,  and  then  successively  under  the 
combined  influence  of  the  earth's  magnetism  and 
of  a  magnet  placed  at  unequal  distances. 
y  The  following  determination  by  Coulomb  will 

I  illustrate  the  use  of  the  method.    A  magnetic  needle 

]  was  used  which  made   1 5  oscillations  in  a  minute 

_A \  under  the  influence  of  the  earth's  magnetism  alone. 

ji.ll '"■'  A  magnetic  bar  about  2  feet  long  was  then  placed 

vertically  in  the  plane  of  the  magnetic  meridian, 

'*'■  '■''■■  so  that  its  north  ])ole  was  downwards  and  presented 

to  the  south  pole  0  of  the  oscillating  needle  (fig.  645),  so  as  to  concur  in  its 

action  with  that  of  the  earth.     He  found  that  at  a  distance  of  4  inches  the 

needle  made  41  oscillations  in  a  minute,  and  at  a  distance  of  8  inches  24 


-706]  Magnetic  Curves.  '671 

oscillations.  Now,  from  the  laws  of  the  pendulum  (55),  the  intensities  of  the 
forces  are  inversely  as  the  squares  of  the  times  of  oscillation.  Hence,  if 
we  call  M  the  force  of  the  earth's  magnetism,  ?n  the  attractive  force  of  the 
magnet  at  the  distance  of  4  inches,  tii'  at  the  distance  of  8  inches,  we  have 

M  :  M  + w  =  15*  141^  and 
M  :  M  +  in'  =15'^:  24', 
eliminating  I\I 

»i  :  w'  =  4i--  15-  :  24--  15-=  1456  :  351  =4  :  I  nearly, 

or  ;//  :  m'  =  4  :  i. 

In  other  words,  the  force  acting  at  4  inches  is  quadruple  that  which  acts  at 
double  the  distance. 

The  above  results  do  not  quite  agree  with  the  numbers  required  by  the 
law  of  inverse  squares.  But  this  could  only  be  expected  to  apply  in  the  case 
in  which  the  repulsive  or  attractive  force  is  exerted  between  two  points,  and 
not,  as  is  here  the  case,  between  the  resultant  of  a  system  of  points.  And  it 
is  to  this  fact  that  the  discrepancy  between  the  theoretical  and  observed 
results  is  due. 

When  a  magnet  acts  upon  a  mass  of  soft  iron,  the  law  of  the  variation 
with  the  distance  is  modified.  The  attraction  in  this  case  is  inversely  pro- 
portional to  the  distance  between  the  magnet  and  the  iron. 

When  the  distance  between  the  magnet  and  the  iron  is  small,  Tyndall 
found  that  the  attraction  is  directly  proportional  to  the  square  of  the  strength 
of  the  magnet  ;  but  when  the  iron  and  the  magnet  are  in  contact,  then  the 
attraction  is  directly  proportional  to  the  strength  of  the  magnet. 

706.  Magnetic  curves. — If  a  stout  sheet  of  paper  stretched  on  a  frame 
be  held  over  ;i  h  '  ....  ^       j^.^^^  filings  be 


Fig.  646. 

strewn  on  the  paper,  on  tapping  the  frame  the  filings  will  be  found  to  arrange 
themselves  in  thread-like  curved  lines,  stretching  from  pole  to  pole  (fig.  646). 
These  lines  form  what  are  called  7nagnetic  curves.  The  direction  of  the 
curve  at  any  point  represents  the  direction  of  the  lines  of  magnetic  force  at 
this  point. 


6/2  On  Magnetism.  [706- 

To  render  these  curves  permanent,  the  paper  on  which  they  are  formed 
should  be  waxed  ;  if  then  a  hot  iron  plate  be  held  over  them,  this  melts  the 
wax,  which  rises  by  capillary  attraction  (131)  between  the  particles  of  filings, 
and  on  subsequent  cooling  connects  them  together.  They  may  also  be  fixed 
by  carefully  placing  on  them  a  sheet  of  paper  coated  with  paste,  which  is 
then  gently  pressed  and  lifted  off;  it  should  be  quickly  dried  to  prevent  the 
iron  from  rusting. 

These  curves  are  a  graphic  representation  of  the  law  of  magnetic  attrac- 
tion and  repulsion  with  regard  to  distance  ;  for  under  the  influence  of  the 
two  poles  of  the  magnet,  each  particle  becomes  itself  a  minute  magnet,  the 
poles  of  which  arrange  themselves  in  a  position  dependent  on  the  resultant 
of  the  forces  exerted  upon  them  by  the  two  poles,  and  this  resultant  varies 
with  the  distance  of  the  two  poles  respectively.  A  small  magnetic  needle 
placed  in  any  position  near  the  magnet  will  take  a  direction  which  is  the 
tangent  to  the  curve  at  this  place. 

707.  Magnetic  definitions. — The  space  in  the  immediate  neighbourhood 
of  any  magnet  undergoes  some  change  in  consequence  of  the  presence  of  this 
magnet,  and  such  a  space  is  spoken  of  as  a  magnetic  field ;  it  is  indeed  the 
sphere  of  action  of  the  magnet  ;  the  effect  produced  by  the  magnet  itself  is 
often  spoken  of  as  due  to  the  magnetic  field.  Magnets  of  different  powers 
produce  magnetic  fields  of  different  intensities.  The  strength  of  the  field 
diminishes  with  the  distance  from  the  magnet. 

The  direction  which  represents  the  resultant  of  the  magnetic  forces  at 
any  position  in  a  magnetic  field  is  spoken  of  as  the  direction  of  the  lines  of 
force  of  this  field.  In  fig.  646  the  magnetic  curves  represent  the  direction  of 
the  lines  of  force  in  the  field  due  to  the  two  opposite  poles. 

A  uniform  magnetic  field  is  one  in  which  the  lines  of  force  are  parallel. 
This  is  practically  the  case  with  a  small  portion  of  a  field  at  some  distance 
from  a  long  thin  magnet  of  uniform  magnetisation.  The  dipping-needle, 
when  free  to  oscillate  in  a  vertical  plane  in  the  magnetic  meridian,  represents 
the  direction  of  the  lines  of  force  due  to  the  terrestrial  magnetic  field.  The 
strength  of  the  field  due  to  this  in  any  one  place  is  uniform  in  much  the 
same  sense  in  which  gravity  is  uniform  in  any  place.  A  field  of  unit  strength 
is  one  which  acts  on  a  unit  pole  with  a  force  equal  to  that  of  a  dyne  (709). 
The  strength  of  any  magnetic  field  is  measured  by  the  number  of  lines  of 
magnetic  force  present  in  the  field. 

The  expression  '  lines  of  force  '  or '  lines  of  magnetic  force '  is  used  in  much 
the  same  sense  as  that  in  which  we  speak  of  rays  of  light.  And  just  as  we 
may  express  the  illumination  of  a  surface  by  the  number  of  rays  of  light 
which  fall  upon  it,  so  also  we  may  say  that  the  strength  of  any  magnetic 
surface  is  proportional  to  the  number  of  lines  of  force  which  it  cuts. 

We  have  seen  that  in  speaking  of  the  pendulum  we  distinguish  between  a 
simple  and  a  compound  one  (79).  The  laws  of  the  pendulum  apply  in  strict- 
ness only  to  the  former,  which  in  practice  cannot  be  realised,  although  we 
])ossess  arrangemenls  which  produce  the  same  cfTcct  as  a  simple  pendulum, 
and  are  equivalent  to  it.  So  too  in  magnetism  we  may  discriminate  between 
an  ideal  and  an  actual  magnet ;  the  former  being  considered  as  a  long, 
infinitely  thin,  bar  of  magnetised  molecules,  to  which  only  do  the  laws  of 
magnetic  action    in   strictness  apply,  although  they   can  be  realised  with 


-707J  Magnetic  Definitions.  6jt, 

ordinary  magnets  with  sufficient  approximation.  Thus  in  the  action  of 
magnets  at  a  distance  we  may  assume  that  all  the  magnetism  is  concen- 
trated in  the  poles,  provided  that  the  length  is  three  to  four  hundred  times 
the  diameter,  or  provided  the  fourth  power  of  half  the  length  of  the  magnet 
may  be  disregarded  in  comparison  with  the  distance  at  which  it  acts  (708). 

In  a  magnet  the  magnetic  moment  is  the  product  of  the  length  of  the 
magnet  into  the  strength  of  one  pole. 

If  a  magnetic  body  be  placed  in  a  magnetic  field,  the  intensity  of  the 
magnetisation  which  it  acquires  will  be  proportional  to  the  strength  of  the 
field,  and  to  a  coefficient  k,  which  depends  on  the  material  itself  and  which 
is  called  the  coefficient  of  magnetisation.  Bodies  such  as  soft  iron,  which  are 
readily  magnetised,  are  said  to  have  great  susceptibility  to  magnetisation. 

The  magnetic  moment  of  a  bar  divided  by  its  mass  represents  the 
specific  magnetism. 

The  intensity  of  magnetisation  in  a  bar,  assumed  to  be  uniformly 
magnetised,  is  the  magnetic  moment  divided  by  the  volume,  that  is  to  say 
the  weight  in  grammes  divided  by  the  specific  gravity. 

The  ratio  of  the  total  magnetic  induction  to  the  force  producing  it  has 
been  called  by  Sir  W.  Thomson  the  magnetic  perineability  of  a  substance, 
and  is  represented  by  the  symbol  /x.  It  represents  in  magnetism  the  specific 
inductive  capacity  of  dielectrics  (745),  and  may  be  regarded  as  expressing 
the  magnetic  inductive  capacity,  or  magnetic  conductivity  for  lines  of  force. 

708.  Total  action  of  two  magrnets  on  eacb  other. — In  the  above  case 
of  the  torsion  balance  one  pole  of  the  magnet  to  be  tested  was  at  so  great 
a  distance  that  it  could  not  appreciably  modify  the  influence  of  the  other. 
When,  however,  the  conditions  are  such  that  both  poles  act,  then  they  follow 
a  different  law,  as  will  now  be  demonstrated. 

Let  ns  (fig.  647)  be  a  small  magnetic  needle,  free  to  move  in  a  horizontal 
plane,  and  let  NS  be  a  bar  magnet  placed  at  right  angles  to  the  magnetic 
meridian,  at  a  distance  which  is  great  compared 
with  its  own  dimensions,  not  less  than  ten  times  as 
great,  and  so  that  the  straight  line  drawn  through 
its  middle  point  and  that  of  the  needle  coincides 
with  the  magnetic  meridian.  In  this  position  the 
magnet  NS  is  said  to  be  'broadside  on.'  The  two 
poles  S  and  s  will  repel  each  other  in  the  direction 
sa  ;  if  mm^  is  the  repellent  force  which  these  two 

poles  would  exert  at  the  unit  distance,  then  — ^'  is 

the  force  which  they  would  exert  at  the  distance 
Sj-  =  r;  let  this  force  be  represented  in  direction 
and  strength  by  the  line  sa.  Similarly,  the  pole  N 
will  act  on  j,  with  a  force  represented  by  the  line 
sc ;  S  and  N  being  at  the  same  distance  r  from  j-, 
sa  and  sc  are  equal,  and  their  resultant  may  be 
represented  by  the  line  sb.  From  the  similarity  of 
the  triangles  (^i-^  and  NSj-  we  have  the  proportion  Sj  :  SN  =rt5- : /;.? ;  if 
/  is  the  value  of  the  resultant  bs,  that  is  the  total  action  of  the  magnet 
SX    on    the    pole   s.,  and  if  /  be  half  the  length   of  the  magnet    SX,   we 

X  X 


6/4  Oyt  Magnetism.  [708- 

have  r\zl=  -"'^  :  f,  from  which  /=3^^^;  that  is,  the  total  action  of  the 

magnet  NS  upon  another  magnet  is  inversely  as  the  cube  of  the  distance  r. 

If  the  two  magnets  be  placed  'end  on'  as  represented  in  fig.  648,  the 

needle  being  in  the  magnetic  meridian,  and  the  deflecting  magnet  at  right 

71  angles  thereto,  and  so  that  the  pro- 
longation of  its  axis  bisects  the  needle, 
then  if  nun,  is  the  force  with  which  the 
pole  N  attracts  the  pole  s  at  the  unit 
distance,  7/1  and  ni,  being  the  strength 
^'S-  648.  Qf  |.j^g   poles  in  the  bar  magnet  and 

the  magnetic  needle  respectively,  the  attracting  force  at  the  distance  Nj  will 

be    "^"'^  ,  /  being,  as  before,  the  half-length  of  the  magnet,  and ;-  the  distance 

(r+/)- 
of  the  pole  J' from  the  middle  of  the  magnet  NS  ;  in  like  manner  the  repellent 

force  with  which  S  acts  upon  s  willl  be -';,.    If  ns  is  small  compared  with 

the  distance  of  the  bar  magnet  NS,  the  direction  of  these  forces  may  be 
assumed  to  be  parallel,  and  at  right  angles  to  ns.  Since  S  is  nearer  than  N 
the  repulsion  will  predominate,  and  the  total  force  with  which  the  magnet 
NS  acts  on  the  pole  s  is 


F=  — 


in/n. 


which,  assuming  that  /  is  so  small  in  comparison  with  r  that  its  square  and 
higher  powers  may  be  neglected,  gives  approximately 

y  _4  nivi,  I 
so  that  compared  with  the  first  position  of  the  magnet 

F  =  2/ 

709.  Setermlnation  of  mag'netlsm  in  absolute  measure. — The  com- 
parisons of  the  intensity  of  the  earth's  magnetism  in  different  places  (701) 
are  only  relative.  Of  late  years  much  attention  has  been  devoted  to  the 
method  of  expressing  not  only  this,  but  all  other  magnetic  forces  in  what  is 
called  absolute  measure.  This  term  is  used  as  opposed  to  relative,  and  does 
not  imply  that  the  measure  is  absolutely  accurate,  or  that  the  units  of  com- 
parison employed  are  of  perfect  construction  ;  it  means  that  the  measure- 
ments, instead  of  being  a  simple  comparison  with  an  arbitrary  quantity  of  the 
same  kind  as  that  measured,  are  referred  to  the  fundamental  units  of  time, 
length,  and  mass  (21). 

The  units  originally  adopted  on  the  proi)osal  of  the  liritish  Association, 
and  now  almost  universally  received,  are  the  second  as  unit  of  time,  the 
centimetre  as  unit  of  length,  and  the  gramme  as  unit  of  mass.  This  system 
is  called  the  ccntiinctrc-gravime-second,  or  CCS.  system,  and  units  referred 
to  this  system  are  spoken  of  as  C.G.S.  units  (61  a). 

The  manner  in  which  this  determination  is  made  in  the  case  of  magnet- 
ism, depends  essentially  on  the  observation  of  the  oscillation  of  a  horizontal 


-709J    Dctcrmhiatiofi  of  Magnetism  in  Absolntc  Measure.    675 

bar  magnet  under  the  influence  of  the  earth's  magnetism  ;  and  in  the  second 
place,  on  observing  the  deflection  of  a  magnetic  needle  under  the  influence 
of  this  same  magnet. 

When  a  bar  magnet  suspended  by  a  thread  without  torsion,  free  to  oscil- 
late in  a  horizontal  plane,  is  deflected  from  its  position  of  equilibrium  and 
then  left  to  itself,  it  vibrates  backwards  and  forwards  through  its  position  of 
equilibrium,  making  oscillations  which,  if  small,  are  isochronous  like  those  of 
the  pendulum.  The  number  of  these  oscillations  in  a  given  time  depends  on  the 
mass  and  dimensions  of  the  bar,  on  its  magnetic  power,  and  on  the  intensity  of 
the  earth's  magnetism  in  the  place  of  obser\ation.    The  time,  /,  of  a  complete 

oscillation  of  such  a  magnet  is  represented  by  the  formula  t^in xl 

where  k  is  the  moment  of  inertia  of  the  magnet ;  that  is,  the  mass  which 
must  be  concentrated  at  the  unit  of  distance  from  the  centre  of  suspension, 
to  present  the  same  resistance  to  change  of  angular  velocity,  about  this  centre, 
as  the  magnet  itself  actually  does.  The  moment  of  inertia  of  a  magnet  may 
be  determined  theoretically  if  it  be  homogeneous  in  structure,  and  of  a 
regular  geometrical  shape  ;  or  it  may  be  determined  experimentally  by  first 
observing  the  time  of  oscillation  of  the  magnet  under  the  influence  of  the 
earth's  magnetism,  and  then  the  time  when  it  has  been  loaded  with  a  mass 
the  inertia  of  which  is  knowTi,  and  which  does  not  alter  the  magnetic  moment 
of  the  bar.  M  is  the  magnetic  moment  of  the  bar  itself,  and  H  is  the  force 
of  the  earth's  magnetism.     Hence 

HM^^';^ (I). 

This  expression  gives  the  force  which,  applied  in  opposite  directions  at 
the  ends  of  a  lever  of  unit  length,  placed  at  right  angles  to  the  direction  of 
this  force,  would  have  the  same  eftect  in  tending  to  turn  the  lever,  as  the 
magnetic  force  of  the  earth  has  in  tending  to  turn  the  magnet  about  a  vertical 
axis  when  it  is  set  at  right  angles  to  the  magnetic  meridian. 

Now  the  value  of  HM  depends  on  the  nature  of  the  bar,  and  on  the  force 
of  the  earth's  magnetism  in  the  place  in  question.  If  the  bar  were  mag- 
netised more  or  less  strongly,  or  if  the  same  bar  were  removed  to  a  different 
locality,  the  product  would  have  a  different  value.  We  must,  therefore,  find 
some  independent  relation  between  H  and  AI,  which  will  give  rise  to  a  new 
equation,  and  thus  M,  the  magnetic  moment  of  the  bar,  would  be  got  rid  of, 
and  an  absolute  value  be  obtained  for  H. 

Such  a  relation  exists  in  the  deflection  from  the  magnetic  meridian,  which 
a  bar  magnet  produces  in  a  magnetic  needle. 

If,  in  the  formula  in  the  preceding  article,  we  put  M  =  2w/,  then—  '^  = 

the  +  or  -  force  acting  on  either  pole  of  the  magnetic  needle,  and,  as  both 
poles  are  acted  on,  the  magnet  will  be  subject  to  the  action  of  a  couple,  the 

moment  of  which  will  be  expressed  by — — -^  2/,  cos  a  ;  where  a  is  the  angle 

of  deflection,  /  the  half-length  of  the  small  magnetic  needle  ;  let  M,  =  2m J. 
In  like  manner  the  earth's  magnetism  will  act  upon  the  magnetic  needle 
with  a  couple,  the  moment  of  which  is  expressed  by  Hw,  2/ sin  «  =  HM 

X  X  J 


6^6  On  Magnetism.  [709- 

sin  a.     Now  when  the  needle  is  in  equihbrium  these  forces  are  equal  ;  that 
is — 

^il!^cosa  =  HM   sina, 

from  which  %—  =  r'  tan  a (2). 

rl 

Combining  (i)  and  (2)  we  get  the  expression 


«  =  ?\/. 


r^  tan  a 

an  expression  which  involves  no  other  physical  units  than  those  of  length 
(involved  in  k  and  r),  mass  (involved  in  y^),  and  time  (involved  in  /),  so  that 
the  value  of  H  can  be  expressed  in  absolute  measure. 

The  value  for  H  in  this  expression  only  gives  the  horizontal  compo- 
nent of  the  earth's  magnetism  ;  the  total  force  is  obtained  by  dividing  the 
value  of  H  by  the  cosine  of  the  angle  of  dip  for  the  place  and  time  of  ob- 
servation.    This  varies  on  the  earth's  surface  from  0-3  to  07. 

The  numerical  value  of  H  will  depend,  moreover,  on  the  units  taken. 
On  the  C.G.S.  system  the  unit  of  force  is  called  a  dyne.  It  is  (as  we  have 
seen,  61  a)  the  force  which  acting  upon  a  gramme  for  a  second  g'enerates  a 
velocity  of  a  centimetre  per  second.  The  value  of  H  at  Greenwich  for  the 
year  1877,  expressed  in  this  unit,  is  0-18079  of  a  dyne;  that  is,  the  horizontal 
component  of  the  earth's  magnetism  at  this  place  acting  on  the  unit  of 
magnetism,  associated  with  one  gramme  of  matter,  would  produce  a  velocity 
of  0-18079  centimetre  at  the  end  of  a  second.  The  angle  of  dip  at  this 
time  and  place  being  67°  y]'.,  we  get  the  total  force  =0-4745  ""it.  If 
British  units — namely,  the  foot,  grain,  second— be  employed,  the  unit  of 
force  is  that  which  by  acting  for  a  second  on  a  grain  gives  to  it  a  velocity 
of  a  foot  per  second,  and  the  unit  magnetic  pole  is  such  that  if  placed  one 
foot  from  a  second  equal  pole  it  will  repel  it  with  a  force  equal  to  the  unit 
just  defined.  To  convert  the  value  of  H,  when  expressed  in  centimetres, 
grammes,  and  seconds,  into  the  equivalent  value  referred  to  British  units,  we 
must  multiply  by  21-69.  In  like  manner,  to  convert  magnetic  forces  referred 
to  British  units   into  the  corresponding  values    e.xpressed    in  centimetres, 

grammes,  and  seconds  we  must  multiply  by  0-0461   =  -    '  -. 

2 1  -69 
If  once  the  value  of  H  in  any  locality  has  been  determined  it  is  easy  to 
determine  the  value  of  M  for  any  magnet  ;  it  is  by  experiments  of  this  kind 
that  the  magnetic  movement  of  minerals  is  arrived  at. 


-713] 


677 


CHAPTER    IV. 

PROCESSES   OF   MAGNETISATION. 


710.  Magnetisation. — The  various  methods  of  magnetisation  are  the 
influence  of  natural  or  artificial  magnets,  terrestrial  magnetism,  and  elec- 
tricity. This  last  method  will  be  described  under  voltaic  electricity.  The 
three  principal  methods  of  magnetisation  by  magnets  are  known  by  the 
technical  names  of  single  toiic/t,  sepa?'ate  touch,  and  double  touch. 

711.  Metbod  of  sing-le  toucta. — This  consists  in  moving  the  pole  of  a 
powerful  magnet  from  one  end  to  the  other  of  the  bar  to  be  magnetised,  and 
repeating  this  operation  several  times  always  in  the  same  direction.  The 
neutral  magnetism  is  thus  gradually  decomposed  throughout  all  the  length 
of  the  bar,  and  that  end  of  the  bar  which  was  touched  last  by  the  magnet  is 
of  opposite  polarity  to  the  end  of  the  magnet  by  which  it  has  been  touched. 
This  method  only  produces  a  feeble  magnetic  power,  and  is,  accordingly, 
only  used  for  small  magnets.  It  has  further  the  disadvantage  of  frequently 
developing  consequent  poles. 

712.  IKXetbod  of  separate  toucb. — This  method,  which  was  first  used 
by  Dr.  Knight  in  1745,  consists  in  placing  the  two  opposite  poles  of  two 
magnets  of  equal  force  in  the  middle  of  the  bar  to  be  magnetised,  and  in 
moving  each  of  them  simultaneously  towards  the  opposite  ends  of  the  bar. 
Each  magnet  is  then  placed  in  its  original  position  and  the  operation  re- 
peated.    After  several  frictions  on  both  faces  of  the  bar  it  is  magnetised. 

In  Knight's  method  the  magnets  are  held  vertically.  Duhamel  improved 
the  method  by  inclining  the  magnets,  as  represented  in  fig.  649  ;  and  still 


Fig.  649. 

more  by  placing  the  bar  to  be  magnetised  on  the  opposite  poles  of  two  fixed 
magnets,  the  action  of  which  strengthens  that  of  the  movable  magnets.  The 
relative  position  of  the  poles  of  the  magnets  is  indicated  in  the  figure.  This 
method  produces  the  most  regular  magnets. 

713.  Metbod  of  double  toucb. — In  this  method,  which  was  invented  by 
Mitchell,  the  two  magnets  are  placed  with  their  poles  opposite  each  other 
in  the  middle  of  the  bar  to  be  magnetised.  But,  instead  of  moving  them  in 
opposite  directions  towards  the  two  ends,  as  in  the  method  of  separate  touch, 


6/8  On  Magnetism.  [713- 

they  are  kept  at  a  fixed  distance  by  means  of  a  piece  of  wood  placed  between 
them  (fig.  649),  and  are  simultaneously  moved  first  towards  one  end,  then 
from  this  to  the  other  end,  repeating  this  operation  several  times,  and  finish- 
ing in  the  middle,  taking  care  that  each  half  of  the  bar  receives  the  same 
number  of  frictions. 

Epinus,  in  1758,  improved  this  method  by  supporting  the  bar  to  be  mag- 
netised, as  in  the  method  of  separate  touch,  on  the  opposite  poles  of  two 
powerful  magnets,  and  by  inclining  the  bars  at  an  angle  of  15°  to  20°.  In 
practice,  instead  of  two  bar  magnets,  it  is  usual  to  employ  a  horse-shoe 
magnet  which  has  its  poles  conveniently  close  together. 

By  this  method  of  double  touch,  powerful  magnets  are  obtained,  but  they 
have  frequently  consequent  poles.  As  this  would  be  objectionable  in  com- 
pass needles,  these  are  best  magnetised  by  separate  touch. 

714.  Mag-netisatlon  by  the  action  of  the  earth. — The  action  of  the 
earth  on  magnetic  substances  resembles  that  of  a  magnet,  and  hence  the 
terrestrial  magnetism  is  constantly  tending  to  separate  the  two  magnetisms 
in  soft  iron  and  in  steel.  But  as  the  coercive  force  is  very  considerable  in 
the  latter  substance,  the  action  of  the  earth  is  inadequate  to  produce  mag- 
netisation, except  when  continued  for  a  long  time.  This  is  not  the  case 
with  perfectly  soft  iron.  When  a  bar  of  this  metal  is  held  in  the  magnetic 
meridian  parallel  to  the  inclination,  the  bar  becomes  at  once  endowed  with 
feeble  magnetic  polarity.  The  lower  extremity  is  a  north  pole,  and  if  the 
north  pole  of  a  small  magnetic  needle  be  approached,  it  will  be  repelled. 
This  magnetism  is  of  course  unstable,  for  if  the  bar  be  turned  the  poles  are 
inverted,  as  pure  soft  iron  is  destitute  of  coercive  force. 

While  the  bar  is  in  this  position,  a  certain  amount  of  coercive  force  may 
be  imparted  to  it  by  giving  it  several  smart  blows  with  a  hammer,  and  the 
bar  retains  for  a  short  time  the  magnetism  which  it  has  thus  obtained.  But 
the  coercive  force  thus  developed  is  very  small,  and  after  a  time  the  mag- 
netism disappears. 

If  a  bar  of  soft  iron  be  twisted  while  held  vertically,  or,  better,  in  the 
plane  of  the  dip,  it  acquires  a  feeble  permanent  magnetism. 

It  is  this  magnetising  action  of  the  earth  which  develops  the  magnetism 
frequently  observed  in  steel  and  iron  instruments,  such  as  fireirons,  rifles, 
lamp-posts,  railings,  gates,  lightning  conductors,  &;c.,  which  remain  for  some 
time  in  a  more  or  less  inclined  position.  They  become  magnetised  with  their 
north  pole  downwards,  just  as  if  placed  over  the  pole  of  a  powerful  magnet. 
The  magnetism  of  native  black  oxide  of  iron  (680)  has  doubtless  been  pro- 
duced by  the  same  causes  ;  the  very  dififcrent  magnetic  power  of  different 
specimens  being  partly  attributable  to  the  ditiferent  positions  of  the  veins  of 
ore  with  regard  to  the  line  of  dip.  The  ordinary  irons  of  commerce  are  not 
quite  pure,  and  possess  a  feeble  coercive  force  ;  hence  a  feeble  magnetic 
polarity  is  generally  found  to  be  possessed  by  the  tools  in  a  smith's  shop. 
Cast-iron,  too,  has  usually  a  great  coercive  force,  and  can  be  permanently 
magnetised.  The  turnings,  also,  of  wrought  iron  and  of  steel  produced  by 
the  powerful  lathes  of  our  ironworks  are  found  to  be  magnetised. 

7 1  5.  Magrnetlsxn  of  Iron  ships. — The  inductive  action  of  terrestrial  mag- 
netism upon  the  masses  of  iron  always  found  in  ships  exerts  a  disturbing 
action  upon  the  compass  needle.     The  local  attraction,  as  it  is  called,  may 


-715]  Magnetism  of  Iron  Ships.  679 

be  so  considerable  as  to  render  the  indications  of  the  needle  almost  useless 
if  it  be  not  guarded  against.  A  full  account  of  the  manner  in  which  local 
attraction  is  produced,  and  in  which  it  is  compensated,  is  inconsistent  with 
the  limits  of  this  book,  but  the  most  important  points  are  the  following  : — 

i.  A  vertical  mass  of  soft  iron  in  the  vessel,  say  in  the  bows,  would 
become  magnetised  under  the  influence  of  the  earth  ;  in  the  northern  hemi- 
sphere, the  lower  end  would  be  a  north  pole,  and  the  upper  end  a  south 
pole  ;  and  as  the  latter  may  be  assumed  to  be  nearer  the  north  pole  of  the 
compass  needle,  its  action  would  preponderate.  So  long  as  the  vessel  was 
sailing  in  the  magnetic  meridian  this  would  have  no  effect ;  but  in  any  other 
direction  the  needle  would  be  drawn  out  of  the  magnetic  meridian,  and  a  little 
consideration  will  show  that  when  the  ship  was  at  right  angles  to  the  magnetic 
meridian  the  effect  would  be  greatest.  This  vertical  uiduction  would  disap- 
pear twice  in  swinging  the  ship  round,  and  would  be  at  its  maximum  twice  ; 
hence  the  deviation  due  to  this  cause  is  knowai  as  semicircular  deviation. 

ii.  Horizontal  masses  again,  such  as  deck  beams,  are  also  acted  upon 
inductively  by  the  earth's  magnetism,  and  their  induced  magnetism  exerts 
a  disturbing  influence  upon  the  magnetic  needle.  The  effect  of  this  hori- 
zontal induction  will  disappear  when  the  ship  is  in  the  magnetic  meridian 
and  also  when  it  is  at  right  angles  thereto.  In  positions  intermediate  to  the 
above  the  disturbing  influence  will  attain  its  maximum.  Hence  in  swinging 
a  ship  round  there  would  be  four  positions  of  the  ship's  head  in  which  the 
influence  would  be  at  a  maximum,  and  four  in  which  it  would  be  at  a  mini- 
mum. The  effect  of  horizontal  induction  is  accordingly  spoken  of  as  quad- 
7-antal  dei'iatioti. 

The  influence  of  both  these  causes,  vertical  and  horizontal  induction, 
may  be  remedied  in  the  process  of  '  swinging  the  ship.'  This  consists  in 
comparing  the  indications  of  the  ship's  compass  with  those  of  a  standard 
compass  placed  on  shore.  The  ship  is  then  swung  round  in  various  posi- 
tions, and  by  arranging  small  vertical  and  horizontal  masses  of  soft  iron  in 
proximity  to  the  steering  compass,  positions  are  found  for  them  in  which  the 
inductive  action  of  the  earth  upon  them  quite  neutralises  the  influence  of  the 
earth's  magnetism  upon  the  ship  ;  and  in  all  positions  of  the  ship,  the  com- 
pass points  in  the  same  direction  as  the  one  on  shore. 

iii.  The  extended  use  of  iron  in  ship-building,  more  especially  when  the 
frames  are  entirely  of  iron,  has  increased  the  difficulty.  In  the  process  of 
building  a  ship,  the  hammering  and  other  mechanical  operations  to  which 
it  is  subject,  while  under  the  influence  of  the  earth's  magnetism,  will  cause 
it  to  become  to  a  certain  extent  permanently  magnetised.  The  distribution 
of  the  magnetism,  the  direction  of  its  magnetic  axis,  will  depend  on  the 
position  in  which  it  has  been  built ;  it  may  or  may  not  coincide  with  the 
direction  of  the  keel.  The  vessel  becomes,  in  short,  a  huge  magnet,  and 
will  exert  an  influence  of  its  own  upon  the  compass  quite  independently  of 
vertical  or  horizontal  induction.  The  influence  is  semicircular ;  that  is,  it 
•disappears  when  the  magnetic  axis  of  the  ship  is  in  the  magnetic  meridian, 
and  is  greatest  at  right  angles  to  it.  It  may  be  compensated  by  two  permanent 
magnets  placed  near  the  compass  in  suitable  positions  found  by  trial  during 
the  process  of  swinging  the  ship.  Supposing  the  inherent  magnetism  of  the 
ship  to  have  the  power  of  drawing  the  compass  a  point  to  the  east,  the  com- 


68o  On  Magnetism.  [715- 

pensating  magnets  may  be  so  arranged  as  to  tend  to  draw  it  a  point  to  the 
west,  and  thus  keep  it  in  the  magnetic  meridian.  If,  however,  the  inherent 
magnetism  be  destroyed,  from  whatever  cause,  it  is  clear  that  the  magnets 
will  now  draw  it  aside  a  point  too  much  to  the  west.  This  is  the  source  of  a 
new  difficulty.  It  has  been  found  that  a  ship  which  at  the  time  of  sailing 
was  properly  compensated,  would,  on  returning  from  a  long  voyage,  have  its 
compasses  over-compensated.  The  buffeting  which  the  ship  had  experienced 
had  destroyed  its  inherent  magnetism,  and  numerous  instances  are  known 
where  the  loss  of  a  vessel  can  be  directly  traced  to  this  cause.  Fortunately, 
it  has  been  found  that  after  some  time  a  ship's  magnetic  condition  is  virtu- 
ally permanent,  and  is  unaltered  by  any  further  wear  and  tear.  The  mag- 
netism which  it  then  retains  is  called  its  ^^r;/zrt;;z^;// magnetism,  in  opposition 
to  the  siib-perina7ient  which  it  loses. 

The  difficulty  of  adequately  compensating  compasses,  which  is  greatly 
increased  by  the  armour-plated  and  turret  ships  now  in  use,  has  induced  one 
school  to  throw  over  any  attempt  at  correction  ;  but  by  careful  observation 
of  the  magnetic  condition  of  a  ship,  and  tabulating  the  errors  to  construct  a 
table,  and  comparing  this  with  the  indications  of  the  compass  at  any  one 
time,  the  true  course  can  be  made  out. 

In  the  Royal  Navy,  the  plan  now  adopted  is  to  combine  both  methods  : 
compensate  the  errors  to  a  considerable  extent,  and  then  construct  a  table 
of  the  residual  errors. 

716.  Mag-netic  saturation. — Experiment  has  shown  that  with  feeble 
magnetising  power  the  magnetic  force  which  can  be  imparted  to  a  steel  bar 
increases  with  the  magnetising  force  used.  It  depends  also  on  the  number  of 
strokes  or  movements  of  the  magnetismg  magnets  or  coils  :  on  the  form  and 
dimensions  of  the  bar,  on  its  density,  on  the  quantity  of  carbon  it  contains,  on 
its  hardness,  and  on  the  manner  in  which  it  is  tempered.  Yet  there  is  a  limit 
to  the  magnetic  force  which  can  be  imparted  to  iron  or  steel,  and  when  this 
is  attained,  the  bar  is  said  to  be  saturated  or  magnetised  to  saturatiojj.  A 
bar  may  indeed  be  magnetised  beyond  this  point,  but  this  excess  is  tem- 
porary ;  it  gradually  diminishes  until  the  magnet  has  sunk  to  its  point  of 
saturation. 

This  is  intelligible,  for  the  magnetisms  once  separated  tend  to  reunite, 
and  when  their  attractive  force  is  equal  to  that  which  opposes  their  separa- 
tion—that is,  the  coercive  force  of  the  metal — equilibrium  is  attained,  and 
tlie  magnet  is  saturated.  Hence,  more  magnetism  ought  to  be  developed 
in  bars  than  they  can  retain,  in  order  that  they  may  decline  to  their  perma- 
nent state  of  saturation.  To  increase  the  magnetism  of  an  unsaturated  bar, 
a  less  feeble  magnet  must  not  be  used  than  that  by  which  it  was  originally 
magnetised. 

In  order  to  attain  a  stationary  condition,  the  magnet  should  be  heated  to 
boiling  for  some  time  after  being  magnetised  ;  it  should  then  be  remagnetised 
and  again  heated  to  boiling,  and  so  forth  ;  and  after  the  last  magnetisation 
it  sliould  be  Ijoiled  for  six  hours  or  more.  Such  magnets  are  far  more  durable 
than  ordinary  ones. 

717.  Mag-netlc  battery. — A  magnetic  battery  or  maga::ine  consists  of 
a  number  of  magnets  joined  together  by  their  similar  poles.  Sometimes 
they  have  the  form  of  a  horse-shoe,  and  sometimes  a  rectilinear  form.     The 


-718]  Armatures.  68 1 

battery  represented  in  fig.  650  consists  of  five  superposed  steel  plates.  That 
in  fig.  651  consists  of  twelve  plates,  arranged  in  three  layers  of  four  each. 
The  horse-shoe  form  is  best  adapted  for  supporting  a  weight,  for  then  both 
poles  are  used  at  once.  In  both  the  bars  are  magnetised  separately,  and 
then  fixed  by  screws. 

The  force  of  a  magnetic  battery  consisting  of  ;/  similar  plates  equally 
magnetised,  is  not  n  times  as  great  as  that  of  a  single  one,  but  is  somewhat 
smaller.  These  magnets  mutually  en- 
feeble each  other  ;  manifestly  because, 
for  instance,  each  north  pole  evokes 
south  magnetism  in  the  adjacent  north 
pole,  and  thereby  diminishes  some  of  its 
north  polarity.  At  the  same  time  the 
strength  is  greater  than  if  the  steel  is  in 
one  coherent  mass  ;  the  reason  doubtless 
is  that  thin  plates  of  steel  are  more  easily 
magnetised  to  saturation  than  thick  ones, 
as  the  inducing  action  does  not  extend 
deep.  The  separate  plates  should  not 
be  in  contact,  as  the  enfeeblement  of  the 
magnetism  is  thereby  less.  It  is  also  ad- 
visable to  connect  the  pieces  by  a  mass 
of  soft  iron  as  shown  in  fig.  651.  The 
magnetism  of  a  plate  which  has  formed 
part  of  such  a  batterj'  will  be  found  to 
be  materially  less  than  it  was  originally. 
Thus  Jamin  found  that  six  equal  plates 
which  separately  had  each  the  portative 
force  18  kilos,  only  lifted  64  kilos  when 
arranged  as  a  battery,  instead  of  108  ;  and  when  removed  from  the  battery, 
each  of  them  had  only  the  portative  force  9  to  10  kilos.  The  force  is  in- 
creased by  making  the  lateral  plates  i  or  2  centimetres  shorter  than  the  one 
in  the  middle  (fig.  650). 

718.  Armatures. — When  even  a  steel  bar  is  at  its  limit  of  saturation,  it 
gradually  loses  its  magnetism.  To  prevent  this,  armatures  or  keepers  are 
used  ;  these  are  pieces  of  soft  iron,  A  and  B  (fig.  651),  which  are  placed  in 
contact  with  the  poles.  Acted  on  inductively,  they  become  powerful  tem- 
porary magnets,  possessing 
opposite  polarity  to  that  of 
the  inducing  pole  ;  they  thus 
react  in  turn  on  the  perma- 
nent magnetism  of  the  bars, 
preserving  and  even  increas- 
ing it. 

\Mien  the  magnets  are  in 
the   form    of  bars,  they  are 

arranged  in  pairs,  as  shown  ^^'   ^" 

in  fig.  652,  with  opposite  poles  in  juxtaposition,  and  the  circuit  is  com])leted 
by  two  small  bars  of  soft  iron,  AB.    Movable  magnetic  needles,  if  not  clamped 


Fig.  650. 


682 


Oft  Magnetism.  [718- 

down,  set  spontaneously  towards  the  magnetic  poles  of  the  earth,  the  influ- 
ence of  which  acts  as  a  keeper. 

A  horse-shoe  magnet  has  a  keeper  attached  to  it,  which  is  usually 
arranged  so  as  to  support  a  weight.  The  keeper  becomes  magnetised  under 
the  influence  of  the  two  poles,  and  adheres  with  great  force  :  the  weight 
which  it  can  support  being  more  than  double  that  which  a  single  pole  would 
hold. 

In  respect  to  this  weight,  a  singular  and  hitherto  inexplicable  pheno- 
menon has  been  observed.  When  contact  is  once  made,  and  the  keeper  is 
charged  with  its  maximum  weight,  any  further  addition 
would  detach  it  :  but  if  left  in  contact  for  a  day,  an 
additional  weight  may  be  added  without  detaching 
it,  and  by  slightly  increasing  the  weight  every  day  it 
may  ultimately  be  brought  to  support  a  far  greater 
load  than  it  would  originally.  But  if  contact  be  once 
broken,  the  weight  it  can  now  support  does  not  much 
exceed  its  original  charge. 

It  is  advantageous  that  the  surface  of  the  magnet 
and  armatures  which  are  in  contact  should  not  be 
plane  but  slightly  cylindrical,  so  that  they  touch  along 
a  line. 

In  providing  a  natural  magnet  with  a  keeper,  the 
line  joining  the  two  poles  may  first  be  approximateh^ 
determined  by  means  of  iron  filings  ;  it  may  also  be 
determined  by  bringing  it  near  a  magnetic  needle,  and 
ascertaining  the  positions  in  which  its  action  is  greatest 
(708).  Two  poles  of  soft  iron  (fig.  653),  each  terminating  in  a  massive  shoe, 
are  then  applied  to  the  faces  corresponding  to  the  poles.  Under  the  in- 
fluence of  the  natural  magnet,  these  plates  become  magnetised,  and  if  the 
letters  A  and  B  represent  the  position  of  the  poles  of  the  natural  magnet, 
the  poles  of  the  armature  are  a  and  b. 

719.  Portative  force.  Power  of  mag-nets. — The  poj'tative  force  is 
the  greatest  weight  which  a  magnet  can  support.  Hacker  found  that  the 
portative  force  of  a  saturated  horse-shoe  magnet,  which,  by  repeatedly  de- 
taching the  keeper,  had  become  constant,  may  be  represented  by  the  formula 

in  which  P  is  the  portative  force  of  the  magnet,  j?^  its  own  weight,  and  a  a 
coefficient  which  varies  with  the  nature  of  the  steel  and  the  mode  of  mag- 
netising. Hence  a  magnet  which  weighs  1000  ounces  only  supports  25 
times  as  much  as  one  weighing  8  ounces  or  ^.^^  as  heavy,  and  25  such  bars 
would  support  as  much  as  a  single  one  which  is  as  heavy  as  125  of  them. 
It  appears  immaterial  whether  the  section  of  the  bar  is  quadratic  or  circular, 
and  the  distance  of  the  legs  is  of  inconsiderable  moment  ;  it  is  important 
however,  that  the  magnet  be  suspended  vertically,  and  that  the  load  be 
exactly  in  the  middle.  In  Hacker's  magnets  the  value  o{  a  was  10-33,  while 
in  Logemann's  it  was  23.  By  arranging  together  several  thin  magnetised 
j)latcs  Jamin  constructed  bar  magnets  which  sujiport  15  times  their  own 
wciiiht. 


Fig.  653' 


-720]    Circumstances  ivhicJi  influence  the  Power  of  Magnets.    683 

The  strength  of  two  bar  magnets  may  be  compared  by  the  following 
simple  method,  which  is  known  as  Kiilp's  compensation  method : — A  small 
magnetic  compass  needle  is  placed  in  the  magnetic  meridian.  One  pole 
of  one  of  the  magnets  to  be  tested  is  then  placed  at  right  angles  to  the 
magnetic  meridian  in  the  same  plane  as  the  needle,  and  so  that  its  axis  pro- 
longed would  bisect  the  needle.  The  compass  needle  is  thereby  deflected 
through  a  certain  angle.  The  similar  pole  of  the  other  magnet  is  then 
placed  similarly  on  the  other  side  of  the  needle,  and  a  position  found  for 
it  in  which  it  exactly  neutralises  the  action  of  the  first  magnet ;  that  is, 
when  the  needle  is  again  in  the  magnetic  meridian.  If  the  magnets  are  not 
too  long,  compared  with  their  distance  from  the  needle,  their  strengths  are 
approximately  as  the  cubes  of  the  distance  of  the  acting  poles  from  the 
magnetic  needle. 

720.  Circumstances  which  influence  the  power  of  mag'nets. — All  bars 
do  not  attain  the  same  state  of  saturation,  for  their  coercive  force  varies. 
Twisting  or  hammering  imparts  to  iron  or  steel  a  considerable  coercive  force. 
But  the  most  powerful  of  these  influences  is  the  operation  of  tempering  (94). 
Coulomb  found  that  a  steel  bar  tempered  at  dull  redness,  and  magnetised  to 
saturation,  made  ten  oscillations  in  93  seconds.  The  same  bar  tempered  at 
a  cheny-red  heat,  and  similarly  magnetised  to  saturation,  only  took  63 
seconds  to  make  ten  oscillations. 

Hence  it  would  seem  that  the  harder  the  steel  the  greater  is  its  coercive 
force  ;  it  undergoes  magnetisation  with  much  greater  difficulty,  but  retains 
it  more  effectually.  It  appears,  however,  from  Jamin's  experiments  that  no 
such  general  rule  of  this  kind  can  be  laid  down  ;  for  each  specimen  of  steel 
there  seems,  according  to  the  proportion  of  carbon  which  it  contains,  to  be 
a  certain  degree  of  tempering  which  is  most  favourable  for  the  development 
of  permanent  magnetisation. 

\'ery  hard  steel  bars  have  the  disadvantage  of  being  very  brittle,  and  in 
the  case  of  long  thin  bars  a  hard  tempering  is  apt  to  produce  consequent 
poles.  Compass  needles  are  usually  tempered  at  the  blue  heat— that  is, 
about  300°  C— by  which  a  high  coercive  force  is  obtained  without  great 
fragility.  Steel  is  magnetised  with  difficulty  even  when  placed  for  some 
time  in  a  coil  through  which  a  powerful  current  is  passing  ;  soft  iron  under 
these  circumstances  is  magnetised  at  once.  If  a  short  coil  covering  only  a 
portion  of  the  steel  bars  be  moved  backwards  and  forwards  the  magnetisa- 
tion is  more  complete. 

The  hardness  of  steel,  and  the  proportion  of  carbon  which  it  contains, 
exert  an  important  influence  on  the  degree  to  which  it  can  be  magnetised. 
For  the  same  degree  of  hardness,  the  magnetisation  increases  with  the  pro- 
portion of  carbon  in  the  steel,  and  more  markedly  the  smaller  this  propor- 
tion ;  with  the  same  proportion  of  carbon  it  increases  with  the  hardness  of 
the  steel.  It  appears  probable  that  the  compound  of  iron  and  carbon  in 
steel  is  the  carrier  of  the  permanent  magnetisation,  and  the  interjacent 
particles  of  iron  the  carriers  of  the  temporary  magnetisation.  Holtz  mag- 
netised plates  of  English  corset  steel  to  saturation  and  determined  their 
magnetic  moment  ;  they  were  then  placed  in  dilute  hydrochloric  acid,  by 
which  the  iron  was  eaten  away,  and  the  magnetic  moment  determined  when 
the  plate  had  been  magnetised  to  saturation  after  each  such  treatment.     It 


684  On  Magnetism.  [720- 

was  thus  found  that,  with  a  diminution  in  the  proportion  of  iron,  there  was 
an  increase  in  the  magnetic  moment  for  the  unit  of  weight.  HoUz  found, 
however,  that  perfectly  pure  iron  prepared  by  electrolysis  can  acquire  per- 
manent magnetism. 

In  ordinary  bar  magnets  the  intensity  of  magnetisation  (707)  varies  from 
200  to  400  C.G.S.  units,  and  in  very  thin  long  ones  may  attain  800,  or  about 
half  the  maximum  of  soft  iron.  Taking  the  specific  gravity  of  steel  at  7-8, 
the  specific  magnetism  is  25  to  50  for  the  ordinary  magnets.  It  is  here 
supposed  that  the  magnetisation  is  uniform,  which  is  not  the  case. 

Jamin  investigated  the  distribution  of  force  in  magnets  by  suspending 
from  one  arm  of  a  delicate  balance  a  small  iron  ball,  and  then  ascertain- 
ing what  force,  applied  at  the  other  arm,  was  required  to  detach  the 
ball  when  placed  in  contact  with  various  positions  of  the  magnet  to  be 
investigated. 

Taking  thus  a  thin  plate  magnetised  to  saturation,  it  was  found  that  the 
magnetisation  increased  with  the  thickness,  but  did  not  materially  vary 
with  the  breadth  of  the  plate.  The  magnetic  force  was  developed  almost 
exclusively  at  the  ends.  The  curve  representing  the  magnetic  force  (721) 
was  convex  towards  the  poles  at  the  ends.  If  now  several  similar  plates  are 
superposed,  the  corresponding  curves  become  steeper  and  prolonged  towards 
the  middle  ;  the  magnetic  force  thus  becomes  increased.  When  the  curves 
run  into  each  other  in  the  middle  the  maximum  of  the  combination  is  reached  ; 
any  additional  plates  produce  no  increase  in  the  strength.  Steel  bars  may 
also  be  magnetised  so  as  to  show  the  same  curves,  and  such  bars  and  com- 
binations of  plates  are  called  by  Jamin  notvfial  magnets. 

Jamin  found  that  magnetisation  extends  deeper  in  a  bar  than  has  been 
usually  supposed  ;  in  soft  and  annealed  steel  it  penetrates  deeply.  The 
depth  diminishes  with  the  hardness  of  the  steel  and  the  proportion  of  carbon 
it  contains.  If  plates  of  varying  thickness  are  so  thin  that  the  magnetisation 
can  entirely  penetrate  them,  the  thicker  of  these  plates  are  more  strongly  mag- 
netised by  the  same  force,  for  the  magnetisation  extends  through  a  thicker 
layer  than  the  thinner  ones  ;  if,  however,  the  plates  are  very  thick,  they  are 
magnetised  to  the  same  extent  by  one  and  the  same  force.  With  equal  bars 
the  thickness  of  the  magnetic  layer  varies  with  the  strength  of  the  magnetising 
force.  Jamin  proved  this  by  placing  the  plates  in  dilute  sulphuric  acid  ;  he 
found  magnetisation  in  bars  which  had  been  exposed  to  the  stronger  force, 
while  those  which  had  been  more  feebly  magnetised  showed  none  when 
they  had  been  eaten  away  by  the  acid  to  the  same  extent.  He  also  showed 
that  the  magnetisation  which  had  penetrated  was  as  strong  as  that  on  the 
surface. 

Holtzhas  made  some  experiments  on  the  influence  of  solid  bars  as  against 
hollow  tubes  in  the  construction  of  permanent  steel  magnets.  The  latter  are 
to  be  preferred  ;  they  are  decidedly  cheaper,  as  they  need  not  be  bored,  but 
may  be  bent  from  steel  plates.  A  bar  and  a  tube  of  the  same  steel,  125  mm. 
in  length  by  13  mm.  diameter,  the  tube  being  175  mm.  thick,  were  magnetised 
to  saturation,  and  their  magnetic  moments  determined  by  the  method  of 
oscillations  (705),  the  tube  being  loaded  with  c(>p])cr.  The  magnetism  of  the 
tube  was  to  that  of  the  bar  as  i-6  :  1.  The  tul)cs  also  retained  their  mag- 
netisation better.    After  the  lapse  of  six  months  the  ratio  of  the  magnetisation 


-720]    Circiii)ista)iccs  tc/iich  iftflncmc  the  Poiucr  of  Magnets.    685 

of  the  tube  was  to  that  of  the  bar  as  27  :  i.  A  magnetised  steel  tube  filled 
with  a  soft  iron  core  has  scarcely  any  directive  force.  Holtz  considers  that 
it  acts  as  a  keeper. 

Temperature.— \\icxQ-\SQ  of  temperature  always  produces  a  diminution  of 
magnetisation.  If  the  changes  of  temperature  are  small — those  of  the  at- 
mosphere, for  instance — the  magnet  is  not  permanently  altered.  Kuppfer 
allowed  a  magnet  to  oscillate  at  different  temperatures,  and  found  a  definite 
decrease  in  its  power  with  increased  temperature,  as  indicated  by  its  slower 
oscillations.  In  the  case  of  a  magnet  2^  inches  in  length,  he  observed  that 
with  an  increase  of  each  degree  of  temperature  the  duration  of  800  oscillations 
was  0-4"  longer.  If  ;/  be  the  number  of  oscillations  at  zero,  and  n^  the 
number  at  /,  then 

«  = ;/,  ( I  -  f/), 

where  c  is  a  constant  depending  in  each  case  on  the  magnet  used.  This 
formula  has  an  important  application  in  the  correction  of  the  observations 
of  magnetic  force  which  are  made  at  different  places  and  at  different 
temperatures,  and  which,  in  order  to  be  comparable,  must  first  be  reduced 
to  a  uniform  temperature. 

When  a  magnet  has  been  more  strongly  heated,  it  does  not  regain  its 
original  force  on  cooling  to  its  original  temperature  ;  and  when  it  has  been 
heated  to  redness,  it  is  demagnetised.  This  was  first  shown  by  Coulomb, 
who  took  a  saturated  magnet,  heated  it  to  progressively  higher  temperatures, 
and  noted  the  number  of  oscillations  after  each  heating.  The  higher  the 
temperature  to  which  it  had  been  heated  the  slower  its  oscillations. 

A  magnet  heated  to  bright  redness  loses  its  magnetism  so  completely 
that  it  is  quite  indifferent,  not  only  towards  iron,  but  also  towards  another 
magnet,  and  this  holds  so  long  as  this  high  temperature  continues.  Incan- 
descent iron  also  does  not  possess  the  property  of  being  attracted  by  the 
magnet.  Hence  there  is  in  the  case  of  iron  a  magnetic  limit.,  beyond  which 
it  is  unaffected  by  magnetism.  Such  a  magnetic  limit  exists  in  the  case  of 
other  magnetic  metals.  With  cobalt.,  for  instance,  it  is  far  beyond  a  white 
heat,  for  at  the  highest  temperatures  hitherto  examined  it  is  still  magnetic  ; 
the  magnetic  limit  of  chromium  is  somewhat  below  red  heat ;  that  of  tiickel 
at  about  350'  C,  and  oi  ma?iganese  at  about  15°  to  20°  C. 

A  change  of  temperature,  whether  from  16°  to  100°  or  from  100°  to  16°, 
increases  the  strength  of  temporary  or  induced  magnetism  both  in  the  case 
of  iron  and  of  steel. 

Percussion  and  Torsion. — When  a  steel  bar  is  hammered  while  beino- 
magnetised  it  acquires  a  much  higher  degree  of  magnetisation  than  it  would 
without  this  treatment.  Conversely  when  a  magnet  is  let  fall,  or  is  otherwise 
violently  disturbed,  it  loses  much  of  its  magnetisation.  Wiedemann  has  inves- 
tigated in  a  very  complete  manner  the  relations  of  torsion  and  magnetisation. 
Torsion  exerts  a  great  influence  on  the  magnetisation  of  a  bar,  and  the  inter- 
esting phenomenon  has  been  observed  that  torsion  influences  magnetism  in 
the  same  manner  as  magnetism  does  torsion.  Thus  the  permanent  mag- 
netisation of  a  steel  bar  is  diminished  by  torsion,  but  not  proportionally  to 
the  increase  of  torsion.  In  like  manner  the  torsion  of  twisted  iron  wires  is 
diminished  by  their  being  magnetised,  though  less  so  than  in  proportion  to 


686 


Oji  Magnetism. 
Repeated   torsions    in   the 


[721- 


their  magnetisation.  Repeated  torsions  in  the  same  direction  scarcely 
diminish  magnetisation,  but  a  torsion  in  the  opposite  direction  produces  a 
new  diminution  of  the  magnetism.  In  a  perfectly  analogous  manner,  re- 
peated magnetisations  in  the  same  direction  scarcely  diminish  torsion,  but  a 
renewed  magnetisation  in  the  opposite  direction  does  so. 

721.  Bistribution  of  free  mag-netism.— Coulomb  investigated  the  dis- 
tribution of  magnetic  force  by  placing  a  large  magnet  in  a  vertical  position 
in  the  magnetic  meridian  ;  he  then  took  a  small  magnetic 
needle  suspended  by  a  cocoon  thread,  and  fixed  at  right 
angles  to  a  stout  copper  wire  so  as  to  retard  the  oscillations 
(fig.  654)  ;  and  having  ascertained  the  number  of  its  oscilla- 
tions under  the  influence  of  the  earth's  magnetism  alone,  he 
presented  it  to  different  parts  of  the  magnet.  The  oscilla- 
tions were  fewer  as  the  needle  was  nearer  the  middle  of  the 
bar,  and  when  they  had  reached  that  position  their  number 
was  the  same  as  under  the  influence  of  the  earth's  magnetism 
alone.  For  saturated  bars  of  more  than  7  inches  in  length 
*^  .  the  distribution  could  always  be  expressed  by  a  curve  whose 

"'   ^"*'  abscissae  were  the  distances  from  the  ends  of  the  magnet, 

and  whose  ordinates  were  the  force  of  magnetism  at  these  points.  With 
magnets  of  the  above  dimensions  the  poles  are  at  the  same  distance  from 
the  end  ;  Coulomb  found  tlie  distance  to  be  r6  inch  in  a  bar  8  inches  long. 
He  also  found  that,  with  shorter  bars,  the  distance  of  the  poles  from  the 
end  is  \  of  the  length  ;  thus  with  a  bar  of  three  inches  it  would  be  half  an 
inch.  These  results  presuppose  that  the  other  dimensions  of  the  bar  are 
very  small  as  compared  with  its  length,  that  it  has  a  regular  shape,  and  is 
uniformly  magnetised.  When  these  conditions  are  not  fulfilled,  the  positions 
of  the  poles  can  only  be  determined  by  direct  trials  with  a  magnetic 
needle.  With  lozenge-shaped  magnets  the  poles  are  nearer  the  middle. 
Coulomb  found  that  these  lozenge-shaped  bars  have  a  -gxtTsX&x  dinxti-ue  force 
than  rectangular  bars  of  the  same  weight,  thickness,  and  hardness. 


p- •,  .*■ r. 


*     *■■     r     •». 


Fig.  655. 

A  short  magnet  is  defined  by  Coulomb  as  one  whose  length  is  less  than 
50  times  its  diameter. 


-722]  Mayers  F/oatnig  Magucts.  687 

Kohlrausch  found  that  the  pole  of  a  magnet,  as  far  as  its  action  at  a 
distance  is  concerned,  is  j',;  from  the  end. 

722.  Mayer's  floating-  magrnets. — The  reciprocal  action  of  magnetic 
poles  may  be  conveniently  illustrated  by  an  elegant  method  devised  by 
Prof  A.  M.  Mayer.  Steel  sewing-needles  are  magnetised  so  that  their 
points  are  north  poles,  and  their  eyes,  which  are  thus  south  poles,  just  pro- 
ject through  minute  cork  discs,  so  that  when  placed  in  water  the  magnets 
float  in  a  vertical  position.  If  the  north  pole  of  a  strong  magnet  is  brought 
near  a  number  of  these  floating  magnets  they  are  attracted  by  it,  and  take  up 
definite  positions,  forming  figures  which  depend  on  the  reciprocal  repulsion 
of  the  floating  magnets,  and  on  their  number.  Some  of  them  are  repre- 
sented in  fig.  655.  The  more  complex  produce  more  than  one  arrangement 
which  are  not  equally  stable,  the  letters  a,  b,  and  c  indicating  the  decreasing 
order  of  stability.  A  slight  shock  often  causes  one  form  to  pass  into  another 
and  more  stable  form. 

These  figures  not  only  illustrate  magnetic  actions,  but  they  suggest  an 
image  of  the  manner  in  which  alteration  of  molecular  groupings  may  give 
rise  to  physical  phenomena,  such  as  those  of  superfusion  (345). 

Such  floating  magnets  as  are  here  described  are  delicate  tests  of  mag- 
netisation, and  are  convenient  for  investigating  the  distribution  of  the  poles 
in  bodies  of  irregular  shape. 


688  Frict tonal  Electricity.  [723- 


BOOK    IX. 

FRICTION AL   ELECTRICITY 


CHAPTER    I. 

FUNDAMENTAL     PRINCIPLES. 

723.  Electricity.  Its  nature. — Electricity  is  a  powerful  physical  agent 
which  manifests  itself  mainly  by  attractions  and  repulsions,  but  also  by 
luminous  and  heating  effects,  by  violent  shocks,  by  chemical  decomposition, 
and  many  other  phenomena.  Unlike  gravity,  it  is  not  inherent  in  bodies, 
but  it  is  evoked  in  them  by  a  variety  of  causes,  among  which  are  friction, 
pressure,  chemical  action,  heat,  and  magnetism. 

Thales,  600  B.C.,  knew  that  when  amber  was  rubbed  with  silk  it  acquired 
the  property  of  attracting  light  bodies  ;  and  from  the  Greek  form  of  this 
word  {fjX(KTpov)  the  term  electricity  has  been  derived.  This  is  nearly  all 
the  knowledge  left  by  the  ancients  ;  it  was  not  until  towards  the  end  of  the 
sixteenth  century  that  Dr.  (Gilbert,  physician  to  Queen  Elizabeth,  showed 
that  this  property  was  not  limited  to  amber,  but  that  other  bodies,  such  as 
sulphur,  wax,  glass,  &c.,  also  possessed  it  in  a  greater  or  less  degree. 

724.  Development  of  electricity  by  friction. — When  a  glass  rod,  or  a 
stick  of  sealing-wax,  or  shellac,  is  held  in  the  hand,  and  is  rubbed  with  a 
piece  of  flannel,  or  with  the  skin  of  a  cat,  the  parts  rubbed  will  be  found  to 
have  the  property  of  attracting  light  bodies,  such  as  pieces  of  silk,  wool, 
feathers,  paper,  bran,  gold  leaf,  &c.,  which,  after  remaining  a  short  time  in 
contact,  are  again  repelled.  They  are  then  said  to  have  become  electrified. 
In  order  to  ascertain  whether  bodies  are  electrified  or  not,  instruments  called 
electroscopes  are  used.  The  simplest  of  these,  the  electric  pendulum  (fig. 
656),  consists  of  a  pith  ball  attached  by  means  of  a  silk  thread  to  a  glass 
support.  When  an  electrified  body  is  brought  near  the  pith  ball,  the  latter 
is  instantly  attracted,  iDut  after  momentary  contact  is  again  repelled  (fig. 
657). 

A  solid  l)ocly  may  also  be  electrified  by  friction  with  a  liquid  or  with  a 
gas.  In  the  Torricellian  vacuum  a  mo\eniL"nt  of  the  mercury  against  the 
sides  of  the  glass  jiroduces  a  disengagement  of  electric  light  visible  in  the 
dark  ;  a  tube  exhausted  of  air,  but  containing  a  few  drops  of  mercury,  be- 
comes also  luminous  when  agitated  in  the  dark. 

If  a  quantity  of  mercury  in  a  dry  glass  vessel  be  connected  with  a  gold- 
leaf  electroscope  by  a  wire,  and  a  dry  glass  rod  be  immersed  in  it,  no  indica- 


-725] 


Conductors  and  Notnwiductors. 


689 


tions  are  observed  during  the  immersion,  but  on  smartly  withdrawinj^  the 
rod,  the  leaves  increasingly  diverge,  attaining  their  maximum  when  the  lod 
lea\es  the  mercury. 

Some  substances,  particularly  metals,  do  not  seem  capable  of  receiving 
the  electric  excitement.  When  a  rod  of  metal  is  held  in  the  hand,  and 
rubbed  with  silk  or  flannel,  no  electrical  eftects  are  produced  in  it  ;  and  bodies 


Fig.  656. 


Fig.  657. 


were  divided  by  Gilbert  into  ideoelectrics,  or  those  which  become  electrical 
by  friction  ;  and  anelectrics,  or  those  which  do  not  possess  this  property. 
These  distinctions  no  longer  obtain  in  any  absolute  sense  ;  under  appropriate 
conditions,  all  bodies  may  be  electrified  by  friction  (726). 

725.  Conductors  and  nonconductors. — When  a  diy  glass  rod,  rubbed 
at  one  end,  is  brought  near  an  electroscope,  that  part  only  will  be  electrified 
which  has  been  rubbed  ;  the  other  end  will  produce  neither  attraction  nor 
repulsion.  The  same  is  the  case  with  a  rod  of  shellac  or  of  sealing-wax. 
In  these  bodies  electricity  does  not  pass  from  one  part  to  another — they  do 
not  conduct  electricity.  Experiment  shows  that,  when  a  metal  has  received 
electricity  in  any  of  its  parts,  the  electricity  instantly  spreads  over  its  entire 
surfl\ce.     Metals  are  hence  said  to  be  good  conductors  of  electricity. 

Bodies  have,  accordingly,  been  divided  into  conductors  and  nonconductors 
or  insulators.  This  distinction  is  not  absolute,  and  we  may  advantageously 
consider  bodies  as  offering  a  resistance  to  the  passage  of  electricity  which 
varies  with  the  nature  of  the  substance.  Those  bodies  which  offer  little 
resistance  are  thus  conductors,  and  those  which  offer  great  resistance  are 
nonconductors  or  insulators  :  electrical  r^«<^«f//7///y  is  accordingly  the  inverse 
of  electrical  resistance.  There  is  no  such  thing  as  an  absolute  nonconductor 
of  electricity,  any  more  than  there  is  an  absolute  nonconductor  of  heat. 
We  are  to  consider  that  between  conductors  and  nonconductors  there  is  a 
quantitative  and  not  a  qualitative  difference  ;  there  is  no  conductor  so  good 

Y  Y 


690 


Frictional  Electricity. 


[725- 


but  that  it  offers  some  resistance  to  the  passage  of  electricity,  nor  is  there  any 
substance  which  insulates  so  completely  but  that  it  allows  some  electricity 
to  pass.  The  transition  from  conductors  to  nonconductors  is  gradual,  and  no 
line  of  sharp  demarcation  can  be  drawn  between  them. 

In  this  sense  we  are  to  understand  the  following  table,  in  which  bodies 
are  classed  as  cofiductors,  semiconductors,  and  nonco?tductors  ;  those  bodies 
being  conveniently  designated  as  conductors  which,  when  applied  to  a 
charged  electroscope,  discharge  it  almost  instantaneously  ;  semiconductors 
being  those  which  discharge  it  in  a  short  but  measurable  time — a  few  seconds, 
for  instance  ;  while  nonconductors  effect  no  perceptible  discharge  in  the 
course  of  a  minute. 


Conductors. 

Metals. 

Well-burnt  charcoal. 

Graphite. 

Acids. 

Aqueous  solutions. 

Water. 

Snow. 

Vegetables. 

Animals. 

Soluble  salts. 

Linen. 

Cotton. 


Seiniconductors. 
Alcohol  and  ether. 
Powdered  glass. 
Flour  of  sulphur. 
Dry  wood. 
Paper. 
Ice  at  0°. 


Nonconductors. 
Dry  oxides. 
Ice  at  —25°  C. 
Lime. 

Caoutchouc. 
Air  and  dry  gases. 
Dry  paper. 
Silk. 
Diamonds  and  precious 

stones. 
Glass. 
Wax. 
Sulphur. 
Resins. 
Amber. 
Shellac. 


This  list  is  arranged  in  the  order  of  decreasing  conductivity,  or,  what  is  the 
same  thing,  of  increasing  resistance.  The  arrangement,  however,  is  not  in- 
variable. Conductivity  depends  on  many  physical  conditions.  Glass,  for 
example,  which  does  not  conduct  at  ordinary  temperatures,  does  so  at  200° 
to  300°  C.  To  show  this,  platinum  wire  is  coiled  on  a  glass  rod  to  within  a 
couple  of  inches  from  the  end.  If  the  coiled  part  is  held  in  the  hand  and 
the  free  end  when  at  the  ordinary  temperature  is  applied  to  a  charged 
electroscope  it  does  not  affect  it  ;  but  if  the  free  end  be  heated  by  placing  it 
in  a  Bunsen's  flame,  it  will  now  be  found  to  discharge  the  electroscope. 
Shellac  and  resin  do  not  insulate  so  well  when  they  are  heated.  Water, 
which  is  a  good  conductor,  conducts  but  little  in  the  state  of  ice  at  0°,  and 
very  badly  at  -25°.  Powdered  glass  and  flour  of  sulphur  conduct  veiy 
well,  while  in  large  masses  they  are  nonconductors  ;  probably  because  in  a 
state  of  powder  each  particle  becomes  covered  \\\\\\  a  film  of  moisture  that 
acts  as  a  conductor.  The  nonconducting  power  of  glass  is  also  greatly 
influenced  by  its  chemical  composition.  Some  specimens  have  an  appreci- 
al)lc  conductivity  even  if  dry  and  at  the  ordinary  temperature. 

Heat  acts  indirectly  by  drying,  Ijy  which  many  bodies  lose  their  conduc- 
tivity either  partially  or  wholly. 

According  to  Said  Effendi,  if  the  conducting  power  of  water  be  taken  at 


-727]  Distinction  of  the   Two  Kinds  of  Electricity.  691 

1,000,  the  conducting  power  of  petroleum  is  72  ;  alcohol  49  ;  ether  40  ; 
turpentine  23  ;  and  benzole  16.  Domalip  obtained  the  following--  numbers 
for  the  respective  conductivities:  Water  144;  ether  6-3;  turpentine  1-9; 
and  benzole  i. 

726.  Insulating-  bodies.  Common  reservoir. —  Bad  conductors  are 
called  ifisidators,  for  they  arc  used  as  supports  for  bodies  in  which  electricity 
is  to  be  retained.  A  conductor  remains  electrified  only  so  long  as  it  is  sur- 
rounded by  insulators.  If  this  were  not  the  case,  as  soon  as  the  electrified 
body  came  in  contact  with  the  earth,  which  is  a  good  conductor,  the  electri- 
city would  pass  into  the  earth,  and  diffuse  itself  through  its  whole  extent, 
On  this  account,  the  earth  has  been  named  the  common  reservoir.  A  body 
is  insulated,  by  being  placed  on  a  support  with  glass  feet,  or  on  a  resinous 
cake,  or  by  being  suspended  by  silk  threads.  No  bodies,  however,  insulate 
perfecdy  ;  all  electrified  bodies  lose  their  electricity  more  or  less  rapidly 
by  means  of  the  supports  on  which  they  rest.  Glass  is  always  somewhat 
hygroscopic,  and  the  aqueous  vapour  which  condenses  on  it  affords  a 
passage  for  the  electricity  ;  the  insulating  power  of  glass  is  materially  im- 
proved by  coating  it  with  shellac  or  copal  varnish.  Dry  air  is  a  good  insu- 
lator ;  but  when  the  air  contains  moisture  it  conducts  electricity,  and  this  is 
the  principal  source  of  the  loss  of  electricity.  Hence  it  is  necessary,  in 
electrical  experiments,  to  rub  the  supports  with  cloths  dried  at  the  fire,  and 
to  surround  electrified  bodies  by  glass  vessels,  containing  substances  which 
absorb  moisture,  such  as  chloride  of  calcium,  or  pumice  soaked  with  sul- 
phuric acid. 

From  their  great  conductivity  metals  do  not  seem  to  become  electrified 
by  friction.  But  if  they  are  insulated,  by  being  held  in  the  hand  by  an  india- 
rubber  glove  or  a  silk  handkerchief  and  then  rubbed,  they  give  good  indi- 
cations.    This  may  also  be  seen  by  the 

following  experiment  (fig.  658).     A  brass    ^        ~^^^         '— -  --^1=^=^ 

tube  is  provided  with  a  glass  handle  by 

which  it  is  held,  and  then   rubbed  with  '  •   :>  • 

silk  or  flannel.  On  approaching  the  metal  to  an  electrical  pendulum  (fig 
656),  the  pith  ball  will  be  attracted.  If  the  metal  is  held  in  the  hand  electri- 
city is  indeed  produced  by  friction — but  it  immediately  passes  through  the 
body  into  the  ground. 

If,  too,  the  cap  of  a  gold-leaf  electroscope  be  briskly  flapped  with  a  dry 
silk  handkerchief,  the  gold  leaves  will  diverge. 

727.  Distinction  of  the  two  kinds  of  electricity. —  If  electricity  be 
developed  on  a  glass  rod  by  friction  with  silk,  and  the  rod  be  brought  near 
an  electrical  pendulum,  the  ball  will  be  attracted  to  the  glass,  and  after 
momentary  contact  will  be  again  repelled.  By  this  contact  the  ball  beconies 
electrified,  and  so  long  as  the  two  bodies  retain  their  electricity,  repulsion 
follows  whenever  they  are  brought  near  each  other.  If  a  stick  of  sealing-wax, 
electrified  by  friction  with  flannel  or  silk,  be  approached  to  another  electrical 
pendulum,  the  same  effects  will  be  produced — the  ball  will  fly  towards  the 
wax,  and  after  contact  will  be  repelled.  Two  bodies,  which  have  been 
charged  with  electricity,  repel  one  another.  But  the  electricities  respectively 
developed  in  the  preceding  cases  are  not  the  same.  If,  after  the  pith  ball 
had  been  touched  with  an  electrified  glass  rod,  an  electrified  stick  of  sealing- 

Y  V  2 


692  Frictional  Electricity.  [727- 

wax,  and  then  an  electrified  glass  rod,  be  alternately  approached  to  it,  the 
pith  ball  will  be  attfacted  by  the  former  and  repelled  by  the  latter.  Simi- 
larly, if  the  pendulum  be  charged  by  contact  with  the  electrified  sealing- 
wax,  it  will  be  repelled  when  this  is  approached  to  it,  but  attracted  by  the 
approach  of  the  excited  glass  rod. 

On  experiments  of  this  nature,  Dufay  first  made  the  observation  that 
there  are  two  different  electricities  :  the  one  developed  by  the  friction  of 
glass  under  certain  circumstances,  the  other  by  the  friction  of  resin  or 
shellac.  To  the  first  the  name  vitreous  electricity  is  given  ;  to  the  second 
the  name  resinous  electricity. 

728.  Theories  of  electricity. — Two  theories  have  been  proposed  to 
account  for  the  different  effects  of  electricity.  Franklin  supposed  that  there 
exists  a  peculiar,  subtle,  imponderable  fluid,  which  acts  by  repulsion  on  its 
own  particles,  and  pervades  all  matter.  This  fluid  is  present  in  every  sub- 
stance in  a  quantity  peculiar  to  it,  and  when  it  contains  this  quantity  it  is  in 
the  natural  state,  or  in  a  state  of  equilibrium.  By  friction  certain  bodies 
acquire  an  additional  quantity  of  the  fluid,  and  are  said  to  be  positively 
electrified  ;  others  by  friction  lose  a  portion,  and  are  said  to  be  tiegatively 
electrified.  The  former  state  corresponds  to  vitreous  electricity,  and  the 
latter  to  resi?ious  electricity.  Positive  electricity  is  represented  by  the 
sign  + ,  and  negative  electricity  by  the  sign  -  ;  a  designation  based  on 
the  algebraical  principle,  that  when  a  plus  quantity  is  added  to  an  equal 
minus  quantity  zero  is  produced.  So  when  a  body  containing  a  quantity  of 
positive  electricity  is  touched  with  a  body  possessing  an  equivalent  cjuantity 
of  negative  electricity,  a  neutral  or  zero  state  is  produced. 

The  theory  of  Syjnmer  ?i?.?,nmQ:?,  that  every  substance  contains  an  inde- 
finite quantity  of  a  subtle,  imponderable  matter,  which  is  called  the  electric 
fluid.  This  fluid  is  formed  by  the  union  of  two  fluids — the  positive  and  the 
negative.  When  they  are  combined  they  neutralise  one  another,  and  the 
body  is  then  in  the  natural  or  neutral  state.  By  friction,  and  by  several 
other  means,  the  two  fluids  may  be  separated,  but  one  of  them  can  never  be 
excited  without  a  simultaneous  production  of  the  other.  There  may,  how- 
ever, be  a  greater  or  less  excess  of  the  one  or  the  other  in  any  body,  and  it 
is  then  said  to  be  electrified  positively  or  negatively.  As  in  Franklin's 
theory,  vitreous  corresponds  to  positive  and  resinous  to  negative  electricity. 
Thi§  distinction  is  merely  conventional :  it  is  adopted  for  the  sake  of  conve- 
nience, and  there  is  no  other  reason  why  resinous  electricity  should  not  be 
called  positive  electricity. 

Electricities  of  the  same  name  repel  one  another,  and  electricities  of 
opposite  kinds  attract  each  other.  The  electricities  can  circulate  freely  on 
the  surface  of  certain  bodies,  which  are  called  conductors,  but  remain  con- 
fined to  certain  parts  of  others,  which  are  called  nonconductors. 

It  must  be  added  that  this  theory  is  quite  hypothetical  ;  but  for  purposes 
of  instruction  its  general  adoption  is  justified  by  the  convenient  explanation 
which  it  gives  of  electrical  phenomena. 

729.  Action  of  electrilied  bodies  on  each  other. — Admitting  the  two- 
fluid  hypothesis,  the  phenomena  of  attraction  a\u\  repulsion  may  be  enun- 
ciated in  the  following  law  :— 


-730]    Lazv  of  the  Development  of  Electricity  by  Friction.     693 

Two  bodies  charged  with  the  same  electricity  repel  each  other ;  two  bodies 
charged  with  opposite  electricities  attract  each  other. 

These  attractions  and  repulsions  take  place  in  \irtue  of  the  action  which 
the  two  electricities  exert  on  themselves,  and  not  in  virtue  of  their  action  on 
the  particles  of  matter. 

730.  Iiaw  of  the  development  of  electricity  by  friction. — Whenever 
two  bodies  are  rubbed  together,  the  neutral  electricity  is  decomposed.  Two 
electricities  are  developed  at  the  same  time  and  in  ecjual  quantities— one 
body  takes  positive  and  the  other  negative  electricity.  This  may  be  proved 
by  the  following  experiment  devised  by  Faraday  : — A  small  flannel  cap 
provided  with  a  silk  thread  (fig.  659)  is  fitted  on  the  end  of  a  stout  rod  of 
shellac,  and  rubbed  round  a  few  times.  When  the  cap  is  removed  by  means 
of  the  silk  thread,  and  presented  to  a  pith  ball  pendulum  charged  with  positive 
electricity,  the  latter  will  be  repelled,  proving  that  the 
flannel  is  charged  with  positive  electricity  ;  while  if  the 
shellac  is  presented  to  the  pith  ball,  it  will  be  attracted, 
showing  that  the  shellac  is  charged  with  negative 
electricity.  Both  electricities  are  present  in  equal 
quantities  ;  for  if  the  rod  be  presented  to  the  electro- 
scopes before  removing  the  cap,  no  action  is  observed. 

The  electricity  developed  on  a  body  by  friction 
depends  on  the  rubber  as  well  as  the  body  rubbed. 
Thus  glass  becomes  negatively  electrified  when  rubbed  Fig.  65q. 

with   catskin,  but  positively  when  rubbed  with  silk. 

In  the  following  list,  which  is  mainly  due  to  Faraday,  the  substances  are 
arranged  in  such  an  order  that  each  becomes  positively  electrified  when 
rubbed  with  any  of  the  bodies  following,  but  negatively  when  rubbed  with 
any  of  those  which  precede  it : — 

1.  Catskin. 

2.  Flannel. 

3.  Ivoiy. 

4.  Rock  crystal. 

The  nature  of  the  electricity  set  free  by  friction  depends  also  on  the 
degree  of  polish,  the  direction  of  the  friction,  and  the  temperature.  If  two 
glass  discs  of  dififerent  degrees  of  polish  are  rubbed  against  each  other,  that 
w^hich  is  most  polished  is  positively,  and  that  which  is  least  polished  is 
negatively,  electrified.  If  two  silk  ribbons  of  the  same  kind  are  rubbed 
across  each  other,  that  which  is  transversely  rubbed  is  negatively  and  the 
other  positively  electrified.  If  two  bodies  of  the  same  substance,  of  the  same 
polish,  but  of  different  temperatures,  are  rubbed  together,  that  which  is  most 
heated  is  negatively  electrified.  Generally  speaking,  the  particles  which  are 
most  readily  displaced  are  negatively  electrified. 

Poggendorff  has  observed  that  many  substances  which  have  hitherto  been 
regarded  as  highly  negative,  such  as  gun-paper,  gun-cotton,  and  ebonite,  yield 
positive  electricity  when  rubbed  with  leather  coated  with  amalgam.  It 
must  be  added  that  the  results  of  experiments  on  the  kind  of  electricity  pro- 
duced by  rubbing  bodies  together  are  somewhat  uncertain,  as  slight  differences 
in  the  surfaces  of  the  bodies  rubbed  may  completely  alter  their  deportment. 


5. 

Glass. 

9- 

W^ood. 

13- 

Resin. 

6. 

Cotton. 

10. 

Metals. 

14. 

Sulphur. 

7- 

Silk. 

II. 

Caoutchouc. 

15- 

Guttapercha. 

8. 

The  hand. 

12. 

Sealing-wax. 

16. 

Gun-cotton. 

694  Frictional  Electricity.  [730- 

A  valuable  source  of  negative  electricity  is  a  strip  of  pyroxyline  or  gunpaper 
drawn  through  the  fingers. 

731.  Development     of    electricity    by     pressure     and     cleavagre. — 

Electrical  excitement  may  be  produced  by  other  causes  than  friction.  If  a 
disc  of  wood,  covered  with  silk,  on  which  some  amalgam  has  been  rubbed, 
and  a  metal  disc,  each  provided  with  an  insulating  handle,  be  placed  in  con- 
tact, and  then  suddenly  separated,  the  metal  disc  is  negatively  electrified. 
A  crystal  of  Iceland  spar  pressed  between  the  fingers  becomes  positively 
electrified,  and  retains  this  state  for  some  time.  The  same  property  is 
observed  in  several  other  minerals,  even  though  conductors,  provided  they 
be  insulated.  If  cork  and  caoutchouc  be  pressed  together,  the  first  becomes 
positively,  and  the  latter  negatively  electrified.  A  disc  of  wood  pressed  on 
an  orange  and  separated  carries  away  a  good  charge  of  electricity  if  the 
contact  be  rapidly  interrupted.  But  if  the  disc  is  slowly  removed  the  quan- 
tity is  smaller,  for  the  two  fluids  recombine  at  the  moment  of  their  separation. 
For  this  reason  there  is  no  apparent  effect  when  the  two  bodies  pressed 
together  are  good  conductors. 

The  contact  of  heterogeneous  bodies  is  no  doubt  the  source  of  electricity. 
Pressure  and  friction  are  but  particular  cases  ;  in  the  former  case  the  con- 
tact is  closer,  and  in  the  latter  case  the  surfaces  are  being  continually  renewed, 
and  the  effect  is  the  same  as  if  there  were  a  series  of  rapidly  succeeding 
contacts. 

Cleavage  also  is  a  source  of  electricity.  If  a  plate  of  mica  be  rapidly 
split  in  the  dark,  a  slight  phosphorescent  light  is  perceived.  Becquerel 
fixed  glass  handles  to  each  side  of  a  plate  of  mica,  and  then  rapidly  separated 
them.  On  presenting  each  of  the  plates  thus  separated  to  an  electroscope, 
he  found  that  one  was  negatively  and  the  other  positively  electrified.  If  a 
stick  of  sealing-wax  be  broken,  the  ends  exhibit  different  electricities. 

All  badly  conducting  crystalline  substances  exhibit  electrical  indications 
by  cleavage.  The  separated  plates  are  always  in  opposite  electrical  condi- 
tions, provided  they  are  not  good  conductors  :  for  if  they  were,  the  separa- 
tion would  not  be  sufficiently  rapid  to  prevent  the  recombination  of  the  two 
electricities.  To  the  phenomena  here  described  is  due  the  luminous  appear- 
ance seen  in  the  dark  when  sugar  is  broken.  If  sulphur  or  resin  be  melted 
in  glass  vessels  and  a  glass  rod  be  placed  in  the  melted  mass,  on  cooling 
the  solid  mass  can  be  lifted  out,  and  will  be  found  to  be  negatively  electrified. 

732.  Pyroelectrlclty.— Certain  minerals,  when  warmed,  acquire  electri- 
cal properties  ;  a  phenomenon  to  which  the  name  pyroelectricity  is  given. 
It  is  best  studied  in  tourmaline^  in  which  it  was  first  disco\ered  from  the 
fact  that  this  mineral  has  the  power  of  first  attracting  and  then  repelling 
hot  ashes  when  placed  among  them. 

To  observe  this  phenomenon,  a  crystal  of  tourmaline  (fig.  660)  is  sus- 
pended horizontally  by  a  silk  thread,  in  a  glass  cylinder  placed  on  a  heated 
metal  plate,  or  in  an  ordinary  hot-air  bath.  On  subsequently  investigating 
the  electric  condition  of  the  ends  by  approaching  to  them  successively  an 
electrified  glass  rod,  one  end  will  be  found  to  be  positively  electrified,  and 
the  other  end  negatively  electrified,  and  each  end  shows  this  polarity  as 
long  as  the  tcmiicrature  rises.  The  arrangement  of  the  electricity  is  thus 
like  that  of  the  magnetism  in  a  magnet.     The  points  at  which  the  intensity 


-732] 


Pyroelectricity, 


695 


Fig.  660. 


of  free  electricity  is  greatest  are  called  the  poles^  and  the  line  connecting 
them  is  the  electric  axis.  When  a  tourmaline,  while  thus  electrified,  is  broken 
in  the  middle,  each  of  the  pieces  has  its  two  poles,  and  the  polarity  of  the 
broken  ends  is  opposite,  resembling  thus  the  experiment  of  the  broken 
magnets  (6S5).  The  quantities  of  electricity  produced  when 
tourmaline  is  heated  are  equal  as  well  as  opposite,  for  if  a 
heated  crystal  be  suspended  by  an  insulating  support  inside  an 
insulated  metal  cylinder,  the  outside  of  which  is  connected  with 
an  electroscope  (745),  no  divergence  in  its  leaves  is  produced. 

These  polar  properties  depend  on  the  change  of  tempera- 
ture. When  a  tourmaline,  which  has  become  electrical  by  being 
warmed,  is  allowed  to  cool  slowly,  it  first  loses  electricity,  and 
then  its  polarity  becomes  reversed  ;  that  is,  the  end  which  was 
positive  now  becomes  negative,  and  that  which  was  negative 
becomes  positive,  and  the  position  of  the  poles  now  remains 
unchanged  so  long  as  the  temperature  sinks.  Tourmaline  only 
becomes  pyroelectric  within  certain  limits  of  temperature  ;  these 
var)'  somewhat  with  the  length,  but  are  usually  between  10°  and 
1 50"  C.  Below  and  above  these  temperatures  it  behaves  like 
any  other  body,  and  shows  no  polarity. 

Tourmaline  belongs  to  the  hexagonal  system,  and  usually  crystallises  in 
hemihedral  forms  ;  those,  that  is  to  say,  which  are  differently  modified  at  the 
ends  of  their  crystallographical  principal  axis.  The  name  analogous  pole  is 
given  to  that  end  A  of  the  crystal  which  shows  positive  electricity  when  the 
temperature  is  rising,  and  negative  electricity  when  it  is  sinking  ;  antilogous 
pole  to  the  end  B  which  becomes  negative  by  being  heated,  and  positive  by 
being  cooled. 

Besides  tourmaline  the  following  minerals  are  found  to  be  pyroelectric, 
though  not  so  markedly — boracite,  topaz,  prehnite,  silicate  of  zinc,  scolezite, 
axenite.  And  the  following  organic  bodies  are  pyroelectric  :  cane-sugar, 
Pasteur's  salt  (racemate  of  sodium  and  ammonium),  tartrate  of  potassium,  &c. 

Sir  W.  Thomson  supposes  that  every  portion  of  tourmaline  and  other 
hemihedral  crystals  possesses  a  definite  electrical  polarity,  the  intensity  of 
which  depends  on  the  temperature.  When  the  surface  is  passed  through  a 
flame  every  part  becomes  electrified  to  such  an  extent  as  to  exactly  neutralise, 
for  all  external  points,  the  effect  of  the  internal  polarity.  The  ciystal  thus  has 
no  external  action,  nor  any  tendency  to  change  its  mode  of  electrification. 
But  if  it  be  heated  or  cooled  the  internal  polarisation  of  each  particle  of  the 
crystal  is  altered,  and  can  no  longer  be  balanced  by  the  superficial  electrifi- 
cation, so  that  there  is  a  resultant  external  action. 

A  very  convenient,  and  at  the  same  time  sensitive,  means  of  investigating 
the  action  of  heat  on  crystals  is  to  sift  on  these,  after  having  been  warmed,  a 
mixture  of  flour  of  sulphur  and  red  lead  through  a  small  cotton  sieve.  By 
the  friction  in  sifting  the  sulphur  acquires  negative  and  the  red  lead  positive 
electricity,  and  the  powders  thus  charged  attach  themselves  to  those  parts  of 
the  crystal  which  have  the  opposite  electricity,  and  thus  by  their  difterent 
colours  give  at  once  an  image  of  its  distribution. 

Crystals  of  fluor-spar  are  not  only  electrified  by  heat,  but  also  when 
they  are  exposed  to  radiation  from  the  sun  and  from  the  electric  light.  This 
phenomenon  is  known  ^s  photo-electricity. 


696 


Frictional  Electricity. 


[733- 


CHAPTER    II. 


QUANTITATIVE   LAWS   OF   ELECTRICAL   ACTIOX. 

733.  Electrical  quantity. — In  the  experiment  with  the  flannel  cap, 
described  above  (730),  each  time  the  experiment  is  made,  the  quantity  of 
positive  electricity  produced,  which  remains  on  the  flannel,  is  equal  to  that 
of  the  negative  electricity,  which  remains  on  the  sealing-wax.  The  flannel, 
with  its  charge  of  positive  electricity,  may  be  detached,  and  if  we  work 
under  precisely  uniform  conditions,  equal  quantities  of  electricity  can  thus 
be  separated. 

If  we  fill  a  cask  with  water  by  means  of  a  measure,  the  quantity  added 
would  be  directly  proportional  to  the  number  of  such  measures.  Now, 
although  in  the  above  experiment  the  quantities  of  electricity  produced  each 
time  are  equal,  yet  when  the  flannel  cap  is  applied  each  time  to  an  insulated 
conductor  it  does  not  necessarily  follow  that  the  quantity  of  electricity  imparted 

is  directly  proportional  to  the  number  of 
such  applications. 

On  the  C.G.S.  system  the  unit  quantity 
of  electricity  is  that  amount  which,  acting, 
at  a  distance  of  one  centimetre  across  air, 
on  a  quantity  of  electricity  of  the  same 
kind  equal  to  itself,  would  repel  it  with  a 
force  equal  to  one  dyne  (709),  and  is  called 
a  Coulomb. 

734.  Iiaws  of  electrical  attraction 
and  repulsion. — The  laws  which  regu- 
late the  attraction  and  repulsion  of  elec- 
trified bodies  may  be  thus  stated  : — 

I.  TJic  repulsions  or  attractions  be- 
tween  tioo   electrified  bodies   are  in    ttie 

J;  -  f     ^  ^_.^      [|ii  invetse  ratio  of  the  squares  of  tJieir  dis- 

","'^j',i^iiiifnii«iiiiia'=»™';^ '„  ''••  *y|^^      tance. 

II.  The  distance  remaining  the  same., 
the  force  of  attraction  or  repulsion  between 
two  electt  ified  bodies  is  directly  as  the  pro- 
duct of  the  quantities  of  electricity  with 
which  they  are  char<^ed. 

These  laws  were  established  by  Cou- 
lomb, by  means  of  llie  torsion  balance,  used  in  determining  the  laws  of  mag- 
netic attractions  and  repulsions  (704),  modified  in  accordance  with  the  re- 
(luirements   of  the  case.     The  wire,  on   the  torsion  of  which  the  method 


-734]        Lazes  of  Electrical  Attraction  atid  Repulsion.  697 

depends,  is  so  fine  that  a  foot  weighs  only  /„  of  a  grain.  At  its  lower  ex- 
tremity there  is  a  fine  shellac  rod,  np  (fig.  661),  at  one  end  of  which  is  a 
small  disc  of  copper-foil,  n.  Instead  of  the  vertical  magnetic  needle,  there 
is  a  glass  rod,  i,  terminated  by  a  gilt  pith  ball,  ;«,  which  passes  through  the 
aperture  r.  The  scale  oc  is  fixed  round  the  sides  of  the  vessel,  and  during 
the  experiment  the  ball,  ;«,  is  opposite  the  zero  point  0.  The  micrometer 
consists  of  a  small  graduated  disc,  e,  movable  independently  of  the  tube  d, 
and  of  affixed  index,  a,  which  shows  by  how  many  degrees  the  disc  is  turned. 
In  the  centre  of  the  disc  there  is  a  small  button,  /,  to  which  is  fixed  the  wire 
which  supports  np. 

i.  The  micrometer  is  turned  until  the  zero  point  is  opposite  the  index, 
and  the  tube  d  is  turned  until  the  knob  n  is  opposite  zero  of  the  graduated 
circle  ;  the  knob  m  is  in  the  same  position,  and  thus  presses  against  71.  The 
knob  in  is  then  removed  and  electrified,  and  replaced  in  the  apparatus, 
through  the  aperture  r.  As  soon  as  the  electrified  knob  m  touches  «,  the 
latter  becomes  electrified,  and  is  repelled,  and  after  a  few  oscillations  re- 
mains constant  at  a  distance  at  which  the  force  of  repulsion  is  equal  to  the 
force  of  torsion.  In  a  special  experiment  Coulomb  found  the  angle  of  tor- 
sion between  the  two  to  be  36°  ;  and  as  the  force  of  torsion  is  proportional 
to  the  angle  of  torsion,  this  angle  represents  the  repulsive  force  between  m 
and  n.  In  order  to  reduce  the  angle  to  18°  it  was  necessary  to  turn  the  disc 
through  126°.  The  wire  was  twisted  126°  in  the  direction  of  the  arrow  at 
its  upper  extremity,  and  18°  in  the  opposite  direction  at  its  lower  extremity, 
and  hence  there  was  a  total  torsion  of  144°.  On  turning  the  micrometer  in 
the  same  direction,  until  the  angle  of  deviation  was  8^°,  567°  of  torsion  was 
necessary.  Hence  the  whole  torsion  was  575^.  Without  sensible  error 
these  angles  of  deviation  may  be  taken  at  36°,  18°,  and  9°  ;  and  on  comparing 
them  with  the  corresponding  angles  of  torsion,  36°,  144°,  and  576°,  we  see 
that  while  the  first  are  as 

I  :  A  :  i, 
the  latter  are  as 

I  :  4  :  16  ; 

that  is,  that  for  a  distance  \  as  great  Llie  angle  of  torsion  is  4  times  as  great, 
and  that  for  a  distance  \  as  great  the  repulsive  force  is  16  times  as  great. 

In  experimenting  with  this  apparatus  the  air  must  be  thoroughly  dry,  in 
order  to  diminish,  as  far  as  possible,  loss  of  electricity.  This  is  effected  by 
placing  in  it  a  small  dish  containing  chloride  of  calcium. 

The  experiments  by  which  the  law  of  attraction  is  proved  are  made  in 
much  the  same  manner,  but  the  two  balls  are  charged  with  opposite  electri- 
cities. A  certain  quantity  of  electricity  is  imparted  to  the  movable  ball,  by 
means  of  an  insulated  pin,  and  the  micrometer  moved  until  there  is  a  certain 
angle  below.  A  charge  of  electricity  of  the  opposite  kind  is  then  imparted 
to  the  fixed  ball.  The  two  balls  tend  to  move  towards  each  other,  but  are 
prevented  by  the  torsion  of  the  wire,  and  the  movable  ball  remains  at  a 
distance  at  which  there  is  equilibrium  between  the  force  of  attraction,  which 
draws  the  balls  together,  and  that  of  torsion,  which  tends  to  separate  them. 
The  micrometer  screw  is  then  turned  to  a  greater  extent,  by  which  more 
torsion  and  a  greater  angle  between  the  two  balls  are  produced.     And  it  is 


698 


Frictiojial  Electricity. 


[734- 


from  the  relation  which  exists  between  the  angle  of  deflection  on  the  one 
hand  and  the  angle  which  expresses  the  force  of  torsion  on  the  other,  that 
the  law  of  attraction  has  been  deduced. 

ii.  To  prove  the  second  law  let  a  charge  be  imparted  \.o  m  ;  n  being  in 
contact  with  it  becomes  charged,  and  is  repelled  to  a  certain  distance.  The 
angle  of  deflection  being  noted,  let  the  ball  ;«  be  touched  by  an  insulated 
but  unelectrified  ball  of  exactly  the  same  size  and  kind.  If  in  this  way  half 
the  charge  on  one  of  the  balls  is  removed  it  will  be  found  that  the  amount 
of  torsion  necessary  to  maintain  the  balls  at  their  original  angular  distance 
is  half  what  it  was  before. 

The  two  laws  are  included  in  the  formula  F  =    ,.,,  where  F  is  the  force, 

d- 

e  and  e'  the  quantities  of  electricity  on  any  two  surfaces,  and  d  the  distance 
between  them.  If  e  and  e'  are  of  opposite  electricities  the  action  is  one  of 
attraction,  while  if  they  are  the  same  it  is  a  repulsive  action. 

Coulomb  also  established  the  law  by  the  method  of  oscillations  which  is 
particularly  applicable  to  the  case  of  attraction,  as  there  are  difficulties  in  ex- 
perimenting with  the  torsion  balance.    An  apparatus  for  this  purpose  consists 


•ig.  662 


of  an  insulated  metal  sphere  (fig.  662),  and  at  a  little  distance  a  short  thin  rod 
of  shellac  hung  by  a  silk  thread  and  with  a  disc  of  metal  foil  at  one  end,  the 
whole  being  enclosed  in  a  glass  cylinder  which  rests  on  an  insulating  plate. 
If  now  the  disc  is  charged  with  the  opposite  electricity  to  that  of  the  sphere, 
and  is  removed  from  its  position  of  equilibrium,  it  will  make  a  series  of 
oscillations  before  coming  to  rest.  It  can  be  proved  that  the  charge  on  the 
sphere  acts  as  if  it  were  concentrated  at  the  centre,  and  if  the  needle  is  short, 
the  distance  at  which  the  force  acts  will  be  that  from  the  centre  of  the  sphere 
to  the  thread  of  suspension.  As  in  the  case  of  magnetic  oscillations  we  may 
use  a  formula  for  the  time  of  a  single  oscillation  analogous  to  that  of  the 


-735] 

pendulum  (55) 


Distribution  of  Electricity. 


699 


■'^Jl\^  in 


that  is  t^Tvx/  ''' ,  in  which  M  is  the  moment  of  inertia 

of  the  needle,  L  its  length,  and  F  the  force  of  attraction.  Now,  all  other 
things  being  the  same,  it  is  found  that  when  the  sphere  is  placed  at  varying 
distances,  d  and  d^,  the  times  of  oscillations,  /  and  /„  vary,  and  therefore 
the  force  varies,  and  the  relation  is  established  that  F  :  F^  =  d'\  :  d'K 

7j'^.  Distribution  of  electricity. — When  an  insulated  sphere  of  conduct- 
ing material  is  charged  with  electricity,  the  electricity  passes  to  the  surface 
of  the  sphere,  and  forms  there  an  extremely  thin  layer.  If,  in  Coulomb's 
balance,  the  fixed  ball  be  replaced  by  another  electrified  sphere,  a  certain 
repulsion  will  be  observed.  If  then  this  sphere  be  touched  with  an  insulated 
sphere  identical  with  the  first,  but  in  the  neutral  state,  the  first  ball  will  be 
found  to  have  lost  half  its  electricity,  and  only  half  the  repulsion  will  be 
observed.  By  repeating  this  experiment  with  spheres  of  various  substances 
solid  and  hollow,  but  all  having  the  same  superficies,  the  result  will  be  the 
same,  excepting  that,  with  imperfectly  conducting  materials,  the  time  required 
for  the  distribution  will  be  greater.  From  this  it  is  concluded  that  the  dis- 
tribution of  electricity  depends  on  the  extent  of  the  surface,  and  not  on  the 
mass,  and,  therefore,  that  electricity  does  not  penetrate  into  the  interior,  but 
is  confined  to  the  surface.  This  conclusion  is  further  established  by  the 
following  experiments  : — 

i.  A  thin  hollow  copper  sphere  provided  with  an  aperture  of  about  an  inch 
in  diameter  (fig.  663),  and  placed  on  an  insulating  support,  is  charged  in  the 
interior  with  electricity.  When  the  carrier  or  proof  plane  (a  small  disc  of 
copper-foil  at  the  end  of  a  slender  glass  or  shellac  rod)  is  applied  to  the  in- 
terior, and  is  then  brought  near  an  electroscope,  no  electrical  indications 
are  produced.  But  if  the  proof  plane  is 
applied  to  the  electroscope  after  having 
been  in  contact  with  the  exterior,  a  con- 
siderable divergence  ensues. 

The  action  of  the  proof  plane  as  a 
measure  of  the  quantity  of  electricity  is 
as  follows  : — When  it  touches  any  surface 
the  proof  plane  becomes  confounded  with 
the  element  touched  ;  it  takes  in  some 
sense  its  place  relatively  to  the  electricity, 
or  rather,  it  becomes  itself  the  element 
on  which  the  electricity  is  diffused.  Thus 
when  the  proof  plane  is  removed  from 
contact  we  have  in  effect  cut  away  from 
the  surface  an  element  of  the  same 
thickness  and  the  same  extent  as  its  own, 
and  have  transferred  it  to  the  balance 
without  its  losing  any  of  the  electricity 
which  covered  it. 

ii.  A  hollow  globe,  fixed  on  an  insu-  '''  '  "*' 

lating  support,  is  provided  with  two  hemispherical  envelopes  which  fit  closely 
and  can  be  separated  by  glass  handles.  The  interior  is  now  electrified  and 
the  two  hemispheres  brought  in  contact.     On  then  rapidly  removing  them 


700 


Frictional  Electricity. 


[735- 


ffig.  664),  the  coverings  will  be  found  to  be  electrified,  while  the  sphere  is  in 
its  natural  condition. 


^  'Mill 


lllllllllllllllllll  III! 

— t=r 


I  iiiiiriii'iiiiir    'iiiiiiiiiiiiili 


This  may  also  be  illustrated  by  the  experiment  represented  in  fig.  665,  in 
which  A  is  a  hollow  brass  hemisphere  resting  on  a  support  of  ebonite,  and  is 
electrified  by  striking  it  with  silk  ;  a  similar 
hemisphere  B  provided  with  a  glass  handle  G  is 
placed  over  it.  A  metal  spring  on  the  inside  of 
1!  is  brought  in  contact  with  A  by  pressing  the 
ebonite  button  E,  and  on  afterwards  examining 
the  two  hemispheres  all  the  electricity  is  found 
on  the  outer  one  B. 

iii.  The  distribution  of  electricity  on  the  sur- 
face may  also  be  shown  by  means  of  the  follow- 
ing apparatus  : — It  consists  of  a  metal  cylinder 
on  insulating  supports,  on  which  is  fixed  a  long 
strip  of  tinfoil  which  can  be  rolled  up  by  means 
of  a  small  insulating  handle  (fig.  666).  A  quad- 
rant electrometer  is  fitted  in  metallic  communi- 
cation with  the  cylinder.  When  the  sphere  is  rolled  up,  a  charge  is  imparted 
to  the  cylinder,  by  which  a  certain  divergence  is  produced.  On  unrolling  the 
tinfoil  this  divergence  gradually  diminishes,  and  increases  as  it  is  again  rolled 
up.  The  quantity  of  electricity  remaining  the  same,  the  electrical  force,  on 
each  unit  of  surface,  is  therefore  less  as  the  surface  is  greater. 

iv.  The  following  ingenious  experiment  by  Faraday  further  illustrates 
this  law  : — A  metal  ring  is  fitted  on  an  insulated  support,  and  a  conical 
gauze  bag,  such  as  is  used  for  catching  butterflies,  is  fitted  to  it  (fig.  667). 

By  means  of  a  silk  thread,  the  bag  can  be  drawn  inside  out.  After 
electrifying  the  bag,  it  is  seen  by  means  of  a  jiroof  plane  that  the  electricity 
is  on  the  exterior  ;  but  if  the  positions  are  reversed  by  drawing  the  bag 
inside  out,  so  that  the  interior  has  now  become  the  exterior,  the  electricity 
will  still  be  found  on  the  exterior. 


-736j 


Distribution  of  Electricity. 


701 


V.  The  same  point  may  be  further  illustrated  by  an  experiment  due  to 
Terquem.  A  bird-cage,  preferably  of  metal  wire,  is  suspended  by  insulators, 
and  contains  either  a  gold-leaf  electroscope  or  pieces  of  Dutch  metal,  feathers, 

pith  balls,  &c.  When 
the  cage  is  connected 
with  an  electrical  ma- 
chine, the  articles  in 
the  interior  are  quite 
unaffected,  although 
strong  sparks  may  be 
taken  from  the  outside. 


Fig.  666. 


Bands  of  paper  may  be  fixed  to  the  inside  ;  while  those  fixed  to  the  outside 
diverge  widely.  A  bird  in  the  inside  is  quite  unaffected  by  the  charge  or 
discharge  of  the  electricity  of  the  cage. 

The  property  of  electricity,  of  accumulating  on  the  outside  of  bodies, 
is  ascribed  to  the  repulsion  which  the  particles  exert  on  each  other.  Elec- 
tricity tends  constantly  to  pass  to  the  surface  of  bodies,  whence  it  continually 
tends  to  escape,  but  is  prevented  by  the  resistance  of  the  feebly  conducting 
atmosphere. 

To  the  statement  that  electricity  resides  on  the  surface  of  bodies,  two 
exceptions  may  be  noted.  When  two  opposite  electricities  are  discharged 
through  a  wure— a  phenomenon  which,  when  continuous,  forms  an  electrical 
current — the  discharge  is  effected  throughout  the  whole  mass  of  the  con- 
ductor. Also  a  body  placed  inside  another  may,  if  insulated  from  it,  receive 
charges  of  electricity.  On  this  depends  the  possibility  of  electrical  experi- 
ments in  ordinary  rooms. 

736.  Electric  density. — On  a  metal  sphere  the  distribution  of  the 
electricity  is  everywhere  the  same,  simply  from  its  symmetry.  This  can  be 
demonstrated  by  means  of  the  proof  plane  and  the  torsion  balance.  A  metal 
sphere  placed  on  an  insulating  support  is  electrified,  and  touched  at  different 
parts  of  its  surface  with  the  proof  plane,  which  each  time  is  applied  to  the 
movable  needle  of  the  torsion  balance.     As  in  all  cases  the  torsion  observed 


702 


Frictional  Electricity. 


[736- 


is  sensibly  the  same,  it  is  concluded  that  the  proof  plane  each  time  receives 
the  same  quantity  of  electricity.  In  the  case  of  an  elongated  ellipsoid  (fig. 
668)  it  is  found  that  the  distribution  of  electricity  is  different  at  different 
points  of  the  surface.  The  electricity  accumulates  at  the  most  acute  points. 
This  is  demonstrated  by  successively  touching  the  ellipsoid  at  different  parts 
with  the  proof  plane,  and  then  bringing  this  into  the  torsion  balance.  By 
this  means  Coulomb  found  that  the  greatest  deflection  was  produced  when 
the  proof  plane  had  been  in  contact  with  the  point  a^  and  the  least  by  con- 
tact with  the  middle  space  c. 

The   elect}  ic  density   or   electric   thickness  is  the  term  used  to  express 
the  quantity  of  electricity  found   at    any  moment  on  a  given  surface.     If 

S  represents  the 
surface  and  Q  the 
quantity  of  elec- 
tricity on  that  sur- 
face, then,  assuming 
that  the  electricity 
is  equally  distri- 
buted, its  electrical 
density     is      equal 

-I 

Coulomb  found 
.by  quantitative  ex- 
periments, that  in 
an  ellipsoid  the 
density  of  the  elec- 
tricity, at  the  equa- 
tor of  the  ellipsoid,  is  to  that  at  the  ends  in  the  same  ratio  as  the  length  of 
the  minor  to  the  major  axis.  On  an  insulated  cylinder,  terminated  by  two 
hemispheres,  the  density  of  the  electrical  layer  at  the  ends  is  greater  than 
in  the  middle.  In  one  case,  the  ratio  of  the  two  densities  was  found  to  be 
as  2-3  :  I.     On  a  circular  disc  the  density  is  greatest  at  the  edges. 

"J-^J.  Force  outside  an  electrified  body. — The  force  F  which  a  sphere, 
charged  with  a  quantity  of  electricity  Q,  exerts  on  a  point  at  a  distance  d 

from  its  centre,  is  -^  ;  this  is  equal  to  '^,  if  S  is  the  area  of  the  sphere,  and 
d-  d~ 

p  the    density  of  electricity  on  the  unit   of  surface. 
Now  the  area  of  the  sphere  is  47rR-  ;  and  if  the  dis- 
tance d  is  equal  to  the  radius  R,  then  the  force  at  the 
47rpR2      . 


Fig. 


surface  S  =  - 


This  holds  also  if  the  point  considered  is  at  a  very 

small  distance  just  outside  the  sphere.     Let  a  small 

segment  at>  be  cut  in  a  sphere  (fig.  669).     Then   its 

Fie  66q.  action  on  a  point/^  just  inside  the  sphere  will  be  exactly 

neutralised  by  the  action  of  the  rest  of  the  sphere  ncd 

on  this  point,  since  there  is  no  electrical  force  inside  a  sphere  (735) ;  that 

is,  the  action  of  the  two  portions  is  equal,  but  in  opposite  directions.     Now 


-738]  Potential.  703 

for  a  point^',  just  outside  the  sphere,  the  actions  will  also  be  equal,  but  in 
the  same  directions.  Ikit  the  total  action  of  the  whole  sphere  is  47r/)  :  hence 
the  action  of  each  portion  is  half  of  this  ;  that  is,  Znp. 

It  may  be  shown  in  like  manner  that  the  whole  force  of  any  closed  con- 
ductor is  47rp  per  unit  area. 

On  an  insulated  conductor,  where  the  electricity  is  in  ecjuilibrium,  a 
particle  of  electricity  will  have  no  tendency  to  move  along  the  surface,  for 
otherwise  there  would  be  no  equilibrium.  But  the  electricity  does  exert  a 
pressure  on  the  external  non-conducting  medium,  which  is  always  directed 
outwards,  and  is  called  the  elect7-ostatic  teiision  or  pressure. 

The  amount  of  this  pressure  is  i-jvp"  for  unit  area,  p  being  the  electrical 
density  at  the  point  considered.  It  is  therefore  proportional  to  the  square  of 
the  density.  The  effect  of  this  on  a  soap-bubble,  for  instance,  if  electrified 
with  either  kind  of  electricity,  is  to  enlarge  it.  In  any  case  the  electrification 
constitutes  a  deduction  from  the  amount  of  atmospheric  pressure  which  the 
body  experiences  when  unelectrified. 

The  term  electric  density  and  electrical  tension  are  often  confounded. 
The  latter  ought  rather  to  be  restricted,  as  Maxwell  proposed,  to  express  the 
state  of  strain  or  pressure  exerted  upon  a  dielectric  in  the  neighbourhood  of 
an  electrified  body  ;  a  strain  which,  if  continually  mcreased,  tends  to  disrup- 
tive discharge.  Electric  tension  may  thus  be  compared  to  the  strain  on  a 
rope  which  supports  a  weight ;  and  the  dielectric  medium  which  can  support 
a  certain  tension  and  no  more  is  said  to  have  a  certain  electrical  strength  in 
the  same  sense  as  a  rope  which  bears  a  certain  weight  without  breaking  is 
said  to  have  a  certain  strength. 

738.  Potential.— In  the  experiment  (fig.  669),  instead  of  applying  the 
test  sphere  directly  to  the  large  sphere,  let  the  two  be  placed  at  a  consider- 
able distance  from  each  other,  and  let  them  be  connected  by  a  long  thin  wire, 
and  then,  detaching  the  small  sphere,  let  the  quantity  upon  it  be  measured 
by  the  torsion  balance:  the  angle  of  deflection  will  show  that  this  quantity 
is  the  same  whatever  part  of  the  large  sphere  be  touched,  as  must  indeed  be 
the  case,  owing  to  symmetry  ;  but  the  amount  of  this  charge  will  be  mate- 
rially difterent  from  the  amount  when  the  small  sphere  is  placed  in  direct 
contact  with  the  larger  one.  Hence  the  quantity  of  electricity  removed 
differs  according  to  the  mode  in  which  connection  is  made. 

If  now  this  experiment  be  repeated  with  the  ellipsoid,  it  will  be  found 
that  whatever  point  of  this  is  put  in  distant  connection  with  the  proof  sphere 
by  the  long  wire,  the  charge  which  the  small  sphere  acquires  is  always  the 
same  ;  although,  as  we  have  seen,  the  proof  sphere  would  remove  very  dif- 
ferent quantities  of  electricity  according  to  the  part  where  it  touches. 

Here,  then,  we  are  dealing  with  experimental  facts  which  our  previous 
notions  are  insufficient  to  explain.  It  is  manifest  that  the  difference  in  the 
results  depends  neither  on  the  total  charge  nor  on  the  density.  We  require 
the  introduction  of  a  new  conception,  which  is  that  of  electrical  potential. 
Introduced  originally  into  electrical  science  by  Green,  out  of  considerations 
arising  from  the  mathematical  treatment  of  the  subject,  the  use  of  the  term 
potential  is  justified  and  recommended  by  the  clearness  with  which  it  brings 
out  the  relations  of  electricity  to  work. 

We  have  already  seen,  that  in  order  to  lift  a  certain  mass  against  the 


704  Frictional  Electricity.  [738- 

attraction  of  gravitation  (59-62)  there  must  be  a  definite  expenditure  of  work, 
and  the  equivalent  of  this  work  is  met  with  in  the  energy  which  the  lifted 
mass  retains,  or  what  is  called  the  potential  energy  of  position. 

Let  us  now  suppose  that  we  have  a  large  insulated  metal  sphere  charged 
with  positive  electricity,  and  that,  at  a  distance  which  is  very  great  in  com- 
parison with  the  size  of  the  sphere,  there  is  a  small  insulated  sphere  charged 
with  the  same  kind  of  electricity.  If  now  we  move  the  small  sphere  to  any 
given  point  nearer  the  larger  one,  we  must  do  a  certain  amount  of  work  upon 
it  to  overcome  the  repulsion  of  the  two  electricities. 

The  work  required  to  be  done  against  electrical  forces,  in  order  to  move 
the  unit  of  positive  electricity  from  an  infinite  distance  to  a  given  point  in 
the  neighbourhood  of  an  electrified  conductor,  is  called  XS\q  potential  2X  this 
point.  If,  in  the  above  case,  the  larger  sphere  were  charged  with  negative 
electricity,  then  instead  of  its  being  needful  to  do  work  in  order  to  bring  a 
unit  of  positive  electricity  towards  it,  work  would  be  done  by  electrical 
attraction,  and  the  potential  of  the  point  near  the  charged  sphere  would  thus 
be  negative. 

The  potential  at  any  point  may  also  be  said  to  be  the  work  done  against 
electrical  force,  in  moving  unit  charge  of  negative  electricity  from  that  point 
to  an  infinite  distance. 

•  The  amount  of  work  required  to  move  the  unit  of  positive  electricity 
against  electrical  force,  from  any  one  position  to  any  other,  is  equal  to  the 
excess  of  the  electrical  potential  of  the  second  position  over  the  electrical 
potential  of  the  first.  This  is,  in  effect,  the  same  as  what  has  been  said 
above,  for  at  an  infinite  distance  the  potential  is  zero. 

We  cannot  speak  of  potential  in  the  abstract,  any  more  than  we  can 
speak  of  any  particular  height,  without  at  least  some  tacit  reference  to  a 
standard  of  level.  Thus,  if  we  say  that  such  and  such  a  place  is  300  feet 
high,  we  usually  imply  that  this  height  is  measured  in  reference  to  the  level 
of  the  sea.  So,  too,  we  refer  the  longitude  of  a  place  to  some  definite 
meridian,  such  as  that  of  Greenwich,  either  expressly  or  by  implication. 

In  like  manner  we  cannot  speak  of  the  potential  of  a  mass  of  electricity 
without,  at  least,  an  implied  reference  to  a  standard  of  potential.  This 
standard  is  usually  the  earth,  which  is  taken  as  being  zero  potential.  If  we 
speak  of  the  potential  at  a  given  point,  the  difference  between  the  potential 
at  this  point  and  the  earth  is  referred  to. 

If,  in  the  imaginary  experiment  described  above,  we  move  the  small 
sphere  round  the  large  electrified  one  always  at  the  same  distance,  no  work 
is  done  by  or  against  it  for  the  purpose  of  overcoming  or  of  yielding  to 
electrical  attractions  or  repulsions,  just  as  if  we  move  a  body  at  a  certain 
constant  level  above  the  earth's  surface,  no  work  is  done  upon  it  as  respects 
gravitation.  An  imaginary  surface  drawn  in  the  neighbourhood  of  an  elec- 
trified body,  such  that  a  given  charge  of  electricity  can  be  moved  from  any 
one  point  of  it  to  any  other  without  any  work  being  done  either  by  or  against 
electrical  force,  is  said  to  be  an  cquipotential  sur/ncc.  Such  a  surface  may 
be  described  as  ha\ing  e\-cryvvhcre  the  sai/w  electrical  level ;  and  the  notion 
of  bodies  at  different  electrical  levels,  in  reference  to  a  particular  standard, 
is  analogous  to  that  of  bodies  at  diflferent  potentials.  In  the  case  of  an 
insulated  electrified  sphere  the  successive  equipolential  surfaces  would  be 


-739]  Electrical  Capacity.  705 

successive  shells  of  gradually  increasing  radii,  like  the  coats  of  an  onion. 
The  space  about  an  electrified  body  or  electrified  system  is  called  the  elec- 
trical field.  The  fall  of  potential  from  one  equipotential  surface  to  another 
is  most  rapid  in  the  direction  of  the  perpendiculars  to  the  two  surfaces. 
These  perpendiculars  represent  the  lines  of  electrical  force,  the  'lines  of 
force'  of  Faraday,  or  the  'lines  of  induction'  of  Ma.xwcll.  On  the  surface 
of  an  insulated  electrified  sphere  at  a  distance  from  other  conductors,  these 
lines  of  force  are  perpendicular  to  the  surface  of  the  sphere.  The  lines  of 
electrical  force  may  be  made  visible  in  the  dark  by  placing  two  small  balls 
at  a  distance  from  each  other  in  conducting  communication  with  an  elec- 
trical machine  at  work,  and  then  sifting  lycopodium  powder  through  a  fine 
sieve  while  the  space  is  simultaneously  illuminated  by  the  lime  or  the  electric 
light. 

As  water  only  flows  from  places  at  a  higher  level  to  places  at  a  lower 
level,  so  also  electricity  only  passes  from  places  at  a  higher  to  places  at  a 
lower  potential.  If  an  electrified  body  is  placed  in  conducting  communica- 
tion with  the  earth,  electricity  will  flow  from  the  body  to  the  earth,  if  the 
body  is  at  a  higher  potential  than  the  earth  ;  and  from  the  earth  to  the 
body,  if  the  body  is  at  a  lower  potential,  and  its  flow  will  be  proportional  to 
the  difference  of  potential.  If  the  potential  of  a  body  is  higher  than  that 
of  the  earth,  it  is  said  to  have  a  positive  potential  ;  and  if  at  a  lower  poten- 
tial, a  negative  potential.  A  body  charged  with  free  negative  electricity  is 
one  at  lower  potential  than  the  earth  ;  one  charged  with  free  positive  elec- 
tricity is  at  a  higher  potential. 

739.  Electrical  capacity. — The  capacity  of  any  conductor  may  be 
measured  by  the  quantity  of  electricity  which  it  can  acquire  when  placed 
in  contact  with  a  body  which  charges  it  to  unit  electrical  potential. 

We  may  illustrate  the  relation  between  capacity  and  potential  by  refer- 
ence to  the  analogous  phenomenon  of  heat.  In  the  interchange  of  heat 
between  bodies  of  different  temperatures  the  final  result  is  that  heat  only 
passes  from  bodies  of  higher  to  bodies  of  lower  temperature.  So  also  elec- 
tricity only  passes  from  bodies  of  higher  to  bodies  of  lower  potential. 
Potential  is  as  regards  electricity  what  temperature  is  as  regards  heat,  and 
might  indeed  be  called  electrical  temperature.  We  may  have  a  small 
quantity  of  heat  at  a  very  high  temperature.  Thus  a  short  thin  wire  heated 
to  incandescence  has  a  far  higher  heat  potential,  or  temperature,  than  a 
bucket  of  warm  water.  But  the  latter  will  have  a  far  larger  quantity.  A 
flash  of  lightning  represents  electricity  at  a  very  high  potential,  but  the 
quantity  is  small. 

The  relation  between  electrical  potential  and  density  may  be  further 
illustrated  by  reference  to  the  head  of  water  in  a  reservoir.  The  pressure 
is  proportional  to  the  depth  ;  the  potential  is  everywhere  the  same.  For 
suppose  we  want  to  introduce  an  additional  pound  of  water  into  the  reser- 
voir, the  same  amount  of  work  is  recjuired  whether  the  water  be  forced  in 
at  the  bottom  or  be  poured  in  at  the  top. 

If  a  hole  be  made  very  near  the  top  of  the  reservoir,  a  quantity  of  water 
in  falling  to  the  ground  would  generate  an  amount  of  heat  proportional  to 
the  fall.  If  the  same  quantity  escaped  through  a  hole  near  the  bottom,  it 
would  not  produce  so  much  heat  by  direct  fall ;  but  it  will  possess  a  certain 

z  7. 


7o6  Frictional  Electricity.  [739- 

velocity,  the  destruction  of  which  will  produce  a  quantity  of  heat  which, 
added  to  that  produced  by  the  fall,  will  give  exactly  as  much  as  the 
other. 

When  the  charge  or  quantity  of  electricity  imparted  to  a  body  increases, 
the  potential  increases  in  the  same  ratio;  so  that,  calling  Q  the  quantity  of 
electricity,  C  the  capacity,  and  V  the  potential,  we  have  Q  =  CV  ;  that  is  to 
say,  that  the  charge,  or  quantity  of  electricity,  that  any  body  possesses,  is 
the  product  of  the  potential  into  the  capacity. 

Now  for  a  sphere  whose  radius  is  R  the  potential  V  =  -^-,  from  which 

R 

we  get  C  =  R  ;  that  is,  that  the  capacity  of  a  spliere  is  equal  to  its  radius. 

While  there  is  a  close  analogy  between  heat  and  electricity,  as  regards 
capacity,  there  are  important  differences  ;  thus  the  capacity  of  a  body  for 
heat  is  influenced  by  the  temperature  (457),  being  greater  at  higher  tem- 
peratures, while  the  capacity  of  a  body  for  electricity  does  not  depend  on 
the  potential.  Again,  the  calorific  capacity  depends  solely  on  the  mass  of 
a  body,  and  in  bodies  of  the  same  material  and  shape  is  proportional  to 
the  cube  of  homologous  dimensions  ;  the  capacity  for  electricity  is  directly 
proportional  to  such  dimensions,  and  not  to  the  weight  or  volume.  Calorific 
capacity  is  proportional  to  a  specific  coefficient,  which  varies  with  the  mate- 
rial, but  is  independent  of  its  shape  ;  while  electrical  capacity  varies  with 
the  shape  of  a  body,  but  not  with  its  material,  provided  the  electricity  can 
move  freely  upon  it.  Calorific  capacity  is  unaffected  by  the  proximity  of 
other  bodies,  while  the  electrical  capacity  depends  on  the  position  and  shape 
of  all  the  adjacent  conductors. 

If  we  have  a  series  of  bodies  at  a  considerable  distance  from  each  other, 

whose  capacities  and  potentials  are  respectively  c,  c\  c'\  &c.,  and  v,  v\  v' \ 

&c.,  then,  if  they  are  all  connected  by  fine  wires  of  no  capacity,  they  all 

instantly  acquire  the  same  potential  V,  which  is  determined  by  the  equation 

Y  _cv  -^  c'v'  +  c"v" 

c  -fC'  +  c" 

The  analogy  of  this  to  the  equalisation  of  temperature  which  takes  place 
when  bodies  at  different  temperatures  are  mixed  together  is  directly 
apparent  (449).  It  may  be  further  illustrated  by  supposing  a  series  of 
tubes  of  different  diameters,  and  connected  by  very  narrow  tubes,  but  in 
which  are  stopcocks  to  cut  off  communication.  If,  while  in  this  state,  water 
be  poured  into  the  tubes  to  different  heights,  it  will  be  manifest  that  they 
will  hold  very  various  quantities  of  water.  If,  however,  the  stopcocks  are 
opened,  the  tubes  will  still  contain  quantities  of  water  proportional  to  their 
capacities,  Ijut  the  level  or  potential  in  all  will  be  the  same. 

740.  IVXeasurement  of  capacity  and  potential. — We  may  use  Coulomb's 
balance  for  the  purpose  of  measuring  the  capacity  C,  or  the  potential  V,  of 
a  body  charged  with  electricity.  For  this  purpose  the  body  in  question  is 
placed,  by  means  of  a  long  fine  wire  of  no  capacity,  in  distant  contact  with 
a  small  neutral  insulated  sphere  of  known  radius  r.  This  small  sphere  is 
then  applied  to  the  torsion  balance,  and  its  charge  q  =  )■%>  is  measured.  Now 
since  the  original  charge  on  the  si)here  is  Q  =  C\',  after  contact  with  the 
small  sphere,  which  is  neutral,  the  system  will  have  a  new  potential  or 
electrical  level,  ?',  such  that  CV  =  (C  +  r)  7>.    Restoring  now  tlie  small  sphere 


-741]  Potential  of  a  Sphere.  707 

to  the  neutral  state,  and  repeating  the  experiment  and  the  measurement, 
we  shall  then  get  a  second  value  n>\  from  which  we  have  the  equation 

C7/  =  (C  +  r)  v'.     Combining  and  reducing,  we  get  the  ratio  V=  ^",  which, 

v' 
seeing  that  7-7'  and  rv'  are  numerical  values,  leads  directly  to  the  desired 
result. 

In  like  manner  it  is  easy  to  determine  the  capacity  by  obvious  transfor- 
mations of  these  equations. 

It  will  thus  be  seen  that  this  process  of  determining  potential  is  analo- 
gous to  that  of  determining  temperature  by  means  of  a  thermometer  ;  and 
the  proof  sphere  plays  the  part,  as  it  were,  of  an  electrical  tJiermometer.  It 
may  be  observed  that  in  the  case  of  heat  we  pass  from  the  conception  of 
temperature  to  that  of  qiiatitity  of  heat,  while  with  electricity,  starting  with 
the  fact  of  quantity,  or  charge  of  electricity,  we  arrive  at  the  conception  of 
potential  of  electricity. 

741.  Potential  of  a  sphere. — \iq^  q\  and  q"  are  any  masses  of  electri- 
city on  the  surface  of  an  insulated  conducting  sphere,  and  d  d'  and  d"  their 

respective  distances  from  any  point  of  the  interior  of  the  sphere,  then  f'  ^, 

d  d' 

and  ^,^  are  the  values  of  the  potentials  v,  v\  and  v"  wjiich  they  would 

severally  produce  at  this  point.     Let  the  point  in  question  be  the  centre, 
and  let  Q  be  the  sum  of  the  whole  quantities  ;  then  V,  the  potential  of  the 

sphere,  equals  l^,  R  being  the  radius. 

If  there  be  a  sphere,  or  uniform  spheroidal  shell  of  matter,  which  acts 
according  to  the  inverse  square  of  the  distance,  then  the  total  action  of  this 
sphere  is  the  same  as  if  the  whole  matter  were  concentrated  at  the  centre. 
This  was  first  proved  by  Newton  in  the  case  of  gravitation  ;  but  it  also 
applies  to  electricity,  and  hence,  in  calculating  the  potential  at  any  point  out- 
side a  sphere  possessing  a  uniform  charge,  we  need  only  consider  its  dis- 
tance from  the  centre,  and  for  such  a  case  we  may  write  the  value  of  the 

potential  V  =  >. 

If  a  charge  of  electricity,  Q,  be  imparted  to  two  insulated  conducting 
spheres  whose  radii  are  respectively  r  and  r',  and  which  are  connected  by 
a  long  fine  wire,  the  quantity  of  which  may  be  neglected,  the  electricity 
will  distribute  itself  over  the  two  spheres,  which  will  possess  the  charges 
q  and  q' ;  that  \%^  q -^^  q'  =  <^.     (i)  The  whole  system  will  be  at  the  same 

potential  V,  such  that  V  =  ?  =  f,.     (2)    Combining  these  two  equations  and 
reducing,  we  get  for  the  quantities  q  and  q'  on  each  sphere  q  = -^^  ,    and 


q 

r  +  r 


r  ■ 
Qr' 


Now,  since  the  diameter  of  any  sphere  with  which  we  can  experiment  is 
infinitely  small  compared  with  that  of  the  earth,  it  follows  that  when  a  sphere 
is  connected  with  the  earth  by  a  fine  wire  the  quantity  of  electricity  which 
it  retains  is  infinitely  small. 

z  z  2 


7o8  Frictional  Electricity.  [741- 

For  the  densities  on  the  two  spheres  we  have  d=    ^  -  and</'  =  ^    ,  from 

47T-r-  47rr 

which  by  equation  (2)  it  is  readily  deduced  that  d :  d'  =  r'  \  r ;  that  is,  that 
the  electrical  densities  on  two  spheres  in  distant  connection  are  inversely  as 
the  radii.  If,  for  instance,  a  fine  wire  be  connected  with  a  charged  insulated 
sphere,  the  distant  pointed  end  of  the  wire  may  be  regarded  as  a  sphere 
with  an  infinitely  small  radius,  and  thus  the  density  upon  it  would  be  in- 
finitely great. 

742.  Action  of  points. — We  have  just  seen  that  on  a  point  in  connection 
with  a  conductor  charged  with  electricity  the  density  may  be  considered  to 
be  infinitely  great,  but  the  greater  the  density  the  greater  will  be  the  tendency 
of  electricity  to  overcome  the  resistance  of  the  air,  and  escape,  for  the  electro- 
static pressure  is  proportional  to  the  square  of  the  density  (J37)-  If  the  hand 
be  brought  near  a  point  on  an  electrified  conductor  a  slight  wind  is  felt ;  and 
if  the  disengagement  of  electricity  takes  place  in  the  dark  a  luminous  brush 
is  seen.  If  an  electrified  conductor  is  to  retain  its  electricity  all  sharp  points 
and  edges  must  be  avoided  ;  on  the  other  hand,  to  facilitate  the  outflow  of 
electricity  in  apparatus  and  experiments  (764),  frequent  use  is  made  of  this 
action  of  points.     A  flame  acts  like  a  very  fine  point  in  diffusing  electricity. 

743.  Jtoss  of  electricity. — Experience  shows  that  electrified  bodies 
gradually  lose  their  electricity,  even  when  placed  on  insulating  supports. 
This  loss  is  mainly  due  to  the  insulating  supports.  The  charge  is  gradually 
dissipated  in  consequence  of  the  electricity  either  passing  through  the  sup- 
ports or  creeping  over  the  surface.  All  substances  conduct  electricity  in 
some  degree  ;  those  which  are  termed  insulators  are  simply  very  bad  con- 
ductors. An  electrified  conductor  resting  on  supports  must  therefore  lose  a 
certain  quantity  of  electricity — either  by  penetration  into  its  mass  or  along 

the  surface.    This  loss  of  electricity  is  a  main  cause 

of  difficulty  in  experiments  on  the  quantitative  laws 

of  electricity  ;    it  varies  with  the  electric  density, 

and  increases  with  the  hygrometric  state  of  the  air, 

though   it  does  not  seem  that  the  loss  from  this 

cause  is  due  to  a  direct  conductivity  by  moist  air. 

Sir  W.  Thomson  ascribes  the  greater  part  of  the  loss 

to  the  conducting  layer  of  moisture  which  covers  the 

supports  ;  and  he  finds  that  in  comparison  with  this, 

the  direct  loss  by  even  moist  air  is  inconsiderable. 

Brown  shellac  or  ebonite  is  the  best  insulator  ; 

-    ^    glass   is   a  hygroscopic    substance,  and   must   be 

dried  with  great  care.     It  is  best  covered  with  a  thin 

'^'   ^'^'  layer  of  shellac  varnish,  as  has  already  been  stated. 

Mascart's  i77sulator  is  admirably  adapted  for  supporting  bodies  charged 

with  electricity.     It  consists  of  a  glass  vessel  of  special  shape  (fig.  67o\  to 

the  glass  vase  of  which  is  fused  the  stem.     This  passes  through  the  neck 

and  supports  the  palate,  P  ;  the  neck  is  closed  by  an  ebonite  stopper,  and 

inside  the  vessel  is  sulphuric  acid,  so  that  the  slcm  A  is  always  dry. 


-744] 


709 


CHAPTEl 


III. 


ACTION   OF   ELECTRIFIED   BODIES   ON   BODIES   IN   THE   NATURAL   STATE. 
INDUCED   ELECTRICITY.      ELECTRICAL  MACHINES. 

744.  Electricity  by  influence  or  induction. — An  insulated  conductor, 
cliarged  with  either  kind  of  electricity,  acts  on  bodies  in  a  neutral  state 
placed  near  it  in  a  manner  analogous  to  that  of  the  action  of  a  magnet  on 
soft  iron  ;  that  is,  it  decomposes  the  neutral  electricity,  attracting  the  oppo- 


tig  67 


site  and  repelling  the  like  kind  of  electricity.     The  action  thus  exerted  is 
said  to  take  place  by  injlucncc  or  induction. 

The  phenomena  of  induction  may  be  demonstrated  by  means  of  a  brass 
cylinder  placed  on  an  insulating  support,  and  provided  at  its  extremities 
with  two  small  electric  pendulums,  which  consist  of  pith  balls  suspended  by 
linen  threads  (fig.  671).  If  this  apparatus  is  placed  near  an  insulated  con- 
ductor ;//,  charged  with  either  kind  of  electricity— for  instance,  the  conductor 
of  an  electrical  machine,  which  is  charged  with  positive  electricity— the 
natural  electricity  of  the  cylinder  is  decomposed,  free  electricity  will  be 
developed  at  each  end,  and  both  pendulums  will  diverge.  If,  while  they  still 
diverge,  a  stick  of  sealing-wax,  excited  by  friction  with  flannel,  be  approached 
to  that  end  of  the  cylinder  nearest  the  conductor,  the  corresponding  pith 
ball  will  be  repelled,  indicating  that  it  is  charged  with  the  same  kind  of 
electricity  as  the  sealing-wax — that  is,  with  negative  electricity  ;  while  if  the 
excited  sealing-wax  is  brought  near  the  other  ball  it  will  be  attracted,  showing 
that  it  is  charged  with  positive  electricity.     If,  further,  a  glass  rod  excited 


710  Frictional  Electricity.  [744- 

by  friction  with  silk,  and  therefore  charged  with  positive  electricity,  be  ap- 
proached to  the  end  nearest  the  conductor,  the  pendulum  will  be  attracted  : 
while  if  brought  near  the  other  end,  the  corresponding  pendulum  will  be  re- 
pelled. If  the  influence  of  the  charged  conductor  be  suppressed,  either  by 
removing  it,  or  placing  it  in  communication  with  the  ground,  the  separated 
electricities  will  recombine,  and  the  pendulums  exhibit  no  divergence. 

The  cause  of  this  phenomenon  is  obviously  a  decomposition  of  the  neutral 
electricity  of  the  cylinder,  by  the  free  positive  electricity  of  the  conductor  ; 
the  opposite  or  negative  electricity  being  attracted  to  that  end  of  the  cylinder 
nearest  the  conductor,  while  the  similar  electricity  is  repelled  to  the  other 
end.  Between  these  two  extremities  there  is  a  space  destitute  of  free 
electricity.  This  is  seen  by  arranging  on  the  cylinders  a  series  of  pairs  of 
pith  balls  suspended  by  threads.  The  divergence  is  greatest  at  each 
extremity,  and  there  is  a  line  at  which  there  is  no  divergence  at  all,  which  is 
called  the  neutral  line.  The  two  electricities,  although  equal  in  quantity,  are 
not  distributed  over  the  cylinder  in  a  symmetrical  manner  ;  the  attraction 
which  accumulates  the  negative  electricity  at  one  end  is,  in  consequence  of 
the  greater  nearness,  greater  than  the  repulsion  which  drives  the  positive 
electricity  to  the  other  end,  and  hence  the  neutral  line  is  nearer  one  end  than 
the  other.  Nor  is  the  electricity  induced  at  the  two  ends  of  the  cylinder 
under  the  same  conditions.  That  which  is  repelled  to  the  distant  extremity 
is  free  to  escape  if  a  communication  be  made  with  the  ground  ;  whilst,  on 
the  other  hand,  the  unlike  electricity  which  is  attracted  is  held  bound  or 
captive  by  the  inducing  action  of  the  electrified  body.  Even  if  contact  be 
made  with  the  ground  on  the  face  of  the  cylinder  adjacent  to  the  inducing 
body,  the  electricity  induced  on  that  face  will  not  escape.  The  repelled 
electricity,  however,  on  the  distant  surface  is  not  thus  bound  ;  it  is  free  to 
escape  by  any  conducting  channel,  and  hence  will  immediately  disappear 
wherever  contact  be  made  between  the  ground  and  the  cylinder.  Both  the 
pith  balls  will  collapse,  and  all  signs  of  electricity  on  the  cylinder  depart  with 
the  escape  of  the  repelled  or  free  electricity.  But  now,  if  communication  with 
the  ground  be  broken,  and  the  inducing  body  be  discharged  or  removed  to  a 
considerable  distance,  the  attracted  or  bound  electricity  is  itself  set  free,  and 
diffusing  over  the  whole  cylinder  causes  the  pith  balls  again  to  diverge,  but 
now  with  the  opposite  electricity  to  that  of  the  original  inducing  body.  The 
reason  for  the  escape  of  the  repelled  electricity  is  as  follows  : — If  the 
cylinder  be  placed  in  connection  with  the  ground,  by  metallic  contact  with 
the  posterior  extremity,  and  the  charged  conductor  be  still  placed  near 
the  anterior  extremity,  the  conductor  will  exert  its  inductive  action  as  before. 
But  it  is  now  no  longer  the  cylinder  alone  which  is  influenced.  It  is  a 
conductor  consisting  of  the  cylinder  itself,  the  wire,  and  the  whole  earth. 
The  neutral  line  will  recede  indefinitely,  and,  since  the  conductor  has 
become  infinite,  the  quantity  of  neutral  fluid  decomposed  will  be  increased. 
Hence,  when  the  posterior  extremity  is  placed  in  contact  with  the  ground, 
the  pendulum  at  the  anterior  extremity  diverges  more  widely.  If  the  con- 
necting-rod be  now  removed,  neither  the  quantity  nor  the  distribution  will 
be  altered  ;  and  if  the  conductor  be  removed  or  be  discharged,  a  charge 
of  negative  electricity  will  be  left  on  the  cylinder.  It  will,  in  fact,  remain 
charged  with  electricity,  the  opposite  of  that  of  the  charged  conductor.    Even 


-745]  Faraday  s  Experiments.  7 1 1 

if,  instead  of  connecting  the  posterior  extremity  of  the  cylinder  with  the 
ground,  any  other  part  had  been  so  connected,  the  general  result  would 
have  been  the  same.  All  the  parts  of  the  cylinder  would  be  charged  with 
negative  electricity,  and,  on  breaking  the  connection  with  the  earth,  would 
remain  so  charged. 

Thus  a  body  can  be  charged  with  electricity  by  induction  as  well  as  by 
conduction.  But,  in  the  latter  case,  the  charging  body  loses  jjart  of  its 
electricity,  which  remains  unchanged  in  the  former  case.  The  electricity 
imparted  by  conduction  is  of  the  same  kind  as  that  of  the  electrified 
body,  while  that  excited  by  induction  is  of  the  opposite  kind.  To  impart 
electricity  by  conduction,  the  body 
must  be  quite  insulated  ;  while  in  the 
case  of  induction  it  must  be  in  con- 
nection with  the  earth — at  all  events 
momentarily. 

A  body  electrified  by  induction 
acts  in  turn  on  bodies  placed  near 
it,  separating  the  two  fluids  in  a 
iTianner  shown  by  the  signs  on  the 
sphere. 

What  has  here  been  said  has 
reference  to  the  inductive  action 
exerted  on  good  conductors.  Bad 
conductors  are  not  so  easily  acted 
upon  by  induction,  owing  to  the  great 
resistance  they  present  to  the  circu- 
lation of  electricity  ;  but,  when  once 
charged,  the  electric  state  is  more 
permanent. 

This  is  analogous  to  what  is  met 
with  in  magnetism  ;  a  magnet  in- 
stantaneously magnetises  a  piece  of 
soft  iron,  but  this  is  only  temporary,  and  depends  on  the  continuance  of  the 
action  of  the  magnet ;  a  magnet  magnetises  steel  with  far  greater  difficulty, 
but  this  magnetisation  is  permanent. 

The  fundamental  phenomena  of  induction  may  be  conveniently  investi- 
gated and  demonstrated  by  means  of  the  apparatus  represented  in  fig. 
672,  which  consists  of  a  narrow  cylindrical  brass  tube  BA,  supported  by  an 
insulating  glass  handle,  and  held  over  the  excited  cake  of  an  electrophorus 
(752). 

745.  Faraday's  experiments. — The  following  experiments  of  P^araday, 
which  are  often  known  as  '  the  ice-pail  experiments,'  from  the  vessels  with 
which  they  were  originally  made,  are  excellent  illustrations  of  the  operation 
of  induction,  and  are  of  great  theoretical  importance  : — 

A  carefully  insulated  metal  cylinder,  A,  fig.  673,  is  connected  by  a  wire 
with  an  electroscope  E,  at  some  distance.  On  slowly  placing  inside  the 
cylinder  an  insulated  brass  ball  C,  charged  with  positive  electricity,  which 
is  small  in  comparison  with  the  size  of  the  cylinder,  the  leaves  of  the  electro- 
scope diverge,  and,   as   can   be  shown,  with  positive  electricity,  and  the 


Fig.  672. 


712 


Frictional  Electricity. 


[745- 


'^^^ISUi^^J 


divergence  increases  until  a  certain  depth  is  attained,  when  there  is  no 
further  increase.  The  divergence  now  remains  constant,  whatever  be  the 
position  of  the  ball,  and  when  the  inside  and  outside  are  tested  with  the 
proof  plane  they  are  found  to  be  charged  with  negative  and  positive  respec- 
tively. If  the  ball  is  withdrawn  the  leaves  of  the  electroscope  collapse,  and 
there  is  no  electrification  on  the  cylinder  ; 
the  quantities  of  negative  and  positive 
electricity  developed  on  the  two  surfaces 
are  accordingly  equal  to  each  other. 

If  now  the   ball,  while    still    charged 
with    positive    electricity,  be   brought  as 
before  into  the  cylinder,  and  be  allowed 
to  touch  the  inside,  there  is  no  alteration, 
^9  i    I  not  even  a  momentary  one,  in  the  diver- 

gence of  the  leaves  of  the  electroscope  ; 
but  if  the  ball  be  withdrawn  it  will  now  be 
found  to  be  neutral,  as  is  also  the  inside 
of  the  cylinder,  while  the  outside  is  charged 
with  positive  electricity.  When  the  ball 
touches  the  interior,  the  system  forms 
only  a  single  conductor,  and  all  the  elec- 
tricity passes  to  the  outside  ;  but  since 
Fig.  673.  the  charge   as  indicated  by  the  electro- 

scope does  not  alter,  it  follows  that  the 
positive  of  the  ball  and  the  negative  of  the  inside  of  the  cylinder  are  equal 
to  each  other. 

If  while  the  ball  charged  with  positive  electricity  is  inside  the  cylinder, 
the  latter  is  momentarily  put  to  earth,  the  gold  leaves  collapse,  and  the  proof 
plane,  if  applied  to  the  outside,  removes  no  trace  of  electricity  ;  for  all 
external  bodies  the  cylinder  behaves  as  if  it  were  neutral.  The  internal 
surface  is,  however,  covered  with  a  layer  of  negative  electricity,  and  this  is 
equivalent  to  the  positive  charge  of  the  ball,  for  all  trace  of  electricity  dis- 
appears if  the  ball  is  made  to  touch  the  side. 

If  the  ball,  after  the  cylinder  has  been  momentarily  connected  to  earth, 
be  removed  without  having  touched  the  sides,  the  negative  passes  to  the 
outside  and  forms  there  a  layer  which  is  distributed  as  was  the  layer  of 
positive  electricity  before  being  connected  with  the  ground.  The  cylinder 
is  thus  finally  charged  with  a  quantity  of  electricity  equal  and  of  opposite 
sign  to  the  inducing  body. 

Four  such  cylinders  (fig.  674)  are  placed  concentrically  within  each  other, 
and  are  insulated  from  each  other  by  discs  of  shellac,  and  tlie  outer  one  is 
connected  with  the  electroscope.  On  introducing  the  charged  ball  into  the 
central  cavity  the  leaves  diverge  just  as  if  the  intermediate  ones  did  not 
exist.  Each  of  these  is  charged  with  equal  quantities  of  opposite  electricities, 
all  equal  in  value  to  that  of  the  sphere.  The  internal  charge  of  the  cylinder 
is  the  same  as  if  all  the  intermediate  cylinders  were  suppressed,  and  the 
charge  does  not  vary  e\cn  when  the  intermediate  ones  arc  connected  with 
each  other  or  are  touched  by  the  electrified  ball  C. 

If,  while  C  is  in  its  original  condition,  the  internal  cylinder,  4,  is  con- 


-746] 


Limit  to  the  Action  of  Induction. 


713 


Fig.  674. 


nected  with  the  ground,  the  leaves  colhipse,  and  the  other  cyHnders  are  in 
the  neutral  state  ;  the  two  layers  which  remain,  positive  on  C,  and  negative 
on  the  adjacent  cylinder,  are  without  action  on  an  external  point.  If  any 
other  cylinder  be  thus  treated  the  external  ones  are  reduced  to  the  neutral 
state. 

With  the  aid  of  the  cylinder  (fig.  674)  it  is  easy  to  demonstrate  that  by 
friction  both  electricities  are  pro- 
duced at  the  same  time,  and  in  l^^^Jt 
equal  quantities.  For  if  the 
flannel  and  sealing-wax  in  fig.  659 
after  being  rubbed  are  placed 
simultaneously  in  the  cylinder 
no  divergence  is  produced,  while 
if  each  is  introduced  separately, 
they  produce  equal  divergence 
but  of  opposite  sign. 

Whenever  a  charge  of  elec- 
tricity exists  there  is  somewhere  a  corresponding  charge  of  electricity  of 
the  opposite  kind.  This  may  seem  inconsistent  with  the  fact  that  an  insu- 
lated sphere  may  have  a  charge  of  one  kind  of  electricity.  But  it  is  to  be 
remembered  that  this  is  the  case  of  a  Leyden  jar  (770)  in  which  the 
dielectric  is  the  layer  of  air  between  the  sphere  and  the  sides  of  the  room 
which  form  the  outer  coating. 

746.  Iilmit  to  the  action  of  induction. — The  inductive  action  which  an 
electrified  body  exerts  on  an  adjacent  body  in  decomposing  its  neutral  fluid 
is  limited.  On  the  surface  of  the  insulated  cylinder,  which  we  have  con- 
sidered in  the  pieceding  paragraph,  let  there  be  at  n  any  small  quantity  of 
neutral  electricity  (fig.  675).  The  positive  electricity  of  the  source  m  first 
decomposes  by  induction  the  neutral  electricity  in  ;/,  attracting  its  negative 
towards  A,  and  repelling  its  positive  towards  B  ;  but  in  the  degree  in  which 
the  extremity  A  becomes  charged  with  negative  electricity,  and  the  extre- 
mity B  with  positive  electricity,  there  are  developed  at  A  and  B  two  forces, 
/"and/',  which  act  in  the  opposite  direction  to  the  original  force.  For  the 
forces/  and  f  concur  in  driving  towards  B  the  negative  of  n,  and  towards 


y 


r  i\-_ 


^ 


> 


Fig.  675. 


A  its  positive.  But  as  the  inducing  force  F  which  is  exerted  at  in  is  con- 
stant, while  the  forces/ and  /  are  increasing,  a  time  arrives  at  which  the 
force  F  is  balanced  by  the  forces  /  and  /.  All  decomposition  of  the 
neutral  condition  then  ceases  ;  the  inducing  action  has  attained  its  limit. 

If  the  cylinder  be  removed  from  the  source  of  electricity,  as  the  inducing 
action  decreases,  a  portion  of  the  free  electricities  at  A  and  B  recombine  to 
form  the  neutral  fluid.  If,  on  the  other  hand,  they  are  brought  nearer,  as 
the  force  F  now  exceeds  the  forces  /  and  /,  a  new  decomposition  of  the 


714  Friclional  Electricity.  [746- 

neutral  fluid  takes  place,  and  fresh  quantities  of  positive  and  negative  elec- 
tricities are  respectively  accumulated  at  A  and  B. 

747.  Faraday's  theory  of  induction. — Hitherto  any  possible  influence 
of  the  medium  which  separates  the  electrified  from  the  unelectrified  body  in 
the  case  of  induction  has  been  disregarded.  It  has  been  tacitly  assumed 
that  electrical  actions  are  exerted  at  a  distance,  and  the  medium  has  been 
looked  upon  as  an  inert  mass  through  which  the  forces  can  act,  but  which 
itself  is  destitute  of  any  active  properties.  The  researches  of  Faraday,  how- 
ever, prove  that  this  is  not  the  case  ;  that  the  medium  is  of  fundamental  im- 
portance, and  that  the  action  is  not  an  action  at  a  distance,  or  at  any  rate 
at  no  greater  distance  than  that  between  any  two  molecules. 

According  to  Faraday's  views  conductors  are  in  a  certain  sense  qualita- 
tively different  from  non-conductors.  He  looked  upon  a  non-conductor  as 
consisting  of  a  number  of  molecules  which  may  be  spherical,  and  which  are 
absolute  conductors,  and  are  disseminated  in  a  non-conducting  medium. 
The  action  of  an  electrified  body  is  either  to  separate  the  electricities  within 
the  molecule  and  arrange  them  in  a  polar  chain,  or  to  impart  to  the  mole- 
cules which  are  themselves  polarised  at  the  outset  a  definite  polar  arrange- 
ment ;  those  ends  of  the  molecule  which  face  the  inducing  body  having  elec- 
tricity of  the  opposite  kind,  and  those  which  are  turned  away  from  it  having 
electricity  of  the  same  kind.  In  the  interior  of  the  medium,  where  succes- 
sively the  positive  end  of  one  molecule  faces  the  negative  end  of  the  next, 
the  two  electricities  neutralise  each  other  ;  but  where  the  non-conductor  is 
bounded  by  a  conductor  the  free  electrification  is  no  longer  neutralised,  but 
constitutes  the  charge  which  is  perceived.  The  action  is  therefore  analogous 
to  that  of  the  pole  of  a  magnet  on  a  piece  of  soft  iron  ;  and  Faraday  called 
i  t  dielectric  polarisation. 

The  following  experiment  was  devised  by  Faraday  to  illustrate  this 
polarisation  of  the  medium,  as  he  called  it.  He  placed  small  filaments  of 
silk  in  a  vessel  of  turpentine  (fig.  676),  and,  having  plunged  two  conductors 
in  the  liquid  on  opposite  sides,  he  charged  one  and  placed  the  other  in  con- 
nection with  the  ground.  The  particles  of  silk  immediately  arranged  them- 
selves end  to  end,  and  adhered 

closely  together,  forming  a  con-  r ^_2!!!\  +e 

tinuous  chain  between  the  two       ^^ [fk^!fi^^^^^''^^^^^-^^^^^^^^?->')T. — /^'^ 

sides.     An  experiment  by  Mat-       W'^W^'^'  '^"Tf~|^'^^^%P 

teucci  also    supports    Faraday's  1^  J 

theory.     He  placed  several  thin 
plates  of  mica  closely  together, 
and  i)rovidcd  the  outside  ones 
with    metallic    coatings,    like    a 
fulminating  pane  (769).     Having  electrified  the  system,  the  coatings  were 
removed  by  insulating  handles,  and  on  e.\amining  the  plates  of  mica  succes- 
sively, each  was  found  charged  with  positive  electricity  on  one  side  and 
negative  electricity  on  the  other. 

748.  Specific  inductive  capacity. —  Faraday  named  the  property  which 
bodies  have  of  transmitting  electrical  induction,  the  specific  inductii^c  capacity., 
or,  as  it  is  often  called,  the  inductive  power.  If  the  dielectric  does  play  the 
essential  part  in  the  phenomena  of  induction  it  is  not  likely  that  all  insu- 


.170. 


-748] 


Specific  Inductive  Capacity. 


715 


lating  bodies  possess  it  in  the  same  degree.  This  seems  to  have  been  known 
to  Cavendish.  To  determine  and  compare  the  inductive  power  Faraday 
used  the  apparatus  represented  in  fig.  677,  and  of  which  fig.  678  represents 
a  vertical  section.  It  consists  of  a  brass  sphere  made  up  of  two  halves,  P 
and  Q,  which  fit  accurately  into  each  other,  like  the  Magdeburg  hemi- 
spheres. In  the  interior  of  this  spherical  envelope  there  is  a  smaller  brass 
sphere  C,  connected  with  a  metal  rod,  terminating  in  a  ball  B.  The  rod  is 
insulated' from  the  envelope  PQ  by  a  thick  layer  of  shellac  A.  The  space 
7)in  receives  the  substance  whose  inductive  power  is  to  be  determined.  The 
foot  of  the  appai^atus  is  provided  with  a  screw  and  stopcock,  so  that  it  can 
be  screwed  on  the  air-pump,  and  the  air  in  imi  either  rarefied  or  exhausted. 
Two  such  apparatus  perfectly  identical  are  used,  and  at  first  they  only 
contain  air.  The  envelopes  PQ  are  connected  with  the  ground,  and  the 
knob  B  of  one  of  them  receives  a  charge  of  electricity.  The  sphere  C  thus 
becomes  charged  like  the  inner  coating  of  a  Leyden  jar  (770).     The  layer 


I  i,'.  077.  Fig.  678. 

mn  represents  the  insulator  which  separates  the  two  coatings.  By  touching 
B  with  the  proof  plane,  which  is  then  applied  to  the  torsion  balance,  the 
quantity  of  free  electricity  is  measured.  In  one  experiment  Faraday  ob- 
served a  torsion  of  250°,  which  represented  the  free  electricity  on  B.  The 
knob  B  was  then  placed  in  metallic  connection  with  the  knob  B'  of  the 
other  apparatus,  and  the  torsion  was  now  found  to  be  125°,  showing  that 
the  electricity  had  become  equally  distributed  on  the  two  spheres,  as  might 
have  been  anticipated,  since  the  pieces  of  apparatus  were  quite  equal,  and 
each  contained  air  in  the  space  mn. 

This  experiment  having  been  made,  the  space  inn  in  the  second  appa- 


yi6  Frictioiial  Electricity.  [748- 

ratus  was  filled  with  the  substance  whose  inductive  power  was  to  be  deter- 
mined :  for  example,  shellac.  The  other  apparatus,  in  which  mn  is  filled 
with  air,  having  been  charged,  the  density  of  the  free  electricity  on  C  was 
measured.  Let  it  be  taken  at  290°,  the  number  observed  by  Faraday  in  a 
special  case.  When  the  knob  B  of  the  first  apparatus  was  connected  with 
the  knob  B'  of  the  second,  the  density  was  not  found  to  be  145°,  as  would 
be  expected.  The  apparatus  containing  air  exhibited  a  density  of  1 14'',  and 
that  with  shellac  of  1 13°.  Hence  the  former  had  lost  176°,  and  had  retained 
114°,  while  the  latter  ought  to  have  exhibited  a  density  of  176°  instead  of 
113°.  The  second  apparatus  had  taken  more  than  half  the  charge,  and 
hence  a  larger  c^uantity  of  electricity  had  been  condensed  by  the  shellac. 
Of  the  total  quantity  of  electricity,  the  shellac  had  taken  176°  and  the  air 
114°  ;  hence  the  specific  inductive  capacity  of  air  is  to  that  of  shellac  as 
114  :  176  ;  or  as  i  :  1-55.  That  is,  the  inductive  power  of  shellac  is  more 
than  half  as  great  again  as  air. 

By  the  following  simple  experiment  the  influence  of  the  dielectric  may 
be  shown  : — At  a  fixed  distance  above  a  gold-leaf  electroscope  let  an  elec- 
trified sphere  be  placed,  by  which  a  certain  divergence  of  the  leaves  is 
produced.  If,  now,  the  charges  remaining  the  same,  a  disc  of  sulphur  or 
of  shellac  be  interposed,  the  divergence  increases,  showing  that  inductive 
action  takes  place  through  the  sulphur  to  a  greater  extent  than  through  a 
layer  of  air  of  the  same  thickness. 

By  various  improved  methods  the  following  are  the  mean  of  the  values 
which  have  been  obtained  for  the  specific  inductive  capacity  of  diclecirics, 
as  they  are  called,  in  opposition  to  anelectrics^  or  conductors  : — 

Air I -GO         Shellac     ....     3-04 

Parafiine  .         .         .     2-02         Sulphur    ....     334 

India-rubber  .         .         .     2-22         Ebonite    ....     3-42 
Gutta-percha  .         .         .     2-46         (jlass        .         .         .         .   5  to  6 

These  values  are  known  as  the  dielectric  constants  ;  and  their  determi- 
nation presents  considerable  difficulty,  owing  to  the  occurrence  of  a  pheno- 
menon to  which  Faraday  gave  the  name  of  electrical  absorption,  and  which 
is  due  to  the  same  cause  as  the  residual  charge  of  condensers. 

A  condenser  with  a  glass  plate  would  thus  have  5  or  6  times  the  capa- 
city of  an  air  condenser  of  the  same  dimensions,  or  the  same  capacity  as  an 
air  condenser  of  the  same  surface,  but  5  or  6  times  as  thin. 

Boltzmann  divides  dielectrics  into  two  classes  :  to  one  of  which  belong 
shellac,  paraffine,  sulphur  and  resin,  which  act  like  perfect  insulators  ;  that 
is,  in  using  them  the  maximum  charge  is  attained,  if  not  instantaneously, 
at  all  events  after  a  very  short  time  :  in  others,  such  as  gutta-percha, 
stearine,  and  glass,  the  chai'ge  increases  appreciably  with  the  time. 

A  very  interesting  relation  probably  exists  between  the  dielectric  con- 
stant and  the  refractive  index  of  certain  substances.  Thus  the  following 
numbers  have  been  found  : — 

d  s/d  n 

Sulphur     ....     3-84  1-96  204 

Resin        ....     2-55  1-59  1-54 

Paraffine  ....     2-32  1-52  1-53 


-750]  Motion  of  Electrified  Bodies.  7 1 7 

where  ;/  is  the  refractive  index  (538),  and  A^d  the  square  root  of  the  di- 
electric constant. 

Hopkinson  found  the  following  numbers  for  the  dielectric  constant  of 
certain  liquids.  Petroleum  2-10,  oil  of  turpentine  2-23,  olive  oil  3-16,  and 
castor  oil  47S. 

Faraday  was  not  able  to  detect  any  difference  in  the  dielectric  constants 
of  various  gases.  Boltzmann  has  shown,  however,  that  there  are  differences 
among  them,  and  that  there  is  a  very  close  agreement  between  the  square 
root  of  their  dielectric  constants  and  their  refractive  indices,  thus  : — 


Air       . 

.     1-00059 

1-000295 

I  -000294 

Carbonic  acid      . 

.     1-00095 

1-000473 

I -000449 

Hydrogen    . 

.     I  -00026 

I -0001 32 

I -000138 

defiant  gas 

.     1-00131 

1-000656 

1-000678 

The  accurate  determination  of  the  dielectric  constant  is  a  matter  of 
great  theoretical  importance,  especially  from  its  bearing  on  Maxwell's 
electro-magnetic  theory  of  light.  According  to  this  theory,  the  medium  in 
which  both  electrical  and  luminous  actions  are  transmitted  is  the  same,  and 
is  in  fact  the  luminiferous  ether  (637),  and  it  is  a  necessary  consequence  of 
this  theory  that  the  above  relation  must  exist  between  the  refractive  index 
of  a  substance  and  its  dielectric  constant. 

749.  Communication  of  electricity  at  a  distance.— In  the  experiment 
represented  in  fig.  677  the  opposite  electricities  of  the  conductor  and  the 
separated  cylinder  tend  to  unite,  but  are  prevented  by  the  resistance  of  the 
air.  If  the  density  is  increased,  or  if  the  distance  of  the  bodies  be  diminished, 
the  opposed  electricities  at  length  overcome  this  obstacle  ;  they  rush  toge- 
ther and  combine,  producing  a  spark,  accompanied  by  a  sharp  sound.  The 
negative  electricity  separated  on  the  cylinder  being  thus  neutralised  by  the 
positive  electricity  of  the  charged  body,  a  charge  of  positive  electricity 
remains  on  the  cylinder.  The  same  phenomenon  is  observed  when  a  finger 
is  presented  to  a  strongly  electrified  conductor.  The  latter  decomposes  by 
induction  the  neutral  electricity  of  the  body,  the  opposite  electricities  com- 
bine with  the  production  of  a  spark,  while  the  electricity  of  the  same  kind 
as  the  electrified  conductor,  which  is  left  on  the  body,  passes  off  into  the 
ground. 

The  striking  distance  varies  with  the  density,  the  shape  of  the  bodies, 
their  conducting  power,  and  with  the  resistance  and  pressure  of  the  inter- 
posed medium. 

750.  Motion  of  electrified  bodies. — The  various  phenomena  of  attrac- 
tion and  repulsion,  which  are  among  the  most  frequent  manifestations  of 
electrical  action,  may  all  be  explained  by  means  of  ^ 
the  laws  of  induction.  If  M  (fig.  679)  be  a  fixed 
insulated  conductor  charged  with  positive  electricity, 
and  N  be  a  movable  insulated  body — for  instance, 
an  electrical  pendulum — there  are  three  cases  to  be 
considered  :— 

i.    The  movable  body  is  iiiielect'fified  and  is  a  con- 
ductor.— In  this  case   M,  acting   inductively   on    N,  '^'   ^^' 
attracts  the  negative  and  repels  the  positive  electricity,  so  that  the  maxima  of 


/1 8  Frktional  Electricity.  [750- 

density  are  respectively  at  the  points  a  and  b.  Now  a  is  nearer  c  than  b 
is  ;  and,  since  attractions  and  repulsions  are  inversely  as  the  square  of  the 
distance,  the  attraction  between  a  and  c  is  greater  than  the  repulsion  be- 
tween b  and  c  ;  and,  therefore,  N  will  be  attracted  to  M  by  a  force  equal 
to  the  excess  of  the  attractive  over  the  repulsive  force. 

ii.  The  tnovable  body  is  a  conductor  and  is  electrified. — If  the  electricity 
of  the  movable  body  is  different  from  that  of  the  fixed  body,  there  is  always 
attraction  ;  but  if  they  are  of  the  same  kind,  there  is  at  first  repulsion 
and  afterwards  attraction.  This  anomaly  may  be  thus  explained  :  Besides 
its  charge  of  electricity,  the  neutral  electricity  is  decomposed  by  the 
induction  of  the  positive  electricity  on  M  ;  and  consequently  the  hemisphere  b 
obtains  an  additional  supply  of  positive  electricity,  while  a  becomes  charged 
with  negative  electricity.  There  is  thus  attraction  and  repulsion,  as  in 
the  foregoing  case.  The  force  of  repulsion  is  at  first  greater,  because  the 
quantity  of  positive  electricity  on  N  is  greater  than  that  of  negative  ; 
but  as  the  distance  ac  diminishes,  the  attractive  force  increases  more  rapidly 
than  the  repulsive  force,  and  finally  exceeds  it. 

iii.  Tlie  movable  body  is  a  bad  conductor. — If  N  is  charged,  repulsion 
or  attraction  takes  place,  according  as  the  electricity  is  of  the  same  or 
opposite  kind  to  that  of  the  fixed  body.  If  it  is  in  the  natural  state,  the 
body  M  will  decompose  the  neutral  electricity  of  N,  and  attraction  will 
take  place  as  in  the  first  case,  since  a  powerful  and  permanent  source  of 
electricity  can  more  or  less  decompose  the  neutral  electricity  even  of  bad 
conductors. 

751.  Gold-leaf  electroscope. — The  name  electroscope  is  given  to  instru- 
ments for  detecting  the  presence  and  determining  the  kind  of  electricity  in 
any  body.  The  original  pith-ball  pendulum  is  an  electroscope  ;  but,  though 
sometimes  convenient,  it  is  not  sufficiently  delicate.  Many  successive  im- 
provements have  been  made  in  it,  and  have  resulted  in  the  form  used,  which 
is  due  to  Bennett. 

Ben?tett^s,  or  the  gold-leaf  electroscope. — This  consists  of  a  tubulated  glass 
shape  B  (fig.  680),  standing  on  a  metal  foot,  which  thus  communicates  with 
the  ground.  A  metal  rod  terminating  at  its  upper  extremity  in  a  knob  C, 
and  holding  at  its  lower  end  two  narrow  strips  of  gold-leaf,  n  n,  fits  in  the 
tubulure  of  the  shade,  the  neck  of  which  is  coated  with  an  insulating 
varnish.  The  air  in  the  interior  is  dried  by  quicklime,  or  by  chloride  of 
calcium,  and  on  the  insidcs  of  the  shade  there  are  two  strips  of  gold-leaf 
a,  communicating  with  the  ground.  These,  being  charged  by  induction  with 
the  opposite  electricity  to  that  of  the  gold  lea\es,  increase  the  divergence,  and 
therefore  the  delicacy  of  the  apparatus.  They  also  prevent  the  leaves  when 
diverging  too  suddenly  from  adhering  to  the  sides,  from  which  it  is  difficult 
to  detach  them. 

When  the  knob  is  touched  with  a  body  charged  with  either  kind  of 
electricity,  the  leaves  diverge  ;  usually,  however,  the  apparatus  is  charged 
by  induction  thus  :— 

If  an  electrified  body — a  stick  of  rubbed  sculing-wax,  for  example— be 
brought  near  the  knoli,  it  will  decompose  the  neutral  electricity  of  the 
system,  attracting  to  the  knob  the  electricity  of  the  opposite  kind,  and 
retaining  it  there,  and  roiiclling  the  electricity  of  tlu>  same  kiml   Id  thr  gold 


-751] 


Gold  Leaf  Electroscope. 


719 

leaves,  which  consequently  diverge.     In  this  way  the  presence  of  an  elec- 
trical charge  is.  ascertained,  but  not  its  quality. 

To  ascertain  ^&kind  of  electricity  the  following  method  is  pursued  :  If, 
while  the  instrument  is  under  the  influence  of  the  body  A,  which  we  will 
suppose  has  a  negative  charge,  the 
knob  be  touched  by  the  finger,  the 
negative  electricity  produced  by  in- 
duction pp.sses  off  into  the  ground,  and 
the  previously  divergent  leaves  will 
collapse  ;  there  only  remains  positive 
electricity,  retained  in  the  knob  by  in- 
duction from  A.  If  now  the  finger  be 
first  removed,  and  then  the  electrified 
body,  the  positive  electricity  previously 
retained  by  A  will  spread  over  the  sys- 
tem, and  cause  the  leaves  to  diverge. 
If  now,  while  the  system  is  charged 
with  positive  electricity,  a  positively 
electrified  body — as,  for  example,  an 
excited  glass  rod — be  approached,  the 
leaves  will  diverge  more  widely  ;  for 
the  electricity  of  the  same  kind  will  be  repelled  to  the  ends.  If,  on  the 
contrar}',  an  excited  shellac  rod  be  presented,  the  leaves  will  tend  to  collapse 
the  electricity  with  which  they  are  charged  being  attracted  by  the  opposite 
electricity.  Hence  we  may  ascertain  the  kind  of  electricity,  either  by 
imparting  to  the  electroscope  electricity  from  the  body  under  examination, 
and  then  bringing  near  it  a  rod  charged  with  positive  or  negative  electricity  ; 
or  the  electroscope  maybe  charged  with  a  known  kind  of  electricity,  and  the 
electrified  body  in  question  brought  near  the  electroscope. 

The  gold-leaf  electroscope  is  sometimes  used  as  an  electrometer,  or 
measurer  of  electricity,  by  measuring  the  angle  of  divergence  of  the  leaves  ; 
this  is  done  by  placing  behind  them  a  graduated  scale  ;  for  small  angles  the 
quantity  of  electricity  is  nearly  proportional  to  the  sine  of  half  the  angle  of 
divergence. 


Fig.  62o. 


'20 


Frictional  Electricity 


[752- 


ELECTRICAL    MACHINES. 

752.  Electrophorus. — It  will  now  be  convenient  to  describe  the  various 
electrical  machines,  or  apparatus  for  generating  and  collecting  large  supplies 
of  statical  electricity.  One  of  the  most  simple  and  inexpensive  of  these  is 
the  electrophorus^  which  was  invented  by  Volta.  It  consists  of  a  cake  of 
resin  B  (fig.  682),  say  about  12  inches  in  diameter,  and  an  inch  thick,  which 
is  placed  on  a  metal  surface,  or  frequently  fits  into  a  wooden  mould  lined 


Fig.  681.  Fig.  682. 

with  tinfoil,  which  is  called  the  form.  Besides  this  there  is  a  metal  disc  A 
(fig.  682),  of  a  diameter  somewhat  less  than  that  of  the  cake,  and  provided 
with  an  insulating  glass  handle  ;  this  is  the  cover.  The  mode  of  working  is 
as  follows  :  All  the  parts  of  the  apparatus  having  been  well  dried,  the 
cake,  which  is  placed  in  the  form,  or  rests  on  a  metal  surface,  is  briskly 
flapped  with  silk,  or,  better,  with  catskin,  by  which  it  becomes  charged  with 
negative  electricity.  The  cover  is  then  placed  on  the  cake.  Owing,  how- 
ever, to  the  minute  rugosities  of  the  surface  of  the  resin,  the  cover  only 
comes  in  contact  with  a  few  points,  and,  from  the  non-conductivity  of  the 
resin,  the  negative  electricity  of  the  cake  does  not  pass  off  to  the  cover.  On 
the  contrary,  it  acts  by  induction  on  the  neutral  electricity  of  the  cover,  and 
decomposes  it,  attracting  the  positive  electricity  to  the  under  surface,  and 
repelling  the  negative  electricity  to  the  upi^er.  If  the  upper  surface  be  now 
touched  with  the  finger,  the  negative  electricity,  because  repelled  and  free, 
passes  off,  and  the  cover  remains  charged  with  positive  electricity,  held, 
however,  by  the  negative  electricity  of  the  cake  ;  the  two  electricities  do 
not  unite,  in  consequence  of  the  non-conductivity  of  the  cake  (fig.  681).  If 
now  the  cover  be  raised  by  its  insulating  handle,  the  charge  diffuses  itself 
over  the  surface  ;  and  if  a  conductor  lie  brought  near  it  (fig.  6S2),  a  smart 
spark  passes. 

The  metal  form  on    which  the  cake    rests  plays    an  important  part    in 


-753J  Plate  Electrical  MacJiine.  721 

the  action  of  the  electrophorus,  as  it  increases  the  quantity  of  electricity,  and 
makes  it  more  permanent.  For  the  negative  electricity  of  the  upper  surface 
of  the  resin,  acting  inductively  on  the  neutral  electricity  of  the  lower,  decom- 
poses it,  retaining  on  the  under  surface  the  positive  electricity,  while  the 
negative  electricity  passes  otif  into  the  ground.  The  positive  electricity  thus 
developed  on  the  under  surface  reacts  on  the  negative  electricity  of  the  upper 
surface,  binding  it,  and  causing  it  to  penetrate  into  the  badly  conducting 
mass,  oji  the  surface  of  which  fresh  quantities  of  electricity  can  be  excited 
far  beyond  the  limits  possible  without  the  action  of  the  form.  It  is  for  this 
reason  that  the  electrophorus,  once  charged,  retains  its  state  for  a  consider- 
able time,  and  sparks  can  be  taken  even  after  a  long  interval.  If  the  form 
be  insulated,  the  charge  obtained  from  it  is  far  less  than  if  it  is  on  a  con- 
ducting support.  For  the  negative  electricity  developed  by  induction  on  the 
lower  surface  being  now  unable  to  escape,  the  condensing  action  referred  to 
cannot  take  place,  and  only  a  feeble  charge  can  be  given  to  the  resin.  The 
retention  of  electricity  is  greatly  promoted  by  keeping  the  cake  on  the  form, 
and  placing  the  cover  upon  it,  by  which  the  access  of  air  is  hindered. 
Instead  of  a  cake  of  resin,  a  disc  of  gutta-percha,  or  vulcanised  cloth,  or 
vulcanite,  may  be  substituted  ;  and,  of  course,  if  glass,  or  any  material  which 
is  positively  electrified  by  friction,  be  used,  the  cover  acquires  a  negative 
charge. 

The  electrophorus  is  a  good  instance  of  the  conversion  of  work  into 
electropotential  energy  (63).  When  the  cover  is  lifted  from  the  excited  cake 
work  must  be  expended  in  order  to  overcome  the  attraction  of  the  electricity 
in  the  cake  for  the  opposite  electricity  developed  by  induction  on  the  cover  ; 
and  the  ecjuivalent  of  this  work  appears  in  the  form  of  the  electricity  thus 
detached.  Thus,  when  a  Leyden  jar  is  charged  either  by  the  machine  or  by 
the  electrophorus,  the  energy  of  the  charge  is  a  transformation  of  the  work 
of  the  operator. 

753.  Plate  electrical  macbine. — The  first  electrical  machine  was  in- 
vented by  Otto  von  Guericke,  the  inventor  also  of  the  air-pump.  It  con- 
sisted of  a  sphere  of  sulphur,  which  was  turned  on  an  axis  by  means  of  the 
hand,  while  the  other,  pressing  against  it,  served  as  a  rubber.  Resin  was 
afterwards  substituted  for  the  sulphur,  which,  in  turn,  Hawksbee  replaced 
by  a  glass  cylinder.  In  all  these  cases  the  hand  served  as  rubber  ;  and 
Winckler,  in  1740,  first  introduced  cushions  of  horsehair,  covered  with  silk, 
as  rubbers.  At  the  same  time  Bose  collected  electricity,  disengaged  by 
friction,  on  an  insulated  cylinder  of  tin  plate.  Lastly,  Ramsden,  in  1760, 
replaced  the  glass  cylinder  by  a  circular  glass  plate,  which  was  rubbed  by 
cushions.  The  form  which  the  machine  has  now  is  but  a  modification  of 
Ramsden's  original  machine. 

Between  two  wooden  supports  (fig.  683)  a  circular  glass  plate  P  is  sus- 
pended by  an  axis  passing  through  the  centre,  and  which  is  turned  by  means 
of  a  handle  M.  The  plate  revolves  between  two  sets  oi  cushions  or  rubbers, 
F,  of  leather  or  of  silk,  one  set  above  the  axis  and  one  below,  which,  by 
means  of  screws,  can  be  pressed  as  tightly  against  the  glass  as  may  be  desired. 
The  plate  also  passes  between  two  brass  rods,  shaped  like  a  horse-shoe,  and 
provided  with  a  series  of  points  on  the  sides  opposite  the  glass  ;  these  rods 
are  fixed  to  larger  metallic  cylinders  C  C,  which  are  called  the  prime  cotiduc- 

3A 


722 


Frictional  Electricity. 


[753- 


tors.     The  latter  are  insulated  by  being  supported  on  glass  feet,  and  are 
connected  with  each  other  by  a  smaller  rod  ;-. 

The  action  of  the  machine  is  thus  explained.     By  friction  with  the  rub- 


bers the  glass  becomes  positively  and  the  rubbers  negatively  electrified. 
If  now  the  rubbers  were  insulated,  they  would  receive  a  certain  charge  ot 
negative  electricity  which  it  would  be  impossible  to  exceed,  for  the  tendency 
of  the  opposed  electricities  to  reunite  would  be  equal  to  the  power  of  the 
friction  to  decompose  the  neutral  state.  But  the  rubbers  communicate  with 
the  ground  by  means  of  a  chain  ;  and,  consequently,  as  fast  as  the  negative 
electricity  is  generated,  it  is  continually  reduced  to  zero  by  contact  with  the 
ground.  The  positive  electricity  of  the  glass  acts  then  by  induction  on  the 
conductor,  attracting  the  negative  electricity.  This  negative  electricity 
collects  on  the  points  opposite  to  the  glass.  Here  its  tendency  to  discharge 
becomes  so  high  that  it  passes  across  the  intervening  space  of  air,  and 
neutralises  the  positive  electricity  on  the  glass  The  conductors  thus  lose 
their  negative  electricity  and  remain  charged  with  positive  electricity.  The 
plate  accordingly  gives  up  nothing  to  the  prime  conductors  ;  in  fact,  it  only 
abstracts  from  them  their  negative  electricity. 


-755]  Maxim  inn  of  Charge.  723 

If  the  hand  be  brought  near  the  conductor  when  charged,  a  spark 
follows,  which  is  renewed  as  the  machine  is  turned.  In  this  case  the  posi- 
tive electricity  decomposes  the  neutral  electricity  of  the  body,  attracting  its 
negative  electricity,  and  combining  with  it  when  the  two  have  a  sufificient 
tension.  Thus,  with  each  spark,  the  conductor  reverts  to  the  neutral  state, 
but  becomes  again  electrified  as  the  plate  is  turned. 

754.  Precautions  In  reference  to  the  machine. — The  glass,  of  which 
the  plate  is  made,  must  be  as  little  hygroscopic  as  possible.  Of  late  ebonite 
has  been  frequently  substituted  for  glass  ;  it  has  the  advantage  of  being 
neither  hygroscopic  nor  fragile,  and  of  readily  becoming  electrified  by 
friction.  It  cannot,  however,  be  relied  on,  as  its  surface  in  time  undergoes  a 
change,  especially  if  exposed  to  the  light,  whereby  it  becomes  a  conductor. 
The  plate  is  usually  from  ^V  to  \  of  an  inch  in  thickness,  and  from  20  to 
30  inches  in  diameter,  though  these  dimensions  are  not  unfrequently  ex- 
ceeded. 

The  rubbers  require  great  care,  both  in  their  construction  and  their  pre- 
servation. They  are  commonly  made  of  leather,  stuffed  with  horsehair. 
Before  use  they  are  coated  either  with  powdered  aiiriim  musivian  (sulphuret 
of  tin),  graphite,  or  amalgam.  The  action  of  these  substances  is  not  very 
clearly  understood.  Some  consider  that  it  merely  consists  in  promoting 
friction.  Others,  agam,  believe  that  a  chemical  action  is  produced,  and 
assign  in  support  of  this  view  the  peculiar  smell  noticed  near  the  rubbers 
when  the  machine  is  worked.  Amalgams,  perhaps,  promote  most  power- 
fully the  disengagement  of  electricity.  Kienmayer's  amalgam  is  the  best 
of  them.  It  is  prepared  as  follows  :  One  part  of  zinc  and  one  part  of  tin 
are  melted  together  and  removed  from  the  fire,  and  two  parts  of  mercury 
stirred  in.  The  mass  is  transferred  to  a  wooden  box  containing  some  chalk, 
and  then  well  shaken.  The  amalgam,  before  it  is  cold,  is  powdered  in  an 
iron  mortar,  and  preserved  in  a  stoppered  glass  vessel.  For  use  a  little  cacao 
butter  or  lard  is  spread  over  the  cushion,  some  of  the  powdered  amalgam 
sprinkled  over  it,  and  the  surface  smoothed  by  a  ball  of  flattened  leather. 

In  order  to  avoid  a  loss  of  electricity,  two  quadrant-shaped  pieces  of 
oiled  silk  are  fixed  to  the  rubbers,  so  as  to  cover  the  plate  on  both  sides : 
one  at  the  upper  part  from  a  to  F,  and  the  other  in  the  corresponding  part 
of  the  lower  rubbers.  These  flaps  are  not  represented  in  the  figure.  Yellow 
oiled  silk  is  the  best,  and  there  must  be  perfect  contact  between  the  plate 
and  the  cloth. 

Ramsden's  machine,  as  represented  in  fig.  683,  only  gives  positive  elec- 
tricity. But  it  may  be  arranged  so  as  to  give  negative  electricity  by  placing 
it  on  a  table  with  insulating  supports.  The  conductor  is  connected  with 
the  ground  by  a  chain,  and  the  machine  worked  as  before.  The  positive 
electricity  passes  off  by  the  chain  into  the  ground,  while  the  negative 
electricity  remains  on  the  supports  and  on  the  insulated  table.  On  bring- 
ing the  finger  near  the  uprights,  a  sharper  spark  than  the  ordinaiy  one  is 
obtained. 

755.  Maximum  of  ctaargre. — It  is  impossible  to  exceed  a  certain  limit 
of  electrical  charge  with  the  machine,  whatever  precautions  are  taken,  or 
however  rapidly  the  plate  is  turned.  This  limit  is  attained  when  the  loss  of 
electricity  equals  its  production.     The  loss  depends  on  three  causes  :  i.  The 

3  A2 


724  Frictional  Electricity.  [755- 

loss  by  the  atmosphere,  and  the  moisture  it  contains,  ii.  The  loss  by  the  sup- 
ports, iii.  The  recombination  of  the  electricities  of  the  rubbers  and  the  glass. 
^^  The  first  two  causes  have  been  already  mentioned. 

H.  L^^  With  reference  to  the  last,  it  must  be  noticed  that  the 

^^  electrical  charge  increases  with  the  rapidity  of  the  rota- 

tion, until  it  reaches  a  point  at  which  it  overcomes  the 
resistance  presented  by  the  non-conductivity  of  the 
glass.  At  this  point,  a  portion  of  the  two  electricities 
separated  on  the  rubbers  and  on  the  glass  recombines, 
and  the  charge  remains  constant.  It  is,  therefore,  ulti- 
mately independent  of  the  rapidity  of  rotation. 

756.  Quadrant  electrometer.  —  The  electrical 
charge  is  roughly  measured  by  the  quadrant  or 
Henley's  electrotneter,  which  is  attached  to  the  con- 
ductor. This  is  a  small  electric  pendulum,  consisting 
of  a  wooden  rod  d,  to  which  is  attached  an  ivorj'  or 
Fig.  684.  cardboard  scale  (fig.  684).     In  the  centre  of  this  is  a 

small  index  of  straw,  movable  on  an  axis,  and  terminating  in  a  pith  ball. 
Being  attached  to  the  conductor,  the  index  diverges  as  the  machine  is 
charged,  ceasing  to  rise  when  the  limit  is  attained.  When  the  rotation  is 
discontinued  the  index  falls  rapidly  if  the  air  is  moist ;  but  in  dry  air  it  only 
falls  slowly,  showing,  therefore,  that  the  loss  of  electricity  in  the  latter  case 
is  less  than  in  the  former. 

757.  Cylinder  electrical  macbine.- — The  construction  of  the  cylinder 
machines,  as  ordinarily  used  in  England,  is  due  to  Nairne.  They  are  well 
adapted  for  obtaining  either  kind  of  electricity.  In  Nairne's  machine  (fig. 
685)  the  cylinder  is  rubbed  by  only  one  cushion  C,  which  is  made  of  leather 


i.u-  685. 

stuffed  with  horsehair,  and  is  screwed  to  an  insulated  conductor  A.  On  the 
opposite  side  of  the  cylinder  there  is  a  similar  insulated  conductor  1>,  pro- 
vided with  a  series  of  points  on  the  sides  next  the  glass.  To  the  lower  part 
of  the  cushion  C  is  attached  a  piece  of  oiled  silk,  which  extends  over  the 


-758]  Armstrongs  Hydro-electric  Machine.  725 

cylinder  to  just  above  the  points.  This  is  not  represented  in  the  figure. 
When  the  cylinder  is  turned,  A  becomes  charged  with  negative  and  B  with 
positive  electricity  by  the  loss  of  its  negative  from  the  points  P.  The  two 
opposite  electricities  will  now  unite  by  a  succession  of  sparks  across  D  and 
E.  If  use  is  to  be  made  of  the  electricity,  either  the  rubber  or  the  prime 
conductor  must  be  connected  with  the  ground.  In  the  former  case  positive 
electricity  is  obtained  ;  in  the  latter,  negative. 

758.  Armstrong-'s  hydro-electric  maclilne. — In  this  machine  electricity 
is  produced  by  the  disengagement  of  aqueous  vapour  through  narrow  orifices. 
The  discovery  of  the  machine  was  occasioned  by  an  accident.  A  work- 
man having  accidentally  held  one  hand  in  a  jet  of  steam,  which  was  issuing 
from  an  orifice  in  a  steam  boiler  at  high  pressure,  while  his  other  hand 
grasped  the  safety-valve,  was  astonished  at  experiencing  a  smart  shock. 
Lord  Armstrong  (then  Mr.  Armstrong,  of  Newcastle),  whose  attention  was 
drawn  to  this  phenomenon,  ascertained  that  the  steam  was  charged  with 
positive  electricity,  and,  by  repeating  the  e.xperiment  with  an  insulated  loco- 
motive, he  found  that  the  boiler  was  negatively  charged.  Armstrong  believed 
that  the  electricity  was  due  to  a  sudden  expansion  of  the  steam  ;  Faraday, 
who  afterwards  examined  the  question,  ascertained  its  true  cause,  which  will 
be  best  understood 
after  describing  a 
machine  which 

Armstrong  devised 
for  reproducing  the 
phenomenon. 

It  consists  of  a 
v.TOught-iron  boiler 
(fig.  686),  with  a 
central  fire,  and 
insulated  on  four 
legs.  It  is  about  5 
feet  long  by  2  feet 
in  diameter,  and 
is  provided  at  the 
side  with  a  gauge 
O,  to  show  the 
height  of  the  water 
in  the  boiler.  C  is 
the  stopcock,  which 
is  opened  when  the 
steam  has  sufficient 
pressure.  Above 
this  is  the  box  B,  in 
which  are  the  tubes 
through  which  the 
steam  is  disen- 
gaged.     On  these 


Fig.  686. 


are  fitted  jets  of  a  peculiar  construction,  which  will  be  understood  from 
the  section  of  one  of  them,  M,  represented  on  a  larger  scale.     They  are 


726 


Frictional  Electricity. 


[758- 


lined  with  hard  wood  in  a  manner  represented  by  the  diagram.  The  box 
B  contains  cold  water.  Thus  the  steam,  before  escaping,  undergoes  partial 
condensation,  and  becomes  charged  with  vesicles  of  water — a  necessary 
condition,  for  Faraday  found  that  no  electricity  is  produced  when  the  steam 
is  perfectly  dry. 

The  development  of  electricity  in  the  machine  was  at  first  attributed  to 
the  condensation  of  the  steam  ;  but  Faraday  found  that  it  is  solely  due  to 
the  friction  of  the  globules  of  water  against  the  jet.  For  if  the  little  cylinders 
which  line  the  jets  are  changed,  the  kind  of  electricity  is  changed  ;  and  if 
ivory  is  substituted,  little  or  no  electricity  is  produced.  The  same  effect  is 
produced  if  any  fatty  matter  is  introduced  into  the  boiler.  In  this  case  the 
linings  are  of  no  use.  It  is  only  in  case  the  water  is  pure  that  electricity  is 
disengaged,  and  the  addition  of  acid  or  saline  solutions,  even  in  minute 
quantity,  prevents  any  disengagement  of  electricity.  If  turpentine  is  added 
to  the  boiler,  the  effect  is  reversed— the  steam  becomes  negatively,  and  the 
boiler  positively,  electrified. 

With  a  current  of  moist  air  Faraday  obtained  effects  similar  to  those  of 
this  apparatus,  but  with  dry  air  no  effect  is  produced. 

759.  Holtz's  electrical  machine. — Before  the  end  of  last  century  elec- 
trical machines  were  known  in  this  country  in  which  the  electricity  was  not 


developed  by  friction,   Init  by  the  continuous   inductive  action  of  a  body 
already  electrified,   as   the  electrophorus  ;  within   the  last  few  years  such 


-759] 


Holtz's  Electrical  Machine. 


727 


machines  have  been  re-invented  and  come  into  use.     The  form  represented 
in  fig.  687  was  invented  by  Holtz,  of  BerHn. 

It  consists  of  two  circular  plates  of  thin  glass  at  a  distance  of  3  mm.  from 
each  other  ;  the  larger  one,  AA,  which  is  2  feet  in  diameter,  is  fixed  by  means 
of  4  wooden  rollers  a,  resting  on  glass  axes  and  glass  feet.  The  diameter  of 
the  second  plate,  B  B,  is  2  inches  less  ;  it  turns  on  a  horizontal  glass  axis, 
which  passes  through  a  hole  in  the  centre  of  the  large  fixed  plate  without 
touching  it.  In  the  plate  A,  on  the  same  diameter,  are  two  large  apertures, 
or  7vi/idoius,  Y  ¥'.  Along  the  lower  edge  of  the  window  F,  on  the  posterior 
face  of  the  plate,  a  band  of  paper,  /,  is  glued,  and  on  the  anterior  face  a  sort 
oi  tongue  of  thin  cardboard,  «,  joined  to/  by  a  thin  strip  of  paper,  and  pro- 
jecting into  the  wmdow.  At  the  upper  edge  of  the  window,  F',  there  are 
corresponding  parts,/'  and  ?t'.  The  papers/  and  /'  constitute  the  armatures. 
The  two  plates,  the  armatures,  and  their  tongues  are  covered  with  shellac 
varnish,  but  more  especially  the  edges  of  the  tongues. 

In  front  of  the  plate  B,  at  the  height  of  the  armatures,  are  two  brass 
combs.,  O  O',  supported  by  two  conductors  of  the  same  metal,  C  C.  In  the 
front  end  of  these  conductors  are  two  moderately  large  brass  knobs,  through 
which  pass  two  brass  rods  terminated  by  smaller  knobs,  r  r\  and  provided 
with  ebonite  handles,  K  K'.  These  rods,  besides  moving  with  gentle  friction 
in  the  knobs,  can  also  be  turned  so  as  to  be  more  or  less  near  and  inclined 
towards  each  other.  The  plate  B  B  is  turned  by  means  of  a  winch  M,and  a 
series  of  pulleys  which  transmit  its  motion  to  the  axis  ;  the  velocity  which 
it  thus  receives  is  12  to  15  turns  in  a  second,  and  the  rotation  should  take 
place  in  the  direction  indicated  by  the  arrows — that  is,  towards  the  points  of 
the  cardboard  tongues  71  ?i'. 

To  work  the  machine,  the  armatures  //'  must  be  first  primed — that  is, 
one  of  the  armatures  is  positively  and  the  other  negatively  electrified.  This 
is  effected  by  means  of  a  plate  of  ebonite,  which  is  excited  by  striking  it 
with  catskin  ;  the  two  knobs  rr'  having  been  connected  so  that  the  two 
conductors  C  C  only  form  one,  as  seen  in  fig.  688,  which  shows  by  a  hori- 


n-     A 


<»"*'«'«'« 


Fig.  63S. 

zontal  section,  through  the  axis  of  rotation,  the  relative  arrangement  of  the 
plates  and  of  the  conductors.  The  electrified  ebonite  is  then  brought  near 
one  of  them — •/,  for  instance — and  the  plate  B  is  turned.  The  ebonite  is 
charged  with  negative  electricity,  and  this  withdraws  the  positive  electricity 
of  the  armature  and  charges  it  negatively.  This  latter  acting  by  induction 
through  the  plate  B  B,  as  it  turns  on  the  conductors  OCC'O'  (fig.  688),  attracts 
through  the  co>nl)  O  the  positive  electricity  which  collects  on  the  front  face  of 
the  movable  plate  ;  while  at  the  same  time  negative  electricity,  repelled  on 
the  comb  O',  collects,  like  the  former,  on  the  front  face  of  the  plate  B. 
Hence,  the  two  electricities  being  carried  along  by  the  rotation,  at  the  end 


728 


Frictional  Electricity. 


[759- 


of  half  a  turn  all  the  lower  half  of  the  plate  B,  from/  to  F'  (fig.  689).  is  posi- 
tively electrified,  and  its  upper  surface  from  p'  to  F  negatively.  But  the  two 
opposite  electricities  above  and  below  the  window  F'  concur  in  decomposing 
the  electricity  of  the  armature  j!^';z'  ;  the  partj?^  is  positively  electrified,  while 
negative  electricity  is  liberated  by  the  tongue  n\  and  is  deposited  on  the 
inner  face  of  the  plate  B  B,  which  from  its  thinness  almost  completely  neu- 
tralises the  positive  electricity  on  the  anterior  face. 

The  two  armatures  are  then  primed,  and  the  same  effect  as  at  F'  is 
produced  at  F  on  the  armature  p  n — that  is,  that  the  opposite  electricities 
above  and  below  p  n,  decomposing  a  new  quantity  of  neutral  electricity, 
the  negative  charge  of  the  part/  increases,  while  the  positive  electricity  which 
is  liberated  by  the  tongue  n  neutralises  the  negative  electricity  which  comes 
from   F'   towards  F  ;  and  so  forth,  until,  the  machine  having  attained  its 


%- 


Fig.  689. 


maximum  charge,  there  is  equilibrium  in  all  its  parts.  From  that  point  it 
only  keeps  itself  up,  and  in  perfectly  dry  air  it  may  work  for  a  long  time 
without  its  l:)eing  necessary  to  employ  the  ebonite  plate.  If  this  be  removed, 
and  the  knobs  r  and  ;-'  are  moved  apart  (fig.  6S7)  to  a  distance  dependent 
on  the  power  of  the  machine,  on  continuing  to  turn,  a  torrent  of  sparks 
strikes  across  from  one  knob  to  the  other. 

With  plates  of  equal  dimensions  Holtz's  machine  is  far  more  powerful 
than  the  ordinary  electrical  machine  (753).  The  power  is  still  further  increased 
by  suspending  to  the  conductors  C  C  two  condensers,  H  H'  (765),  or  small 
Leyden  jars,  which  consist  of  two  glass  tubes  coated  with  tinfoil,  inside  and 
out,  to  within  a  fifth  of  their  height.  Each  of  them  is  closed  by  a  cork 
through  which  passes  a  rod,  communicating  at  one  end  with  the  inner  coat- 
ing, and  suspended  to  one  of  the  conductors  by  a  crook  at  the  other  end- 
The  two  external  coatings  are  connected  by  a  conductor,  G.  They  are,  in 
fact,  only  two  small  Leyden  jars  (770),  one  of  them,  H,  becoming  charged 
with  positive  electricity  on  the  inside  and  negative  on  the  outside  ;  the  other, 
ir,  with  negative  electricity  on  the  inside  and  positive  on  the  outside, 
becoming  charged  by  the  play  of  the  machine,  and  being  discharged  at  the 


-760]  WimsJmrsfs  MacJiine.  729 

same  rate  by  the  knoljs  rr\  they  strengthen  the  spark,  which  may  attain  a 
length  of  6  or  7  inches. 

The  current  of  the  machine  is  utilised  by  placing  in  front  of  the  frame 
two  brass  uprights,  ^(^' ,  with  binding  screws  in  which  are  copper  wires  ;  then, 
by  means  of  the  handles  K  K',  the  rods  which  support  the  knobs  rr'  are  in- 
clined, so  that  they  are  in  contact  with  the  uprights.  The  current  being- 
then  directed  by  the  wires,  a  battery  of  six  jars  can  be  charged  in  a  few 
minutes,  water  can  be  decomposed,  a  galvanometer  deflected,  and  Geissler's 
tubes  illuminated  as  with  the  voltaic  battery. 

Kohlrausch  found  that  a  Holtz  machine  with  a  plate  16  inches  in  dia- 
meter, and  making  5  turns  in  three  seconds,  produced  a  constant  current 
capable  of  decomposing  water  at  the  rate  of  3^  millionths  of  a  milligramme 
in  a  second.  This  is  equal  to  the  effect  produced  by  a  Grove's  cell  in  a  cir- 
cuit of  45,000  ohms  resistance. 

Rossetti,  who  made  a  series  of  measurements  with  a  Holtz  machine, 
found  that  the  strength  of  the  current  is  nearly  proportional  to  the  velocity 
of  the  rotation  ;  it  increases  a  little  more  rapidly  than  the  rotation.  The  ratio 
of  the  velocity  of  rotation  to  the  strength  of  the  current  is  greater  when  the 
hygrometric  state  increases.  The  current  produced  by  a  Holtz  machine  is 
quite  comparable  to  that  of  a  voltaic  couple.  Its  electromotive  force  and 
resistance  are  constant,  provided  the  velocity  of  rotation  and  the  hygrometric 
state  are  constant. 

The  electromotive  force  is  independent  of  the  velocity  of  rotation,  but 
diminishes  as  the  moisture  increases  ;  it  is  nearly  52,000  times  as  great  as 
that  of  a  Daniell's  cell. 

The  internal  resistance  is  independent  of  the  moisture,  but  diminishes 
rapidly  with  increased  velocity  of  rotation.  Thus  with  a  velocity  of  120  turns 
in  a  minute  it  is  represented  by  2,810  million  ohms  (964),  and  with  a  velocity 
of  450  turns  it  is  646  million  ohms. 

Holtz's  machine  is  very  much  affected  by  the  moisture  of  the  air  ;  but 
Ruhmkorfif  found  that  by  spreading  on  the  table  a  few  drops  of  petroleum, 
the  vapours  which  condense  on  the  machine  protect  it  against  the  moisture 
of  the  atmosphere. 

Holtz's  machine  alTords  a  means  of  making  a  curious  experiment  on 
reversibility.  If  the  two  combs  of  a  machine  in  the  ordinary  state  are  con- 
nected with  the  poles  of  a  second  similar  one,  which  is  then  set  in  action, 
the  combs  of  the  first  become  luminous,  and  the  plate  begins  to  rotate,  but 
in  the  opposite  direction  to  its  ordinary  course  ;  the  electricity  thus  transmits 
the  motion  of  the  second  machine  to  the  first  ;  the  one  expends  what  the 
other  produces.  It  may  also  be  observed  that  the  two  machines  are  con- 
nected by  opposite  poles,  and  the  system  constitutes  a  circuit  which  is  tra- 
versed in  a  definite  direction  by  a  continuous  electrical  current. 

A  ver)'  simple  and  efficient  machine  of  this  kind  is  made  by  Voss  of 
Berlin.  One  with  a  plate  of  10  inches  diameter  produces  a  spark  of  4  to  5 
inches. 

760.  'Wimshurst'8  machine. — This  is  the  simplest  and  most  efficient  of 
all  induction  machines. 

It  consists  (fig.  690)  of  two  circular  glass  discs  mounted  on  a  fixed 
horizontal  spindle  in  such  a  way  as  to  be  rotated  in  opposite  directions  at  a 


730  Frictional  Electricity.  [760- 

distance  of  not  more  than  a  quarter  of  an  inch  apart.  Both  discs  are  well 
varpished,  and  attached  to  the  outer  surface  of  each  are  narrow  radial 
sections  of  tinfoil  arranged  at  equal  angular  distances  apart. 


Fig.  690. 


Attached  to  the  fixed  spindle  on  which  the  discs  rotate  is  a  bent  conduct- 
ing rod,  at  the  ends  of  which  are  two  fine  wire  brushes  ;  twice  during  each 
revolution  two  diametrically  opposite  conductors  are  put  in  connection  with 
each  other  by  means  of  this  conductor,  as  they  just  graze  the  tips  of  the 
brushes.  At  the  back  is  a  similar  one  at  right  angles  to  that  in  front,  and 
there  is  a  position  of  maximum  efficiency,  which  is  when  they  make  an  angle 
of  45°  with  the  fixed  collectors.  There  are  two  forks  provided  with  combs 
directed  towards  one  another,  and  towards  the  t\\o  discs  which  rotate  between 
them  ;  they  are  supported  horizontally  on  glass  Leyden  jars,  to  which  are 
also  attached  the  terminal  electrodes  or  dischargers,  the  distance  apart  of 
which  can  be  varied  by  turning  the  Leyden  jar  from  which  they  rise. 

The  machine  is  quite  self-exciting,  and  requires  neither  friction,  nor  the 
spark  from  any  outside  exciter,  to  start  it.  This  is  one  of  the  most  remark- 
able features  of  this  machine,  that  under  ordinary  conditions  it  attains  its 
full  power  after  the  second  or  third  turn.  The  initial  discharge  is  probably 
obtained  from  the  electricity  of  the  air,  or  from  the  frictional  resistance 
against  it. 


-761]       JVor/c  Required  for  the  Production  of  Electricity,         731 

With  a  machine  having  plates  17  inches  in  diameter,  a  powerful  spark 
discharge  passes  between  the  two  electrodes  when  they  are  4  to  5  inches 
apart,  in  regular  succession,  at  the  rate  of  2  or  3  for  every  turn  of  the  handle. 
A  machine  with  12  plates,  30  inches  in  diameter,  when  driven  at  a  speed  of 
200  turns  per  minute,  produces  sparks  between  the  terminals  of  13^  inches 
in  length  ;  and  when  the  terminals  are  closed  by  a  wire  of  3,000  ohms 
resistance  (964)  a  current  of  §  of  a  millampere  is  produced.  With  these 
machines  the  increase  of  electricity  has  been  found  proportional  to  the 
speed  of  rotation  up  to  5,000  turns  in  a  minute. 

It  is  not  easy  to  give  a  satisfactory  account  of  the  theory  of  the  machine. 
Its  inventor  considers  that  the  remarkable  efficiency  may  be  partly  due 
to  the  duplex  action  of  the  apparatus,  both  plates  being  active  and  con- 
tributing electricity  to  the  collecting  combs,  the  sector-shaped  plates  of  tin- 
foil acting  as  inductors  when  in  their  position  of  lowest  efficiency  as  carriers, 
and  as  carriers  when  in  the  positions  at  which  their  inductive  effect  is  at  a 
minimum,  and  vice  versa,  and  as  it  follows  from  the  construction  of  the 
instrument  that  the  inductors  of  the  one  disc  are  at  a  position  of  highest 
efficiency  when  those  of  the  other  are  at  their  lowest,  and  vice  versa,  and  as 
this  applies  with  equal  force  to  the  sectors  when  considered  as  carriers,  it 
also  follows  that  the  charging  of  the  electrodes,  and  therefore  the  discharge 
between  them,  is  by  mutual  compensation  maintained  constant. 

761.  Work  required  for  the  production  of  electricity.— In  all  electrical 
machines  electricity  is  only  produced  by  the  expenditure  of  a  definite  amount 
of  force,  as  will  at  once  be  seen  by  a  perusal  of  the  preceding  descriptions. 
The  action  of  those  machines,  however,  which  work  continuously,  is  some- 
what complex.  Not  only  is  electricity  produced,  but  heat  also  ;  and  it  has 
been  hitherto  impossible  to  estimate  separately  the  work  required  for  the 
heat  from  that  required  for  the  electricity.  This  is  easily  done  in  theory,  but 
not  in  practice  :  it  would  be,  for  instance,  difficult  to  determine  the  tem- 
perature of  the  cushion,  or  of  the  plate  of  a  Ramsden  machine. 

By  means  of  a  Lane  electrometer  (717)  it  was  found  that  taking  as  unity 
the  quantity  of  electricity  produced  by  one  turn  of  a  Ramsden  machine  with 
a  plate  39  inches  in  diameter,  that  produced  by  a  Holtz  machine  with  a 
plate  of  21  inches  was  o-86  ;  but  as  for  the  same  work  the  former  made  i 
and  the  latter  10  turns  in  a  second,  it  follows  that  the  quantities  produced 
were  as  i  :  8-6.  Comparing  the  quantities  per  unit  of  surface,  the  yield  of 
the  Holtz  machine  is  more  than  12  times  that  of  the  Ramsden. 

In  lifting  the  plate  off  a  charged  electrophorus  a  certairk  expenditure  of 
force  is  needed,  though  it  be  too  slight  to  be  directly  estimated  (752).  With 
a  Holtz  machine  it  may  be  readily  shown  by  experiment  that  there  is  a 
definite  expenditure  of  force  in  working  it.  If  such  a  machine  be  turned 
without  having  been  charged,  the  work  required  is  only  that  necessary  to 
overcome  the  passive  resistances  due  to  friction.  If,  however,  a  charged 
ebonite  plate  is  approached  to  one  of  the  sectors,  as  soon  as  the  peculiar 
sound  indicates  that  the  machine  is  at  work,  it  will  be  observed  that  there 
must  be  a  distinct  increase  in  the  mechanical  effort  necessary  to  work  the 
machine. 

The  work  required  to  charge  an  unelectrified  conductor  to  a  given  poten- 
tial may  be  deduced  from  the  following  considerations  : — To  impart  to  a  body 


7^^ 


Frictional  Electricity. 


[761- 


which  is  at  potential  V  a  quantity  of  electricity  Q  would  require  an  amount 
of  work  represented  by  QV  (739).  But  in  the  case  of  an  unelectrified  body  it 
is  neutral  at  the  outset — that  is,  at  zero  potential  ;  and  we  may  conceive  the 
electricity  imparted  to  it  in  a  series  oi  11  very  small  charges  of  q  each,  such 
that  71  q  =  Q  ;  and  as  the  potential  rises  proportionally  to  the  number  of 
charges,  it  may  be  assumed  that  the  work  done  is  equal  to  that  required  to 
charge  the  body  to  an  average  potential  of  W  ;  hence  the  work  in  question 
W  =  ^QV. 

From  the  relation  between  the  quantity  of  heat  produced  by  the  current 
of  a  Holtz  machine  working  under  definite  conditions,  and  the  amount  of 
work  expended  in  producing  the  rotation  of  the  plate,  Rossetti  has  made  a 
determination  of  the  mechanical  equivalent  of  heat,  which  gave  the  number 
1,397,  agreeing  therefore  very  well  with  the  numbers  obtained  by  other 
methods  (497). 

761(7.  Thomson's  water-dropping-  collector. — This  may  be  given  as  an 
illustration  of  an  arrangement  by  which  a  known  charge  may  be  almost  in- 
definitely multiplied.  In  fig.  691  I  is  an  insulated  metal  cylinder  called  the 
niductor,  and  water  falls  in  drops  from  an  uninsulated  metal  tap  the  nozzle 
of  which  is  in  the  centre  of  the  cylinder.  Directly  below  the  inductor  is  a 
second  similar  insulated  metal  cylinder  R,  with  a  funnel  the  nozzle  of  which 
is  also  in  the  centre.  This  second  cylinder  is  called 
the  receiver.  If  now  a  very  feeble  positive  charge  be 
given  to  the  inductor  I,  the  drops  of  water  .as  they 
issue  will  be  charged  with  positive  electricity,  and  will 
repel  each  other  as  they  issue.  Falling  on  the  funnel 
of  the  receiver  they  will  give  up  to  this  the  whole  of 
their  charge,  and  the  water  as  it  issues  will  be  neutral. 
The  charge  thus  imparted  to  R  will  go  on  increasing 
until  the  loss  equals  the  production,  or  until  the  drops 
issuing  from  the  inductor  are  repelled  by  the  receiver, 
so  that  they  do  not  fall  into  the  funnel. 

Suppose  two  such  apparatus  I  I'  and  R  R'  be 
arranged  near  each  other,  and  in  such  a  manner  that 
the  inductor  I  of  the  one  is  in  metallic  connection  with 
the  receiver  R'  of  the  other,  and  conversely  the  in- 
ductor r  in  connection  with  the  receiver  R  of  the  other. 
By  this  means  they  will  act  on  each  other  and  recipro- 
cally increase  their  charges.  If  a  feeble  charge  be 
given  to  one  of  the  inductors,  the  charges  will  go  on 
increasing  until  sparks  pass  between.  It  is  not  even 
necessary  to  give  a  charge  at  the  outset,  the  ordinary  electricity  of  the  atmo- 
sphere is  sufficient. 

The  energy  in  this  apparatus  is  derived  from  that  of  the  falling  body,  and 
would  be  exactly  equivalent  to  it  if  there  were  no  loss,  and  if  the  drops 
reached  the  funnel  without  any  velocity. 


Fig.  631 


-762] 


Spark. 


733 


EXPERIMENTS    WITH   THE    ELECTRICAL    MACHINE. 

762.  Spark. — One  of  the  most  curious  phenomena  observed  with  the 
electrical  machine  is  the  spark  drawn  from  the  conductor  when  a  finger  is 
presented  to  it,  The  positive  electricity  of  the  conductor,  acting  inductively 
on  the  neutral  electricity  of  the  body,  decomposes  it,  repelling  the  positive 
and  attracting  the  negative.  When  the  attraction  of  the  opposite  electricities 
is  sufficiently  great  to  overcome  the  resistance  of  the  air,  they  recombine 
with  a  smart  crack  and  a  spark.  The  spark  is  instantaneous,  and  is  accom- 
panied by  a  sharp  prickly  sensation,  more  especially  with  a  powerful  machine. 
Its  shape  varies.  When  it  strikes  at  a  short  distance  it  is  rectilinear,  as  seen 
in  fig.  692.  Beyond  two  or  three  inches  in  length  the  spark  becomes  irre- 
gular, and  has  the  form  of  a  sinuous  curve  with  branches  (fig.  693).  If  the 
discharge  is  very  powerful,  the  spark  takes  a  zigzag  shape  (fig.  694).  These 
two  latter  appearances  are  seen  in  the  discharge  of  lightning. 


Fig.  692 


f 


Fig.  693. 


Fig.  694. 


A  spark  may  be  taken  from  the  human  body  by  aid  of  the  insiilati7ig 
stool,  which  is  simply  a  low  stool  with  stout  glass  legs.  The  person  standing 
on  this^stooi  touches  the  prime  conductor,  and,  as  the  human  body  is  a  con- 
ductor, the  electricity  is  distributed  over  its  surface  as  over  an  ordinary 
insulated  metallic  conductor.  The  hair  diverges  in  consequence  of  repulsion, 
a  peculiar  sensation  is  felt  on  the  face,  and  if  another  person,  standing  on 
the  ground,  presents  his  hand  to  any  part  of  the  body,  a  smart  crack  with  a 
pricking  sensation  is  produced. 


734 


Friciional  Electricity. 


[762- 


001 


Gi^— 


A  person  standing  on  an  insulated  stool  may  be  positively  electrified  by 
being  struck  with  a  catskin.     If  the  person  holding  the  catskin  stands  on  an 
_  insulated   stool,   the    striker   becomes 

positively  and  the  person  struck  nega- 
tively electrified. 

763.  Electrical  ctalmes.  —  The 
electrical cJiimcs  is  a  piece  of  apparatus 
consisting  of  three  bells  suspended  to 
a  horizontal  metal  rod  (fig.  695).  Two 
of  them,  A  and  B,  are  in  metallic  con- 
nection with  the  conductor ;  the  middle 
bell  hangs  by  a  silk  thread,  and  is  thus 
insulated  from  the  conductor,  but  is 
connected  with  the  ground  by  means 
of  a  chain.  Between  the  bells  are 
small  copper  balls  suspended  by  silk  threads.  When  the  machine  is  worked, 
the  bells  A  and  B,  being  positively  electrified,  attract  the  copper  balls,  and 
after  contact  repel  them.  Being  now  positively  electrified,  they  are  in  turn 
attracted  by  the  middle  bell,  C,  which  is  charged  with  negative  electricity 
by  induction  from  A  to  B.  After  contact  they  are  again  repelled,  and  this 
process  is  repeated  as  long  as  the  machine  is  in  action. 

Fig.  696  represents  an  apparatus   originally  devised  by  Volta  for  the 
purpose  of  illustrating  what  he  supposed  to  be  the  motion  of  hail  between 


Fig.  695 


Fig.  696. 


Fig.  697. 


two  clouds  oppositely  electrified.  It  consists  of  a  tubulated  glass  shade, 
with  a  metal  base,  on  which  are  some  pith  balls.  The  tubulure  has  a  metal 
cap,  through  which  passes  a  brass  rod,  provided  with  a  metal  disc  or  sphere 
at  the  lower  end,  and  at  the  upper  with  a  ring,  which  touches  the  prime 
conductor. 

When  the  madiinc  is  worked,  the  sphere  l)(.'c()ming  positively  electrified 
attracts  the  light  pith  l)alls,  which  arc  then  immeiliately  repelled,  and,  having 


-764] 


Electrical  Whirl  or   Vane. 


735 


lost  their  charge  of  positive  electricity,  are  again  attracted,  again  repelled, 
and  so  on,  as  long  as  the  machine  continues  to  be  worked.  An  amusing 
modification  of  this  experiment  is  frequently  made  by  placing  between  the 
two  plates  small  pith  figures,  somewhat  loaded  at  the  base.  When  the 
machine  is  worked,  the  figures  execute  a  regular  dance. 

764.  Electrical  wblrl  or  vane. — The  electrical  whirl  or  vatie  consists 
of  5  or  6  wires,  terminating  in  points,  all  bent  in  the  same  direction,  and 
fixed  in  a  central  cap,  which  rotates  on  a  pivot  (fig.  697).  When  the  appa- 
ratus is  placed  on  the  conductor,  and  the  machine  worked,  the  whirl  begms 
to  revolve  in  a  direction  opposite  that  of  the  points.  This  motion  is  not 
analogous  to  that  of  the  hydraulic  tourniquet  (149).  It  is  not  caused  by  a 
flow  of  material  fluid,  but  is  owing  to  a  repulsion  between  the  electricity  of 
the  points  and  that  which  they  impart  to  the  adjacent  air  by  conduction.  The 
electricity,  being  accumulated  on  the  points  in  a  high  state  of  density,  passes 
into  the  air,  and,  imparting  thus  a  charge  of  electricity,  repels  this  electricity, 
while  it  is  itself  repelled.  That  this  is  the  case  is  evident  from  the  fact  that 
on  approaching  the  hand  to  the  .whirl  while  in  motion,  a  slight  draught  is 
felt,  due  to  the  movement  of  the  electrified  air,  while  in  vacuo  the  apparatus 
does  not  act  at  all.     This  draught  or  wind  is  known  as  the  electrical  aura. 

If  the  experiment  be  made  in  water,  the  fly  remains  stationary,  for  water 
is  a  good  conductor  ;  but  in  olive  oil,  which  is  a  bad  conductor,  the  whirl 
rotates. 

When  the  electricity  thus  escapes  by  a  point,  the  electrified  air  is  repelled 
so  strongly  as  not  only  to  be  perceptible  to  the  hand,  but  also  to  engender 
a  current  strong  enough  to  blow  out  a  candle.  Fig.  698  shows  this  experi- 
ment. The  same  efifect  is  produced  by  placing  a  taper  on  the  conductor 
and  bringing  near  it  a  pointed  wire  held  in  the  hand  (fig.  699).    The  current 


Fig.  698. 

arises  in  this  case  from  the  flow  of  air  electrified  with  the  contrary  electricity 
which  escapes  by  the  point  under  the  influence  of  the  machine.  The  loss 
of  electricity  in  this  way  by  contact  with  easily-moving  bodies  is  analogous 
to  the  transmission  of  heat  by  convection. 

The  electrical  orrery  and  the  electrical  Inclined  plane  are  analogous  in 
their  action  to  these  pieces  of  apparatus. 

The  velocity  of  the  electrical  aura  has  been  determined  by  placing  a 
wire  gauze  connected  with  earth  at  a  fixed  distance  from  the  point,  and  an 
anemometer  at  varying  distances  behind  the  gauze.     The  velocity  of  the 


•36 


Frictional  Electricity 


[764- 


wind  was  found  to  diminish  with  the  distance,  but  not  in  direct  proportion  ; 
at  a  distance  of  22  inches  it  was  5^  feet  per  second,  while  at  60  inches  its 
velocity  was  2  feet  per  second. 

The  production  of  the  electi'ical  aura  is  accompanied  by  luminous 
phenomena  which  can  be  seen  in  the  dark.  If  positive  electricity  escapes 
from  the  point  a  violet  aigrette  is  formed  ;  while  when  the  electricity  is 
negative  a  small  brilliant  star  forms  on  the  point. 

It  is  pretty  certain  that  in  these  experiments  it  is  not  the  air  itself,  but 
the  particles  in  it,  whether  of  dust  or  of  moisture,  which  become  electrified. 

This  may  be  illustrated  by 
the  following  simple  ex- 
penment.  A  glass  globe 
is  filled  with  dense  smoke 
of  turpentine  or  petro- 
leum (fig.  700),  and  the 
bared  end  of  a  gutta- 
percha-covered  wire  is 
held  in  it  while  the  other 
end  is  connected  with  an 
electrical  machine.  On 
giving  two  or  three  turns 
to  the  machine  the  smoke 
is  rapidly  deposited,  and 
the  inside  becomes  quite 
clear.  Here  the  smoke 
consists  of  solid  particles, 
which  become  polarised  by  induction  and  attract  each  other  like  the  particles 
of  silk  in  fig.  676.  They  thereby  become  agglomerated,  and  fall  to  the 
bottom  of  the  globe.  Nahrwold  proves  that  if  air  is  freed  from  dust  by 
filtration  it  takes  little  or  no  charge  from  an  electrified  point. 

This  phenomenon  is  employed  industrially  in  the  deposition  of  finely 
suspended  powders,  as  in  lead  works.  Two  conductors  provided  with  points 
arc  connected  respectively  with  a  positive  and  negative  source  of  electricity  ; 
the  powder  electrified  by  the  one  point  is  repelled  and  is  precipitated  on  the 
other. 


-765J 


Condensers  or  Accuniulators. 


717 


CHAPTER    IV. 

CONDENSATION   OR   ACCUMULATION   OF   ELECTRICITY. 

765.  Condensers  or  Accumulators. — A  condenser  is  an  apparatus  for 
condensing  a  large  quantity  of  electricity  on  a  comparatively  small  surface. 
The  form  may  vary  considerably,  but  in  all  cases  consists  essentially  of  two 
insulated  conductors,  separated  by  a  non-conductor,  and  the  working  depends 
on  the  action  of  induction.  When  an  insulated  conductor  is  near  other 
conductors,  and  particularly  when  these  latter  are  connected  with  the  earth, 
the  capacity  of  the  conductor  is  increased  ;  that  is  to  say,  it  requires  a 
greater  quantity  of  electricity  to  raise  it  to  a  given  potential  than  when  the 
other  conductors  are  away.  An  arrangement  of  this  kind  is  called  a  con- 
denser or  acciamdator,  the  latter  term,  though  less  usual,  being  preferable,  as 
the  former  tacitly  implies  some  hypothesis  of  the  nature  of  electricity. 

Epinus's  condenser  consists  of  two  circular  brass  plates,  A  and  B  (fig. 
701),  with  a  sheet  of  glass,  C,  between  them.     The  plates,  each  provided 


Fig.  701. 


with  a  pith-ball  pendulum,  are  mounted  on  insulated  glass  legs,  and  can  be 
moved  along  a  support  and  fixed  in  any  position.  When  electricity  is  to  be 
accumulated,  the  plates  are  placed  in  contact  with  the  glass,  and  then  one  of 
them,  B  for  instance,  is  connected  with  the  electrical  machine,  and  the  other 
placed  in  connection  with  the  ground,  as  shown  in  fig.  702. 


73^ 


Frictional  Electricity. 


[765- 


In  explaining  the  action  of  the  condenser,  it  will  be  convenient  in  each 
case  to  call  that  side  of  the  metal  plate  nearest  the  glass  the  cwtcrio}'  and 
the  other  the  posteftor  side.  And  first  let  A  be  at  such  distance  from  B  as 
to  be  out  of  the  sphere  of  its  action.  The  plate  B,  which  is  then  connected 
with  the  conductor  of  the  electrical  machine,  takes  its  maximum  charge, 
which  is  distributed  equally  on  its  two  faces,  and  the  pendulum  diverges 


Fig.  702. 

widely.  If  the  connection  with  the  machine  be  interrupted,  nothing  would 
be  changed  ;  but  if  the  plate  A  be  slowly  approached,  its  neutral  state  being 
decomposed  by  the  influence  of  B,  negative  electricity  is  accumulated  on  its 
anterior  face,  ft  (fig.  703),  and  positive  passes  into  the  ground.  But  as 
the  negative  electricity  of  the  plate  A  reacts  in  its  turn  on  the  positive  of 
the  plate  B,  the  latter  ceases  to  be  equally  distributed  on  both  faces,  and 
is  accumulated  on  its  anterior  face,  m.  The  posterior  ia.ce.,p,  having  thus 
lost  a  portion  of  its  electricity,  its  density  has  diminished,  and  is  no  longer 
equal  to  that  of  the  machine,  and  the  pendulum  b  diverges  less  widely. 
Hence  B  can  receive  a  fresh  quantity  from  the  machine,  which,  acting  as  just 
described,  decomposes  by  induction  a  second  quantity  of  neutral  electricity 
on  the  plate  A.  There  is  then  a  new  accumulation  of  negative  electricity 
on  the  face  «,  and  consequently  of  posi- 
tive electricity  on  m.  But  each  time  that 
the  machine  gives  off  electricity  to  the 
plate,  only  a  part  of  this  passes  to  the 
face  f/i,  the  other  remaining  on  the  face 
p  ;  the  density  here,  therefore,  continues 
to  increase  until  it  equals  that  of  the 
machine.  From  this  moment  equilibrium 
is  established,  and  a  limit  to  the  charge 
is  attained  which  cannot  be  exceeded. 
The  quantity  of  electricity  accumulated 
now  on  the  two  faces  /ii  and  ;/  is  very  considerable,  and  yet  the  pendulum 
diverges  just  as  much  as  it  did  when  A  was  absent,  and  no  more  ;  in  fact, 
the  density  at/  is  just  what  it  was  then — namely,  that  of  the  machine. 


-766J       Shzu  Discharge  and  Instantaneous  Discharge.  739 

When  the  condenser  is  charged— that  is,  when  the  opposite  electricities 
are  accumulated  on  the  anterior  faces— connection  with  the  ground  is  broken 
by  raising  the  wires.  The  plate  A  is  charged  with  negative  electricity,  but 
simply  on  its  anterior  face  (fig.  703),  the  other  side  being  neutral.  The 
plate  B,  on  the  contrary,  is  electrified  on  both  sides,  but  unequally  ;  the  ac- 
cumulation is  only  on  its  anterior  face,  while  on  the  posterior,/,  the  density 
is  simply  equal  to  that  of  the  machine  at  the  moment  the  connections 
are  interrupted.  In  fact,  the  pendulum  b  diverges,  and  a  remains  vertical. 
But  if  the  two  plates  are  removed,  the  two  pendulums  diverge  (fig.  701), 
which  is  owing  to  the  circumstance  that,  as  the  plates  no  longer  act  on  each 
other,  the  positive  electricity  is  equally  distributed  on  the  two  faces  of  the  plate 
B,  and  the  negative  on  those  of  the  plate  A. 

766.  Slow  dlscharg-e  and  Instantaneous  discbargre. — While  the  plates 
A  and  B  are  in  contact  with  the  glass  (fig.  702),  and  the  connections  inter- 
rupted, the  condenser  may  be  discharged — that  is,  restored  to  the  neutral 
state — in  two  ways  ;  either  by  a  slow  or  by  an  instantaneous  discharge.  To 
discharge  it  slowly,  the  plate  B— that  is,  the  one  containing  an  excess  of  elec- 
tricity— is  touched  with  the  finger  ;  a  spark  passes,  all  the  electricity  on  p 
passes  into  the  ground,  the  pendulum  b  falls,  but  a  diverges.  For  B,  having 
lost  part  of  its  electricity,  only  retains  on  the  face  m  that  held  by  the  inductive 
influence  of  the  negative  on  A.  But  the  quantity  thus  retained  at  B  is  less 
than  that  on  A ;  this  has  free  electricity,  which  makes  the  pendulum  a  diverge  ; 
and  if  it  be  now  touched,  a  spark  passes,  the  pendulum  a  sinks  while  b  rises, 
and  so  on  by  continuing  to  touch  alternately  the  two  plates.  The  discharge 
only  takes  place  slowly  ;  in  very  dry  air  it  may  require  several  hours.  If  the 
plate  A  were  touched  first,  no  electricity  would  be  removed,  for  all  it  has  is 
retained  by  that  of  the  plate  B.  To  remove  the  total  quantity  of  electricity 
by  the  method  of  alternate  contacts,  an  infinite  number  of  such  contacts  would 
theoretically  be  required. 

An  instantaneous  discharge  may  be  effected  by  means  of  the  discharging 
rod  (fig.  704).  This  consists  of  two  bent  brass  rods,  terminating  in  knobs 
and  joined  by  a  hinge.  When  provided  with  glass 
handles,  as  in  fig.  704,  it  forms  a  glass  discharging 
rod.  In  using  this  apparatus  one  of  the  knobs  is 
pressed  against  one  plate  of  the  condenser,  and  the 
other  knob  brought  near  the  other.  At  a  certain  dis- 
tance a  spark  strikes  from  the  plate  to  the  knob,  caused 
by  the  sudden  recomposition  of  the  two  opposite  elec- 
tricities. 

When  the  condenser  is  discharged  by  the  dis- 
charger no  sensation  is  experienced,  even  though  the 
latter  be  held  in  the  hand  ;  of  the  two  conductors, 
the   electricity   chooses   the   better,   and   hence    the  pig_  ^^^ 

discharge    is   effected   through   the   metal,   and   not 

through  the  body.  But  if,  while  one  hand  is  in  contact  with  one  plate 
the  other  touches  the  second,  the  discharge  takes  place  through  the  breast 
and  arms,  and  a  considerable  shock  is  felt  ;  and  the  larger  the  surface  of 
the  condenser,  and  the  greater  the  electric  density,  the  more  violent  is  the 
shock. 

3  B  2 


740 


Frictional  Electricity. 


[767- 


767.  Condensing-  force. — The  cofidensing  force  is  the  relation  between 
the  whole  charge,  which  the  collecting  plate  can  take  while  under  the  in- 
fluence of  the  second  plate,  and  that  which  it  would  take  if  alone  ;  in  other 
words,  it  is  the  ratio  of  the  capacities  under  the  two  conditions. 

768.  Xlmit  of  the  charge  of  condensers. — The  quantity  of  electricity 
which  can  be  accumulated  on  each  plate  is,  cceteris  paribus.,  proportional  to 
the  potential  of  the  electricity  on  the  conductor,  and  to  the  surface  of  the 
plates  ;  it  decreases  as  the  insulating  plate  is  thicker,  and  it  differs  with  the 
specific  inductive  capacity  of  the  substance.  There  is,  however,  a  limit  in 
the  case  of  each  condenser  beyond  which  it  cannot  be  charged.  The  effect 
of  dielectric  polarisation  (747)  is  to  put  the  medium  into  a  state  of  strain 
from  which  it  is  always  trying  to  release  itself,  and  which  is  the  equivalent 
of  the  work  done  in  charging  a  condenser.  This  is,  indeed,  the  seat  of  the 
electrical  energy.  It  is  as  if  two  surfaces  were  pulled  together  by  elastic 
threads  which  repelled  each  other  laterally.  When  the  strain  exceeds  a 
certain  limit,  a  discharge  takes  place  through  the  mass  of  the  dielectric, 
generally  accompanied  by  light  and  sound,  and  with  a  temporary  or  perma- 
nent rupture  of  the  dielectric  according  as  it  is  fluid  or  solid.  This  is  what 
takes  place  when  a  substance — glass,  for  instance— is  exposed  to  a  continually 
increasing  weight  ;  a  point  is  ultimately  reached  at  which  the  glass  gives 
way,  and  the  weight  at  that  point  is  a  measure  of  the  resistance  to  fracture 
of  the  glass.  In  like  manner,  the  point  at  which  the  electrical  discharge  takes 
place  is  a  measure  of  the  electrical  strength  of  the  dielectric.  This  electrical 
strength  is  greater  in  glass  than  in  air,  and  in  dense  than  in  rarefied  air. 

Thus  to  produce  a  spark  of  0-5  cm.  in  wire  at  the  pressures  20,  180,  and 
685  mm.  respectively,  the  only  potentials  required  were  3-23,  12-2,  and  36. 

We  may,  following  Maxwell,  further  illustrate  this  point  by  the  twisting 
of  a  wire :  a  wire  in  which  a  small  force  produces  a  permanent  twist  corre- 
sponds to  the  case 
of  the  conduction 
of  electricity  in  a 
good  conductor  ; 
one  which  having 
been  twisted,  re- 
\erts  to  its  former 
shape  when  the 
twisting  force  is 
removed,  is  com- 
pletely elastic,  and 
corresponds  to  a 
perfect  insulator 
with  respect  to  the 
charge  employed. 
If  no  permanent 
twist  can  be  given 
to  the  wire  by  a 
f'S-  705.  force  which  doesnot 

break  it,  the  wire  is  brittle.    A  dielectric  such  as  air,  which  does  not  transmit 
electricity  except  by  disruptive  discharge,  may  be  said  to  be  electrically  brittle. 


770] 


Lcydcn  Jar. 


741 


769.  Fulminating-  pane.  Franklin's  plate. — This  is  a  simple  form  of 
the  condenser,  and  is  more  suitable  for  giving  strong  shocks  and  sparks.  It 
consists  of  a  glass  plate  fixed  in  a  wooden  frame  (fig.  705)  ;  on  each  side  of 
the  glass,  pieces  of  tinfoil  are  fastened  opposite  each  other,  leaving  a  space 
free  between  the  edge  and  the  frame.  It  is  well  to  cover  this  part  of  the 
glass  with  an  insulating  layer  of  shellac  varnish.  One  of  the  sheets  of  tin- 
foil is  connected  with  the  ring  on  the  frame  by  a  strip  of  tinfoil,  so  that  it  can 
be  connected  with  the  ground  by  means  of  a  chain.  To  charge  the  pane  the 
insulated  side  is  connected  with  the  machine.  As  the  other  side  communi- 
cates with  the  ground,  the  two  coatings  play  exactly  the  part  of  the  condenser. 
On  both  plates  there  are  accumulated  large  quantities  of  contrary  electricities. 

The  pane  may  be  discharged  by  touching  one  knob  of  the  discharger 
against  the  lower  surface,  while  the  other  is  brought  near  the  upper  coating. 
A  spark  ensues,  due  to  the  recombination  of  the  two  electricities  ;  but  the 
operator  experiences  no  sensation,  for  the  discharge  takes  place  through  the 
wire.  But  if  the  connection  between  the  two  coatings  be  made  by  touching 
them  with  the  hands,  a  violent  shock  is  felt  in  the  hands  and  breast,  for  the 
combination  then  takes  place  through  the  body. 

770.  SCieyden  jar. — The  Ley  den  jar  ^  so  named  from  the  town  of  Leyden, 
where  it  was  invented,  is  essentially  a  modified  condenser,  or  fulminating 
pane  rolled  up.  Fig.  706  represents  a  Leyden  jar  of  the  usual  French  shape 
in  the  process  of  being  charged.  It  consists  of  a  glass  jar  of  any  conve- 
nient size,  the  interior  of  which  is  either  coated  with  tinfoil  or  filled  with  thin 
leaves  of  copper,  or  with  gold-leaf.  Up  to  a  certain  distance  from  the  neck 
the  outside  is  coated  with  tinfoil.  The  neck  is  provided  with  a  cork,  through 
which  passes  a  brass  rod, 

which    terminates  at  one  /^^^  A 

end  in  a  knob,  and  com- 
municates with  the  metal 
in  the  interior.  The  me- 
tallic coatings  are  called 
respectively  the  inner  and 
outer  coatings  or  arma- 
tures. Like  any  other  con- 
denser, the  jar  is  charged 
by  connecting  one  of  the 
coatings  with  the  ground, 
and  the  other  with  the 
source  of  electricity.  When  it  is  held  in  the  hand  by  the  outer  coating,  and 
the  knob  presented  to  the  positive  conductor  of  the  machine,  positive  elec- 
tricity is  accumulated  on  the  inner  and  negative  electricity  on  the  outer 
coating.  The  reverse  is  the  case  if  the  jar  is  held  by  the  knob,  and  the 
outer  coating  presented  to  the  machine.  The  positive  charge  acting 
inductively  across  the  dielectric  glass,  decomposes  the  electricity  of  the 
outer  coating,  attracting  the  negative  and  repelling  the  positive,  which 
escapes  by  the  hand  to  the  ground.  Thus  it  will  be  seen  that  the  action  of 
the  jar  is  the  same  as  that  of  the  condenser,  and  all  that  has  been  said  of 
this  applies  to  the  jar,  substituting  the  two  coatings  for  the  two  plates  A  and 
B  of  fig.  702. 


Fig.  706. 


742 


F}'ictional  Elcctncity. 


[770- 


Like  any  other  condenser,  the  Leyden  jar  may  be  discharged  either 
slowly  or  instantaneously.  For  the  latter  purpose  it  is  held  in  the  hand  by 
the  outside  coating  (fig.  707),  and  the  two  coatings  are  then  connected  by 
means  of  the  simple  discharger.  Care  must  be  taken  to  touch  first  the 
external  coating  with  the  discharger,  otherwise  a  smart  shock  will  be  felt. 
To  discharge  it  slowly  the  jar  is  placed  on  an  insulated  plate,  and  first  the 
inner  and  then  the  outer  coating  touched,  either  with  the  hand  or  with  a 
metallic  conductor.     A  slight  spark  is  seen  at  each  discharge. 

Fig.  708  represents  a  very  pretty  experiment  for  illustrating  the  slow 
discharge.     The  rod  terminates  in  a  small  bell,  d^  and  the  outside  coating- 


Fig.  707. 

is  connected  with  an  upright  metal  support,  on  which  is  a  similar  bell,  e. 
Between  the  two  bells  a  light  brass  ball  is  suspended  by  a  silk  thread.  The 
jar  is  then  charged  in  the  usual  manner  and  placed  on  the  support  m.  The 
internal  coating  contains  a  quantity  of  free  electricity ;  the  pendulum  is 
attracted  and  immediately  repelled,  striking  against  the  second  bell,  to 
which  it  imparts  its  free  electricity.     Being  now  neutralised,  it  is  again 


attracted  l^y  the  first  bell,  and  so  on  for  some  time,  especially  if  the  air  be 
dry,  and  the  jar  somewhat  large. 


-772  J 


Residua/  Charoc. 


743 


771.  Iieyden  jar  with  movable  coatings. — This  apparatus  (fig.  709)  is 
used  i;o  demonstrate  that  in  the  Leyden  jar  the  opposite  electricities  are  not 
accumulated  on  the  coatings  merely,  but  are  stored  up  in  the  state  of  strain 
into  which  the  glass  is  put,  and  this  state  of  strain  is  the  mechanical  equiva- 
lent of  the  work  done  in  charging  the  jar.  It  consists  of  a  somewhat 
conical  glass  vessel,  B,  with  movable  coatings  of  zinc  or  tin,  C  and  D.  These 
separate  pieces  placed  one  in  the  other,  as  shown  in  figure  A,  form  a 
complete  Leyden  jar.  After  having  charged  the  jar,  it  is  placed  on  an  insu- 
lating cake  ;  the  inner  coating  is  first  removed  by  the  hand,  or  better  by  a 

glass  rod,  and  then  the  glass  vessel.  The  coatings  are  found  to  contain 
little  or  no  electricity,  and  if  they  are  placed  on  the  table  they  are  restored 
to  the  neutral  state.  Nevertheless,  when  the  jar  is  put  together  again,  as 
represented  in  the  figure  at  A,  a  shock  may  be  taken  from  it  almost  as  strong 
as  if  the  coatings  had  not  been  removed.  It  is  therefore  concluded  that  the 
coatings  principally  play  the  part  of  conductors,  distributing  the  electricity 
over  the  surface  of  the  glass,  which  thus  becomes  polarised,  and  retains  this 
state  even  when  placed  on  the  table,  owing  to  its  imperfect  conductivity. 

The  experiment  may  be  conveniently  made  without  any  special  form  of 
apparatus  by  forming  a  Leyden  jar,  of  which  the  inside  and  outside  coatings 
are  of  mercury,  charging  it ;  then  having  mixed  the  two  coatings,  the  apparatus 
is  put  together  again,  upon  which  a  discharge  may  be  once  more  taken. 

772.  Xiicbtenberg-'s  fig-ures. — This  experiment  well  illustrates  the  oppo- 
site electrical  conditions  of  the  two  coatings  of  a  Leyden  jar.     Holding  a 

jar  charged  with  positive  elec- 
tricity by  the  hand,  a  series  of 
lines  are  drawn  with  the  knob 
on  a  cake  of  resin  or  vulcanite  ; 
then  having  placed  the  jar  on 
an  insulator,  it  is  held  by  the 
knob,  and  another  series  traced 
by  means  of  the  outer  coating. 
If  now  a  mixture  of  red-lead  and 
flour  of  sulphur  be  projected  on 
the  cake,  the  sulphur  will  attach 
itself  to  the  positive  lines,  and 
the  red  lead  to  the  negative 
lines  ;  the  reason  being  that  in 
mixing  the  powders  the  sulphur 
has  become  negatively  electri- 
fied, and  the  red  lead  positively. 
The  sulphur  will  arrange  itself 
in  tufts  with  numerous  diverging" 
branches,  while  the  red  lead  will  take  the  form  of  small  circular  spots,  in- 
dicating a  difference  in  the  two  electricities  on  the  surface  of  the  resin. 
These  figures  form,  in  short,  a  very  sensitive  electroscope  for  investigating 
the  distribution  of  electricity  on  an  insulating  surface  {"jyj). 

Fig.  710  represents  the  appearance  of  a  plate  of  resin,  which  has  been 
touched  by  the  knob  of  a  Leyden  jar  charged  with  positive  electricity,  and 
has  then  been  dusted  with  lycopodium  powder. 


744  Frictio7ial  Electricity.  [773- 

'J12,.  Residual  charg-e. — Not  only  do  the  electricities  adhere  to  the  two 
surfaces  of  the  insulating  medium  which,  separates  them,  but  they  penetrate 
to  a  certain  extent  into  the  interior,  as  is  shown  by  the  following  experi- 
ment : — A  condenser  is  formed  of  a  plate  of  shellac  and  movable  metal  plates. 
It  is  then  charged,  retained  in  that  state  for  some  time,  and  afterwards  com- 
pletely discharged.  On  removing  the  metal  coatings  and  examining  both 
surfaces  of  the  insulator,  they  show  no  signs  of  electricity.  After  some  time, 
however,  each  face  exhibits  the  presence  of  some  electricity  of  the  same 
kind  as  that  of  the  plate  with  which  it  was  in  contact  while  the  apparatus  was 
charged.      This  is  explained,  by  some,  as  a  kind  of  elect7'ical  absorption. 

A  phenomenon  frequently  olaserved  in  Leyden  jars  is  of  the  same  nature. 
When  a  jar  has  been  completely  discharged  by  bringing  the  inner  and 
outer  coatings  in  metallic  contact,  and  allowed  to  stand  a  short  time,  it 
exhibits  a  second  charge,  which  is  called  the  electric  residue.  The  jar  may 
be  again  discharged,  and  a  second  residue  will  be  left,  feebler  than  the  first, 
and  so  on,  for  three  or  four  times.  Indeed,  with  a  delicate  electroscope  a 
long  succession  of  such  residues  may  be  demonstrated.  The  residue  is 
greater  the  longer  the  jar  has  remained  charged.  The  magnitude  of  the 
residue  further  depends  on  the  amount  of  the  charge,  and  also  on  the 
degree  in  which  the  metal  plates  are  in  contact  with  the  insulator.  It 
varies  with  the  nature  of  the  substance,  but  there  is  no  residue  with 
either  liquids  or  gaseous  insulators.  Faraday  found  that  with  parafifine 
the  residue  was  greatest,  then  with  shellac,  while  with  glass  and  sulphur  it 
was  least  of  all.  Kohlrausch  has  found  that  the  residue  is  nearly  proportional 
to  the  thickness  of  the  insulator.  If  successive  small  charges,  alternately 
positive  and  negative,  be  imparted  to  the  jar,  it  is  found  that  the  residual 
charges  come  out  in  the  reverse  order  to  that  in  which  the  original  charges  go 
in.  This  residue  is  not  to  be  confounded  with  that  observed  when  a  Leyden 
jar  is  discharged  at  the  greatest  striking  distance  (788),  and  which  residue 
Reiss  found  to  be  always  in  a  constant  proportion,  y-\,of  the  entire  charge. 

Maxwell  proved  that  a  dielectric  composed  of  strata  of  different  materials 
may  exhibit  the  phenomena  of  the  residual  charge,  even  though  none  of  the 
substances  composing  it  exhibit  it  when  alone. 

From  what  has  been  said  as  to  the  state  of  mechanical  strain  in  which 
the  dielectric  of  a  condenser  is  thrown  when  charged  with  electricity,  it  is 
not  difficult  to  account  for  the  phenomenon  of  the  residual  charge.     An 
elastic    body,  such  as  a  steel  plate,  which  has  been 
twisted  or  bent,  reverts  to  its  original  state  when  the 
force  which  brought  about  the  deformation  ceases  to 
act,  but  not  at  once  quite  completely.    A  certain  length 
of  time  is  required  for  this  alteration  to  take  place,  but 
I      the    change    is   promoted  by  any  gentle  mechanical 
\     action,  such  as  tapping,  which  gives  the  molecules  a 
^    certain  freedom  of  motion.     Dr.  Hopkinson  has  made 
an  experiment  with  a  Leyden  jar  which  is  quite  ana- 
„.  logous  to  this.     A  glass  vessel  (fig.  711)  contains  sul- 

phuric acid,  and  in  it  is  placed  a  thinner  one,  about  half 
full  of  the  same  ]i(|uid.  Platinum  wires  dip  in  the  two  liquids,  one  of  which 
is  in  connection  wiili  the  prime  conductor  of  an  electrical  machine,  while  the 


-775] 


Electric  Batteries. 


745 


other  is  connected  with  the  earth.  The  arrangement  forms,  in  short,  a  con- 
denser, the  coatings  of  which  are  sulphuric  acid.  When,  after  being  thus 
charged,  the  jar  is  discharged,  after  some  time  a  residual  discharge  may  be 
taken  by  again  connecting  the  wires  ;  if,  however,  the  inner  jar  be  gently 
struck  with  a  piece  of  wood,  the  residue  makes  its  appearance  much  more 
rapidly.  The  same  observer  draws  a  parallel  between  the  phenomena  of  the 
residual  charge  and  those  of  residual  magnetism  (715). 

774.  Electric  batteries.— The  charge  which  a  Leyden  jar  can  take 
depends  on  the  extent  of  the  coated  surface,  and  for  small  thicknesses  is 
inversely  proportional  to  the  thickness  of  the  insulator.  Hence,  the  larger 
and  thinner  the  jar  the  more  powerful  the  charge.  But  veiy  large  jars 
are  expensive,  and  liable  to  break  ;  and  when  too  thin,  the  accumulated 
electricities  discharge  themselves  through  the  glass,  especially  if  it  is 
not  quite  homogeneous.  Leyden  jars  have  usually  from  ^  to  3  square  feet 
of  coated  surface.     For  more  powerful  charges  electric  batteries  are  used. 

An  electric  battery  consists  of  a  series  of  Leyden  jars,  whose  internal 
and  external  coatings  are  respectively  connected  with  each  other  (fig.  712). 
They  are  usually  placed  in  a  wooden  box  lined  on  the  bottom  with  tinfoil. 
This  lining  is  connected  with  two  metal  handles  in  the  sides  of  the  box. 
The  inner  coatings  are  connected  with  each  other  by  metal  rods,  and  the 
battery  is  charged  by  placing  the  inner  coatings  in  connection  with  the  prime 
conductor,  while  the  outer  coatings  are  connected  with  the  ground  by  means 
of  a  chain  fixed  to  the  handles.  A  quadrant  electrometer  fixed  to  one  jar 
indicates  the  charge 
of  the  battery.  Al- 
though there  is  a 
large  quantity  of 
electricity  accumu- 
lated in  the  appara- 
tus, the  divergence 
is  not  great,  for  it 
is  simply  due  to 
the  free  electricity 
on  the  inner  coat- 
ing. The  larger 
and  more  numerous 
they  are,  the  longer 
is  the  time  required 
to  charge  the  bat- 
tery, but  the  effects 
are  so  much  the 
more  powerful  (784).  Fig- 7x2. 

When  a  battery  is  to  be  discharged,  the  coatings  are  connected  by  means 
of  the  discharging  rod,  the  outside  coating  being  touched  first.  Great  care  is 
required,  for  with  large  batteries  serious  and  even  fatal  accidents  may  occur. 

775.  The  universal  discbargrer. — This  is  an  almost  indispensable  appa- 
ratus in  experiments  with  the  electric  battery.  On  a  wooden  stand  (fig.  713) 
are  two  glass  legs,  each  provided  with  universal  joints,  in  which  movable 
brass  rods  are  fitted.     Between  these  legs  is  a  small  ivory  table,  on  which  is 


746  Frictional  Electricity.  [775- 

placed  the  object  under  experiment.  The  two  metal  knobs  being  directed 
towards  the  objects,  one  of  them  is  connected  with  the  outer  coating  of  the 
battery,  and  the  moment  communication  is  made  between  the  outer  and  the 
inner  coating  by  means  of  the  glass  discharging  rod,  a  violent  shock  passes 
through  the  object  on  the  table. 

776.  Cbarging:  by  cascade. — A  series  of  Leyden  jars  are  placed  each 
separately  on  insulating  supports.  The  knob  of  the  first  is  in  connection 
with  the  prime  conductor  of  the  machme,  and  its  outer  coating  joined  to  the 
knob  of  the  second,  the  outer  coating  of  the  second  to  the  knob  of  the  third, 
and  so  on,  the  outer  coating  of  the  last  communicating  with  the  ground. 
The  inner  coating  of  the  first  receives  a  charge  of  positive  electricity  from 


Fig.  713. 

the  machine,  and  the  corresponding  positive  electricity  set  free  by  induction 
on  its  outer  coating,  instead  of  passing  to  the  ground,  gives  a  positive  charge 
to  the  inner  coating  of  the  second,  which,  acting  in  like  manner,  develops  a 
charge  in  the  third  jar,  and  so  on  to  the  last,  where  the  positive  electricity 
ilcvelopcd  by  induction  on  the  outer  coating  passes  to  the  ground.  The  jars 
may  be  discharged  either  singly  by  connecting  the  inner  and  outer  coatings 
of  each  jar,  or  simultaneously  by  connecting  the  inner  coating  of  the  first 
with  the  outer  of  the  last.  In  this  way  the  quantity  of  electricity  necessary 
lo  charge  one  jar  is  available  for  charging  a  series  of  jars. 

IT].  Measurement  of  tbe  cbargre  of  a  battery,  pane's  electro- 
meter. \\'hcn  the  duler  and  inner  coatings  of  a  charged  Lcytliu  jar  arc 
gradually  Ijrought  nearer  each   other,  at  a  certain   ilistance  a  spontaneous 


-778]  Harris  s  Utiit  Jar.  y^y 

discharge  ensues.  The  distance  is  called  the  striking  or  sparkitJg  iiisia7ue. 
For  the  same  charge  it  is  inversely  proportional  to  the  pressure  of  the  air 
(768),  and,  with  the  same  jar,  but  different  charges,  directly  proportional  to  the 
electric  density  of  that  point  of  the  inner  coating  at  which  the  discharge 
takes  place.  As  the  density  of  any  point  of  the  inner  coating,  other  things 
remaining  the  same,  is  proportional  to  the  entire  charge,  the  striking  distance 
is  proportional  to  the  quantity  of  electricity  in  a  jar.  The  measurement  of 
the  charge  of  a  battery,  however,  by  means  of  the  striking  distance,  can  only 
take  place  when  the  charge  dis- 
appears. 

By  means  of  Lane's  electro- 
meter, which  depends  on  an 
application  of  this  principle,  the 
charge  of  a  jar  or  batteiy  may 
be  measured.  This  apparatus, 
c  (fig.  714),  consists  of  an  ordi- 
nary Leyden  jar,  near  which 
there  is  a  vertical  metallic  sup- 
port. At  the  upper  end  is  a 
brass  rod,  with  a  knob  at  one 


Fig.  714. 


end,  which  can  be  placed  in  metallic  connection  with  the  outside  of  the  jar : 
the  rod  being  movable,  the  knob  can  be  kept  at  a  measured  distance  from 
the  knob  of  the  inner  coating.  Fig.  714  represents  the  operation  of  measur- 
ing the  charge  of  a  jar  by  means  of  this  apparatus.  The  jar  b^  whose  charge 
is  to  be  measured,  is  placed  on  an  insulated  stool  with  its  outer  coating  in 
metallic  connection  with  the  inner  coating  of  Lane's  jar  t",  the  outer  coating 
of  which  is  in  connection  with  the  ground,  or  still  better  with  a  system  of  gas 
or  water  pipes ;  a  is  the  conductor  of  the  machine.  When  the  machine  is 
worked,  positive  electricity  passes  into  the  jar  b  ;  a  proportionate  cjuantity  of 
positive  electricity  is  repelled  from  its  outer  coating,  passes  into  the  inner 
coating  of  the  electrometer,  and  there  produces  a  charge.  When  this  has 
reached  a  certain  limit,  it  discharges  itself  between  the  two  knobs,  and  as 
often  as  such  a  discharge  takes  place,  the  same  quantity  of  positive  electricity 
will  have  passed  from  the  machine  into  the  battery ;  hence  its  charge  is  pro- 
portional to  the  number  of  discharges  of  the  electrometer. 

77S.  Harris's  unit  jar.— Harris's  unit  jar  (fig.  715)  is  an  application 
of  the  same  principle,  and  is  often  convenient  for  measuring  quantities 
of  electricity.  It  consists  of  a  small 
Leyden  phial,  4  inches  in  length  and 
f  inch  in  diameter,  coated  to  about 
an  inch  from  the  end,  so  as  to  expose 
about  6  inches  of  coated  surface.  It  is 
fixed  horizontally  on  a  long  insulator, 
and  the  charging  rod  connected  at  P 
with  the  conductor  of  the  machine, 
while  the  outer  coating  is  connected 
with  the  jar  or  batter)^  by  the  rod  /  /. 
When  the  accumulation  of  electricity  in  the  interior  has  reached  a  ceitain 
height  depending  on  the  distance  of  the  two  balls  in  and ;/,  a  discharge  ensues, 


748 


Frictional  Electricity. 


[779- 


and  marks  a  certain  quantity  of  electricity  received  as  a  charge  by  the 
battery,  in  terms  of  the  small  jar. 

779.  Volta's  condensing-  electroscope. — The  condensing  electroscope 
invented  by  Volta  is  a  modification  of  the  ordinary  gold-leaf  electroscope 
(751).  The  rod  to  which  the  gold-leaves  are  affixed  terminates  in  a  disc 
instead  of  in  a  knob,  and  there  is  another  disc  of  the  same  size  provided  with 
an  insulating  glass  handle.  The  discs  are  covered  with  a  layer  of  insulating 
shellac  varnish  (fig.  716). 

To  render  very  small  quantities  of  electricity  perceptible  by  this  apparatus 
one  of  the  plates,  which  thus  becomes  the  collecting  plate,  is  touched  with 
the  body  under  examination.  The  other  plate,  the  cofide/isifig plate,  is  con- 
nected with  the  ground  by  touching  it  with  the  finger.     The  electricity  of 


Fig.  716.  Fig.  717. 

the  body,  being  diffused  over  the  collecting  plate,  acts  inductively  through 
the  varnish  on  the  other  plate,  attracting  the  opposite  electricity,  but 
repelling  that  of  like  kind.  The  two  electricities  thus  become  accumulated 
on  the  two  plates  just  as  in  a  condenser,  but  there  is  no  divergence  of  the 
leaves,  for  the  opposite  electricities  counteract  each  other.  The  finger  is 
now  removed,  and  then  the  source  of  electricity,  and  still  there  is  no  diver- 
gence ;  but  if  the  upper  plate  be  raised  (fig.  717)  the  neutralisation  ceases, 
and  the  electricity  being  free  to  move  diffuses  itself  over  the  rod  and  the 
leaves,  which  then  diverge  widely.  The  delicacy  of  this  electroscope  is  in- 
creased by  adapting  to  the  foot  of  the  apparatus  two  metal  rods,  terminating 
in  knobs  ;  for  these  knobs,  being  excited  by  induction  from  the  gold-leaves, 
react  upon  them. 

A  still  further  degree  of  delicacy  is  attained  if  the  rods  be  replaced  by  two 


-781]  TJiomsons  Absolute  lilcctronicter.  749 

Bohnenbergers  dry  piles,  one  of  which  presents  its  positive  and  the  other  its 
negative  pole.  Instead  of  two  gold-leaves  there  is  only  one  ;  the  least  trace 
of  electricity  causes  it  to  oscillate  cither  to  one  side  or  to  the  other,  and  at 
the  same  time  shows  the  kind  of  electricity. 

780.  Thomson's  quadrant  electrometer. — Sir  William  Thomson  has 
devised  a  new  and  delicate  form  of  electrometer,  by  which  accurate  measure- 
ments of  the  amount  of  electrical 
charge  may  be  made.  The  prin- 
ciple of  this  instrument  may  be 
understood  from  the  following"  de- 
scription of  a  form  of  it  constructed 
for  lecture  purposes  by  Messrs. 
Elliott. 

A  light  flat  broad  aluminium 
needle  (fig.  7 1 8)  hangs  by  a  very  fine 
wire  from  the  inner  coating  of  a 
charged  Leyden  jar,  the  outer  coat- 
ing being  in  conducting  communi- 
cation with  the  earth.  The  whole 
apparatus  is  enclosed  within  a  glass 
shade,  and  the  air  is  kept  dry  by 
means  of  a  dish  of  sulphuric  acid  ; 
there  is,  therefore,  very  little  loss  of 
electricity,  and  the  needle  remains 
at  a  virtually  constant  charge. 

The  needle  is  suspended  over 
four  quadrantal  metal  plates,  insu- 
lated from  each  other  and  from  the 
ground   by  resting  on  glass  rods. 


Fig.  71 


The  alternate  quadrants  are  in  conducting  communication  with  each  other 
by  means  of  wires.  If  now  all  the  quadrants  are  in  the  same  electrical  con- 
dition, the  needle  will  be  at  rest  when  it  is  directly  over  one  of  the  diametrical 
slits.  But  if  the  two  pairs  of  quadrants  are  charged  with  opposite  kinds  of 
electricity,  as  when,  for  instance,  they  are  connected  with  the  two  poles  of 
an  insulated  voltaic  cell  by  means  of  the  knobs,  then  each  end  of  the  needle 
will  be  repelled  by  the  pair  of  quadrants  which  are  electrified  like  itself,  and 
will  be  attracted  by  the  other  pair.  It  will  thus  be  subject  to  the  action  of 
a  couple  tending  to  set  it  obliquely  to  the  slit. 

In  order  to  render  the  slightest  motion  of  the  needle  visible,  a  small  silver 
concave  mirror  with  a  radius  of  about  a  metre  is  fixed  above  it.  The  light  of 
a  petroleum  lamp,  not  represented  in  the  figure,  strikes  against  this,  and  is 
reflected  as  a  spot  on  a  horizontal  scale.  Any  deflection  of  the  needle,  either 
on  one  side  or  the  other,  is  indicated  by  the  motion  of  the  spot  of  light  on 
the  scale  (520). 

781.  Thomson's  absolute  electrometer. — Another  class  of  electro- 
meters, also  invented  by  Sir  W.  Thomson,  have  the  advantage  of  furnishing 
a  direct  measure  of  electrical  constants  in  absolute  measure.  Fig.  719 
represents  the  essential  features  of  a  modified  form  of  the  electrometer, 
which  has  been  devised  by  Professor  Foster  for  class  experiments. 


750 


Frictional  Electricity. 


[781- 


Two  plane  metal  discs  A  and  B,  about  lo  cm.  in  diameter,  are  kept  at  a 
distance  from  each  other,  which  is  small  in  proportion  to  their  diameters, 
but  which  can  be  very  accurately  measured.  Out  of  the  centre  of  the  upper 
one  is  cut  a  disc  c  ;  this  is  suspended  by  insulating  threads  from  one  end  of 
the  arm  a  b  oi  7i  balance,  at  the  other  end  of  which  is  a  counterpoise,  or  a 
scale  pan/.  At  the  end  of  the  arm  is  a  fork,  across  which  is  stretched  a 
fine  wire  ;  when  the  disc  is  exactly  in  the  plane  of  the  circular  band  or  ring 

which  surrounds  it,  and  which 
is  called  the  guard  ring^  this 
fine  wire  is  exactly  across  the 
interval  between  two  marks 
in  the  upright,  and  the  posi- 
tion of  which  can  be  accu- 
rately determined  by  means 
of  the  lens  C.  The  disc  and 
the  guard  ring  are  kept  at 
a  constant  potential,  being 
connected  by  a  wire  with  a 
constant  source  of  electricity, 
while  the  other  can  be  kept 
at  any  potential. 

Suppose  now  that  the 
whole  system  is  at  the  same 
potential,  and  that  the  disc  is  exactly  balanced  so  as  to  be  in  the  plane  of  the 
guard  ring.  If  now  A  be  electrified  to  a  given  potential,  while  the  plate  B 
is  connected  with  the  earth,  then  the  body  charged  with  electricity  of  higher 
potential— that  is,  the  disc — will  be  urged  towards  the  body  of  lower  potential, 
the  fixed  plate  ;  and  in  order  to  retain  it  exactly  in  the  plane  of  the  guard 
ring  the  force  applied  at  the  other  end  of  the  lever  must  be  increased.  This 
may  be  done  by  altering  the  distance  of  the  counterpoise,  or  by  adding  weights 
to  a  scale  pan,  and  the  additional  weight  thus  applied  is  a  measure  of  the 
attractive  force. 

Now,  it  can  be  shown  that  the  attractive  force  between  any  two  plates 
electrified  to  different  potentials  is  proportional  to  the  square  of  the  differ- 
ence of  potentials,  provided  the  distance  between  them  is  small  in  comparison 
with  their  area,  and  that  the  portions  of  the  plates  opposite  each  other  are 
at  some  distance  from  the  edge.  These  conditions  are  fulfilled  in  the  above 
case.  If  S  is  the  area  of  the  disc,  ^the  distance  of  the  plates,  V-A',  the 
difference  of  potentials,  and  F  the  force  required  to  balance  a  certain  attrac- 
tion, then 


Fig.  719. 


for  V 


V'S 
this  is  ^    -,..  and  \  =  d  \ 
and-  V 


Zndr 
/SttF 

/   s  • 


Now  as  F  is  expressed  Ijy  a  weight,  and  S  and  (/ depend  on  measures  of 
length,  we  have  a  means  of  expressing  difference  of  potentials  in  absolute 
measure  (709). 

It  is  also  clear  that  the  experiments  may  be  modified  by  making  the 


-782]  Potctitial  and  Capacity  of  a  Ley  den  Jar.  751 

weight  constant,  and  the  distance  variable.  By  means  of  micromctric 
arrangements  the  distance  of  the  plates  maybe  varied  and  measured  with 
very  great  accuracy. 

782.  Potential  and  capacity  of  a  Xicyden  jar — These  may  be  most 
conveniently  investigated  by  considering  the  case  of  a  spherical  jar.  Let  us 
suppose  A  (fig.  720)  to  represent  an  insulated  metal  sphere,  and  let  us  con- 
sider it  placed  in  conducting  communication  with  a  source  of,  say,  positive 
electricity,  which  is  supposed  to  be  at  a  constant   potential  V.     Then  its 

potential  V  is  ^  ,  and  its  charge  (^  =  VR,  R  being  the  radius  of  the  sphere  A. 

Suppose  now  it  be  possible  to  surround  this  sphere  by  an  external  conduct- 
ing shell  or  envelope  B,  which  is  in  connection  with  the  ground  ;  movements  of 
electricity  will  take  place  ;  a  new  equilibrium 
will  be  established,  and  there  will  now  be  two 
electrical  layers — one  on  the  sphere  A,  and 
the  other  on  the  sphere  B.  These  will  have 
no  action  on  any  external  point,  which  is  only 
possible  provided  the  charges  are  equal  and 
contrary.  If -t-  Q  is  the  charge  on  the  inner, 
then-Q  is  that  on  the  outer  sphere  (745). 

The  charge  of  the  original  sphere  is  at 
first  not  altered  by  this  operation,  but  its 
potential  is  less,  its  capacity  being  now 
greater ;  but,  as  it  is  in  contact  with  the 
source,  which  is  constant,  it  receives  fresh 
charges  of  electricity  until  it  is  again  at  the 
potential  of  the  source  V. 

Now  let  us  suppose  that  the  insulating  layer  which  separates  the  inner 
from  the  outer  coating  is  air,  and  that  its  thickness  is  t ;  then  the  potential 
y  of  the  whole  system  is  made  up  of  two  parts,  the  first  due  to  the  elec- 
trical charge  of  the  inner  sphere  V  =  -t-  ^,  and  the  second  due  to  the  charge 

Q_Q^Q(R'-R)         o  =  ^^^^^" 
R"  '  R     R'  RR'      '         ^     R'-R 

VR;  hence  ^  ^R'-R^    But 
Q         R' 
R'-R  is  the  thickness  of  the  dielectric,  which,  for  the  sake  of  simplicity,  we 

O     R' 

will   suppose  is  air,  and  calling   this   /,  we   have  - ^  =  —  ;  that  is,  that  the 

charge  is  inversely  as  the  thickness  of  the  dielectric. 

It  is  to  be  observed  that  the  results  here  obtained  apply  strictly  only  to 
the  supposed  case  in  which  the  inner  conductor  is  completely  surrounded  by 
the  outer  one  (745),  which  is  not  the  case  with  the  ordinary  form  of  a  Leyden 
jar.     It  may,  however,  be  applied  to  them  if  we  compare  homologous  jars  ; 

in  the  above  formula  Q  =  ^,        ,now  if  R  and  R' are  nearly  equal,  then 


Fig.  72 


of  the  outer  sphere  =  —  ^i,;  that  is,  V 

Now,  the  charge  of  the  insulated  sphere  ^ 


47r^' 


■here  47rR'-  =  S  is  the  coated 


752  Frictional  Electricity.  [782- 

surface  of  one  side  and  /  the  thickness  of  the  dielectric.     In  this  formula 

is  a  constant  for  a  Leyden  jar  of  given  dimensions,  and  represents  the 
47r/ 
capacity  of  the  jar. 

If  instead  of  air  there  be  a  solid  or  liquid  dielectric,  whose  specific  induc- 
tive capacity  is  /c,  the  formula  becomes  Q  =  ~^  = !^-     If  the  dielectric  be 

^Tvt        A,T:t 

partly  air  and  partly  some  other  material  such  as  glass,  then  if  the  thick- 

VS 
ness  of  this  latter  is  ^,  Q  =  — - —  .  The    expression    6   is    sometimes 


47r 


('--D 


written  /',  and  represents  the  thickness  of  the  layer  of  air  equivalent  to  it  in 

specific  inductive  capacity.     It  is  also  called  the  reduced  thickness. 

VRR'  RR' 

From  the  expression  Q  =    _  we   get  the  capacity  C  =  ^- — —  ;  or  as 

R  —  R  R  —  R 

above   =  — — ,  so  that  the  presence  of  the  envelope  multiplies  the  capacity 

of  the  sphere  by       . 

If  R'  is  so  great  that  the  value  of  R  in  the  denominator  may  be  disre- 
garded, we  get  C  =  R,  which  is  the  expression  for  the  capacity  of  an  insulated 
sphere  (739)  ;  such  a  sphere  may  indeed  be  regarded  as  a  condenser,  in 
which  the  layer  of  air,  between  it  and  the  sides  of  the  room,  represents  the 
dielectric.     This  represents  in  effect  the  condensing  force  (267). 

If  a  series  of  n  identical  jars  are  joined  in  surface,  we  have  a  condenser 
whose  capacity  is  equal  to  the  «-fold  capacity  of  a  single  jar. 

If  these  n  jars  are  joined  in  cascade,  the  capacity  of  the  system  is  that  of 
a  single  jar,  the  dielectric  of  which  is  n  times  as  thick. 

A  cylindrical  Leyden  jar  with  the  diameter  10  cm.  and  coated  to  a  height 
of  20  cm.  will  have  a  total  coated  surface  of  706-5  ;  if  the  glass  has  the  di- 
electric constant  5,  and  its  thickness  is  3  mm.  the  capacity  of  the  jar  will  be 
937-5  ;  and  as  the  capacity  of  a  sphere  is  equal  to  its  radius  (739),  it  will  be 
equal  to  the  capacity  of  a  freely  suspended  sphere  I9'75  metres  in  diameter 
(748). 


-783]  Effects  of  the  Electric  Discharge.  753 


THE  ELECTRIC   DISCHARGE. 

7^3-  Effects  of  the  electric  dlschargre. — The  recombination  of  the  two 
electricities  which  constitutes  the  electrical  discharge  may  be  either  con- 
tinuous or  sudden  :  continuous.,  or  of  the  nature  of  a  current,  as  when  the 
two  conductors  of  a  Holtz's  machine  are  joined  by  a  chain  or  a  wire  ;  and 
sudden  or  disruptive,  as  when  the  opposite  electricities  accumulate  on  the 
surface  of  two  adjacent  conductors,  till  their  mutual  attraction  is  strong 
enough  to  overcome  the  intervening  resistances,  whatever  they  may  be.  But 
the  difference  between  a  sudden  and  a  continuous  discharge  is  one  of  degree, 
and  not  of  kind,  for  there  is  no  such  thing  as  an  absolute  non-conductor,  and 
the  very  best  conductors,  the  metals,  offer  an  appreciable  resistance  to  the 
passage  of  electricity.  Still  the  difference  at  the  two  extremes  of  the  scale 
is  sufficiently  great  to  give  rise  to  a  wide  range  of  phenomena. 

Riess  has  shown  that  the  discharge  of  a  battery  does  not  consist  in  a 
simple  union  of  the  positive  with  the  negative  electricity,  but  that  it  consists 
of  a  series  of  successive  partial  discharges.  The  direction  of  the  discharge 
depends  mainly  on  the  length  and  nature  of  the  circuit. 

Feddersen  examined  the  discharge  of  a  Leyden  jar  in  a  rapidly  rotating 
mirror  (796),  when  it  was  seen  as  a  narrowband  of  light  the  length  of  which 
varied  with  the  duration  of  the  discharge.  The  duration  was  found  to  increase 
with  the  striking  distance,  and  with  the  number  of  jars. 

When  the  resistance  through  which  the  circuit  took  place  was  small,  it 
was  found  that  the  discharge  was  an  oscillatory  one,  consisting  of  a  series  of 
separate  discharges  in  alternating  directions  ;  the  image  was  traversed  by  a 
number  of  dark  lines. 

When  the  resistance  was  greater  the  discharge  was  a  single  continuous 
one,  and  its  image  was  that  of  a  continuous  band  of  light.  With  very  great 
resistance  the  discharge  was  an  intermitteiit  one,  and  consisted  of  sparks 
following  each  other  at  irregular  intervals. 

These  oscillator)'  discharges  may  be  illustrated  by  means  of  a  simple 
hydrostatical  experiment.     Suppose  that  in  the  U-tube  (fig.  721)  is  a  valve  j-, 
by  which  the  two  tubes  are  separated,  and  that  water  is 
poured  in  one  so  that  it  is  at  the  height  -1-  L  above  the 
level  00,  and  in  the  other  in  the  corresponding  distance 
—  L  below  the  level.     When  the  valve  is  suddenly  opened, 
the   water  passes  through  and  only  comes  to  rest  in  the 
position  00  after  several  oscillations  about  this  level.     Sup- 
pose the  valve  to  be  suddenly  closed  during  the  oscillation,  ^ 
it  may  easily  happen  that  the  water  is  higher  in  that  limb           p- 
in  which   it  was  previously  lower.     This  would  represent 
the  case  observed  by  Oettingen  with  the  electrical  residues,  who  found  them 
to  be  sometimes  negative  and  sometimes  positive. 

Again,  if  the  valve  be  only  slightly  opened,  so  that  great  resistance  is 
offered,  the  water  slowly  sinks  to  its  level,  the  discharge  is  continuous,  and 
there  are  no  oscillations. 

The  oscillator)'  nature  of  the  discharge  was  confirmed  by  the  observations 

3  c 


754  Frictional  Elect ncity.  [783- 

of  Paalzow  on  the  luminous  phenomena  seen  in  highly  rarefied  gases 
when  it  takes  place  in  them,  as  well  as  by  the  manner  in  which  a  magnet 
affects  the  phenomena.  Helmholtz  had  already  deduced  the  necessity  of 
such  an  oscillating  motion  from  the  laws  of  the  conservation  of  energy, 
and  Thomson  and  Kirchhoff  had  deduced  the  conditions  under  which  it 
occurs. 

784.  "Work  effected  by  the  discharg-e  of  a  Iieyden  jar. — The  work 

required  to  charge  a  Leyden  jar  is  W  =      QV  = =  ^-^  = V'^ ;  that  is, 

is  proportional  to  the  surface  and  to  the  square  of  the  potential,  and  is 
inversely  as  the  thickness  of  the  insulator.  From  the  principle  of  the  con- 
servation of  energy,  this  stored-up  energy  reappears  when  the  jar  is  dis- 
charged. This  occurs  partly  in  the  form  of  a  spark,  partly  in  the  heating 
effect  of  the  whole  system  of  conductors  through  which  the  discharge  takes 
place.  When  the  armatures  are  connected  by  a  thick  short  wire,  the  spark 
is  strong  and  the  heating  effect  small  :  if,  on  the  contrary,  the  jar  is  dis- 
charged through  a  long  fine  wire,  this  beconies  more  heated,  but  the  spark 
is  weaker. 

If  a  series  of  identical  jars  are  each  separately  charged  from  the  same 
source,  they  will  each  acquire  the  same  potential,  which  will  not  be  altered 
if  all  the  jars  are  connected  by  their  inner  and  outer  coatings  respectively. 
The  total  charge  will  be  the  same  as  if  the  battery  had  been  charged  directly 
from  the  source,  and  its  energy  will  be  W  =  ^  Vttq  =  ^VQ  :  that  is,  the  energy 
of  a  battery  of  n  equal  jars  is  the  same  as  that  of  a  single  jar  of  the  same 
thickness  but  of  ;z  times  the  surface. 

Let  us  consider  two  similar  Leyden  jars  having  respectively  the  capaci- 
ties c  and  c',  and  let  one  of  them  be  charged  to  potential  V  and  let  the  other 
remain  uncharged.  Suppose  now  that  the  inner  and  outer  coatings  of  the 
jars  are  respectively  connected  with  each  other.     Then  the  energy  of  the 

charged  jar  alone  is  W  =  i-^,  and  when  it  is  connected  with  the  other,  the 

original  charge  will  spread   itself  over  the  two,  so  that  the  energy  of  the 

charge  in  the  two  jars  is  W  =  ---^ — r.     Hence  W :  W  =  c  +  c' :  c  ;  and  there- 

2{c  +  c') 
fore,  since  c  +  c'  \s  always  greater  than  c,  there  must  be  a  loss  of  energy.     In 
point  of  fact,  when  a  charged  jar  is  connected  with  an  uncharged  one,  a  spark 
passes  which  is  the  equivalent  of  this  loss  of  energy. 

It  follows,  further,  that  when  two  jars  at  different  potentials  are  united 
there  is  always  a  loss  of  energy. 

If  a  series  of  n  similar  jars  are  joined  in  surface,  and  a  given  charge 
of  electricity  is  imparted  to  them,  the  energy  is  inversely  as  the  number 
of  jars;  but,  when  they  are  charged  from  a  source  of  constant  potential, 
the  energy  is  proportional  to  the  number  of  jars.  If,  however,  the  jars 
are  arranged  in  cascade,  then  for  a  given  charge  the  energy  is  n  times 
that  of  a  single  jar,  while  for  a  given  potential  it  is  n  times  smaller.  It  is 
sometimes  convenient  to  arrange  the  jars  in  a  combination  of  the  two 
systems. 

785.  Physiological  effects. — The  shock  from  the  electrical  machine 
has  been  already  noticed  (770).     The  shock  taken  from  a  charged  Leyden 


-787J  Spark  and  Brush  Discharge.  755 

jar  by  grasping  the  outer  coating  with  one  hand  and  touching  the  inner 
with  the  other  is  much  more  violent,  and  has  a  peculiar  character.  With  a 
small  jar  the  shock  is  felt  in  the  elbow ;  with  a  jar  of  about  a  quart  capacity 
it  is  felt  across  the  chest,  and  with  jars  of  still  larger  dimensions  in  the 
stomach. 

A  shock  may  be  given  to  a  large  number  of  persons  simultaneously  by 
means  of  the  Leyden  jar.  For  this  purpose  they  must  form  a  chain  by  join- 
ing hands.  If  then  the  first  touches  the  outside  coating  of  a  charged  jar, 
while  the  last  at  the  same  time  touches  the  knob,  all  receive  a  simultaneous 
shock,  the  intensity  of  which  depends  on  the  charge,  and  on  the  number  of 
persons  receiving  it.  Those  in  the  centre  of  the  chain  are  found  to  receive 
a  less  violent  shock  than  those  near  the  extremities.  The  Abbe  Nollet  dis- 
charged a  Leyden  jar  through  an  entire  regiment  of  1,500  men,  who  all 
received  a  violent  shock  in  the  arms  and  shoulders. 

With  large  Leyden  jars  and  batteries  the  shock  is  sometimes  very  dan- 
gerous. Priestley  killed  rats  with  batteries  of  7  square  feet  coated  surface, 
and  cats  with  a  battery  of  about  4^  square  yards  coating. 

Experience  shows  that  the  physiological  effect  varies  with  the  electrical 
energy  ;  thus  a  discharge  from  an  ordinary  electrical  machine  which  gives 
a  spark  of  nearly  a  foot  may  be  taken  without  danger,  while  one  from  a 
batter}^  of  large  capacity  of  a  few  millimetres  could  not  be  borne.  The 
duration  of  the  discharge  has  also  an  influence  ;  a  battery  which  gives  a 
violent  shock  when  discharged  in  ordinary  conditions  only  gives  a  feeble 
one  when  discharged  through  a  moist  cord,  which  only  delays  the  rapidity 
of  the  discharge. 

786.  luminous  effects. — The  recombination  of  two  electricities  of  high 
potential  (738)  is  always  accompanied  by  a  disengagement  of  light,  as  is  seen 
when  sparks  are  taken  from  a  machine,  or  when  a  Leyden  jar  is  discharged. 
The  better  the  conductors  on  which  the  electricities  are  accumulated,  the 
more  brilliant  is  the  spark ;  its  colour  varies  not  only  with  the  nature  of  the 
bodies,  but  also  with  the  nature  of  the  surrounding  medium  and  with  the 
pressure.  The  spark  between  two  charcoal  points  is  yellow,  between  two 
balls  of  silvered  copper  it  is  green,  between  knobs  of  wood  or  ivory  it  is 
crimson.  In  atmospheric  air  at  the  ordinary  pressure  the  electric  spark  is 
white  and  brilliant ;  in  rarefied  air  it  is  reddish  ;  and  in  vacuo  it  is  violet. 
In  oxygen,  as  in  air,  the  spark  is  white ;  in  hydrogen  it  is  reddish,  and  green 
in  the  vapour  of  mercury ;  in  carbonic  acid  it  is  also  green,  while  in  nitrogen 
it  is  blue  or  purple,  and  accompanied  by  a  peculiar  sound.  Generally  speak- 
ing, the  higher  the  potential  the  greater  is  the  lustre  of  the  spark. 

When  these  sparks  are  examined  by  the  spectroscope  (576)  it  is  seen  that 
they  show  the  lines  characteristic  of  the  metals  between  which  the  spark 
passes,  and  also  of  the  gas  in  which  it  takes  place.  If  the  knobs  are  of 
different  metals  the  lines  of  both  are  seen.  Part  of  the  energy  is  accordingly 
consumed  in  detaching  and  volatilising  the  metal  particles  on  the  two 
electrodes  ;  when  a  powerful  discharge  takes  place  between  a  knob  of  gold 
and  one  of  silver,  the  latter  metal  is  found  on  the  gold  ball,  while  some  gold 
is  found  on  the  silver. 

787.  Spark  and  brusb  discbargre. — The  shapes  which  luminous  electric 
phenomena  assume  may  be  classed  under  two  heads — the  spark  and  the 

3  c  2 


756  Frictiotial  Electricity.  [787- 

brush.  The  brush  forms  when  the  electricity  leaves  the  conductor  in  a 
continuous  flow  ;  the  spark,  when  the  discharge  is  discontinuous.  The 
formation  of  one  or  the  other  of  these  depends  on  the  nature  of  the  con- 
ductor and  on  the  nature  of  the  conductors  in  its  vicinity  ;  and  small  altera- 
tions in  the  position  of  the  surrounding  conductors  transform  the  one  into 
the  other. 

The  spark  which  at  short  distances  appears  straight,  at  longer  distances 
has  a  zigzag  shape  with  diverging  branches.  Its  length  depends  on  the 
density  at  the  part  of  the  conductor  from  which  it  is  taken  ;  and  to  obtain 
the  longest  sparks  the  electricity  must  be  of  as  high  a  density  as  possible,  but 
not  so  high  as  to  discharge  spontaneously.  With  long  sparks  the  luminosity 
is  different  in  different  parts  of  the  spark. 

The  brush  derives  its  name  from  the  radiating  divergent  arrangement 
of  the  light,  and  presents  the  appearance  of  a  luminous  cone,  whose  apex 
touches  the  conductor.  Its  size  and  colour  differ  with  the  nature  and  form  of 
the  conductor  ;  it  is  accompanied  by  a  peculiar  hissing  noise,  very  different 
from  the  sharp  crack  of  the  spark.  Its  luminosity  is  far  less  than  that  of 
the  spark  ;  for  while  the  latter  can  easily  be  seen  by  daylight,  the  former  is 
only  visible  in  a  darkened  room.  The  brush  discharge  may  be  obtained  by 
placing  on  the  conductor  a  wire  filed  round  at  the  end,  or,  with  a  powerful 
machine,  by  placing  a  small  bullet  on  the  conductor.  The  brush  from  a 
negative  conductor  is  less  than  from  a  positive  conductor  ;  the  cause  of 
this  difference  has  not  been  satisfactorily  made  out,  but  may  originate  in  the 
fact,  which  Faraday  has  observed,  that  negative  electricity  discharges  into 
the  air  at  a  somewhat  lower  density  than  positive  electricity  ;  so  that  a  nega- 
tively charged  knob  sooner  attains  that  density  at  which  spontaneous 
discharge  takes  place,  than  does  a  positively  charged  one,  and  therefore 
discharges  the  electricity  at  smaller  intervals  and  in  less  quantities. 

When  electricity,  in  virtue  of  its  high  density,  issues  from  a  conductor,  no 
other  conductor  being  near,  the  discharge  takes  place  without  noise,  and  at 
the  places  at  which  it  appears  there  is  a  pale  blue  luminosity  called  the 
electrical  glow  ^  ox  ox\  points,  a  star-like  centre  of  light.  It  is  seen  in  the  dark 
by  placing  a  point  on  the  conductor  of  the  machine.  It  may  be  regarded  as 
a  very  short  brush. 

788.  striking-  distance.- — Sir  W.  Harris  by  means  of  experiments  with 
his  unit  jar  suitably  modified,  and  Riess  by  independent  researches,  found 
that  for  small  distances  the  striking  distance  is  directly  proportional  to  the 
quantity  of  electricity,  and  inversely  proportional  to  the  coated  surface  ;  in 
other  words,  it  is  proportional  to  the  potential.  For  his  experiments  Riess 
used  the  spark  micrometer.,  which  consists  of  two  metal  knobs  on  insulating 
supports,  the  distance  of  which  from  each  other  could  be  varied  by  a  micro- 
metric  screw. 

The  striking  distance  varies  slightly  with  the  shape  of  the  electrodes  ; 
thus  for  the  same  distance  the  difference  of  potential  required  is  slightly 
greater  for  two  spheres  than  for  two  plates. 

P'or  greater  distances  the  difference  of  potential  increases  less  rapidly 
than  the  distance,  and  the  greater  the  distance  the  less  is  the  rate  of  increase; 
this  is  seen  in  the  following  experiments,  where  the  discharge  took  place 
between  two  knobs  2 '2  cm.  in  diameter. 


-789] 


Luminous  Tube  and  Square. 


7S7 


Distance 

Volts 

Distance 

Volts 

cm. 

cm. 

o-i 

5,490 

5-0 

94,800 

0-5 

26,730 

TO 

107,700 

ro 

48,600        . 

lo-o 

119,100 

2-0 

64,800 

I2-0 

124,200 

j-o 

76,800 

I5-0 

127,800 

The  striking  distance  in  air  is  virtually  the  same  for  the  spark  proper  as 
for  the  brush. 

The  influence  of  pressure  on  the  electric  discharge  may  be  studied  by 
means  of  the  electric  egg.  This  consists  of  an  ellipsoidal  glass  vessel  (fig. 
722),  with  metal  caps  at  each  end.  The  lower  cap  is 
provided  with  a  stopcock,  so  that  it  can  be  screwed 
into  an  air-pump,  and  also  into  a  heavy  metallic  foot. 
The  upper  metal  rod  moves  up  and  down  in  a  leather 
stuffing-box  ;  the  lower  one  is  fixed  to  the  cap.  A 
vacuum  having  been  made,  the  stopcock  is  turned, 
and  the  vessel  screwed  into  its  foot ;  the  upper  part 
is  then  connected  with  a  powerful  electrical  machine, 
and  the  lower  one  with  the  ground.  On  working  the 
machine,  the  globe  becomes  filled  with  a  feeble  violet 
light  continuous  from  one  end  to  the  other,  and 
resulting  from  the  recomposition  of  the  positive  elec- 
tricity of  the  upper  cap  with  the  negative  of  the  lower. 
If  the  air  be  gradually  allowed  to  enter  by  opening 
the  stopcock,  the  light  now  appears  white  and 
brilliant,  and  is  only  seen  as  an  ordinary  intermittent 
spark. 

Some  beautiful  effects  of  the  electric  discharge 
are  obtained  by  means  of  Geissler^s  tubes,  which  will 
be  noticed  under  Dynamical  Electricity. 

789.  Iiumlnous  tube  and  square. — The  linninous 
tube  (fig.  723)  is  a  glass  tube  about  a  yard  long,  round 
which  are  arranged  in  a  spiral  form  a  series  of  lozenge- 
shaped  pieces  of  tinfoil,  between  which  are  veiy  short 
intervals.  There  is  a  brass  cap  with  hooks  at  each  end,  in  which  the  spiral 
terminates.     If  one  end  be  presented  to  a  machine  in  action,  while  the  other 


Fi?.  7=3. 
is  held  in  the  hand,  sparks  appear  simultaneously  at  each  interval,  and   pro- 
duce a  brilliant  luminous  appearance,  especially  in  the  dark. 


758  Frictional  Electricity.  [789- 

The  luminous  pane  (fig.  724)  is  constructed  on  the  same  principle,  and 
consists  of  a  square  of  ordinary  glass,  on  which  is  fastened  a  narrow  strip  of 
tinfoil  folded  parallel  to  itself  for  a  great  number  of  times.  Spaces  are  cut 
out  of  this  strip  so  as  to  represent  any  figure,  a  portico  for  example. 
The  pane  being  fixed  between  two  insulating  supports,  the  upper  extre- 
mity of  the  strip  is  connected  with 

^"""Y^. ^—         the    electrical    machine,    and    the 

'^  '  ^^  ^^ —  lower  part  with  the  ground.  When 
the  machine  is  in  operation,  a  spark 
appears  at  each  interval,  and  repro- 
duces in  liiminous  flashes  the  ob- 
ject represented  on  the  glass. 

790.  Keating'  effects. — Besides 
being  luminous,  the  electric  spark 
is  a  source  of  great  heat.  When  it 
passes  through  inflammable  liquids, 
as  ether  or  alcohol,  it  inflames  them. 
An  arrangement  for  efl"ecting  this  is 
represented  in  fig.  725.  It  is  a  small 
glass  cup  through  the  bottom  of 
which  passes  a  metal  rod,  termi- 
nating in  a  knob  and  fixed  to  a 
metal  foot.  A  quantity  of  liquid 
sufficient  to  cover  the  knob  is 
placed  in  the  vessel.  The  outer 
coating  of  the  jar  having  been 
connected  with  the  foot  by  means  of  a  chain,  the  spark  which  passes  when 
the  two  knobs  are  brought  near  each  other  inflames  the  liquid.  With  ether 
the  experiment  succeeds  very  well,  but  alcohol  requires  to  be  first  warmed. 

Coal  gas  may  also  be  ignited  by  means  of  the  electric  spark.     A  person 
standing  on  an   insulated   stool   places  one  hand  on  the  conductor  of  a 

machine  which  is  then  worked,  while 
he  presents  the  other  to  the  jet  of  gas 
issuing  from  a  metallic  burner.  The 
spark  which  passes  ignites  the  gas. 
When  a  battery  is  discharged  through 
an  iron  or  steel  wire  it  becomes 
heated,  and  even  made  incandescent 
or  melted  if  the  discharge  is  very 
powerful. 

If,  in  discharging  a  jar,  the  dis- 
charge does  no  other  work,  then  the 
whole  of  the  energy  of  the  charge 
(784)  apjiears  in  the  form  of  heat  ;  and 
if  we  divide  this  by  Joule's  equivalent 
(497),  we  have  the  total  heating  due 
to  any  charge. 

The    laws    of  this   heating   effect    were    investigated  independently  by 
Harris  and  b)'  Ricss  by  means  of  the  electric  tlier/no/zictcr.     This  consists  of 


Fig.  724. 


-790]        Heating  Effects  of  the  Electrical  Discharge.  759 

a  glass  bulb,  fig.  726,  closed  by  a  stopper  c,  and  to  which  is  fixed  a  capillary 
tube  bent  twice,  and  terminating  in  an  enlargement  ;  this  contains  coloured 
liquid.  The  whole  apparatus  is  fixed  on  a  hinged  support  A,  which  works 
on  the  base  B,  so  that  it  can  be  inclined  and  fixed  at  any  given  angle.  The 
diameter  of  the  tube  being  very  small  compared  with  that  of  the  enlarge- 
ment, a  consider- 
able displacement 
of  the  liquid  may 
take  place  along 
the  scale  without 
any  material  alter- 
ation in  pressure, 
and  before  making 
the  experiment  the 
stopper  c  is  opened 
so  as  to  equalise 
the  pressure.  Be- 
tween the  binding 
screws  a  and  b 
a  fine  platinum 
wire    is    stretched. 

When     a     Leyden  ~"         

jar    is     discharged  ^'=-  ^-^■ 

through  the  wire  this  becomes  heated,  expands  the  air  in  the  bulb,  and  the 
expansion  is  indicated  by  the  motion  of  the  liquid  along  the  graduated  stem 
of  the  thermometer.  In  this  way  it  has  been  found  that  the  increase  in 
temperature  in  the  wire  is  proportional  to  the  square  of  the  quantity  of 
electricity  divided  by  the  surface — a  result  which  follows  from  the  formula 
already  given  (784).  Riess  also  found  that  wilh  the  satne  charge,  but  with 
wires  of  different  dimensions,  the  rise  of  temperature  is  i7iversely  as  the 
fourth  power  of  the  diameter.  Thus,  compared  with  a  given  wire  as  unity, 
the  rise  of  te7iiperature  in  a  wire  of  double  or  treble  the  diameter  would  be 
j\  or  g\  as  small ;  but  as  the  masses  of  these  wires  are  four  and  nine  times 
as  great,  the  heat  produced  would  be  respectively  \  and  |  as  great  as  in 
a  wire  of  unit  thickness. 

If  a  jar  charged  to  a  given  potential  be  discharged  through  the  electrical 
thermometer,  the  discharge  will  take  place  at  a  certain  striking  distance, 
and  a  certain  depression  will  be  produced  which  is  a  measure  of  the  heating 
effect  in  the  thermometer.  If  now  a  card  be  interposed  in  the  path  of 
the  discharge,  a  certain  proportion  of  its  energy  will  be  expended  in  the 
mechanical  perforation  of  the  card,  and  the  proportion  in  the  thermo- 
meter will  be  less.  Thus  Riess  found  that  that  charge  which  when  passed 
through  air  produced  a  depression  of  15-9,  when  passed  in  addition 
through  one  card,  two  cards,  and  a  plate  of  mica,  produced  depressions 
of  117,  8-0,  and  6-8  respectively  ;  showing  then  that  the  heating  effect  was 
less  according  as  more  of  the  energ^y  of  the  discharge  was  used  for  other 
purposes. 

When  an  electric  discharge  is  sent  through  gunpowder  placed  on  the 
table  of  a  Henley's  discharger,  it  is   not  ignited,  but   is   projected    in  all 


760 


Frictional  Electricity. 


[790- 


directions.  But  if  a  wet  string  be  interposed  in  the  circuit,  a  spark  passes 
which  ignites  the  powder.  This  arises  from  the  retardation  which  electricity 
experiences  in  traversing  a  semi-conductor,  such  as  a  wet  string  ;  for  the 
heating  effect  is  proportional  to  the  duration  of  the  discharge. 

When  a  charge  is  passed  through  sugar,  heavy  spar,  fluor-spar,  and  other 
substances,  they  afterwards  become  phosphorescent  in  the  dark.  Eggs, 
fruit,  &c.,  may  be  made  luminous  in  the  dark  in  this  way. 

When  a  battery  is  discharged  through  a  gold  leaf  pressed  between  two 
glass  plates  or  between  two  silk  ribbons,  the  gold  is  volatilised  in  a  violet 
powder  which  is  finely  divided  gold.  In  this  way  what  are  called  electric 
portraits  are  obtained. 

Siemens  has  shown  that  when  a  jar  is  charged  and  discharged  sev'eral 
times  in  succession  the  glass  becomes  heated.  Hence  during  the  discharge 
there  must  be  movements  of  the  molecules  of  the  glass,  as  Faraday  sup- 
posed (747) ;  we  have  here,  probably,  something  analogous  to  the  heating 
produced  in  iron  when  it  is  rapidly  magnetised  and  demagnetised. 

791.  IVXag-netic  eflFects. — By  the  discharge  of  a  large  Leyden  jar  or 
battery,  a  steel  wire  may  be  magnetised  if  it  is  laid  at  right  angles  to  a  con- 
ducting wire  through  which  the  discharge  is 
effected,  either  in  contact  with  the  wire  or  at 
some  distance.  And  even  a  steel  rod  or  needle 
may  be  magnetised  by  placing  it  inside  a  spiral 
of  insulated  copper  wire  A  (fig.  727),  and  passing 
one  or  more  discharges  through  it.  The  polarity 
depends  on  the  direction  in  which  the  electricity 
enters  the  coil,  and  the  way  in  which  the  wire 
is  coiled.  Thus  if  the  jar  is  charged  in  the  in- 
side with  positive  electricity,  and  the  direction 

"''^'  ''^^"  in  which  the  wire  is  coiled  is  that  in  which  the 

hands  of  a  watch  move,  that  end  at  which  the  positive  electricity  enters  will 
be  a  south  pole. 

It  is,  however,  frequently  observed  that  the  magnetism  is  abnormal,  and 
that  for  the  same  charge  of  the  jar  the  north  pole  is  first  at  one  end  and  then 
at  the  other.  This  is  to  be  referred  to  the  residue  in  the  jar,  which  changes 
the  sign  in  an  irregular  manner  (783). 

To  effect  a  deflection  of  the  magnetic  needle  by  the  electric  current  pro- 
duced by  frictional  electricity  is  more  difficult.  It  may  be  accomplished 
by  making  use  of  a  galvanometer  consisting  of  400  or  500  turns  of  fine  silk- 
covered  wire,  which  is  further  insulated  by  being  coated  with  shellac  varnish, 
and  by  separating  the  layers  by  means  of  oiled  silk.  When  the  prime  con- 
ductor of  a  machine  in  action  is  connected  with  one  end  of  the  galvanometer 
wire,  and  the  other  with  the  ground,  a  deflection  of  the  needle  is  produced. 

792.  iwechanlcal  effects. — The  mechanical  effects  are  the  violent  lacera- 
tions, fractures,  and  sudden  expansions  which  ensue  when  a  powerful  dis- 
charge is  passed  through  a  badly  conducting  substance.  Glass  is  perforated, 
wood  and  stones  are  fractured,  and  gases  and  liquids  are  violently  disturbed. 
The  mechanical  effects  of  the  electric  spark  may  be  demonstrated  by  a 
variety  of  experiments. 

Fig.  728  represents  an  arrangement  for  perforating  a  piece  of  glass  or 


(miiiimiiiimiiiiiiiiiiii iiTi'iii! 

Iimiiiiiiiiiiiir 


-792]      Mechanical  Effects  of  the  Electrical  Discharge.  761 

card.  It  consists  of  two  glass  columns,  with  a  horizontal  cross-piece,  in 
which  is  a  pointed  conductor,  B.  The  piece  of  glass.  A,  is  placed  on  an 
insulating  glass  support,  in  which  is  placed  a  second  conductor,  terminating 
also  in  a  point,  which  is  _ 

connected  with  the  outside 
of  the  battery,  while  the 
knob  of  the  inner  coating 
is  brought  near  the  knob 
of  B.  When  the  discharge 
passes  between  the  two 
conductors,  the  glass  is 
perforated.  The  experi- 
ment only  succeeds  with 
a  single  jar  when  the  glass 
is  very  thin  ;  otherwise  a 
battery  must  be  used. 

When  the  discharge 
takes  place  through  a 
piece  of  cardboard  be- 
tween two  points  exactly 
opposite  each  other  the 
line  of  perforation  is  quite 
straight  ;  but  if  not  exactly 
opposite  a  slight  hole  is 
seen  near  the  negative  point.  This  phenomenon,  which  is  known  as  LulliTis 
experiment,  is  probably  connected  with  the  greater  facility  with  which  elec- 
tricity discharges  into  air  accord- 
mg  as  it  is  negative  or  positive 
(787). 

The  perturbation  and  sudden 
expansion  which  the  discharge 
produces  may  be  illustrated  by 
means  of  what  is  known  as 
Kznnersleys  thermometer.  This 
consists  of  two  glass  tubes  (fig. 
729),  which  fit  into  metallic  caps 
and  communicate  with  each 
other.  At  the  top  of  the  large 
tube  is  a  rod  terminating  in  a 
knob,  and  moving  in  a  stuffing- 
box,  and  at  the  bottom  there  is  a 
similar  rod  with  a  knob.  The 
apparatus  contains  water  up  to 
the  level  of  the  lower  knob. 
When  the  electric  discharge 
passes  between  the  two  knobs, 
the  water  is  driven  out  of  the 
larger  tube  and  rises  to  a  slight  extent  in  the  small  one.  The  level  is 
immediately  re-established,  and  therefore  the  phenomenon  is  not  due  to  a 
rise  of  temperature. 


y(>2 


Frictional  Electricity. 


[792- 


If  the  upper  knob  inside  a  Kinnersley's  thermometer  be  replaced  by  a 
point,  and  the  outside  knob  is  connected  with  the  prime  conductor  of  a 
machine  at  work,  the  electricity  discharges  itself  in  the  form  of  a  brush, 
and  a  permanent  displacement  of  the  liquid  in  the  stem  shows  that  this 
is  due  to  the  heating  effect  of  the  brush  discharge. 

For  the  production  of  mechanical  effects  the  universal  discharger  (fig. 
713)  is  of  great  service.  A  piece  of  wood,  for  instance,  placed  on  the  table 
between  the  two  conductors,  is  split  when  the  discharge  passes. 

When  a  Leyden  jar  is  charged  it  undergoes  a  true 
expansion  which  is  not  that  due  to  heat.  This  was 
shown  by  Quincke,  one  of  whose  experiments  is  repre- 
sented in  fig.  730.  It  consists  of  a  glass  bulb  A  about 
2  inches  in  diameter  at  the  end  of  a  narrow  capillary 
tube  K,  on  an  enlargement  in  which  a  platinum  wire  k 
is  fused.  The  bulb  and  a  portion  of  the  stem  contains 
a  conducting  liquid,  such  as  water  or  sulphuric  acid, 
and  it  is  placed  in  a  vessel  of  ice-cold  water,  K,  which 
can  be  connected  with  the  earth  by  a  conducting  wire, 
G.  If  now  this  condenser  is  charged  by  connecting 
the  wire  B  with  an  electrical  machine,  while  G  is  in 
connection  with  the  earth,  there  is  a  distinct  depres- 
sion of  the  liquid  in  the  tube.  When  the  jar  is  dis- 
charged the  liquid  resumes  its  original  level.  Hence 
this  cannot  have  been  due  to  heat,  apart  from  the 
fact  that  the  temperature  was  kept  constant  ;  nor  is 
it  due  to  a  contraction  of  the  thickness  of  the  glass. 
The  same  results  are  obtained  if  the  outer  coating  is  insulated  by  resting  it 
on  shellac  T,  which  in  turn  is  insulated  by  resting  on  a  slab  of  india-rubber, 
the  inner  coating  being  put  to  earth.  Similar  effects  are  observed  with 
solid  condensers  of  other  materials,  and  also  with  liquids. 

793.  Cbemical  effects. — The  chemical  effects  are  the  decompositions 
and  recombinations  effected  by  the  passage  of  the  electric  discharge.  When 
two  gases  which  act  on  each  other  are  mixed  in  the  proportions  in  which 
they  combine,  a  single  spark  is  often  sufficient  to  determine  their  combina- 
tion ;  but  when  either  of  them  is  in  great  excess,  a  succession  of  sparks  is 
necessary.  Priestley  found  that  when  a  series  of  electric  sparks  was  passed 
through  moist  air,  its  volume  diminished,  and  blue  litmus  introduced  into 
the  vessel  was  reddened.  This,  Cavendish  discovered,  was  due  to  the  for- 
mation of  nitric  acid. 

Several  compound  gases  are  decomposed  by  the  continued  action  of  the 
electric  spark.  With  olefiant  gas,  sulphuretted  hydrogen,  and  ammonia,  the 
decomposition  is  complete  ;  while  carbonic  acid  is  partially  decomposed 
into  oxygen  and  carbonic  oxide.  The  electric  discharge  also  by  suitable 
means  can  feebly  decompose  water,  oxides,  and  salts  ;  but,  though  the  same 
in  kind,  the  chemical  effects  of  statical  electricity  are  by  no  means  so  powerful 
and  varied  as  those  of  dynamical  electricity.  The  chemical  action  of  the 
spark  is  easily  demonstrated  by  means  of  a  solution  of  iodide  of  potassium. 
A  small  lozenge-shaped  piece  of  filtering  paper,  impregnated  with  iodide  of 
potassium,  is  placed  on  a  glass  plate,  and  one  corner  connected  with  the 


Fig.  730. 


-793]        Chemical  Effects  of  the  Electrical  Discharge. 


^63 


ground.  When  a  few  sparks  from  a  conductor  charged  with  positive  elec- 
tricity are  taken  at  the  other  corner,  brown  spots  are  produced,  due  to  the 
separation  of  iodine. 

The  electric  pistol  is  a  small  apparatus  which  serves  to  demonstrate  the 
chemical  effects  of  the  spark.  It  consists  of  a  brass  vessel  (fig.  731),  in 
which  is  introduced  a  detonating  mixture  of  two  volumes  of  hydrogen  and 


V 


ITd 


? 


ij 


-r 


Fig.  731.  Fig.  732. 

one  of  oxygen,  and  which  is  then  closed  with  a  cork.  In  a  tubulure  in  the 
side  there  is  a  glass  tube,  in  which  fits  a  metal  rod,  terminated  by  the 
knobs  A  and  B.  The  vessel  is  held  as  represented  in  fig.  732,  and  brought 
near  the  machine.  The  knob  A  becomes  negatively,  and  B  positively,  elec- 
trified by  induction  from  the  machine,  and  a  spark  passes  between  the  con- 
ductor and  A.  Another  spark  passes  at 
the  same  time  between  the  knob  B  and 
the  side  ;  this  determines  the  combina- 
tion of  the  gases,  which  is  accompanied 
by  a  great  disengagement  of  heat,  and  the 
vapour  of  water  formed  acquires  such  an 
expansive  force,  that  the  cork  is  pro- 
jected with  a  report  like  that  of  a  pistol. 

Among  the  chemical  effects  must  be 
enumerated  the  formation  of  ozoiie,  which 
is  recognised  by  its  peculiar  odour,  and 
by  certain  chemical  properties.  The 
odour  is  perceiv'ed  when  electricity  issues 
from  a  conductor  into  the  air  through 
a  series  of  points.  It  has  been  estab- 
lished that  ozone  is  an  allotropic  modi- 
fication of  oxygen. 

With  these  effects  may  be  associated 
a  certain  class  of  phenomena  observed 
when  gases  are  made  to  act  as  the  dielec- 
tric in  a  charged  Leyden  jar.  An  appa- 
ratus by  which  this  is  effected  is  repre- 
sented in  fig.  733  ;  it  is  a  modification  of 
one  invented  by  Siemens.  It  consists 
of  a  glass  cylinder  E,  containing  dilute 
sulphuric  acid  ;  «  is  a  glass  tube  closed  at  the  bottom,  and  also  containing 
sulphuric  acid,  in  an  enlargement  of  which  at  the  top  the  inner  tube  ec  fits. 


Fig.  733- 


764 


Frictional  Electricity. 


[793- 


There  is  a  tube  /,  by  which  gas  enters,  and  one  dt'  by  which  it  emerges. 
When  the  acids  in  E  and  e  are  respectively  connected  with  the  two  combs  of 
a  Holtz  machine,  or  with  the  two  terminals  of  a  Ruhmkorfif's  coil,  a  certain 
condition  or  strain  (747)  is  produced  in  the  dielectric,  which  is  known  as  the 
silent  discharge  or  the  electric  effluvium.  \\'hat  that  condition  is  cannot  be 
definitely  stated  ;  but  it  gives  rise  to  powerful  and  characteristic  chemical 
actions,  often  differing  from  those  produced  by  the  spark. 

By  this  apparatus  large  quantities  of  ozone  may  be  produced. 
794.  Application  of  the  electrical  discharg-e  to  firing-  mines. — By  the 
labours  of  Sir  F.  Abel  in  this  country,  and  of  Baron  Von  Ebner  in  Austria,  the 
electrical  discharge  has  been  applied  to  firing  mines  for  military  purposes, 
and  the  methods  have  acquired  a  high  degree  of  perfection.  The  principle  on 
which  the  method  is  based  maybe  understood  from  the  following  statement : — 
One  end  of  an  insulated  wire  in  which  is  a  small  break  is  placed  in  con- 
tact with  the  outside  of  a  charged  Leyden  jar,  the  other  end  being  placed 
near  the  inner  coating.  If  now  this  end  be  brought  in  contact  with  the  inner 
coating  the  jar  is  discharged,  and  a  spark  strikes  across  the  break  ;  and 
if  there  be  here  some  explosive  compound  it  is  ignited,  and  this  ignition 
may  of  course  be  communicated  to  any  gunpowder  in  which  it  is  placed. 
If  on  one  side  of  the  break,  instead  of  having  an  insulated  wire  direct 
back   to   the   outer  coating  of  the  Leyden  jar,  an  uncovered  wire  be  led 

into  the  ground,  the  out- 
side of  the  jar  being 
also  connected  with  the 
ground,  the  result  is  un- 
changed, the  earth  acting 
as  a  return  wire.  More- 
over, if  there  be  several 
breaks,  the  explosion  will 
still  ensue  at  each  of  them, 
provided  the  charge  be 
sufficiently  powerful. 

In  the  actual  applica- 
tion it  is  of  course  neces- 
sary to  have  an  arrange- 
ment for  generating 
frictional  electricity  which 
shall  be  simple,  portable, 
powerful,  and  capable  of 
working  in  any  weather. 
Fig.  734  represents  a  \iew 
of  Von  Ebner's  instrument 
as  constructed  by  Messrs. 
Elliott,  part  of  the  case 
being  removed  to  show 
the  internal  construction. 
Itconsists  of  two  circu- 
lar plates  of  ebonite,  a,  mounted  on  an  axis  so  that  they  are  turned  by  a 
handle  b,  between  rubber,  which  are  so  arranged  as  to  be  easily  removed 


F'g-  734- 


-794]    Application  of  Electrical  Disc Jiargc  to  Firing  Mines     765 

for  the  purposes  of  amalgamation,  &€.  Fastened  to  a  knob  on  the  base  of 
the  apparatus  and  projecting  between  the  plates  is  a  pointed  brass  rod, 
which  acts  as  a  collector  of  the  electricity.  The  condenser  or  Leyden  jar 
arrangement  is  inside  the  case,  part  of  which  has  been  removed  to  show  the 
arrangement.  It  consists  of  india-rubber  cloth,  coated  on  each  side  with 
tinfoil,  and  formed  into  a  roll  for  the  purpose  of  greater  compactness. 
By  means  of  a  metal  button  the  knob  is  in  contact  with  one  tinfoil  coating, 
which  thus  receives  the  electricity  of  the  machine,  and  corresponds  to  the 
inner  coating  of  the  Leyden  jar.  Another  button,  connected  with  the 
other  tinfoil  coating,  rests  on  a  brass  band  at  the  base  of  the'  apparatus 
which  is  in  metallic  contact  with  the  cushions,  the  knob  d,  and  the  per- 
forated knob  in  which  slides  a  rod  at  the  front  of  the 
apparatus.  These  are  all  in  connection  with  the  earth. 
The  knob  e  is  in  metallic  connection  with  a  disc  _^  pro- 
vided with  a  light  arm.  By  means  of  a  flexible  chain  this 
is  so  connected  with  a  trigger  on  the  side  of  the  apparatus 
not  represented  in  the  figure,  that  when  the  trigger  is 
depressed,  the  arm,  and  therewith  the  knob  e,  is  brought 
into  contact  with  the  inner  coating  of  the  condenser. 

On  depressing  the  trigger,  after  a  certain  number  of 
turns,  a  spark  passes  between  the  knob  e  and  the  sliding 
rod,  and  the  striking  distance  is  a  measure  of  the 
working  condition  of  the  instrument. 

The  fuse  used  is  known  as  AbeVs  electrical  fuse,  and 
has  the  following  construction  : — The  ends  of  two  fine 
copper  wires  (fig.  735)  are  imbedded  in  a  thin  soHd 
gutta-percha  rod,  parallel  to  each  other,  but  at  a  dis- 
tance of  about  I  "5  mm.  At  one  end  of  the  gutta-percha 
a  small  cap  of  paper  c  c  \s  fastened,  in  which  is  placed 
a  small  quantity  of  the  priming  composition,  which  con- 
sists of  an  intimate  mixture  of  subsulphide  of  copper, 
subphosphide  of  copper,  and  chlorate  of  potassium. 
The  paper  is  fastened  down  so  that  the  exposed  ends  of 
the  wires  are  in  close  contact  with  the  powder. 

This  is  the  actual  fuse  ;  for  service  the  capped  end  of  the  fuse  is 
placed  in  a  perforation  in  the  rounded  head  of  a  wooden  cylinder,  so  as  to 
project  slightly  into  the  cavity  g  of  the  cylinder.     This  «„ 

cavity  is  filled  with  meal  powder,  which  is  well  rammed 
down,  so  that  the  fuse  is  firmly  imbedded.  It  is  after- 
wards closed  by  a  plug  of  gutta-percha,  and  the  whole 
is  finally  coated  with  black  varnish. 

The  free  ends  of  the  wire  a  a  are  pressed  into  small 
grooves  in  the  head  of  the  cylinder  (fig.  736),  and  each 
end  is  bent  into  one  of  the  small  channels  with  which  the 
cylinder  is  provided,  and  which  are  at  right  angles  to 
the  central  perforation.  They  are  wedged  in  here  by 
driving  in  small  copper  tubes,  the  ends  of  which  are 
then  filed  flush  with  the  surface  of  the  cylinder.  The 
bared  ends  of  two  insulated  conducting  wires  are  then  pressed  into  one  of 


Fig.  735- 


Fig.  736. 


766  Frictiojial  Electricity.  [794- 

the  small  copper  tubes  or  eyes,  and  fixed  there  by  bending  the  wire  round 
on  to  the  wood,  as  shown  at  e. 

The  conducting  wire  used  in  firing  may  be  thin,  but  it  must  be  w-ell 
insulated.  One  end  which  is  bared,  having  been  pressed  into  the  hole  d 
of  the  fuse  (fig.  735),  the  other  is  placed  near  the  exploder.  In  the  other 
hole  d'  of  the  fuse  a  wire  is  placed  which  serves  as  earth  wire,  care  being 
taken  that  there  is  no  connection  between  the  two  wires.  The  fuse  having 
been  introduced  into  the  charge,  the  earth  wire  is  placed  in  good  connection 
with  the  ground.  The  knob  /  of  the  exploder  is  also  connected  with  the 
earth  by  leading  the  bare  wire  into  water  or  moist  earth,  and  the  condi- 
tion of  the  machine  tested.  The  end  of  the  insulated  wire  is  then  connected 
with  the  knob  c  and  the  rod  drawn  down  ;  at  the  proper  signal  the  handle 
is  turned  the  requisite  number  of  times,  and  when  the  signal  is  given  the 
trigger  is  depressed,  and  the  explosion  ensues. 

When  a  number  of  charges  are  to  be  fired  they  are  best  placed  in  a  single 
circuit,  care  being  taken  that  the  insulation  is  good. 

795.  Duration  of  the  electric  spark. — Wheatstone  measured  the  dura- 
tion of  the  electric  spark  by  means  of  the  rotating  mirror  which  he  invented 
for  this  purpose.  At  some  distance  from  this  instrument,  which  can  be  made 
to  rotate  with  a  measured  velocity,  a  Leyden  jar  is  so  arranged  that  the  spark 
of  its  discharge  is  reflected  from  the  mirror.  Now,  from  the  laws  of  reflec- 
tion (520)  the  image  of  the  luminous  point  describes  an  arc  of  double  the 
number  of  degrees  which  the  mirror  describes,  in  the  time  in  which  the 
mirror  passes  from  the  position  in  which  the  image  is  visible  to  that  in  which 
it  ceases  to  be  so.  If  the  duration  of  the  image  were  absolutely  instanta- 
neous the  arc  would  be  reduced  to  a  mere  point.  Knowing  the  number  of 
turns  which  the  mirror  makes  in  a  second,  and  measuring,  by  means  of  a 
divided  circle,  the  number  of  degrees  occupied  by  the  image,  the  duration  of 
the  spark  would  be  determined.  In  one  experiment  Wheatstone  found  that 
this  arc  was  24°.  Nov/,  in  the  time  in  which  the  mirror  traverses  360°  the 
image  traverses  720°  ;  but  in  the  experiment  the  mirror  made  800  turns  in  a 
second,  and  therefore  the  image  traversed  576,000°  in  this  time  ;  and  as  the 
arc  was  24°,  the  image  must  have  lasted  the  time  expressed  by^r.!^,  or  ^j^^- 
of  a  second.  Thus  the  discharge  is  not  instantaneous,  but  has  a  certain 
duration,  which,  however,  is  excessively  short. 

Feddersen  found  that  when  greater  resistances  were  interposed  in  the 
circuit  through  which  the  discharge  was  effected,  the  duration  of  the  spark 
was  increased.  W'ith  a  tube  of  water  9  mm.  in  length,  the  spark  lasted  0-0014 
second  ;  and  with  one  of  180  mm.  its  duration  was  0-0183  second.  The 
duration  increased  also  with  the  striking  distance,  and  with  the  dimensions 
of  the  battery. 

To  determine  the  duration  of  the  electric  spark  Lucas  and  Cazin  used  a 
method  by  which  it  maybe  measured  in  millionths  of  a  second.  The  method 
is  an  application  of  the  vernier  (10).  A  disc  of  mica  15  centimetres  in  dia- 
meter is  blackened  on  one  face,  and  at  the  edge  are  traced  180  equal  divi- 
sions in  very  fine  transparent  lines.  The  disc  is  mounted  on  a  horizontal 
axis,  and  by  means  of  a  gas  engine  it  may  be  made  to  turn  with  a  velocity 
of  100  to  300  turns  in  a  second.  A  second  disc  of  silvered  glass  of  the  same 
radius  is  mounted  on  the  same  axis  as  the  other  and  very  close  to  it  ;  at  its 
upper  edge  six  equidistant  transparent  lines  are  traced,  forming  a  vernier 


-795] 


Duration  of  the  Electric  Spark. 


767 


with  the  lines  on  the  mica.  P'or  this,  the  distance  between  two  consecutive 
Hnes  on  the  two  discs  is  such  that  five  divisions  of  the  mica  disc  DC  corre- 
spond to  six  divisions  of  the  glass  disc  AB,  as  seen  in  fig.  72)7-  Thus  the 
vernier  gives  the  sixths  of  a  division  of  the  mica  disc  (10).  In  the  apparatus 
the  lines  AB  are  not  above  the  lines  CD,  but 
are  at  the  same  distance  from  the  axis,  so 
that  the  latter  coincide  successively  with 
the  former. 

The  mica  disc  is  contained  in  a  brass 
box  D  (fig.  738),  on   the  hinder  face  of 
which  is  fixed  the  vernier.     In  the  front 
face  is  a  glass  window  O,  through  which  the  coincidence  of  the  two  sets  of 
lines  can  be  observed  by  means  of  a  magnifying  lens  L. 

The  source  of  electricity  is  a  battery  of  2  to  8  jars,  each  having  a  coated 
surface  of  1,243  square  centimetres,  and  charged  continuously  by  a  Holtz 
machine.     The  spark  strikes  between  two  metal  balls  a  and  b,  1 1  millimetres 


Fig-  737- 


in  diameter.  Their  distance  can  be  varied,  and  at  the  same  time  measured, 
by  means  of  a  micrometric  screw,  r.  The  two  opposite  electricities  arrive 
by  wires  ;;?  and  ;/,  and  the  sparks  strike  at  the  principal  focus  of  a  condensing 
lens  placed  in  the  collimator  C,  so  that  the  rays  which  fall  on  the  \-crnier  are 
parallel. 


y6^  Frictional  Electricity.  [795- 

The  motion  is  transmitted  to  the  toothed  wheels  and  to  the  mica  disc  by 
means  of  an  endless  band,  which  can  be  placed  on  any  one  of  three  pulleys 
P,  so  that  the  velocity  may  be  varied.  At  the  end  of  the  axis  of  the  pulleys 
is  a  bent  wire  which  moves  a  counter,  V,  that  marks  on  three  dials  the 
number  of  turns  of  the  disc. 

These  details  being  premised,  suppose  the  velocity  of  the  disc  is  400 
turns  in  a  second.  In  each  second  400+  180,  or  72,000  lines  pass  before  the 
observer's  eye  in  each  second  ;  hence  an  interval  of  ~~^  of  a  second  elapses 
between  two  consecutive  lines.  But  as  the  spark  is  only  seen  when 
one  of  the  lines  of  the  disc  coincides  with  one  of  the  six  hnes  of  the  ver- 
nier ;  and  as  this  gives  sixths  of  a  division  of  the  movable  disc,  when  the 
latter  has  turned  through  a  sixth  of  a  division,  a  second  coincidence  is 
produced ;    so  that   the  interval   between  two    successive    coincidences    is 

7- =  0-0000023  of  a  second. 

72000  X  6  -^ 

That  being  the  case,  let  the  duration  of  a  spark  be  something  between 
23  and  46  ten-millionths  of  a  second  ;  if  it  strikes  exactly  at  the  moment  of 
a  coincidence,  it  will  last  until  the  next  coincidence  ;  and  owing  to  the  per- 
sistence of  impressions  on  the  retina  (625)  the  observer  will  see  two  luminous 
lines.  But  if  the  spark  strikes  between  two  coincidences  and  has  ceased 
when  the  thu'd  is  produced,  only  one  brilliant  line  is  seen.  Thus,  if  with  the 
above  velocity  sometimes  i  and  sometimes  2  bright  lines  are  seen,  the  dura- 
tion of  the  spark  is  comprised  between  23  and  46  ten-millionths  of  a  second. 

By  experiments  of  this  kind,  with  a  striking  distance  of  5  millimetres 
between  the  balls  a  and  <5,  and  varying  the  number  of  the  jars,  MM.  Lucas 
and  Cazin  obtained  the  following  results  : — 

Duration  in  millionths 
Number  of  jars                                                                of  a  second. 
2 26 

4 41 

6 45 

8 47 

It  will  thus  be  seen  that  the  duration  of  the  spark  increases  with  the 
number  of  jars.     It  also  increases  with  the  striking  distance  ;  but  it  is  inde- 
pendent of  the  diameter  of  the  balls  between  which 
the  spark  strikes. 

The  spark  of  electrical  machines  has  so  short  a 
duration    that    it    could   not    be    measured  with   the 
/^'  \      chrnnoscope. 

^.o.       /<?  •  <is      |<r"7  796.  Velocity  Of  electricity. — To  determine  the 

'    '  \^^J\  — \z^ —       velocity    of    electricity    Wheatstone    constructed   an 

apparatus  the  principle  of  which  will  be  understood 

from  fig.   739.      Six  insulated   metal  knobs   were  ar- 

— <!r]~L>'~  ranged  in  a  horizontal  line  on  a  piece  of  wood  called 

Pig  ^3g_  a  spark  board ;  of  these  the  knob   i  was  connected 

with  the  outer,  while  6  could  be  connected  with  the 

inner  coating  of  a  charged  Leyden  jar  ;  the  knob  i  was  a  tenth  of  an  inch 

distant   from  the  knob  2  ;    while  between   2  and  3  a  quarter  of  a  mile  of 

insulated  wire  was  interposed  ;  3  was  likewise  a  tenth  of  an  inch  from  4,  and 


-796]  Velocity  of  lilcctricity.  769 

there  was  a  quarter  of  a  mile  of  wire  between  4  and  5  ;  lastly,  5  was  a  tenth 
of  an  inch  from  6,  from  which  a  wire  led  directly  to  the  inner  coatinj^-  of  the 
Leyden  jar.  Hence,  when  the  jar  was  discharged  by  connecting  the  wire 
from  6  with  the  inner  coating  of  the  jar,  sparks  would  pass  between  i  and  2, 
between  3  and  4,  and  between  5  and  6. .  Thus  the  discharge,  supposing  it  to 
proceed  from  the  inner  coating,  has  to  pass  in  its  course  through  a  quarter  of 
a  mile  of  wire  between  the  first  and  second  spark,  and  through  the  same 
distance  between  the  second  and  third. 

The  spark  board  was  arranged  at  a  distance  of  10  feet  from  the  rotating 
mirror,  and  at  the  same  height,  both  being  horizontal  ;  and  the  observer 
looked  down  on  the  mirror.  Thus  the  sparks  were  visible  when  the  mirror 
made  an  angle  of  45°  with  the  horizon. 

Now,  if  the  mirror  were  at  rest,  or  had  only  a  small  velocity,  the  images 
of  the  three  spots  would  be  seen  as  three  dots  \ ,  but  when  the  mirror  had 
a  certain  velocity  these  dots  appeared  as  lines,  which  were  longer  as  the 
rotation  was  more  rapid.  The  greatest  length  observed  was  24°,  which, 
with  800  revolutions  in  a  second,  can  be  shown  to  correspond  to  a  duration 
of  jJ^^  of  a  second.  With  a  slow  rotation  the  lines  present  the  appearance 
^== ;  they  are  quite  parallel,  and  the  ends  in  the  same  line.  But  with 
greater  velocity,  and  when  the  rotation  took  place  from  left  to  right,  they 
presented  the  appearance  —  ,  and  when  it  turned  from  right  to  left 

the  appearance      == — ,  because  the  image  of  the  centre  spark  was  formed 

after  the  lateral  ones.  Wheatstone  found  that  this  displacement  amounted 
to  half  a  degree  before  or  behind  the  others  ;  accordingly  this  arc  corre- 
sponds to  a  duration  of  about  the  jy.^|^o  °f  ^  second  ;  the  space  traversed 
in  this  time  being  a  quarter  of  a  mile,  gives  for  the  velocity  of  electricity 
288,000  miles  in  a  second,  which  is  greater  than  that  of  light.  The  velocity 
obtained  from  experiments  with  dynamical  electricity  is  far  less  ;  and,  owing 
to  induction,  the  transmission  of  a  current  through  submarine  wires  is  com- 
paratively slow. 

In  the  above  experiment  the  images  of  the  two  outer  sparks  appear 
simultaneously  in  the  mirror,  from  which  it  follows  that  the  electric  current 
issues  simultaneously  from  the  two  coatings  of  the  Leyden  jar. 

From  theoretical  considerations  based  upon  measurements  of  constant 
electrical  currents  Kirchhoff  concluded  that  the  motion  of  electricity  in  a  wire 
in  which  it  meets  with  no  resistance  is  like  that  of  a  wave  in  a  stretched 
string,  and  has  the  velocity  of  192,924  miles  in  a  second,  which  is  about  that 
of  light  in  vacuo  (507). 

According  to  Walker,  the  velocity  of  electricity  is  18,400  miles,  and 
according  to  Fizeau  and  Gounclle  it  is  62,100  miles  in  iron,  and  1 1 1,780  in 
copper  wire.  These  measurements,  however,  were  made  with  telegraph  wires, 
which  induce  opposite  electricities  in  the  surrounding  media  ;  there  is  thus 
produced  a  resistance  which  diminishes  the  velocity.  The  velocity  is  less 
in  insulated  wires  in  water  than  in  air.  The  nature  of  the  conductor  appears 
to  have  some  influence  on  the  velocity ;  but  not  the  thickness  of  the  wire 
nor  the  potential  of  the  electricity. 

For  atmospheric  electricity,  reference  must  be  made  to  the  chapter  on 
Meteorology. 

3D 


770 


Dynamical  Electricity. 


[797- 


BOOK   X. 

DYNAMICAL   ELECTRICITY. 


CHAPTER    I. 

VOLTAIC  PILE.      ITS  INIODIFICATIONS. 

797.  Galvani's  experiment  and  theory. — The  fundamental  experiment 
which  led  to  the  discovery  of  dynamical  electricity  is  due  to  Galvani,  Pro- 
fessor of  Anatomy  in  Bologna.  Occupied  with  investigations  on  the  in- 
fluence of  electricity  on  the  nervous  excitability  of  animals,  and  especially  of 

the  frog,  he  observed 
that  when  the  lum- 
bar nerves  of  a  dead 
frog  were  connected 
with  the  crural  mus- 
cles by  a  metallic 
circuit,  the  latter  be- 
came briskly  con- 
tracted. 

To  repeat  this 
celebrated  experi- 
ment, the  legs  of  a 
recently  killed  frog 
are  prepared,  and 
the  lumbar  nerves 
on  each  side  of  the 
vertebral  column  are 
exposed  in  the  form 
of  white  threads. 
A  metal  conductor, 
composed  of  zinc 
and  copper,  is  then 
taken  (fig.  740),  and  one  end  introduced  between  the  nerves  and  the  vertebral 
column,  while  the  other  touches  one  of  the  muscles  of  the  thighs  or  legs  ; 
at  each  contact  a  smart  contraction  of  the  muscles  ensues. 

Galvani  had  some  time  before  observed  that  the  electricity  of  machines 
produced  in  dead  frogs  analogous  contractions,  and  he  attributed  the  pheno- 
mena first  described  to  an  electricity  inherent  in  the  animal.     He  assumed 


Fig.  740. 


-799]      Disengagement  of  Electricity  in  Clieniical  Actions.       yyi 

that  this  electricity,  which  he  called  vital  fluid,  passed  from  the  nerves  to 
the  muscles  by  the  metallic  arc,  and  was  thus  the  cause  of  contraction. 
This  theory  met  with  great  support,  especially  among  physiologists,  but  it 
was  not  without  opponents.  The  most  considerable  of  these  was  Alexander 
Volta,  Professor  of  Physics  in  Pavia. 

798.  Volta's  fundamental  experiment. — Galvani's  attention  had  been 
exclusively  devoted  to  the  nerves  and  muscles  of  the  frog  ;  Volta's  was 
directed  upon  the  connecting  metal.  Resting  on  the  observation,  which 
Galvani  had  also  made,  that  the  contraction  is  more  energetic  when  the  con- 
necting arc  is  composed  of  two  metals,  than  when  there  is  only  one,  Volta 
attributed  to  the  metals  the  active  part  in  the  phenomenon  of  contraction. 
He  assumed  that  the  disengagement  of  electricity  was  due  to  their  contact, 
and  that  the  animal  parts  only  officiated  as  conductors,  and  at  the  same  time 
as  a  very  sensitive  electroscope. 

By  means  of  the  condensing  electroscope,  which  he  had  then  recently 
invented,  Volta  devised  several  modes  of  showing  the  disengagement  of  elec- 
tricity on  the  contact  of  metals,  of  which  the  following  is  the  easiest  to  per- 
form : — 

The  moistened  finger  being  placed  on  the  upper  plate  of  a  condensing 
electroscope  (fig.  716),  the  lower  plate  is  touched  with  a  plate  of  copper,  c, 
soldered  to  a  plate  of  zinc,  2,  which  is  held  in  the  other  hand.  On  breaking 
the  connection  and  lifting  the  upper  plate  (fig.  717),  the  gold  leaves  diverge, 
and,  as  may  be  proved,  with  negative  electricity.  Hence,  when  soldered 
together,  the  copper  is  charged  with  negative  electricity,  and  the  zinc  with 
positive  electricity.  The  electricity  could  not  be  due  either  to  friction  or 
pressure  ;  for  if  the  condensing  plate,  which  is  of  copper,  is  touched  with 
the  zinc  plate  2,  the  copper  plate  to  which  it  is  soldered  being  held  in  the 
hand,  no  trace  of  electricity  is  observed. 

A  memorable  controversy  arose  between  Galvani  and  Volta.  The  latter 
was  led  to  give  greater  extension  to  his  contact  theory,  and  propounded  the 
principle  that  when  two  heterogeneous  substances  are  placed  in  contact,  one 
of  them  always  assumes  the  positive  and  the  other  the  ftegative  electrical 
condition.  In  this  form  Volta's  theory  obtained  the  assent  of  the  principal 
philosophers  of  his  time.  Galvani,  however,  made  a  number  of  highly 
interesting  experiments  with  animal  tissues.  In  some  of  these  he  obtained 
indications  of  contraction,  even  though  the  substances  in  contact  were  quite 
homogeneous. 

799.  Disengagrement  of  electricity  In  chemical  actions. — The  contact 
theory  which  Volta  had  propounded,  and  by  which  he  explained  the  action  of 
the  pile,  soon  encountered  objectors.  Fabroni,  a  countryman  of  Volta,  having 
observed  that,  in  the  pile,  the  discs  of  zinc  became  oxidised  in  contact  with 
the  acidulated  water,  thought  that  this  oxidation  was  the  principal  cause  of 
the  disengagement  of  electricity.  In  England  Wollaston  soon  advanced  the 
same  opinion,  and  Davy  supported  it  by  many  ingenious  experiments. 

It  is  true  that  in  the  fundamental  experiment  of  the  contact  theory  (798) 
Volta  obtained  signs  of  electricity.  But  De  la  Rive  showed  that  if  the  zinc 
be  held  in  a  wooden  clamp,  all  signs  of  electricity  disappear,  and  that  the 
same  is  the  case  if  the  zinc  be  placed  in  gases,  such  as  hydrogen  or  nitrogen, 
which  exert  upon  it  no  chemical  action.     De  la  Rive  accordingly  concluded 

3  D  2 


772  Dynamical  Electricity.  [799- 

that  in  Volta's  original  experiment  the  disengagement  of  electricity  is  due  to 
the  chemical  actions  which  result  from  the  perspiration  and  from  the  oxygen 
of  the  atmosphere. 

The  development  of  electricity  in  chemical  actions  may  be  demonstrated 
in  the  following  manner  by  means  of  the  condensing  electroscope  (786)  : — A 
disc  of  moistened  paper  is  placed  on  the  upper  plate  of  the  condenser,  and 
on  this  a  zinc  capsule,  in  which  some  very  dilute  sulphuric  acid  is  poured.  A 
platinum  wire,  communicating  with  the  ground,  but  insulated  from  the  sides 
of  the  vessel,  is  immersed  in  the  liquid,  and  at  the  same  time  the  lower  plate 
of  the  condenser  is  also  connected  with  the  ground  by  touching  it  with  the 
moistened  finger.  On  breaking  contact  and  removing  the  upper  plate,  the 
gold  leaves  are  found  to  be  positively  electrified,  proving  that  the  upper  plate 
has  received  a  charge  of  negative  electricity. 

By  a  variety  of  analogous  experiments  it  may  be  shown  that  various 
chemical  actions  are  accompanied  by  a  disturbance  of  the  electrical  equili- 
brium ;  though  of  all  chemical  actions  those  between  metals  and  liquids  are 
the  most  productive  of  electricity.  All  the  various  resultant  effects  are  in 
accordance  with  the  general  rule,  that  when  a  liquid  acts  chemically  on  a 
metal  the  liquid  assumes  the  positive,  and  the  metal  the  negative,  con- 
dition. In  the  above  experiment  the  sulphuric  acid,  by  its  action  on 
zinc,  becomes  positively  electrified,  and  its  electricity  passes  off  through 
the  platinum  wire  into  the  ground,  while  the  negative  electricity  excited 
on  the  zinc  acts  on  the  condenser  just  as  an  excited  rod  of  sealing-wax 
would  do. 

In  many  cases  the  electrical  indications  accompanying  chemical  actions 
are  but  feeble,  and  require  the  use  of  a  veiy  delicate  electroscope  to  render 
them  apparent.  Thus,  one  of  the  most  energetic  chemical  actions,  that  of 
sulphuric  acid  upon  zinc,  gives  no  more  free  electricity  than  water  alone  does 
with  zinc. 

Opinion — which  in  this  country,  at  least,  had,  mainly  by  the  iniluence  of 
Faraday's  experiments,  tended  in  favour  of  the  purely  chemical  origin  of 
the  electricity  produced  in  voltaic  action — has  of  late  inclined  more  and  more 
towards  the  contact  theory.  The  following  experiments,  due  to  Sir  W. 
Thomson,  afford  perhaps  the  most  conclusive  arguments  hitherto  adduced 
in  favour  of  the  latter  view  : — 

A  very  light  metal  bar  is  suspended  by  fine  wire,  so  as  to  be  movable 
about  an  axis  perpendicular  to  the  plane  of  a  disc  made  up  of  two  half  discs, 
one  of  zinc,  Z,  and  the  other  of  copper,  C  (fig. 
■^j!^i^^^  741).     The  light  bar  is  counterpoised  so  as  to 

iDe  exactly  over  one  half  of  the  line  of  separa- 
tion of  the  two  discs.  When  the  discs  are 
placed  in  contact  and  the  bar  is  charged  posi- 
tively by  being  connected  with  a  Leydcn  jar, 
the  bar  moves  from  the  zinc  towards  the  copper  ; 
'^  ^■'''  if  the  jar,  and  therefore  the  bar,  is  charged 

negatively,  its  motion  is  in  the  opposite  direction.  The  same  results  are  ob- 
tained when  the  discs  are  connected  by  a  wire,  thus  showing  that  the  contact 
of  the  two  metals  causes  them  to  assume  different  electrical  conditions,  the 
zinc  taking  the  positive,  and  the  copper  the  negative  electricity. 


-800]  Current  Electricity.  773 

\\'hen,  however,  the  two  halves,  instead  of  being  in  metalHc  contact,  are 
connected  by  a  drop  of  water,  no  change  is  produced  in  the  position  of  the 
bar  by  altering  its  electrification,  provided  it  hangs  quite  symmetrically  rela- 
tive to  the  two  halves  of  the  ring.  This  result  shows  that,  under  the  circum- 
stances mentioned,  no  difference  is  produced  in  the  electrical  condition  of 
the  two  metals.  Hence  the  conclusion  has  been  drawn  by  Sir  W.  Thomson 
and  others,  that  the  movement  of  electricity  in  the  galvanic  circuit  is  entirely 
due  to  the  electrical  difference  produced  at  the  surfaces  of  contact  of  the  dis- 
similar metals.  These  results  have  been  confirmed  by  some  recent  very 
careful  experiments  by  Professor  Clifton. 

There  are,  however,  other  facts  which  are  not  easily  harmonised  with  this 
view  ;  and  indeed  the  last-mentioned  experiment  can  hardly  be  regarded  as 
proving  that  in  all  cases  two  different  metals  connected  by  an  electrolytic 
(8 1 6)  liquid  assume  the  same  electrical  condition.  It  may,  therefore,  still  be 
regarded  as  possible,  or  even  probable,  that  the  contact  between  the  metals 
and  the  liquids  of  a  cell  contributes,  at  least  in  some  cases,  to  the  production 
of  the  current. 

A  most  complete  discussion  of  the  question  as  to  the  seat  of  electromotive 
forces  in  the  voltaic  cell  is  published  in  a  series  of  papers  by  Prof.  Lodge  in 
the  nineteenth  volume  of  the  '  Philosophical  Magazine.' 

Soo.  Curreut  electricity. — When  a  plate  of  zinc  and  a  plate  of  copper  are 
partially  immersed  in  dilute  sulphuric  acid,  no  electrical  or  chemical  change 
is  apparent  beyond  perhaps  a  slight  disengagement  of  hydrogen  from  the 
surface  of  the  zinc  plate.     If  now  the  plates  are 
placed  in  direct  contact,  or,  more  conveniently,  ». 

are  connected  by  a  metal  wire,  the  chemical  if 

action  sets  in,  a  large  quantity  of  hydrogen  is 
disengaged  ;  but  this  hydrogen  is  no  longer  dis- 
engaged at  the  surface  of  the  zinc,  but  at  the 
surface  of  the  copper  plate.  Here  then  we  have 
to  deal  with  something  more  than  mere  chemical 

action,  for  chemical  action  would  be  unable  to  

explain  either  the  increase  in  the  quantity  of  \  ly-" 

hydrogen  disengaged  when  the  metals  touch,  or  ~  "^.i- 

the  fact  that  this  hydrogen  is  now  given  off  at 

the  surface  of  the  copper  plate.     At  the  same  ■"'    ' 

time,  if  the  wire  is  examined  it  will  be  found  to  possess  many  remarkable 

thermal,  magnetic,  and  other  properties  which  will  be  afterwards  described. 

In  order  to  understand  what  here  takes  place,  let  us  suppose  that  we  have 
two  insulated  metal  spheres,  and  that  one  is  charged  with  positive  and  the 
other  with  negative  electricity,  and  that  they  are  momentarily  connected  by 
means  of  a  wire.  Electricity  will  pass  from  a  place  of  higher  to  a  place  of 
lower  potential — that  is,  from  the  positive  along  the  wire  to  the  negative — 
and  the  potentials  become  equal.  This  is,  indeed,  nothing  more  than  an 
electrical  discharge  taking  place  through  the  wire  ;  and  during  the  infinitely 
short  time  in  which  this  is  accomplished,  it  can  be  shown  that  the  wire 
exhibits  certain  heating  and  magnetising  effects,  of  which  the  increase  of 
temperature  is  perhaps  the  easiest  to  observe.  If  now  we  can  imagine  some 
agency  by  which  the  different  electrical  conditions  of  the  two  spheres  are 


m 


774  Dynamical  Electricity.  [800- 

renevved  as  fast  as  they  are  discharged,  which  is  what  very  nearly  takes 
place  when  the  two  spheres  are  respectively  connected  with  the  two  con- 
ductors r  and  7\  of  a  Holtz  machine  (figs.  687,  688),  this  equalisation  of 
potentials,  thus  taking  place,  is  virtually  continuous,  and  the  phenomena 
above  mentioned  are  also  continuous. 

Now  this  is  what  takes  place  when  the  two  metals  are  in  contact  in  a 
liquid  which  acts  upon  them  unequally.  This  is  independent  of  hypothesis 
as  to  the  cause  of  the  phenomena — whether  the  electrical  difference  is  only 
produced  at  the  moment  of  contact  of  the  metals,  or  whether  it  is  due  to  the 
chemical  action,  or  tendency  to  chemical  action,  between  the  metal  and  the 
liquid.  The  rapidly  succeeding  series  of  equalisations  of  potential,  which 
takes  place  in  the  wire,  being  continuous,  so  long  as  the  chemical  action 
continues,  is  what  is  ordinarily  spoken  of  as  the  electrical  cm-rent. 

If  we  represent  by  +^  the  potential  of  the  copper  plate,  and  by  —e  the 
potential  of  the  zinc,  then  the  electrical  difference — that  is,  the  difference  of 
potentials — is  +£?  —  (  —  ^)  =  2i?.  And  this  is  general  ;  the  essential  point  of  any 
such  combination  as  the  above  is,  that  it  maintains,  or  tends  to  maintain,  a 
difference  of  potentials,  which  difference  is  constant.  If,  for  instance,  the 
zinc  plate  be  connected  with  the  earth  which  is  at  zero  potential,  its  potential 
also  becomes  zero  ;  and  since  the  electrical  difference  remains  constant,  we 
have  for  the  potential  of  the  copper  plate  +  ■2e.  Similarly,  if  the  copper  be 
connected  with  the  earth  the  potential  of  the  zinc  plate  is  negative  and  is  —  2e. 
The  conditions  under  which  a  current  of  electricity  is  formed  in  the  above 
experiment  may  be  further  illustrated  by  reference  to  the  conditions  which 
determine  the  flow  of  water  between  two  reservoirs  containing  water  at  dif- 
ferent levels.  If  they  are  connected  by  a  pipe,  water  will  flow  from  the 
one  at  a  higher  level  to  the  one  at  a  lower  If  vel  until  the  water  in  the  two 
is  at  the  same  level,  when  of  course  the  flow  ceases.  If  we  imagine  the 
lower  reservoir  so  large  that  any  water  added  to  it  would  not  affect  its  level — 
if  it  were  the  sea,  for  example — that  would  represent  zero  level,  and  if  the 
higher  reservoir  could  be  kept  at  a  constant  level  there  would  be  a  constant 
flow  in  the  pipe. 

We  must  here  be  careful  not  to  dwell  too  much  on  this  analogy.  It  is  not 
to  be  supposed  that  in  speaking  of  current  of  electricity  we  mean  to  assert 
that  anything  actually  flows — that  there  is  any  actual  transfer  of  matter. 
We  say  '  electricity  flows  '  or  '  a  current  is  produced,'  in  much  the  same  sense 
as  that  in  which  we  say  '  sound  or  light  tra\els.' 

801.  Voltaic  couple.  Electromotive  series. — The  arrangement  just 
described,  consisting  of  two  metals  in  metallic  contact,  and  a  conducting 
liquid  in  which  they  are  placed,  constitutes  Tvsintple  voltaic  element  or  couple. 
So  long  as  the  metals  are  not  in  contact,  the  couple  is  said  to  be  open^  and 
when  connected  it  is  closed. 

According  to  the  chemical  view,  to  which  wc  shall  for  the  present  pro- 
visionally adhere,  it  is  not  necessary  for  the  jnoduction  of  a  current  that  one 
of  the  metals  be  unaffected  by  the  liquid,  but  merely  thatthe  chemical  action 
upon  the  one  be  greater  than  upon  the  other.  "  For  then  we  may  assume 
that  the  current  produced  would  be  due  to  the  difference  between  the  differ- 
ences of  potential  which  each  of  the  metals  separately  produces  by  its  con- 
tact with  the  liquid.     If  the  differences  of  potentials  were  absolutely  equal — 


-802]  Elect r 01  native  Force.  775 

a  condition,  however,  impossible  of  realisation  with  two  distinct  metals — we 
must  assume  that  when  the  metals  are  joined  no  current  would  be  produced. 
The  metal  which  is  most  attacked  is  called  ihc  positive  or  generating-  plate, 
and  that  which  is  least  attacked  the  negative  or  collecting  plate.  The  posi- 
tive metal  determines  the  direction  of  the  current,  which  proceeds  i?i  the 
liquid  from  the  positive  to  the  negative  plate,  and  out  of  the  liquid  through 
the  connecting  wire  from  the  negative  to  the  positive  plate. 

In  speaking  of  the  direction  of  the  current  the  direction  of  the  positive 
electricity  is  always  understood. 

In  the  fundamental  experiment,  not  only  the  connecting  wire,  but  also  the 
liquid  and  the  plates  arc  traversed  by  the  electrical  current — are  the  scene 
of  electrical  actions. 

The  mere  immersion  of  two  different  metals  in  a  liquid  Is  not  alone 
sufficient  to  produce  a  current  ;  there  must  be  chemical  action.  When  a 
platinum  and  a  gold  plate  are  connected  with  a  delicate  galvanometer,  and 
immersed  in  pure  nitric  acid,  no  current  is  produced  ;  but  on  adding  a  drop 
of  hydrochloric  acid  a  strong  current  is  excited,  which  proceeds  in  the  liquid 
from  the  gold  to  the  platinum,  because  the  gold  is  attacked  by  the  nitro- 
hydrochloric  acid,  while  the  platinum  is  less  so,  if  at  all. 

As  a  voltaic  current  is  produced  whenever  two  metals  are  placed  in 
metallic  contact  in  a  liquid  which  acts  more  powerfully  upon  one  than  upon 
the  other,  there  is  a  great  choice  in  the  mode  of  producing  such  currents. ' 
In  reference  to  their  electrical  deportment,  the  metals  have.been  arranged  in 
what  is  called  an  elcctroniotive  series^  in  which  the  most  electropositive  are 
at  one  end,  and  the  most  electro?tegative  at  the  other.  Hence  when  any  two  of 
these  are  placed  in  contact  in  dilute  acid,  the  current  in  the  connecting  wire 
proceeds  from  the  one  lower  in  the  list  to  the  one  higher.  The  principal 
metals  are  as  follows  : — 

1.  Zinc  5.   Iron  10.  Silver 

2.  Cadmium  6.  Nickel  11.  Gold 

3.  Tin  7.  Bismuth  12.  Platinum 

4.  Lead  8.  Antimony  13.  Graphite 

9.  Copper 

It  will  be  seen  that  the  electrical  deportment  of  any  metal  depends  on  the 
metal  with  which  it  is  associated.  Iron,  for  example,  in  dilute  sulphuric  acid 
is  electronegative  towards  zinc,  but  is  electropositive  towards  copper  ;  copper 
in  turn  is  electronegative  towards  iron  and  zinc,  but  is  electropositive  towards 
silver,  platinum,  or  graphite. 

802.  Electromotive  force. — The  force  in  virtue  of  which  continuous 
electrical  effects  are  produced  throughout  a  circuit  consisting  of  two  metals 
in  metallic  contact  in  a  liquid  which  acts  unequally  upon  them,  is  usually 
called  the  electromotive  force.  Electromotive  force  and  difference  of  potentials 
are  commonly  used  in  the  same  sense.  It  is,  however,  more  correct  to  regard 
difference  of  potentials  as  a  particular  case  of  electromotive  force  ;  for  as  we 
shall  afterwards  see,  there  are  cases  in  which  electrical  currents  are  pro- 
duced without  the  occurrence  of  that  particular  condition  which  we  have  called 
difference  of  potentials.  The  electromotive  force  is  greater  in  proportion  to 
the  distance  of  the  two  metals  from  one  another  in  the  series.     I'hat  is  to 


776 


Dynamical  Electricity. 


[802- 


/ 

say,  it  is  greater  the  greater  the  difference  between  the  chemical  action  upon 
the  two  metals  immersed.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  greater  than  that  between  zinc  and  iron,  or  between  zinc  and 
copper.  The  law  extablished  by  experiment  is,  that  the  electromotive  force 
between  any  two  metals  is  equal  to  the  sum  of  the  electromotive  forces  between 
all  the  intervening  metals.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  equal  to  the  sum  of  the  electromotive  forces  between  zinc  and 
iron,  iron  and  copper,  and  copper  and  platinum. 

The  electromotive  force  is  influenced  by  the  condition  of  the  metal  ; 
rolled  zinc,  for  instance,  is  negative  towards  cast  zinc.  It  also  depends  on 
the  degree  of  concentration  of  the  liquid  ;  in  dilute  nitric  acid  zinc  is  positive 
towards  tin,  and  mercury  positive  towards  lead  ;  while  in  concentrated  nitric 
acid  the  reverse  is  the  case,  mercury  and  zinc  being  respectively  electro- 
negative towards  lead  and  tin. 

The  nature  of  the  liquid  also  influences  the  direction  of  the  current.  If 
two  plates,  one  of  copper  and  one  of  iron,  are  immersed  in  dilute  sulphuric 
acid,  a  current  is  set  up  proceeding  through  the  liquid  from  the  iron  to  the 
copper ;  but  if  the  plates,  after  being  washed,  are  placed  in  solution  of 
potassium  sulphide,  a  current  is  produced  in  the  opposite  direction — the 
copper  is  now  the  positive  metal.  Other  examples  may  be  drawn  from  the 
following  table,  which  shows  the  electric  deportment  of  the  principal  metals 
with  three  different  liquids.  It  is  arranged  like  the  preceding  one  ;  each 
metal  being  electropositive  towards  any  one  lower  in  the  list,  and  electro- 
negative towards  any  one  higher. 


Caustic  potass 

Zinc 

Tin 

Cadmium 

Antimony 

Lead 

Bismuth 

Iron 

Copper 

Nickel 

Silver 


Sulphide  of 
potassium 

Zinc 

Copper 

Cadmium 

Tin 

Silver 

Antimony 

Lead 

Bismuth 

Nickel 

Iron 


Hydrochloric  acid 

Zinc 

Cadmium 

Tin 

Lead 

Iron 

Copper 

Bismuth 

Nickel 

Silver 

Antimony . 

voltaic  current  may  also  be  produced  by  means  of  two  liquids  and 
_  one  metal.  This  may  be  shown  by  the  following 
experiment : — In  a  beaker  containing  strong  nitric 
acid  is  placed  a  small  porous  pot  (fig.  743),  con- 
taining strong  solution  of  caustic  potass.  If  now 
two  platinum  wires  connected  with  the  two  ends 
of  a  galvanometer  (821)  are  immersed  respectively 
in  the  alkali  and  in  the  acid,  a  voltaic  current  is 
produced,  proceeding  in  the  wire  from  the  nitric 
acid  to  the  potass,  which  thus  correspond  re- 
s])ectively  to  the  negative  and  positive  plates  in 
ordinary  couples. 
A  metal  which  is  acted  upon  by  a  liquid  can  be  protected  from  solution 


Fifi. 


-804]  Voltaic  Pile.      Voltaic  Battery.  777 

by  placing  in  contact  with  it  a  more  electropositive  metal,  and  thus  forming 
a  simple  voltaic  circuit.  This  principle  is  the  basis  of  Davy's  proposal  to 
protect  the  copper  sheathings  of  ships,  which  are  rapidly  acted  upon  by  sea- 
water.  If  zinc  or  iron  be  connected  with  the  copper,  these  metals  are  dis- 
solved and  the  copper  protected.  Davy  found  that  a  piece  of  zinc  the  size 
of  a  nail  was  sufficient  to  protect  a  surface  of  forty  or  fifty  square  inches  ; 
unfortunately  the  proposal  has  not  been  of  practical  value,  for  the  copper 
must  be  attacked  to  a  certain  extent  to  prevent  the  adherence  of  marine 
plants  and  shellfish. 

803.  Poles  and  electrodes.— If  the  wire  connecting  the  two  terminal 
plates  of  a  voltaic  couple  be  cut,  it  is  clear,  from  what  has  been  said  about 
the  origin  and  direction  of  the  current,  that  positive  electricity  will  tend  to 
accumulate  at  the  end  of  the  wire  attached  to  the  copper  or  negative  plate, 
and  negative  electricity  on  the  wire  attached  to  the  zinc  or  positive  plate. 
These  terminals  have  been  called  the  poles  of  the 
battery.  For  experimental  purposes,  more  especi- 
ally in  the  decomposition  of  salts,  plates  of  platinum 
are  attached  to  the  ends  of  the  wires.  Instead  of  the 
term  poles,  the  word  electrode  (t'j^eKTpoi',  and  686s,  a 
way)  is  now  commonly  used  ;  for  these  are  the  ways 
through  which  the  respective  electricities  emerge.  It 
is  important  not  to  confound  the  positive  plate  with 
the  positive /^/^  or  electrode.  The  positive  electrode 
is  that  connected  with  the  negative  plate,  while  the 
negative  electrode  is  connected  with  the  positive  plate. 

804.  Voltaic  pile.  Voltaic  battery. — When  a 
series  of  voltaic  elements  or  pairs  is  arranged  so 
that  the  zinc  of  one  element  is  connected  with  the 
copper  of  another,  the  zinc  of  this  with  the  copper 
of  another,  and  so  on,  the  arrangement  is  called  a 
voltaic  battery  ;  and  by  its  means  the  effects  pro- 
duced by  a  single  element  are  capable  of  being  very 
greatly  increased. 

The  earliest  of  these  arrangements  was  devised  by 
Volta  himself.  It  consists  (fig.  744)  of  a  series  of  discs 
piled  one  over  the  other  in  the  following  order  : — At 
the  bottom,  on  a  frame  of  wood,  is  a  disc  of  copper, 
then  a  disc  of  cloth  moistened  by  acidulated  water,  or 
by  brine,  then  a  disc  of  zinc  ;  on  this  a  disc  of  copper,  ^ 
and  another  disc  of  moistened  cloth,  to  which  again 
follow  as  many  sets  of  copper-cloth-zinc,  always  in  the 
same  order,  as  may  be  convenient,  the  highest  disc 
being  of  zinc.     The  discs  are  kept  in  a  vertical  position  by  glass  rods. 

It  will  be  readily  seen  that  we  have  here  a  series  of  simple  voltaic  couples, 
the  moisture  in  the  cloth  acting  as  the  Iic|uid  in  the  cases  already  mentioned, 
and  that  the  terminal  zinc  is  the  negative  and  the  terminal  copper  the 
positive  pole.  From  the  mode  of  its  arrangement,  and  from  its  discoverer, 
the  apparatus  is  known  as  the  voltaic  pile,  a  term  applied  to  all  apparatus  of 
this  kind  for  accumulating  the  effects  of  dynamical  electricity. 


Fig.  744. 


yT^ 


Dynamical  Electricity. 


[804- 


The  distribution  of  electricity  in  the  pile  varies  according  as  it  is  in  con- 
nection with  the  earth  by  one  of  its  extremities,  or  as  it  is  insulated  by  being 
placed  on  a  non-conducting  cake  of  resin  or  glass. 

Jn  the  former  case,  the  end  in  contact  with  the  ground  is  neutral,  and  the 
rest  of  the  apparatus  contains  only  one  kind  of  electricity  ;  this  is  negative 
if  the  copper  disc,  and  positive  if  the  zinc  disc,  is  in  contact  with  the  ground. 

In  the  insulated  pile  the  electricity  is  not  uniformly  distributed.  By 
means  of  a  proof-plane  and  electroscope  it  may  be  demonstrated  that  the 
middle  part  is  in  a  neutral  state,  and  that  one-half  is  charged  with  positive 
and  the  other  with  negative  electricity,  the  potential  increasing  from  the 
middle  to  the  ends.  The  half  terminated  by  a  zinc  disc  is  charged  with  nega- 
tive electricity,  and  that  by  a  copper  with  positive  electricity.  The  pile  is 
thus  similar  to  a  charged  Leyden  jar  ;  with  this  difference,  however,  that 
when  the  jar  has  been  discharged  by  connecting  its  two  coatings,  the  elec- 
trical effects  cease  ;  while  in  the  case  of  the  pile,  the  cause  which  originally 
brought  about  the  distribution  of  electricity  restores  this  state  of  charge  after 
the  discharge  ;  and  the  continuous  succession  of  charges  and  discharges 
forms  the  current.     The  effects  of  the  pile  will  be  discussed  in  other  places. 

805.  -Wollaston's  battery. — The  original  form  of  the  voltaic  pile  has  a 
great  many  inconveniences,  and  possesses  now  only  an  historical  interest. 


Fig.  745- 


It  has  received  a  great  many  improvements,  the  principal  object  of  which 
has  been  to  facilitate  manipulation,  and  to  produce  greater  electromotive  ^ 
force. 

One  of  the  earliest  of  these  modifications  was  the  crown  of  cups,  or 
coiironiie  des  tasscs,  invented  by  Volta  himself.  An  improved  form  of  this  is 
known  as  Wollastons  battery  (fig.  745)  ;  it  is  arranged  so  that  when  the 
current  is  not  wanted,  the  action  of  the  battery  can  be  stopped. 

The  plates  Z  are  of  thick  rolled  zinc,  and  usually  about  eight  inches  in 
length  by  six  in  breadth.     The  copper  plates,  C,  are  of  thin  sheet,  and  bent 


-806]  Enfccblenient  of  the  Current  in  Batteries.  779 

so  as  to  surround  the  zincs  without  touching  them,  contact  being  prevented 
by  small  pieces  of  cork.  To  each  copper  plate  a  narrow  strip  of  copper,  <?, 
is  soldered,  which  is  bent  twice  at  right  angles  and  is  soldered  to  the  next 
zinc  plate  ;  and  the  first  zinc,  Z,  is  surrounded  by  the  first  copper  C  ;  these 
two  constitute  a  couple,  and  each  couple  is  immersed  in  a  glass  vessel,  con- 
taining acidulated  water.  The  copper,  C,  is  soldered  to  the  second  zinc  by 
the  strip  o,  and  this  zinc  is  in  turn  surrounded  by  a  second  copper,  and  so  on. 

Fig.  745  represents  a  pile  of  sixteen  couples  united  in  two  parallel  series 
of  eight  each.  All  these  couples  are  fixed  to  a  cross  frame  of  wood,  by  which 
they  can  be  raised  or  lowered  at  pleasure.  When  the  battery  is  not  wanted, 
the  couples  are  lifted  out  of  the  liquid.  The  water  in  these  vessels  is  usually 
acidulated  with  j^^  sulphuric  and  ^^  nitric  acid. 

Hare's  dcjlagrator. — This  is  a  simple  voltaic  arrangement,  consisting  of 
two  large  sheets  of  copper  and  zinc  rolled  together  in  a  spiral,  but  preserved 
from  direct  contact  by  bands  of  leather  or  horsehair.  The  whole  is  immersed 
in  a  vessel  containing  acidulated  water,  and  the  two  plates  are  connected 
outside  the  liquid  by  a  conducting  wire. 

806.  Enfeeblement  of  the  current  in  batteries.  Secondary  currents. 
The  various  batteries  already  described — ^'olta's,  Wollaston's,  and  Hare's, 
which  consist  essentially  of  two  metals  and  one  liciuid— labour  under  the 
objection  that  the  currents  produced  rapidly  diminish  in  strength. 

This  is  due  principally  to  three  causes  :  the  first  is  the  decrease  in  the 
chemical  action  owing  to  the  neutralisation  of  the  sulphuric  acid  by  its  com- 
bination with  the  zinc.  This  is  a  necessary  action,  for  upon  it  depends  the 
current ;  it  therefore  occurs  in  all  batteries,  and  is  without  remedy  except  by 
replacement  of  acid  and  zinc.  The  second  is  due  to  what  is  called  local 
action  ;  that  is,  the  production  of  small  closed  circuits  in  the  active  metal, 
owing  to  the  impurities  it  contains.  These  local  currents  rapidly  wear  away 
the  active  plate,  without  contributing  anything  to  the  continuance  of  the 
general  current.  They  are  remedied  by  amalgamating  the  zinc  with  mercury, 
by  which  chemical  action  is  prevented  until  the  circuit  is  closed,  as  will  be 
more  fully  explained  (816).  The  third  arises  from  the  production  of  an 
inverse  electromotive  force,  which  tends  to  produce  a  current  in  a  contrary 
direction  to  the  principal  current,  and  therefore  to  destroy  it  either  totally 
or  partially.  In  the  fundamental  experiment  (fig.  742),  when  the  circuit  is 
closed,  zinc  sulphate  is  formed,  which  dissolves  in  the  licjuid,  and  at  the 
same  time  a  layer  of  hydrogen  gas  is  gradually  formed  on  the  surface  of  the 
copper  plate.  This  diminishes  the  activity  of  the  combination  in  more  than 
one  way.  In  the  first  place,  it  interferes  with  the  contact  between  the  metal 
and  the  liquid  ;  in  the  second  place,  in  proportion  as  the  copper  becomes 
coated  with  hydrogen,  we  have  virtually  a  plate  of  hydrogen  instead  of  a 
plate  of  copper  opposed  to  the  zinc,  and  in  addition,  the  hydrogen,  by  react- 
ing on  the  zinc  sulphate,  which  accumulates  in  the  liquid,  gradually  causes  a 
deposition  of  zinc  on  the  surface  of  the  copper  ;  hence,  instead  of  having 
two  different  metals  unequally  attacked,  the  two  metals  become  gradually 
lees  different,  and,  consequently,  the  total  effect  and  the  current  become 
weaker  and  weaker. 

The  polarisation  of  the  plate  (as  this  phenomenon  is  termed)  may  be 
destroyed  by  breaking  the  circuit  and  exposing  the  copper  plate  to  the  air  ; 


78o 


Dynamical  Electricity. 


[806- 


the  deposited  hydrogen  is  thus  more  or  less  completely  got  rid  of,  and  on 
again  closing  the  circuit  the  current  has  nearly  its  original  strength.  The 
same  result  is  obtained  when  the  current  of  another  battery  is  transmitted 
through  the  battery  in  a  direction  opposite  to  that  of  the  first. 

_  When  platinum  electrodes  are  used 

to  decompose  water,  a  similar  pheno- 
menon is  produced,  called ^cJA^r/^a/ztfiw 
of  tJte  electrodes,  which  may  be  illus- 
trated by  an  arrangement  represented 
in  fig.  746,  in  which  B  is  a  constant 
element,  V  a  voltameter  (846),  G  a 
galvanometer  (821),  and  H  a  mercury 
cup.  The  wire  L  being  disconnected 
from  H,  a  current  is  produced  in  the 
voltameter,  the  direction  of  which  is 
from  P  to  P' ;  if  now  the  wire  F  be 
detached  from  H,  and  L  be  connected  therewith,  a  current  is  produced 
through  the  galvanometer  the  direction  of  which  is  from  P'  to  P  ;  that  is,  the 
opposite  of  that  which  the  element  had  previously  produced.  Becquerel  and 
Faraday  have  shown  that  this  polarisation  of  the  metals  results  from  the 
deposits  caused  by  the  passage  of  the  current,  and  an  important  application 
of  this  phenomenon  will  be  found  described  farther  on  (849). 


Fi?.  740. 


CONSTANT  CURRENTS. 

807.  Constant  currents. — With  few  exceptions,  batteries  composed  of 
elements  with  a  single  liquid  have  almost  gone  out  of  use,  in  consequence 
of  the  rapid  enfeeblemcnt  of  the  current  produced.  They  have  been  replaced 
l^y  batteries  with  two  liquids,  which  are  called  constant  batteries  because 
their  action  continues  without  material  alteration  for  a  considerable  period 
of  time.  The  essential  point  to  be  attended  to  in  securing  a  constant  current 
is  to  prevent  the  polarisation  of  the  inactive  metal ;  in  other  words,  to  hinder 
any  permanent  deposition  of  hydrogen  on  its  surface.  This  is  eflTected  by 
placing  the  inactive  metal  in  a  liquid  upon  which  the  deposited  hydrogen 
tan  act  chemically 

80S.  Baniell's  battery. — This  was  the  first  form  of  the  constant  batteiy, 
and  was  invented  by  Daniell  in  the  year  1836.  As  regards  the  constancy 
of  its  action,  it  is  perhaps  still  the  best  of  all  constant  batteries.  P'ig.  747 
represents  a  single  element.  A  glass  or  porcelain  vessel,  V,  contains 
a  saturated  solution  of  copper  sulphate,  in  which  is  immersed  a  copper 
cylinder,  (i,  open  at  both  ends,  and  perforated  by  holes.  At  the  upper  part 
of  this  cylinder  there  is  an  annular  shelf,  (1,  also  perforated  by  small  holes, 
and  below  the  level  of  the  solution  ;  this  is  intended  to  support  crystals  of 
copper  sulphate  to  replace  that  decomposed  as  the  electrical  action  pro- 
ceeds. Inside  the  cylinder  is  a  thin  porous  vessel,  P,  of  unglazed  earthen- 
ware. This  contains  either  water,  or  solution  of  common  salt,  or  dilute 
sulphuric  acid,  in  which  is  placed  the  cylinder  of  amalgamated  zinc,  Z.  Two 
thin  strips  of  copper/  and  //,  fixed  by  binding  screws  to  the  copper  and  to 
the  zinc,  serve  for  connecting  the  elements  in  series. 


-809] 


Grove's  Battery. 


781 


Fig.  747. 


When  a  DanielFs  element  is  closed,  the  hydrogen  resulting  from  the 
action  of  the  dilute  acid  on  the  zinc  is  liberated  on  the  surface  of  the  copper 
plate,  but  meets  there  the  copper  sulphate,  which  is  reduced,  forming  sul- 
phuric acid  and  metallic  copper,  which  is  deposited  on  the  surface  of  the 
copper  plate.  In  this  way  copper  sulphate  in 
solution  is  taken  up  ;  and  if  it  were  all  con- 
sumed, hydrogen  would  be  deposited  on  the 
copper,  and  the  current  would  lose  its  con- 
stancy. This  is  prevented  by  the  crystals  of 
copper  sulphate  which  keep  the  solution  satu- 
rated. The  sulphuric  acid  produced  by  the 
decomposition  of  the  sulphate  permeates  the 
porous  cylinder,  and  tends  to  replace  the  acid 
used  by  its  action  on  the  zinc  ;  and  as  the 
quantity  of  sulphuric  acid  formed  in  the  solu- 
tion of  copper  sulphate  is  regular,  and  propor- 
tional to  the  acid  used  in  dissolving  the  zinc,  the 
action  of  this  acid  on  the  zinc  is  regular  also,  and 
thus  a  constant  current  is  produced. 

In  order  to  join  together  several  of  these 
elements  to  form  a  battery,  the  zinc  of  one  is  connected  either  by  a  copper 
wire  or  strip  with  the  copper  of  the  next,  and  so  on  from  one  element  to 
another,  as  shown  in  fig.  751,  for  another  kind  of  battery. 

Instead  of  a  porous  earthenware  vessel,  a  bag  of  sailcloth  may  be  used 
for  the  diaphragm  separating  the  two  liquids.  The  effect  is  at  first  more 
powerful,  but  the  two  solutions  mix  more  rapidly,  which  weakens  the  current. 
The  object  of  the  diaphragm  is  to  allow  the  current  to  pass,  but  to  prevent 
as  much  as  possible  the  mixture  of  the  two  liquids. 

The  current  produced  by  a  Daniell's  battery  is  constant  for  some  hours  ; 
its   action   is    stronger  when    it    is 
placed  in  hot  water.      Its  electro- 
motive force  is  about  i  -08  volt. 

809.  Grove's  battery. — In  this 
battery  the  copper  sulphate  solution 
is  replaced  by  nitric  acid,  and  the 
copper  by  platinum,  by  which 
greater  electromotive  force  is  ob- 
tained. Fig.  748  represents  one 
of  the  forms  of  a  couple  of  this 
battery.  It  consists  of  a  glass 
vessel.  A,  partially  filled  with  dilute 
sulphuric  acid  (i  :  8) ;  of  a  cyhnder 
of  zinc,  Z,  open  at  both  ends  ;  of  a 
vessel,  \\  made  of  porous  earthen- 
ware, and  containing  ordinary  nitric 
acid;  of  a  plate  of  platinum,  P  (fig.  749),)  bent  in  the  form  of  an  S,  and  fixed 
to  a  cover,  c,  which  rests  on  the  porous  vessel.  The  platinum  is  con- 
nected with  a  binding  screw,  (5,  and  there  is  a  similar  binding  screw  on  the 
zinc.     In  this  battery  the  hydrogen,  which   would  be  disengaged  on  the 


^VJ 


Fig.  748. 


782 


Dynamical  Electricity. 


[809- 


platinum,  meeting,'-  the  nitric  acid,  decomposes  it,  forming  hyponitrous  acid, 
which  dissolves,  or  is  disengaged  as  nitrous  fumes.  Grove's  battery  is  the 
most  convenient,  and  one  of  the  most  powerful  of  the  two  fluid  batteries. 
It  is,  however,  expensive,  owing  to  the  high  price  of  platinum;  besides 
v/hich  the  platinum  is  liable,  after  some  time,  to  become  brittle  and  break 
very  easily.  But  as  the  platinum  is  not  consumed,  it  retains  most  of  its 
value,  and  when  the  plates  which  have  been  used  in  a  battery  are  heated  to 
redness  they  regain  their  elasticity. 

8io.  Bunsen's  battery .^ — Bunsen's,  also  known  as  the  sine  carbon 
battery,  was  invented  in  1843  ;  it  is  in  effect  a  Grove's  battery,  where 
the  plate  of  platinum  is  replaced  by  a  cylinder  of  carbon.  This  is  made 
either  of  the  graphitoidal  carbon  deposited  in  gas  retorts,  or  by  calcining 
in  an  iron  mould  an  intimate  mixture  of  coke  and  bituminous  coal,  finely 
powdered  and  strongly  compressed.  Both  those  modifications  of  carbon 
are  good  conductors.  Each  element  consists  of  the  following  parts  :  i,  a 
vessel,  F  (fig.  750),  either  of  stoneware  or  of  glass,  containing  dilute  sul- 
phuric acid ;  2,  a  hollow  cylinder,  Z,  of  amalgamed  zinc  ;  3,  a  'porous 
vessel,  V,  in  which  is  ordinary  nitric  acid  ;  4,  a  rod  of  carbon,  C,  prepared 


t'ig-  75 


in  the  above  manner.  In  the  vessel  F  the  zinc  is  first  placed,  and  in  it  the 
carbon  C  in  the  porous  vessel  V  as  seen  in  P.  To  the  carbon  is  fixed  a 
binding  screw,  /;/,  to  which  a  copper  wire  is  attached,  forming  the  positive 
pole.  The  zinc  is  provided  with  a  similar  binding  screw,  ;/,  and  wire,  which 
is  thus  a  negative  pole. 

A  single  cell  of  the  ordinary  dimensions,  20  cm.  in  height  and  9  cm.  in 
diameter,  has  a  resistance  of  about  o"i4  ohm,  and  taking  its  E.M.F.  at  r82 
(814),  gives  a  current  of  12  to  13  amperes  when  on  short  circuit,  that  is, 
when  it  is  closed  without  measurable  external  resistance. 

The  elements  are  arranged  to  form  a  battery  (fig.  751)  by  connecting  each' 
carbon  to  the  zinc  of  the  following  one  by  means  of  the  clamps  w//,  and  a 
strip  of  copper,  c,  represented  in  the  top  of  the  figure.  The  copper  is  pressed 
at  one  end  between  the  carbon  and  the  clamp,  and  at  the  other  it  is  soldered 
to  the  clamp  ti,  which  is  fitted  on  the  zinc  of  the  following  element,  and  so 
forth.  The  clamp  of  the  first  carbon  and  that  of  the  last  zinc  are  alone 
provided  with  binding  screws,  to  which  are  attached  the  wires. 


-811]  Since  s  Battery.  783 

The  chemical  action  of  Bunsen's  battery  is  the  same  as  that  of  Grove's, 
and  being  equally  powerful,  while  less  costly,  is  very  generally  used  on  the 
Continent.  But  though  its  first  cost  is  less  than  that  of  Grove's  battery,  it 
is  more  expensive  to  work,  and  is  not  so  convenient  to  manipulate. 


Vig.  751. 

Callaiis  battery  is  a  modified  form  of  Grove's.  Instead  of  zinc  and  plati- 
num, zinc  and  platinised  lead  are  used  ;  and  instead  of  pure  nitric  acid  Callan 
used  a  mixture  of  sulphuric  acid,  nitric  acid,  and  saturated  solution  of  nitre. 
The  batter)^  is  said  to  be  equal  in  its  action  to  Grove's,  and  is  much  cheaper. 

Callan  has  also  constructed  a  battery  in  which  zinc  in  dilute  sulphuric 
acid  forms  the  positive  plate,  and  cast  iron  in  strong  nitric  acid  the  negative. 
Under  these  circumstances  the  iron  becomes  passive  ;  it  is  strongly  electro- 
negative, and  does  not  dissolve.  If,  however,  the  nitric  acid  becomes  too 
weak,  the  iron  is  dissolved  with  simultaneous  disengagement  of  nitrous  fumes. 

After  being  in  use  some  time,  all  the  batteries  in  which  the  polarisation 
is  prevented  by  nitric  acid  disengage  nitrous  fumes  in  large  quantities,  and 
this  is  a  serious  objection  to  their  use,  especially  in  closed  rooms.  To  pre- 
vent this,  nitric  acid  is  frequently  replaced  by  chromic  acid,  or,  better,  by  a 
mixture  of  4  parts  potassium  bichromate,  4  parts  sulphuric  acid,  and  18 
water.  The  liberated  hydrogen  reduces  the  chromic  acid  to  the  state  of 
oxide  of  chromium,  which  remains  dissolved  in  sulphuric  acid.  With  the 
same  view,  sesquichloride  of  iron  is  sometimes  substituted  for  nitric  acid  ; 
it  becomes  reduced  to  protochloride.  But  the  action  of  the  elements  thus 
modified  is  considerably  less  than  when  nitric  acid  is  used,  owing  to  the 
increased  resistance. 

811.  Smee's  battery, — In  this  battery  the  polarisation  of  the  negative 
plate  is  prevented  by  mechanical  means.  Each  element  consists  of  a  sheet  of 
platinum  placed  between  two  vertical  plates  of  zinc,  as  in  Grove's  battery  ; 
but  as  there  is  only  a  single  liquid,  dilute  sulphuric  acid,  the  elements  have 
much  the  form  of  those  in  Wollaston's  battery.  The  adherence  of  hydrogen 
to  the  negative  plate  is  prevented  by  covering  the  platinum  with  a  deposit  of 
finely  divided  platinum.  In  this  manner  the  surface  is  roughened,  which 
facilitates  the  disengagement  of  hydrogen  to  a  remarkable  extent,  and  con- 


784 


Dynamical  Electricity. 


[811- 


sequently  diminishes  the  resistance  of  a  couple.  Instead  of  platinum,  silver 
coveied  with  a  deposit  of  finely  divided  platinum  is  frequently  substituted, as 
being  cheaper. 

Walker'' s  battery. — This  resembles  Smee's  battery,  but  the  electronegative 
plate  is  either  gas  graphite  or  platinised  graphite  ;  it  is  excited  by  dilute 
sulphuric  acid.  This  battery  is  used  in  all  the  stations  of  the  South-Eastern 
Railway  ;  it  has  considerable  electromotive  force^is  convenient  and  economi- 
cal in  manipulation,  and  large-sized  elements  can  be  constructed  at  a  cheap  rate. 

812.  Kecent  batteries. — The  mercury  sulpJiate  battery  (fig.  752)  de- 
vised by  Marie  Davy,  is  essentially  a  zinc-carbon  element,  but  of  smaller 
dimensions  than  those  elements  usually  are.  In  the  outer  vessel,  \\  ordi- 
nary water  or  brine  is  placed,  and  in  the  porous  vessel  mercury  sulphate. 
This  salt  is  agitated  with  about  three  times  its  volume  of  water,  in  which  it  is 
difficultly  soluble,  and  the  liquid  poured  off  from  the  pasty  mass.  The  carbon 
being  placed  in  the  porous  vessel,  the  spaces  are  filled  with  the  residue,  and 
then  the  decanted  liquor  poured  into  it. 

Chemical  action  takes  place  when  the  cell  is  closed.  The  zinc  then 
decomposes  the  water,  liberating  hydrogen,  which,   traversing   the  porous 


rorff^ra 


I*'ig.  752-  l''K-  7.rv  Fig.  754. 

vessel,  reduces  the  mercury  sulphate,  forming  metallic  mercury,  which  collects 
at  the  iDOttom  of  the  vessel,  while  the  sulphuric  acid  formed  at  the  same  time 
traverses  the  diaphragm  to  act  on  the  zinc,  and  thus  increases  the  action. 

The  mercury  which  is  deposited  may  be  used  to  prepare  a  quantity  of 
sulphate  equal  to  that  which  has  been  consumed.  A  small  quanti  ty  of  the 
solution  of  mercury  sulphate  may  also  pass  through  the  diaphragm  ;  but  this 
is  rather  advantageous,  as  its  effect  is  to  amalgamate  the  zinc. 

The  electromotive  force  of  this  element  is  about  a  quarter  greater  than  that 
of  Danicll's  clement,  but  it  has  greater  resistance  ;  it  is  rapidly  exhausted 
when  continuously  worked,  though  it  appears  well  suited  for  discontinuous 
work,  as  with  the  telegraph,  and  with  alarums. 

Gravity  batteries. — The  use  of  porous  \essels  is  open  to  many  objections, 
more  especially  in  the  case  of  Daniell's  battery,  in  which  they  gradually 
become  encrusted  with  copper,  which  destroys  them.  A  kind  of  battery  has 
been  devised  in  which  the  porous  vessel  is  entirely  dispensed  with,  and  the 
separation  of  the  liquids  is  effected  by  the  difference  of  density.  Such 
batteries  are  called  gravity  battel ics.     Fig.  753  represents  a  form  dc\ised 


-812 j  Recent  Batteries.  785 

by  Callaud.  V  is  a  glass  or  earthenware  vessel  in  which  is  a  copper  plate 
soldered  to  a  wire  insulated  by  gutta-percha.  On  the  plate  is  a  layer  of  crys- 
tals of  copper  sulphate,  C  ;  the  whole  is  then  filled  with  water,  and  the  zinc 
cylinder,  Z,  is  immersed  in  it.  The  lower  part  of  the  liquid  becomes  saturated 
with  copper  sulphate  ;  the  action  of  the  battery  is  that  of  a  Daniell,  and  the  zinc 
sulphate  which  gradually  forms,  floats  on  the  solution  of  copper  sulphate  owing 
to  its  lower  density.  This  battery  is  easily  manipulated,  the  consumption  of 
copper  sulphate  is  economical,  and  when  not  agitated  it  works  constantly  for 
some  time,  provided  care  be  taken  to  replace  the  water  lost  by  evaporation. 

Meidingcr's  element,  which  is  much  used  in  Germany,  is  essentially  a 
gravity  battery  of  special  construction,  with  zinc  in  solution  of  magnesium 
sulphate,  and  copper  in  solution  of  copper  sulphate. 

Mhwttds  battery. — This  may  be  described  as  a  Daniell's  element,  in 
which  the  porous  vessel  is  replaced  by  a  layer  of  sawdust  or  of  sand.  At 
the  bottom  of  an  earthenware  vessel  (fig.  754)  is  placed  a  layer  of  coarsely- 
powdered  copper  sulphate  «,  and  on  this  a  copper  plate  provided  with  an 
insulated  copper  wire  i.  On  this  there  is  a  layer  of  sand  or  of  sawdust  be, 
and  then  the  whole  is  filled  with  water,  in  which  rests  a  zinc  cylinder  Z. 
The  action  is  just  that  of  a  Daniell ;  the  sawdust  prevents  the  mixture  of  the 
liquids,  but  it  also  offers  great  resistance,  which  increases  with  its  thickness. 
From  its  simplicity  and  economy,  and  the  facility  with  which  it  is  constructed, 
the  battery  merits  increased  attention. 

Dc  la  Rue  and  Mailer's  element  consists  of  a  glass  tube  about  6  inches 
long  by  075  inch  in  diameter,  closed  by  a  vulcanised  india-rubber  stopper 
through  which  passes  a  zinc  rod  o-i8  inch  in  diameter  and  5  inches  long. 
A  flattened  silver  wire  also  passes  through  the  stopper  to  the  bottom  of  the 
tube,  in  which  is  placed  about  half  an  ounce  of  silver  chloride,  the  greater 
part  of  the  cell  being  filled  with  solution  of  sal-ammoniac.  The  hydrogen 
evolved  at  the  negative  plate  reduces  the  chloride  to  metallic  silver,  which 
is  thereby  recovered.  Since  there  is  only  one  liquid,  and  the  solid  electro- 
lyte is  not  acted  upon  when  the  circuit  is  open,  the  element  is  easily  worked 
and  requires  little  attention.  It  is  very  compact,  1,000  elements  occupying 
a  space  of  less  than  a  cubic  yard  ;  De  la  Rue  and  Miiller  have  used  as  many 
as  14,400  such  cells  in  investigations  on  the  stratification  of  the  electric  light. 
A  battery  of  8,040  of  these  cells  gave  a  spark  \  of  an  inch  in  length  in  air 
under  the  ordinary  atmospheric  pressure  ;  while  under  a  pressure  of  a  cjuarter 
of  an  atmosphere  the  striking  distance  was  i^_  inch. 

The  electromotive  force  of  a  silver  chloride  cell  is  1-03  of  a  volt,  and  that 
of  one  made  with  silver  bromide  is  0-908  ;  hence  a  series  of  4  cells,  three  of 
the  silver  chloride  cells  with  one  of  bromide,  gives  an  average  electromotive 
force  of  I  volt  (814). 

Latimer  Clark's  element  consists  of  perfectly  pure  mercury  as  a  negati\e 
plate  covered  with  a  paste  obtained  by  boiling  sulphateof  mercury  in  a  satu- 
rated solution  of  zinc  sulphate.  The  positive  metal  is  a  plate  of  zinc  resting  on 
this  paste  of  sulphate.  Insulated  wire?,  leading  to  the  mercury  and  the  zinc 
respectively,  form  the  connections.  This  battery  is  not  well  adapted  for 
continuous  work,  but  it  furnishes  a  standard  of  electromotive  force,  which  is 
constant  and  can  be  relied  upon.  Its  electromotive  force  is  i"495  volt  at 
15°,  and  it  diminishes  by  0-00078  for  an  increase  of  1°  C. 


786 


Dynamical  Electricity 


[812- 


Fig.  755 


A  convenient  form  of  element  for  many  purposes  is  Xh^  potassium  bichro- 
mate,or, zs  it  is  frequently  teniied,  the  bichromate  of  potass  ^Xttrntnl  (fig.  755). 
It  consists  of  a  zinc  plate  Z,  attached  to  a  brass 
rod,  which  slides  up  and  down  in  a  brass  tube  in  an 
ebonite  or  porcelain  cover,  so  that  it  can  be  wholly 
or  partially  immersed  in  the  liquid.  Two  graphite 
plates,  C  C,  are  similarly  fitted  in  the  cover,  and  by 
means  of  strips  of  brass  the  carbon  and  the  zinc 
plates  are  respectively  in  connection  with  the  binding 
IJJJHJI  jll  screws,    which   thus    form   the   poles.      The   exciting 

|H|i  I  liquid  is  a  mixture  of  i  part  of  potassium  bichromate, 

JIMA  "V  -  of  sulphuric  acid,  and  10  of  water. 

The  electromotive  force  is  about  rS  or  1-9  that 
of  a  Daniell  ;  when  the  element  is  closed  by  a  wire 
of  small  resistance  its  E.M.F.  increases  slightly  at 
first,  then  remains  constant  for  some  time,  after  which 
it  rapidly  sinks  to  half  its  original  amount. 

In  Niaiidefs   eloiietit    a    zinc   cylinder   dips  in    a 

solution  of  common  salt  and  surrounds  a  porous  cell, 

in   which  is   a  carbon  plate  surrounded  by  pieces  of 

carbon  and  filled  with  chloride  of  lime,  which  does  not  act  on  the  zinc  even 

when  the  circuit  is  closed.     The  electromotive  force  is  i  -6  that  of  a  Daniell. 

The  element  of  Lalandc  a?id  Chaperon 

^  is  zinc  in  a  30  per  cent,  solution  of  caustic 

CTn  potass  and  copper  in  contact  with  oxide 

^  of  copper  which  acts  as  depolariser.     The 

E.M.F.  is  0-85  volt,  and  there  is  no  action 
unless  the  circuit  is  closed.  To  prevent 
the  absorption  of  carbonic  acid  the  solu- 
tion is  covered  with  paraffine  oil. 

813.  licclanclie's  element.  —  This 
consists  (fig.  756)  of  a  rod  of  carbon, 
C,  placed  in  a  porous  pot,  which  is  then 
very  tightly  packed  with  a  mixture  of 
pyrolusite  (peroxide  of  manganese)  and 
gas  grajjhite,  M.  This  is  covered  over 
with  a  layer  of  pitch.  At  the  top  of  the 
carbon  is  soldered  a  mass  of  lead,  L,  to 
which  is  affixed  a  binding  screw.  The 
positive  plate  is  a  rod  of  zinc,  Z,  in  which 
is  fixed  a  copper  wire.  The  exciting 
liquid  consists  of  a  strong  solution  of  sal- 
ammoniac,  contained  in  a  glass  vessel  G, 
which  is  not  more  than  one-third  full. 
The  electromotive  force  of  the  element 
is  said  to  be  about  one-third  greater  than  that  of  a  Danicll's  element  ;  its  in- 
ternal resistance  varies  of  course  with  the  size,  but  is  stated  to  be  from  ri  to 
5  times  that  of  an  ohm.  The  battery  is  not  adapted  for  continuous  work 
as  in  heavy  telegraphic  circuits,  or  in  electro-plating,  since  it  soon  becomes 


Fig.  756. 


-814]  Electromotive  Force  of  Different  Elements.  787 

polarised  ;  it  has,  however,  the  valuable  property  of  quickly  regaining  its 
original  strength  when  left  at  rest,  and  is  extremely  well  adapted  for  dis- 
continuous work,  such  as  that  of  electrical  bells. 

A  rod  of  carbon  4|  x  i|  x  y^^  inches  should  have  a  maximum  resistance  of 
I  ohm  ;  but  good  plates  made  from  the  carbon  of  gas  retorts  do  not  average 
more  than  0-5,  and  in  some  cases  o-i  ohm.  If  the  resistance  equals  an  ohm, 
the  conducting  power  of  carbon  is  about  0-003  that  of  mercury. 

A  drawback  to  the  use  of  carbon  is  that,  from  its  porosity,  the  exciting 
liquid  rises,  and  forms  local  currents  at  the  junction  with  the  binding 
screw,  which  injure  or  destroy  contact.  This  may  be  remedied  to  a  very 
great  extent  by  soaking  the  plates  before  use  in  hot  melted  paraffine,  which 
penetrates  into  the  pores,  expelling  the  air.  On  cooling,  it  solidifies  and 
prevents  the  capillaiy  action  mentioned  above.  By  carefully  scraping  the 
paraffine  from  the  outside,  a  surface  is  exposed  which  is  as  good  a  conductor 
as  if  the  pores  were  filled  with  air.  IVIeasurements  have  shown  that  the 
resistance  of  a  rod  thus  prepared  is  not  altered. 

In  a  recent  modification  of  his  element  Leclanche  dispensed  with  the 
porous  cell,  and  placed  the  carbon  plate  C  between  two  similar  flat  prisms, 
made  by  compressing  a  mixture  of  55  parts  of  graphite,  40  parts  of  pyrolusite, 
and  5  parts  of  shellac  in  steel  moulds  at  a  temperature  of  100°  under  a  pressure 
of  300  atmospheres. 

814.  Electromotive  force  of  different  elements. — The  following  num- 
bers represent  the  electromotive  force  of  some  of  the  elements  most  frequently 
used,  compared  with  that  of  an  ordinary  Daniell's  cell  charged  as  above 
described  ;  they  are  the  means  of  many  careful  determinations  : — 

Daniell's  element  .         .     set  up  with  water      .         .         .         .     i-oo 
„  „        .         .     pure  zinc  and  pure  water,  with  pure 

copper  and  pure  saturated  solution 
of  copper  sulphate         .         .         .1-02 
Leclanche's  „        .         .     zinc    in    saturated   solution    of  am- 
monium chloride  .         .         .         .1-32 

Latimer  Clark's  element i  -496 

Bunsen's  „  carbon  in  nitric  acid         .         .         .177 

„  „  carbon  in  chromic  acid     .         .         .1-87 

Grove's  „         platinum  in  nitric  acid      .         .         .182 

The  greatest  electromotive  force  as  yet  observed  is  by  Beetz  in  a  couple 
consisting  of  potassium  amalgam  in  caustic  potash,  combined  with  pyrolusite 
in  a  solution  of  potassium  permanganate.  It  is  three  times  as  much  as  that 
of  a  Daniell's  element. 

The  standard  of  electromotive  force  on  the  C.  G.  S.  system  is  the  Volt. 
This  is  equal  to  1,000,000,000  or  10'  absolute  electromagnetic  units  (709). 
The  volt  is  rather  less  than  the  electromotive  force  of  a  Daniell's  cell,  the 
mean  value  of  which  may  be  taken  at  ro8  volt.  The  unit  of  current,  which 
is  called  an  Ampere,  is  the  current  due  to  an  electromotive  force  of  one  volt 
working  through  a  resistance  of  one  ohm. 

The  Coulomb  is  the  practical  unit  of  electrical  quantity  ;  it  is  that  quantity 
which,  in  a  second,  passes  through  the  section  of  a  conductor  traversed  by 
a  current  of  an  ampere. 

3  E2 


788  Djmamical  Electricity.  [815- 

815.  Comparison  of  the  voltaic  battery  with  a  frictlonal  electrical 
machine. — Except  in  the  case  of  batteries  consisting  of  a  very  large  number 
of  couples,  the  difference  of  potentials  between  the  terminals  is  far  weaker 
than  in  frictional  electrical  machines,  and  is  insufficient  to  give  any  visible 
spark.  With  De  la  Rue  and  Miiller's  great  battery  the  striking  distance 
between  two  terminals  was  found  to  increase  with  the  potential,  but  for  high 
potentials  rather  more  rapidly  than  in  direct  ratio.  Thus  while  the  striking 
distance  was  o'oi2  in.,  with  the  potential  due  to  1,200  of  their  cells,  it  was 
0-049  i"-  with  4,800  cells,  and  0-133  i"-  "^^'ith  11,000  cells. 

In  the  case  of  a  small  battery  or  of  a  single  cell,  very  delicate  tests  are 
required  to  detect  any  signs  of  free  electrification.  But  by  means  of  a  deli- 
cate condensing  electroscope,  and  by  extremely  careful  insulation,  it  can  be 
shown  that  one  pole  possesses  a  positive  and  the  other  a  negative  charge. 
For  this  purpose  one  of  the  plates  of  the  electroscope  is  connected  with 
one  pole,  and  the  other  with  the  other  pole  or  with  the  ground.  The  electro- 
scope thus  becomes  charged,  and  on  breaking  the  connection  electroscopic 
indications  are  observed. 

On  the  other  hand,  the  strength  of  current  which  a  voltaic  element  can 
produce  in  a  good  conductor  is  much  greater  than  that  which  can  be  pro- 
duced by  a  machine.  Faraday  immersed  two  wires — one  of  zinc,  and  the 
other  of  platinum,  each  y^  of  an  inch  in  diameter — in  acidulated  water  for  ~ 
of  a  second.  The  effect  thus  produced  on  a  magnetic  needle  in  this  short 
time  was  greater  than  that  produced  by  23  turns  of  the  large  electrical 
machine  of  the  Royal  Institution. 

Nystrom  has  ascertained  by  quantitative  measurements  that  the  potential 
of  the  charge  of  the  cover  of  an  ordinary  electrophorus  is  not  less  than  50,000 
times  as  great  as  the  potential  of  a  Meidinger's  cell  (812)  ;  that  is,  that  not 
less  than  50,000  of  those  elements  would  be  required  to  produce  the  same 
potential  as  the  electrophorus.  In  practice,  a  far  greater  number  would  be 
needed,  owing  to  the  difficulty  of  getting  good  insulation. 

816.  Amalgamated  zinc.  I.ocal  currents.— Perfectly  pure  distilled 
zinc  is  not  attacked  by  dilute  sulphuric  acid,  but  becomes  so  when  immersed 
in  that  liquid  in  contact  with  a  plate  of  copper  or  of  platinum.  Ordinaiy 
coinmercial  zinc,  on  the  contrary,  is  rapidly  dissolved  by  dilute  acid.  This, 
doubtless,  arises  from  the  impurity  of  the  zinc,  which  always  contains  traces 
either  of  iron  or  lead.  Being  electronegative  towards  zinc,  they  tend  to  pro- 
duce local  electrical  currc?Jts,  which  accelerate  the  chemical  action  without 
increasing  the  quantity  of  electricity  in  the  connecting  wire. 

Zinc,  when  amalgamated,  acquires  the  properties  of  perfectly  pure  zinc, 
and  is  unaltered  by  dilute  acid,  so  long  as  it  is  not  in  contact  with  a  copper 
or  platinum  plate  immersed  in  the  same  liquid.  To  amalgamate  a  zinc  plate, 
it  is  first  immersed  in  dilute  sulphuric  or  hydrochloric  acid  so  as  to  obtain  a 
clean  surface,  and  then  a  drop  of  mercury  is  placed  on  the  plate  and  spread 
over  it  with  a  brush.  The  amalgamation  takes  place  immediately,  and  the 
plate  has  the  brilliant  aspect  of  mercury.  Zinc  as  well  as  other  metals  are 
readily  amalgamated  by  dipping  them  in  an  amalgam  of  one  part  sodium 
and  200  parts  of  mercury.  Zinc  plates  may  also  be  amalgamated  by  dipping 
them  in  a  solution  of  mercury  prepared  by  dissohing  one  pound  of  mercury 


-818]  Bohncnberger's  Electroscope.  789 

in  live  pounds  of  aqua  regia  (one  part  of  nitric  to  three  of  hydrochloric  acid), 
and  then  adding  five  parts  more  of  hydrochloric  acid. 

The  amalgamation  of  the  zinc  removes  from  its  surface  all  the  impurities, 
especially  the  iron.  The  mercury  effects  a  solution  of  pure  zinc,  which  covers 
the  surface  of  the  plate,  as  with  a  liquid  layer.  The  process  was  first  applied 
to  electrical  batteries  by  Kemp.  Amalgamated  zinc  is  not  attacked  so  long 
as  the  circuit  is  not  closed — that  is,  when  there  is  no  current  ;  when  closed 
the  current  is  more  regular,  and  at  the  same  time  stronger,  for  the  same 
quantity  of  metal  dissolved. 

817.  Dry  piles.— In  dry  piles  the  liquid  is  replaced  by  a  solid  hygrometric 
substance,  such  as  paper  or  leather.  They  are  of  various  kinds  ;  in  Zamboni's, 
which  is  most  extensively  used,  the  electromotors  are  tin  or  silver,  and  bin- 
oxide  of  manganese.  To  construct  one  of  these  a  piece  of  paper  silvered  or 
tinned  on  one  side  is  taken  ;  the  other  side  of  the  paper  is  coated  with  finely- 
powdered  binoxide  of  manganese  by  slightly  moistening  it,  and  rubbing  the 
powder  on  with  a  cork.  Having  placed  together  seven  or  eight  of  these 
sheets,  they  are  cut  by  means  of  a  punch  into  discs  an  inch  in  diameter. 
These  discs  are  then  arranged  in  the  same  order,  so  that  the  tin  or  silver  of 
each  disc  is  in  contact  with  the  manganese  of  the  next.  Having  piled  up  1,200 
or  1,800  couples,  they  are  placed  in  a  glass  tube,  which  is  provided  with  a 
brass  cap  at  each  end.  In  each  cap  there  is  a  rod  and  knob,  by  which  the 
leaves  can  be  pressed  together,  so  as  to  produce  better  contact.  The  knob 
in  contact  with  the  manganese  corresponds  to  the  positive  pole,  while  that 
at  the  other  end,  which  is  in  contact  with  the  silver  or  tin,  is  the  negative 
pole. 

Dry  piles  are  remai'kable  for  the  permanence  of  their  action,  which  may 
continue  for  several  years.  Their  action  depends  greatly  on  the  temperature 
and  on  the  hygrometric  state  of  the  air.  It  is  stronger  in  summer  than  in 
winter,  and  the  action  of  a  strong  heat  revives  it  when  it  appears  extinct.  A 
Zamboni's  pile  of  2,000  couples  gives  neither  shock  nor  spark,  but  can  charge 
a  Leyden  jar  and  other  condensers.  A  certain  time  is,  however,  necessary', 
for  electricity  only  moves  slowly  in  the  interior. 

Si 8.  Bohnenbergrer's  electroscope. — Bohnenberger  constructed  a  dry- 
pile  electroscope  of  great  delicacy.  It  is  a  condensing  electroscope  (fig.  716), 
from  the  rod  of  which  is  suspended  a  single  gold  leaf.  This  is  at  an  equal 
distance  from  the  opposite  poles  of  two  dry  piles  placed  vertically,  inside  the 
bell  jar,  on  the  plate  of  the  apparatus.  As  soon  as  the  gold  leaf  possesses 
any  free  electricity  it  is  attracted  by  one  of  the  poles  and  repelled  by  the 
other,  and  its  electricity  is  obviously  contrary  to  that  of  the  pole  towards 
which  it  moves. 


790  Dynamical  Electricity.  [819- 


CHAPTER   II. 

DETECTION   AND   MEASUREMENT  OF   VOLTAIC   CURRENTS. 

819.  Detection  and  measurement  of  voltaic  currents. — The  remark- 
able phenomena  of  the  voltaic  battery  may  be  classed  under  the  heads  phy- 
siological, chemical,  mechanical,  and  physical  effects  ;  and  these  latter  may 
be  again  subdivided  into  the  thermal,  luminous,  and  magnetic  effects.  For 
ascertaining  the  existence  and  measuring  the  strength  of  voltaic  currents, 
the  magnetic  effects  are  more  suitable  than  any  of  the  others,  and,  accord- 
ingly, the  fundamental  magnetic  phenomena  will  be  described  here,  and  the 
description  of  the  rest  postponed  to  a  special  chapter  on  electro-magnetism. 

820.  Oersted's  experiment. — Oersted  published  in  1 8 19  a  discovery 
which  connected  magnetism  and  electricity  in  a  most  intimate  manner,  and 
became,  in  the  hands  of  Ampere  and  of  Faraday,  the  source  of  a  new  branch 
of  physics.  The  fact  discovered  by  Oersted  is  the  directive  action  which  a 
fixed  current  exerts  at  a  distance  on  a  magnetic  needle. 

To  make  this  experiment  a  copper  wire  is  suspended  horizontally  in  the 
direction  of  the  magnetic  meridian  over 
a  movable  magnetic  needle,  as  repre- 
sented in  fig.  757.  So  long  as  the  wire 
is  not  traversed  by  a  current,  the  needle 
remains  parallel  to  it  ;  but  as  soon  as 
the  ends  of  the  wire  are  respectively 
connected  with  the  poles  of  a  battery 
or  of  a  single  element,  the  needle  is  de- 
flected, and  te?tds  to  take  a  position 
which  is  the  more  nearly  at  right  angles 
to  the  magnetic  metidian  in  proportion 
Fig-  757-  as  the  current  is  stronger. 

In  reference  to  the  direction  in  which  the  poles  are  deflected,  there  are 
several  cases  which  may,  however,  be  referred  to  a  single  principle.  Re- 
membering our  assumption  as  to  the  direction  of  the  current  in  the  con- 
necting wire  (803)  the  preceding  experiment  presents  the  following  four 
cases  :  — 

i.  If  the  current  passes  above  the  needle,  and  goes  from  south  to  north, 
the  north  pole  of  the  magnet  is  deflected  towards  the  west  ;  this  arrangement 
is  represented  in  the  above  figure. 

ii.  If  the  current  passes  below  the  needle,  also  from  south  to  north,  the 
north  pole  is  deflected  towards  the  east. 

iii.  When  the  current  passes  above  the  needle,  but  from  north  to  south, 
the  north  pole  is  deflected  towards  the  east. 


-821] 


Gahanovietcr  or  Multiplie 


791 

iv.  Lastly,  the  deflection  is  towards  the  west  when  the  current  goes  from 
north  to  south  below  the  needle. 

Ampere  has  given  the  following  mcinoria  tccJuiica  by  which  all  the  various 
directions  of  the  needle  under  the  influence  of  a  current  may  be  remembered. 
If  we  imagine  an  observer  placed  in  the  connecting  wire  in  such  a  manner 
that  the  current  entering  by  his  feet  issues  by  his  head,  and  that  his  face  is 
always  turned  towards  the  needle,  we  shall  see  that  in  the  above  four  posi- 
tions the  north  pole  is  always  deflected  towards  the  left  of  the  observer.  By 
thus  personifying  the  current,  the  different  cases  may  be  comprised  in  this 
general  principle  :  In  the  directive  action  of  currents  on  magnets,  the  north 
pole  is  always  deflected  towards  the  left  of  the  current. 

821.  Galvanometer  or  multiplier. — The  r\a.mQ  galvattomcter,  or  some- 
times iiiifltiplicr  or  rheoinetcr,  is  given  to  a  very  delicate  apparatus  by  which 
the  existence,  direction,  and  intensity  of  currents  may  be  determined.  It 
was  invented  by  Schweigger  a  short  time  after  Oersted's  discovery. 

In  order  to  understand  its  principle,  let  us  suppose  a  magnetic  needle 
suspended  by  a  filament  of  silk  (fig.  758),  and  surrounded  in  the  plane  of  the 


c 

« 

n 

1- 

N, 

J 

t— - 

■ —      a 

'^_ 

, — . 

'I  p 

Fig-  758. 


r 

1,-'-^ 

n 

^,,,— ^ 

^          f 

^''               i 

^-^■'^" 

i 

f^-^^ 

'I  I' 

Fig.  759. 


magnetic  meridian  by  a  copper  wire,  mnopq,  forming  a  complete  circuit 
round  the  needle  in  the  direction  of  its  length.  When  this  wire  is  traversed 
by  a  current,  it  follows,  from  what  has  been  said  in  the  previous  paragraph, 
that  in  every  part  of  the  circuit  an  observer  lying  in  the  wire  in  the  direction 
of  the  arrows,  and  looking  at  the  needle  ab^  would  have  his  left  always  turned 
towards  the  same  point  of  the  horizon,  and  consequently,  that  the  action  of 
the  current  in  every  part  would  tend  to  turn  the  north  pole  in  the  same 
direction  ;  that  is  to  say,  that  the  actions  of  the  four  branches  of  the  circuit 
concur  to  give  the  north  pole  the  same  direction.  By  coiling  the  copper 
wire  in  the  direction  of  the  needle,  as  represented  in  the  figure,  the  action 
of  the  current  has  been  multiplied.  If,  instead  of  a  single  one,  there  are 
several  circuits,  provided  they  are  insulated,  the  action  becomes  still  more 
multiplied,  and  the  deflection  of  the  needle  increases.  Nevertheless,  the 
action  of  the  current  cannot  be  multiplied  indefinitely  by  increasing  the 
number  of  windings,  for,  as  we  shall  presently  see,  the  strength  of  a  current 
diminishes  as  the  length  of  the  circuit  is  increased. 

As  the  directive  action  of  the  earth  continually  tends  to  keep  the  needle 
in  the  magnetic  meridian,  and  thus  opposes  the  action  of  the  current,  the 
effect  of  the  latter  is  increased  by  using  an  astatic  system  of  two  needles, 


792  Dynamical  Electricity.  [821- 

as  shown  in  fig.  759.  The  action  of  the  earth  on  the  needle  is  then  very 
feeble,  and,  further,  the  actions  of  the  current  on  the  two  needles  become 
accumulated.  In  fact,  the  action  of  the  circuit,  from  the  direction  of  the 
current  indicated  by  the  arrows,  tends  to  deflect  the  north  pole  of  the  lower 
needle  towards  the  west.  The  upper  needle  a'b\  is  subjected  to  the  action 
of  two  contrary  currents,  no  and  qp,  but  as  the  first  is  nearer,  its  action  pre- 
ponderates. Now  this  current  passing  below  the  needle,  evidently  tends  to 
turn  the  pole  a'  towards  the  east,  and,  consequently,  the  pole  b'  towards  the 
west  ;  that  is  to  say,  in  the  same  direction  as  the  pole  a  of  the  other  needle. 
From  these  principles  it  will  be  easy  to  understand  the  action  of  the 
multiplier.    The  apparatus  represented  in  fig.  760  consists  of  a  thick  copper 

plate,  D,  resting  on  levelling 
screws  ;  on  this  is  a  rotating 
plate,  P,  of  the  same  metal, 
to  which  is  fixed  a  copper 
frame,  the  breadth  of  which 
is  almost  equal  to  the  length 
of  the  needles.  On  this  is 
coiled  a  great  number  of 
turns  of  wire  covered  with 
silk.  The  two  ends  terminate 
in  binding  screws,  /  and  0. 
Above  the  frame  is  a  gradu- 
ated circle,  C,  with  a  central 
slit  parallel  to  the  direction 
in  which  the  wire  is  coiled. 
The  zero  corresponds  to  the 
position  of  this  slit,  and  there 
are  two  graduations  on  the 
scale,  the  one  on  the  right 
and  the  other  on  the  left  of 
zero,  but  they  only  extend  to 
90°.  By  means  of  a  very  fine 
filament  of  silk,  an  astatic 
system  is  suspended  ;  it  con- 
sists of  two  needles  ab  and 
a'b\  one  above  the  scale, 
and  the  other  within  the  cir- 
cuit itself.  These  needles, 
which  are  joined  together  by  a  copper  wire,  like  those  in  fig.  642  and  fig. 
759,  and  cannot  move  separately,  must  not  have  exactly  the  same  magnetic 
intensity  ;  for  if  they  are  exactly  equal,  every  current,  strong  or  weak,  would 
always  put  them  at  right  angles  with  itself. 

In  using  this  instrument  the  diameter,  to  which  corresponds  the  zero  of 
the  graduation,  is  brought  into  the  magnetic  meridian  by  turning  the  plate 
P  until  the  end  of  the  needle  (xb  corresponds  to  zero.  The  instrument  is 
fixed  in  this  position  by  means  of  the  screw-clanip  T. 

The  length  and  diameter  of  the  wire  vary  with  the  purpose  for  w  hicli  the 
galvanometer  is  intcMulcd.      l'"or  one  which  is  to  be  used  in  observing  the 


Fig.  760. 


-821]  Galvimonietcr  or  Multiplier.  793 

currents  due  to  chemical  actions,  a  wire  about  \  millimetre  in  diameter,  and 
making-  about  Soo  turns,  is  well  adapted.  Those  for  thermo-electric  currents, 
which  have  low  intensity,  require  a  thicker  and  shorter  wire  ;  for  example, 
thirty  turns  of  a  wire  |  millimetre  in  diameter.  For  very  deHcate  experi- 
ments, as  in  physiological  investigations,  galvanometers  with  as  many  as 
30,000  turns  have  been  used. 

By  means  of  a  delicate  galvanometer  consisting  of  2,000  or  3,000  turns 
of  fine  wire,  the  coils  of  which  are  carefully  insulated  by  means  of  silk  and 
shellac,  currents  of  high  potential,  as  those  of  the  electrical  machine  (791) 
may  be  shown.  One  end  of  the  galvanometer  is  connected  with  the  con- 
ductor, and  the  other  with  the  ground,  and  on  working  the  machine  the 
needle  is  deflected,  affording  thus  an  illustration  of  the  identity  of  statical 
with  dynamical  electricity. 

The  deflection  of  the  needle  increases  with  the  strength  of  the  current  ; 
the  relation  between  the  two  is,  however,  so  complex,  that  it  cannot  well 
be  deduced  from  theoretical  considerations,  but  requires  to  be  determined 
experimentally  for  each  instrument.  And  in  the  majority  of  cases  the  in- 
strument is  used  as  a  galvanoscope  or  rheoscope — that  is,  to  ascertain  the 
presence  and  direction  of  currents — rather  than  as  a  galvanometer  or  rheo- 
>neter  in  the  strict  sense  ;  that  is,  as  a  measurer  of  their  intensity.  The 
term  galvanometer  is,  however,  commonly  used. 

The  differential  galvanometer  consists  of  a  needle,  as  in  an  ordinary 
galvanometer,  but  round  the  frame  of  which  are  coiled  two  wires  of  the  same 
kind  and  dimensions,  carefully  insulated  from  each  other,  and  provided  with 
suitable  binding  screws,  so  that  separate  currents  can  be  passed  through 
each  of  them.  If  the  currents  are  of  the  same  strength  but  in  different 
directions,  no  deflection  is  produced  ;  where  the  needle  is  deflected  one 
of  the  currents  differs  from  the  other.  Hence  the  apparatus  is  used  to 
ascertain  a  difference  in  strength  of  two  currents,  and  to  this  it  owes  its 
name. 

When  a  current  is  passed  through  a  galvanometer,  the  needle  does  not 
usually  at  once  attain  its  final  position  of  equilibrium,  but  oscillates  about 
this  position,  which  in  observations  causes  much  loss  of  time.  If  such  a 
needle  is  surrounded  by  a  mass  of  a  good  conductor  such  as  copper,  currents 
are  induced  in  the  mass  which,  as  will  afterwards  be  explained  (905),  impede, 
or  damp  the  motion  of  the  magnetic  needle  and  tend  to  bring  it  to  rest. 
Such  an  arrangement  is  called  a  da7nper.,  and  in  practice  is  frequently  used  ; 
the  copper  frame  on  which  the  wires  of  the  galvanometer  are  coiled,  and 
the  wires  themselves,  act  in  this  way.  The  natural  logarithm  of  the  ratio  of 
the  amplitudes  of  two  successive  oscillations  of  the  needle,  is  called  the 
logarithmic  decrement.  The  logarithmic  decrement  X  is  proportional  to 
the  product  of  the  damping  power  e  and  the  time  of  an  oscillation  / ;  that 
is,  A  =  d.  By  diminishing  the  directive  power  of  the  earth  on  the  magnet  by 
making  it  astatic,  the  logarithmic  decrement  becomes  infinite,  and  the 
needle  attains  its  position  of  equilibrium  without  oscillations.  Galvano- 
meters in  which  the  needle  acquires  at  once  this  final  deflection  are  known 
as  aperiodic,  or  dead-beat  galvanometers. 

To  this  class  belong  that  of  Deprez  and  D'Arsonval  represented  in  fig. 
761.     Between  the  branches  of  a  strong  horse-shoe  magnet  is  a  light  iron 


794  Dynamical  Electricity.  [821- 

cylinder  supported  independently,  and  which  becomes  magnetised  by  in- 
duction. Between  this  and  the  magnet  is  a  light  rectangular  wire  coil, 
supported  by  wires  conveying  the  current  which  are  in  connection  with 
binding  screws.    When  the  current  passes,  the  coil  is  deflected  at  right  angles 

to  the  field,  and  equilibrium 
is  established  when  the  electro- 
magnetic action  is  equalled  by 
the  torsion  of  the  wire.  The 
motion  of  the  coil  can  be  read 
off  by  a  spot  of  light  reflected 
from  a  mirror  (822)  attached  to 
it,  and  for  small  angles  the  cur- 
rent is  proportional  to  tangent 
of  the  angle  of  deflection  (823). 
Induction  currents  due  to  the 
motion  of  the  coil  in  the  field 
are  produced,  and  as  this  is  very 
powerful  the  galvanometer  is 
virtually  dead-beat  when  closed 
by  a  small  resistance. 

When  a  current  of  very  small 
duration  is  passed  through  a 
galvanometer,  a  momentary  de- 
flection or  switig  or  throw  of  the 
needle  will  be   produced.     The 


Fig.  761. 


product  of  a  constant  into  the  sine  of  half  the  angle  of  the  first  swing  is  then 
a  measure  of  the  strength  of  the  current,  so  that  if  momentary  currents  of 
different  strengths  are  passed  through  one  and  the  same  galvanometer  they 
will  be  measured  by  the  sines  of  the  corresponding  angles  of  deflection,  or 
by  the  angles  themselves  where  these  are  small.  This  is  known  as  the  ballistic 
7iietIiod  of  measuring  currents,  and  the  galvanometers  adapted  for  the  pur- 
pose are  known  as  ballistic  galvatiometers. 

822.  Sir  'W.  Thomson's  marine  gralvanometer. — In  laying  submarine 
cables  the  want  was  felt  of  a  galvanometer  sufficiently  sensitive  to  test  insula- 
tion, which  at  the  same  time  was  not  affected  by  the  pitching  and  rolling  of  the 
ship.  For  this  purpose,  Sir  W.  Thomson  invented  his  marine  galvanometer. 
B  (fig.  762)  represents  a  coil  of  many  thousand  turns  of  the  finest  copper  wire, 
carefully  insulated  throughout,  terminating  in  the  binding  screws,  EE.  In 
the  centre  of  this  coil  is  a  slide,  which  carries  the  magnet,  the  arrangement  of 
which  is  represented  on  a  larger  scale  in  D.  The  magnet  itself  is  made  of  a 
piece  of  fine  watch-spring  about  \  of  an  inch  in  length,  and  does  not  weigh 
more  than  a  grain  ;  it  is  attached  to  a  small  and  very  slightly  concave  mirror 
of  very  thin  silvered  glass.  A  single  fibre  of  silk  is  stretched  across  the  slide, 
and  the  mirror  and  magnet  are  attached  to  it  in  such  a  manner  that  the 
fibre  passes  exactly  through  the  centre  of  gravity  in  every  position.  As  the 
mirror  and  magnet  weigh  only  a  few  grains,  they  retain  their  position  rela- 
tively to  the  instrument,  however  the  ship  may  pitch  and  roll.  The  slide  fits  in 
a  groove  in  the  coil,  and  the  whole  is  enclosed  within  a  wrought-iron  case 
with  an  aperture  in  front  and  a  wrought-iron  lid  on  the  top.     The  eflfect  of 


Sir   JJ^.    TJiomsoiis  Maritie  Galvanometer. 


795 


-822] 

this  is  to  act  as  a  viagnetic  screen  and  thereby  counteract  the  influence  of 
terrestrial  magnetism  when  the  ship  changes  its  course. 

Underneath  the  coil  is  a  large  bent  steel  magnet  N,  which  compensates 
the  earth's  directive  action  upon  the  magnet  D  (700) ;  and  in  the  side  of  the 
case,  and  on  a  level  with  D,  a  pair  of  magnets,  C,  are  placed  with  opposite 
poles  together.  By  a  screw,  suitably  adjusted,  the  poles  of  the  magnets  may 
be  brought  together  ;  in  which  case  they  quite  neutralise  each  other,  and  thus 
e.xert  no  action  on  the  suspended  magnet,  or  they  may  be  slid  apart  from 
each  other  in  such  a  manner  that  the  action  of  either  pole  on  D  prepon- 
derates to  any  desired  extent.  This  small  magnet  is  thus  capable  of  very 
delicate  adjustment.  The  large  magnet  N,  and  the  pair  of  magnets,  C,  are 
analogous  to  the  coarse  and  fine  adjustment  of  a  microscope. 

.At  a  distance  of  about  three  feet,  there  is  a  scale  with  the  zero  in  the 
centre  and  the  graduation  extending  on  each  side.     Underneath  this  zero 


Fig.  762. 

point  is  a  narrow  slit,  through  which  passes  the  light  of  a  paraffine  lamp,  and 
which,  traversing  the  window,  is  reflected  from  the  bent  mirror  against  the 
graduated  scale.  By  means  of  the  adjusting  magnets  the  image  of  the  slit 
is  made  to  fall  on  the  centre  of  the  graduation. 

This  being  the  case,  if  any  arrangement  for  producing  a  current,  however 
weak,  be  connected  with  the  terminal,  the  spot  of  light  is  deflected  either  to 
one  side  or  the  other,  according  to  the  direction  of  the  current  ;  the  stronger 
the  current  the  greater  the  deflection  of  the  spot ;  and  if  the  current  remains 
of  constant  strength  for  any  length  of  time,  the  spot  is  stationary  in  a  cor- 
responding position. 

The  movement,  on  a  screen,  of  a  spot  of  light  reflected  from  a  body,  is  the 
most  delicate  and  convenient  means  of  observing  motions  which  of  them- 
selves are  too  small  for  direct  measurement  or  observation.  Hence  this 
principle  is  frequently  applied  in  experimental  investigations  and  in  lecture 
illustrations  (522).  It  is  used  in  observing  the  motion  of  oscillating  bodies, 
in  measuring  the  variations  of  magnetism,  in  determining  the  expansion  of 
solids,  &c. 


79<5 


Dynamical  Electricity. 


[823- 


It  will  be  seen  from  the  article  on  the  Electric  Telegraph,  how  alternate 
deflections  of  the  spot  of  light  may  be  utilised  in  forming  a  code  of  signals. 

823.  Tang-ent  compass,  or  tangent  galvanometer. — When  a  magnetic 
needle  is  suspended  in  the  centre  of  a  voltaic  current  in  the  plane  of  the 
magnetic  meridian,  it  can  be  proved  that  the  strength  of  a  current  is  directly 

proportional  to  the  tangent  of  the 
angle  of  deflection,  provided  the 
dimensions  of  the  needle  are  suffi- 
ciently small  as  compared  with  the 
diameter  of  the  circuit.  An  instru- 
ment based  on  this  principle  is 
called  the  tangetit  galva7iometer  or 
tangeitt  compass.  It  consists  of  a 
copper  ring,  12  inches  in  diameter 
(fig.  763),  and  about  an  inch  in 
breadth,  mounted  vertically  on  a 
stand  ;  the  lower  half  of  the  ring  is 
generally  fitted  in  a  semicircular 
frame  of  wood  to  keep  it  steady.  In 
the  centre  of  the  ring  is  suspended 
a  delicate  magnetic  needle,  whose 
length  must  not  exceed  ~  or  i  of 
the  diameter  of  the  circle.  Under- 
'^'  ''  ^'  neath  the  needle  there  is  a  graduated 

circle.  The  ends  of  the  ring  are  prolonged  in  copper  wires,  fitted  with 
mercury  cups,  ab.,  by  which  it  can  be  connected  with  a  battery  or  element. 
The  circle  is  placed  in  the  plane  of  the  magnetic  meridian,  and  the  deflection 
of  the  needle  is  directly  read  off  on  the  circle,  and  its  corresponding  value 
obtained  from  a  table  of  tangents. 

On  account  of  its  small  resistance,  the  tangent  galvanometer  is  well 
adapted  for  currents  of  low  potential,  but  in  which  a  considerable  quantity 
of  electricity  is  set  in  motion. 

To  prove  that  the  intensities  of  various  currents  are  proportional  to  the 
tangents  of  the  corresponding  angles  of  deflection,  let  NS,  fig.  764,  represent 
the  wire  of  the  galvanometer  and  ns  the  needle,  and  let  (^  be  the  angle  of 
deflection  produced  when  a  current  C  is  passed.  Two  forces  now  act  upon 
the  needle — the  force  of  the  earth's  magnetism,  which  we  will  denote  by  H, 
which  tends  to  place  the  needle  in  the  magnetic  meridian,  and  the  strength 
of  the  current  C,  which  strives  to  place  it  at  right  angles  to  the  magnetic 
meridian.  Let  the  magnitudes  of  these  forces  be  represented  by  the  corre- 
sponding lines  a7t  and  bn.  Now  the  whole  intensities  of  these  forces  do  not 
act  so  as  to  turn  the  point  of  the  needle  round,  but  only  those  components 
which  are  at  right  angles  to  the  needle.  Resolving  them,  we  have  ng  and  nf 
as  the  forces  acting  in  opposite  directions  on  the  needle  ;  and  since  the 
needle  is  at  rest  these  forces  must  be  equal. 

The  angle  nag  is  equal  to  the  angle  (/),  and  therefore  ng=an  sin  </>  ;  and 
in  like  manner  the  angle  bfif  is  equal  to  (^  and  nf^bn  cos  ^  ;  and  therefore 

since  ;//=  ng^  bn  cos  <\i 
C  =  H  tan  (/). 


an  sin  0,  or  bn  =  an 


sm  cj) 
cos  (j> 


tan  (j)  ;    that   is. 


-824]  Tangent  Galvanometer.  7g7 

If  any  other  current  be  passed  through  the  galvanometer  we  shall  ha\'e 
sunilarly  C'=  H  tan  (/>' ;  and  shice  the  earth's  magnetism  does  not  appreci- 
ably alter  in  one  and  the  same  place  C  :  C'  =  tan  </>  :  tan  ^'. 

In  this  reasoning  it  has  been  assumed  that  the  action  of  the  current  on 
the  needle  is  the  same  whatever  be  the  angle  by  which  it  is  deflected.  This 
is  only  the  case  when  the  dimensions  of  the  needle  are 
small  compared  with  the  diameter  of  the  ring  :  it  should 
not  be  more  than  J  or  {-^  the  diameter.  In  order  to  mea- 
sure with  accuracy  the  deflection  a  light  index  is  placed 
at  right  angles  to  the  needle. 

Wiedoiianns  tangent  galvanometer  consists  of  a  short 
thick  copper  tube,  in  which  is  suspended,  instead  of  a 
needle,  a  thin  piece  of  soft  iron,  silvered  on  one  side  so  as 
to  act  as  a  mirror,  the  position  of  which  can  be  observed 
by  a  microscope  and  scale  (522).  On  each  side  of  the 
copper  tube,  and  sliding  in  grooves,  are  coils  of  wire  which 
can  be  pushed  over  the  tube.  By  this  lateral  arrangement 
of  the  current  in  reference  to  the  magnetic  needle,  the 
error  of  the  tangent  galvanometer  is  diminished  ;  for 
when  the  needle  is  deflected,  though  one  end  moves  away  Fig.  764. 

from  the  current,  the  other  approaches  it. 

In  the  tangent  galvanometer  of  Helmholtz  and  of  Gaugain  the  wires  are 
coiled  on  the  surface  of  a  cone  the  angle  of  which  is  120°,  and  the  point  on 
which  the  needle  works  is  placed  in  the  position  of  the  corresponding  apex 
of  the  cone  :  the  law  of  the  tangent  holds  then  even  with  longer  needles,  and 
especially  if  the  wire  is  divided  between  two  such  cones,  one  on  opposite 
sides  of  the  needle. 

If  the  ring  of  the  tangent  galvanometer  is  so  constructed  that  it  can  turn 
about  its  axis,  which  is  in  the  magnetic  meridian,  the  action  of  the  current 
on  the  needle  is  inversely  proportional  to  the  cosine  of  the  angle  (9,  through 
which  the  ring  is  turned.  Hence  by  increasing  (9,  the  action  of  any  current 
on  the  needle  may  be  made  as  small  as  we  please. 

S24.  Sine  gralvanometer. — This  is  another  form  of  galvanometer  for 
measuring  powerful  currents.  Round  the  circular  frame  M  (fig.  765),  several 
turns  of  stout  insulated  copper  wire  are  coiled,  the  two  ends  of  which,  z, 
terminate  on  the  binding  screws  at  E.  On  a  table  in  the  centre  of  the  ring 
there  is  a  magnetic  needle,  m  ;  a  second  light  needle,  n,  fixed  to  the  first", 
serves  as  pointer  along  the  graduated  circle  N.  Two  copper  wires,  a^  b, 
from  the  sources  of  electricity  to  be  measured,  are  connected  with  E.  The 
circles  M  and  N  are  supported  on  a  foot  O,  which  can  move  about  a  ver- 
tical axis  passing  through  the  centre  of  a  fixed  horizontal  circle  H. 

The  circle  M  being  then  placed  in  the  magnetic  meridian,  and  therefore 
in  the  same  plane  as  the  needle,  the  current  is  allowed  to  pass.  The  needle 
being  deflected,  the  circuit  M  is  turned  until  it  coincides  with  the  vertical 
plane  passing  through  the  magnetic  needle  m.  The  directive  action  of  the 
current  is  now  exerted  perpendicularly  to  the  direction  of  the  magnetic 
needle,  and  it  may  be  shown  that  the  strength  of  the  current  is  propor- 
tional to  the  sine  of  the  angle  of  deflection  :  this  angle  is  measured  on  the 
circle  II  by  means  of  a  vernier  on  the  piece  C.     This  piece  C,  fixed  to  the 


798 


Dynamical  Electricity. 


[824- 


foot  O,  turns  it  by  means  of  a  knob  A.  This  angle  of  deflection,  and  hence 
its  sine,  being  known,  the  intensity  of  the  current  may  be  thus  deduced  : 
let  mm'  be  the  direction  of  the  magnetic  meridian,  d  the  angle  of  deflection, 
C  the  strength  of  the  current,  and   H  the  directive  action  of  the  earth.     If 

the  direction  and  intensity  of 
this  latter  force  be  represented 
by  ak,  it  may  be  replaced  by 
two  components,  ah  and  ac  (fig. 
766).  Now,  as  the  first  has  no 
III     .  -''^^-^^-^■^■^^^^^^^^giJI^  directive  action  on  the  needle, 

*''         ..*=:*-«®«*6te^^!!*^H\  tl^g   component   ac   must  alone 

counterpoise  the  force  C  ;  that 
is,  C  =  ac.  But  in  the  triangle 
ack.,  ac  =  ak  cos  cak^  from  which 


S^« 


Fig.  765 


Fig.  766. 


ac  =  H  sin  </,  for  the  angle  cak  is  the  complement  of  the  angle  d,  and  ak  is 
equal  to  H  ;  hence,  lastly,  C  =  H  sin  d,  which  was  to  be  proved.  In  like 
manner  for  any  other  current  C,  which  produces  a  deflection  (/',  we  shall 
have  C  =  H  sin  d\  whence  C  :  C'  =  sin  ^  :  sin  d'. 

825.  Ohm's  law. — For  a  knowledge  of  the  conditions  which  regulate 
the  action  of  the  voltaic  current,  science  is  indebted  to  the  late  G.  S.  Ohm. 
His  results  were  at  first  deduced  from  theoretical  considerations  ;  but  by 
his  own  researches  as  well  as  by  those  of  Fechncr,  Pouillet,  Daniell,  De  la 
Rive,  Wheatstone,  and  others,  they  received  the  fullest  confirmation,  and 
their  great  theoretical  and  practical  importance  has  been  fully  established. 

i.  The  force  or  cause  by  which  electricity  is  set  in  motion  in  the  voltaic 
circuit  is  called  the  electromotive  force.  The  quantity  of  electricity  which  in 
any  unit  of  time  flows  through  a  section  of  the  circuit  is  called  the  intensity^ 
or,  perhaps  better,  ttie  strefigth  of  the  current.  Ohm  found  that  this  strength 
is  the  same  in  all  parts  of  one  and  the  same  circuit,  however  heterogeneous 
they  were  ;  one  and  the  same  magnetic  needle  is  deflected  to  the  same 
extent  over  whatever  part  of  the  circuit  it  is  suspended  ;  and  the  same 
voltameter,  wherever  interposed  in  the  circuit,  indicates  the  same  disengage- 
ment of  gas  ;  he  also  found  that  the  strength  is  proimrlional  to  the  electro- 
motive force. 


-825]  Ohm's  Law.  799 

It  has  further  been  found  that  when  the  current  from  the  same  element 
is  passed  respectively  through  a  short  and  through  a  long  wire  of  the  same 
material,  its  action  on  the  magnetic  needle  is  less  in  the  latter  case  than  in 
the  former.  Ohm  accordingly  supposed  that  in  the  latter  case  there  was  a 
greater  resistance  to  the  passage  of  the  current  than  in  the  former  ;  and  he 
proved  that  '■the  resistance  is  inversely  proportional  to  the  strength  of  the 
cun-ent.^ 

On  tliese  principles  Ohm  founded  the  celebrated  law  which  bears  his 
name,  that  the  strength  of  the  current  is  equal  to  the  electromotive  force 
divided  by  the  resistance. 

This  is  expressed  by  the  simple  formula 

-^- 

where  C  is  the  strength  of  the  current,  E  the  electromotive  force,  and  R  the 
resistance. 

ii.  The  resistance  of  a  conductor  depends  on  three  elements  ;  its  conduc- 
tivity., which  is  a  constant,  determined  for  each  conductor  ;  its  section  ;  and 
its  length.  The  resistance  is  obviously  'nversely  proportional  to  the  conduc- 
tivity ;  that  is,  the  less  the  conducting  power,  the  greater  the  resistance.  It 
has  been  pro\-ed  that  the  resistance  is  inversely  as  the  section  and  directly 
as  the  length  of  a  conductor.  If  then  k  is  the  conductivity,  w  the  section,  and  \ 
the  length  of  a  conductor,  we  have 

RA  ,   ^       E      xtojE 

■-=    -and  C  =  —  =    ^-  ; 

KU)  A  A 

that  is,  the  strength  of  a  current  is  inversely  proportional  to  the  lotgth  of  the 
conductor,  and  directly  proportional  to  its  section  and  conductivity. 

iii.  In  a  voltaic  battery  composed  of  different  elements,  the  strength  of 
the  current  is  equal  to  the  sum  of  the  electromotive  forces  of  all  the  elements 
divided  by  the  sum  of  the  resistances.  Usually,  however,  a  batteiy  is  com- 
posed of  elements  of  the  same  kind,  each  having,  in  intention  at  least,  the 
same  electromotive  force  and  the  same  resistance. 

In  an  ordinary  element  there  are  essentially  two  resistances  to  be  con- 
sidered :  I.  That  offered  by  the  liquid  conductor  between  the  two  plates, 
which  is  frequently  called  the  internal  or  essefttial  resistance  ;  and  2.  That 
offered  by  the  interpolar  conductor  which  connects  the  two  plates  outside  the 
liquid  ;  this  conductor  may  consist  either  wholly  of  metal,  or  may  be  partly  of 
metal  and  partly  of  liquids  to  be  decomposed  ;  it  is  the  external  or  non-essential 
resistafice.     Calling  the  former  R  and  the  latter  r,  Ohm's  formula  becomes 

R  +  r 

iv.  If  any  number,  ;/,  of  similar  elements  are  joined  together,  there  is  // 
times  the  electromotive   force,  but  at  the  same  time  n  times  the  internal 

resistance,  and  the  formula  becomes  -^       ,     If  the  resistance  in  the  inter- 

n\\  +  r 

polar,  r,  is  very  small — which  is  the  case,  for  instance,  when  it  is  a  short.. 


8oo  Dynamical  Electricity.  [825- 

thick  copper  wire — it  may  be  neglected  in  comparison  with  the  internal 
resistance,  and  then  we  have 

C  -  "^  -  ^  ■ 
~  nR  ~  R  ' 

that  is,  a  battery  consisting  of  several  elements  produces  in  this  case  no 
greater  effect  than  a  single  element. 

V.  If,  however,  the  external  resistance  is  verj'  great,  as  when  the  current 
has  to  produce  the  electric  light,  or  to  work  a  long  telegraphic  circuit,  advan- 
tage is  gained  by  using  a  large  number  of  elements,  for  then  we  have  the 
formula 

C  -    ^^ 
~nRV?' 

If  r  is  very  great  as  compared  with  ;/R,  the  latter  may  be  neglected,  and  the 
expression  becomes 

r 

that  is,  that  the  strength,  within  certain  limits,  is  proportional  to  the  number 
of  elements. 

In  a  thermo-electric  pile,  which  consists  of  very  short  metallic  conductors, 
the  internal  resistance  R  is  so  small  that  it  may  be  neglected,  and  the 
strength  is  inversely  as  the  length  of  the  connecting  wire. 

vi.  If  the  plates  of  an  element  be  made  in  times  as  large,  there  is  no 
increase  in  the  electromotive  force,  for  this  depends  solely  on  the  nature 
of  the  metals  and  of  the  liquid  (802)  ;  but  the  resistance  is  vi  times  as  small, 
for  the  section  is  711  times  larger  :  the  expression  becomes  then 

„  _    E    _    wE 
~  R         R-i- w;-' 

+  ;- 
m 

Hence,  an  increase  in  the  size  of  the  plate — or,  what  is  the  same  thing,  a 
decrease  in  the  internal  resistance — does  not  increase  the  strength  to  an 
indefinite  extent ;  for  ultimately  the  resistance  of  the  element  R  vanishes  in 
comparison  with  the  resistance  r,  and  the  strength  continually  approximates 

to  the  value  C  =     . 
?• 

vii.  Ohm's  law  enables  us  to  arrange  a  battery  so  as  to  obtain  the  greatest 
effect  in  any  given  case.  For  instance,  with  a  battery  of  six  elements  there 
are  the  following  four  ways  of  arranging  them  : — i.  In  a  single  series  (fig. 
767),  in  which  the  zinc  Z  of  one  element  is  united  with  the  copper  C  of  the 
second,  the  zinc  of  this  with  the  copper  of  the  third,  and  so  on.  2.  Arranged 
in  a  system  of  three  double  elements,  each  element  being  formed  by  joining 
two  of  the  former  (fig.  768).  3.  In  a  system  of  two  elements,  each  of  which 
consists  of  three  of  the  original  elements  joined,  so  as  to  form  one  of  triple 
the  surface  (fig.  769).  Lastly,  of  one  large  element,  all  the  zincs  and  all  the 
coppers  being  joined,  so  as  to  form  a  pair  of  six  times  the  surface  (fig.  770). 

With  a  series  of  twelve  elements  there  maybe  six  different  combinations, 
and  so  on  for  a  larger  number. 


-825]  Ohm's  Laiv.  80  r 

Now  let  us  suppose  that  in  the  particular  case  of  a  battery  of  six  elements 
the  internal  resistance  R  of  each  element  is  3,  and  the  external  resistance 
r=i2.  Then  in  the  first  case  where  there  are  six  elements  arranged  in 
series  we  have  the  value 

6R  +  r6x3+i2     30  '         ^  ' 

If  they  were  united  so  as  to  form  three  elements,  each  of  double  the 
surface  as  in  the  second  case  (fig.  768),  the  electromotive  force  would  then 


be  the  electromotive  force  in  each  element  :  there  would  also  be  a  resistance 
R  in  each  element,  but  this  would  be  only  half  as  great,  for  the  section  of 
the  plate  is  now  double  ;  hence  the  strength  in  this  case  would  be 

r'_    3E^    _      3E    _6E. 


3R 

--  +  r 
2 


(2) 


:th. 


accordingly  this  change  would  lessen  the  stren;.. 

If,  with  the  same  elements,  the  resistance  in  the  connecting  wire  were 
only  r  =  2,  we  should  have  the  values  in  the  two  cases  respectively — 
6xE       6E 
20' 

.3  F 


C  = 


6x3  +  2 


8o2  Dynamical  Electricity.  [825- 

,  „,       3E  6E       6E 

andC  =-^ =• =       . 

,3R^^      9+12      13 
2 

The  result  in  the  latter  case  is,  therefore,  more  favourable.  If  the  re- 
sistance r  were  9,  the  strength  would  be  the  same  in  both  cases.  Hence, 
then,  by  altering  the  size  of  the  plates  or  their  arrangement,  favourable 
or  unfavourable  results  are  obtained  according  to  the  relation  between  R 
and  r. 

826.  Arrang-ement  of  multiple  battery  for  maximuin  current. — It  can 
be  shown  that  in  any  given  co/nbination  the  viaxinium  e^cct  is  obtainedwhen 
the  total  resistance  in  the  elements  is  equal  to  the  resistance  of  the  intcrpolar. 
For  let  N  be  the  total  number  of  cells  available  for  a  given  combination,  and 
let  n  be  the  number  of  cells  arranged  tandem.,  or  in  series — that  is,  when. 
the  zinc  of  one  is  connected  with  the  copper  of  the  next,  and  so  on  ;  then 

there  will  be       elements  arranged  abreast.     If  e  be  the  electromotive  force 
n 

and  r  the  resistance  of  one  cell,  while  /  is  the  external  resistance,  then  the 

strength  of  the  current  will  be 

C  -     ^'^     -      '^^      -        ^ 
~nr^~rri'r^fnrl 
-^^     N-^^     n"^^ 
n 

Therefore    C    is   a   maximum  when  .,7  +  -  is  a  minimum.      But  -7  x - 

N      n  N     n 

=  ''    is  a  constant,  therefore  the  sum  ^+      is    a   minimum    when  ^^    =      ; 
N  N      «  N         ;/ 

that  is,  when'' ^^  =  /,  or  when  the  total    internal  resistance  is    equal    to    the 

external  resistance. 

For  if  X  and  —  are  any  two  quantities  whose  product  is  A-,  then 

A-  ^ x"-  +  A- - 2kx  +  2A.t-^ (.r-  A)-  ^  ^^ 

X  X  X 

This  is  greater  than  2A  unless  .t--A  =  o,  in  which  case  it  is  equal  to  2A,and 
is  a  minimum.     In  that  case  .i-  =  A,  and  therefore 

X 

It  follows  thus  from  the  above  formula  that  the  best  eftect  is  obtained 

wheny;=^/-^_-. 

If  in  a  given  case  we  have  8  elements,  each  oflcring  a  resistance  15,  and 
an  interpolar  with  the  resistance  40,  we  get  n^^-^.  But  this  is  an  im- 
possil)le  arrangement,  for  it  is  not  a  whole  number,  and  the  nearest  whole 
numljcr  must  be  taken.  This  is  4  ;  and  it  will  be  found,  on  making  a  calcu- 
lalinn  analogous  to  that  above,  that  when  arranged  so  as  to  form  4  elements,, 
each  of  double  surface,  the  greatest  eftccl  is  obtained. 


-826]  Arrangement  of  JSIidlipk  Battery.  803 

The  formula  for  the  strength  of  current  from  several  elements,  C=  -^-, 

may  also  be  applied  to  the  currents  produced  l^y  a  magneto-electrical  ma- 
chine (920).  In  that  case  n  stands  for  the  number  of  coils  which  in  a  given 
time  cut  the  lines  offeree  of  a  magnetic  field. 

The  principle  that  the  best  eftect  is  obtained  when  the  total  internal  is 
equal  to  the  total  external  resistance,  holds  also  for  the  currents  produced  by 
these  machines. 


3F2 


8o4  Dynamical  Electricity.  [827- 


CH AFTER   III. 

EFFECTS   OF   THE   CURRENT. 

S27.  Physlolog-ical  actions. — Under  this  name  are  included  the  effects 
produced  by  a  battery  current  on  living  organisms  or  tissues. 

When  the  electrodes  of  a  battery  of  many  cells  are  held  in  the  two  hands  a 
violent  shock  is  felt,  especially  if  the  hands  are  moistened  with  acidulated 
water,  which  increases  the  conductivity.  The  violence  of  the  shock  increases 
with  the  number  of  elements  used,  and  with  a  large  number— as  200  Bunsen's 
cells — is  even  dangerous. 

The  power  of  contracting  upon  the  application  of  a  voltaic  current  seems 
to  be  a  very  general  property  oi  protoplasiti — the  physical  basis  of  both 
animal  and  vegetable  life  ;  if,  for  example,  a  current  of  moderate  strength  be 
passed  through  such  a  simple  form  of  protoplasm  as  an  amoeba,  it  imme- 
diately withdraws  its  processes,  ceases  its  changes  of  form,  and  contracts  into 
a  rounded  ball — soon,  however,  resuming  its  activity  upon  the  cessation  of 
the  current.  Essentially  similar  effects  of  the  current  have  been  observed  in 
the  protoplasm  of  young  vegetable  cells. 

If  a  frog's  fresh  muscle  (which  will  retain  its  vitality  for  a  considerable 
time  after  removal  from  the  body  of  the  animal)  be  introduced  into  a  galvanic 
circuit,  no  apparent  effect  will  be  observed  during  the  steady  passage  of  the 
current,  but  every  opening  or  closure  of  the  circuit  will  cause  a  muscular 
contraction,  as  will  also  any  sudden  and  considerable  alteration  in  its  in- 
tensity. By  very  rapidly  interrupting  the  current,  the  muscle  can  be  thrown 
into  a  state  of  uninterrupted  contraction,  or  physiological  tetanus^  each  new 
contraction  occurring  before  the  previous  one  has  passed  off.  Other  things 
being  equal,  the  amount  of  shortening  exhibited  by  the  muscles  increases, 
up  to  a  certain  limit,  with  the  intensity  of  the  current.  These  phenomena 
entirely  disappear  with  the  life  of  the  muscle  ;  hence  the  experiments  are 
somewhat  more  difficult  with  warm-blooded  animals,  the  vitality  of  whose 
muscles,  after  exposure  or  removal  from  the  body,  is  maintained  with  more 
difficulty ;  but  the  results  of  careful  experiment  are  exactly  the  same  here  as 
in  the  case  of  the  frog. 

The  influence  of  an  electric  current  upon  living  nerves  is  very  remark- 
able ;  as  a  general  rule,  it  may  be  stated  that  its  effect  is  to  throw  the  nerve 
into  a  state  of  activity,  whatever  its  special  function  may  be  :  thus,  if  the 
nerve  be  one  going  to  a  muscle,  the  latter  will  be  caused  to  contract  ;  if  it 
be  one  of  common  sensation,  pain  will  be  produced  ;  if  one  of  special  sense, 
the  sensation  of  a  flash  of  light,  or  of  a  taste,  iSic,  will  be  produced,  accord- 
ing to  the  nerve  irritated.  These  effects  do  not  manifest  themselves  during 
the  even  passage  of  the  current,  Ijut  only  when  the  circuit  is  cither  opened  or 


-828]  Elect  rotomts.  805 

closed,  or  both.  Of  course  the  continuity  of  the  nerve  with  the  organ  where 
its  activity  manifests  itself  must  be  maintained  intact.  The  changes  set  up 
by  the  current  in  the  different  nerve-trunks  are  probably  similar,  the  various 
sensations,  &c.,  produced  depending  on  the  difterent  terminal  organs  with 
which  the  nerves  are  connected. 

Professor  Burdon  Sanderson  has  ascertained  that  the  movement  which 
causes  the  Diomca  musciptda  (Venus's  tly-trap),  one  of  what  are  called  car- 
nivorous plants^  to  close  its  hairy  leaves  ancl  thereby  entrap  insects  which 
alight  upon  it,  is  accompanied  by  an  electrical  current  in  a  manner  analogous 
to  that  manifested  in  muscular  contraction.  The  manner  in  which  the  irrita- 
tion is  caused  seems  immaterial. 

828.  Slectrotonus. — In  a  living  nerve,  as  will  be  stated  more  fully  in 
Chapter  X.,  certain  parts  of  the  surface  are  electropositive  to  certain  other 
parts,  so  that  if  a  pair  of  electrodes  connected  with  a  galvanometer  be  applied 
to  these  two  points,  a  current  will  be  indicated  ;  if  now  another  part  of  the 
nerve  be  interposed  in  a  galvanic  circuit,  it  will  be  found  that,  if  this  extra- 
neous current  be  passing  in  the  same  direction  as  the  proper  nerve-current, 
the  latter  is  increased,  and  vice  versa  ;  and  this  although  it  has  previously 
been  demonstrated  experimentally  that  none  of  the  battery  current  escapes 
down  the  nerve,  so  as  to  exert  any  influence  of  its  own  on  the  galvanometer. 
This  alteration  of  its  natural  electromotive  condition,  produced  through  the 
whole  of  a  nerve  by  the  passage  of  a  constant  current  through  part  of  it,  is 
known  as  the  elcctrotonic  state  ;  it  is  most  intense  near  the  extraneous,  or,  as 
it  is  called,  the  exciting  cicrrent.  It  continues  as  long  as  the  latter  is  pass- 
ing, and  is  attended  with  important  changes  in  the  excitability  of  the  nerve, 
or,  m  other  words,  the  readiness  with  which  the  nerve  is  thrown  into  a  state 
of  functional  activity  by  any  stimulus  applied  to  it.  Pfliiger,  who  has  inves- 
tigated these  changes,  has  named  the  part  of  the  nerve  through  which  the 
exciting  current  is  passing  the  intrapolar  region  :  the  condition  of  the  nerve 
close  to  the  positive  pole  is  called  aiielectrotonus  ;  that  near  the  negative 
pole,  kathelcctrotoniis.  The  excitability  of  the  nerve  is  diminished  in  the 
anelectrotonic  region,  so  that  with  a  motor  nerve,  for  example,  a  stronger 
stimulus  than  before  would  need  to  be  applied  at  this  part  in  order  to  obtain 
a  muscular  contraction  ;  in  the  kathelectrotonic  region,  on  the  contrary,  the 
excitability  of  the  nerve  is  heightened.  Moreover,  with  an  exciting  current 
of  moderate  strength,  the  power  of  the  nerve  to  conduct  a  stimulus  is  lowered 
in  the  anelectrotonic  region,  and  increased  in  the  kathelectrotonic  ;  with 
strong  currents  it  is  said  to  be  diminished  in  both. 

These  facts  have  to  be  taken  into  account  in  the  scientific  application  of 
galvanism  to  medical  purposes.  If,  for  instance,  it  is  wished  to  diminish  the 
excitability  of  the  sensory  nerves  of  any  part  of  the  body,  the  current  should 
be  passed  in  such  a  direction  as  to  throw  the  nerves  of  that  part  into  a  state 
of  anelectrotonus — and  similarly  in  other  cases. 

If  a  powerful  electric  current  be  passed  through  the  body  of  a  recently 
killed  animal,  violent  movements  are  produced,  as  the  muscles  ordinarily 
retain  their  vitality  for  a  considerable  time  after  general  systematic  death  : 
by  this  means,  also,  life  has  been  re-established  in  animals  which  were  appa- 
rently dead — a  properly  applied  current  stimulating  the  respiratory  muscles 
to  contract. 


8o6 


Dynamical  Electricity. 


[829- 


S29.  Heating:  effects. — When  a  voltaic  current  is  passed  through  a  metal 
wire  the  same  effects  are  produced  as  by  the  discharge  of  an  electric  battery 
(790)  ;  the  wire  becomes  heated,  and  even  incandescent  if  it  is  veiy  short 
and  thin.  With  a  powerful  battery  all  metals  are  melted,  even  iridium  and 
platinum,  the  least  fusible  of  metals.  Carbon  is  the  only  element  which  has 
not  hitherto  been  fused  by  it.  Despretz,  however,  with  a  battery  composed 
of  600  Bunsen's  elements  joined  in  six  series  (825),  raised  rods  of  very  pure 
carbon  to  such  a  temperature  that  they  were  softened  and  could  be  welded 
together,  yielding  an  incipient  fusion. 

A  battery  of  30  to  40  Bunsen's  elements  is  sufficient  to  melt  and  volatilise 
fine  wires  of  lead,  tin,  zinc,  copper,  gold,  silver,  iron,  and  even  platinum,  with 
differently  coloured  sparks.  Iron  and  platinum  burn  with  a  brilliant  white 
light ;  lead  with  a  purple  light ;  the  light  of  tin  and  of  gold  is  bluish-white  ; 

the  light  of  zinc 
is  a  mixture  of 
white  and  gold  ; 
finally,  copper 
and  silver  give 
a  green  light. 

The  thermal 
effects  of  the 
voltaic  current 
are  used  for 
firing  mines  for 
military  pur- 
poses and  for 
blasting  opera- 
tions. The  fol- 
lowing arrange- 
ment was  de- 
vised by  Colo- 
nel Schaw,  and 
serves  to  illustrate  the  principle  :— Fig.  771  represents  a  small  wooden  box 
provided  with  a  lid.  Two  moderately  stout  cojiper  wires,  bb\  insulated  by 
being  covered  with  gutta-percha,  are  deprived  of  this  coating  at  the  ends, 
which  arc  then  passed  through  and  through  the  box  in  the  manner  repre- 
sented in  the  figure.  The  distance  between  them  is  f  of  an  inch,  and  a  very 
fine  platinum  wire  (one  weighing  1-92  grain  to  the  yard  is  the  regulation 
size)  is  soldered  across.  The  object  of  arranging  the  wires  in  this  manner 
is  that  they  shall  not  be  in  contact,  and  that  the  strain  which  they  exert  may 
be  spent  on  the  box,  and  not  on  the  jilatinum  wire  joining  them,  which, 
being  extremely  thin,  would  be  broken  by  even  a  very  slight  pull.  Th.e  box 
is  then  filled  with  fine  grained  powder,  and  the  lid  tied  down.  The  wires  of 
the  fuse  are  then  carefully  joined  to  the  long  conducting  wires  which  lead  to 
the  battery  :  these  should  be  of  copper,  and  as  thick  as  is  convenient,  so  as 
to  offer  very  little  resistance  :  No.  16  gauge  copper  wire  is  a  suitable  size. 
The  fuse  is  then  introduced  into  the  charge  to  be  fired  :  if  it  is  for  a  sub- 
marine explosion  the  powder  is  contained  in  a  canister,  the  neck  of  which, 
after  the  introduction  of  the  fuse,  is  carefully  fastened  by  means  of  cement. 


Fig.  771. 


-830]     Laws  of  Heating  Effects.     Galvanothennoinetcr.        807 

When  contact  is  made  with  the  battery,  which  is  effected  throuj^h  the  inter- 
vention of  mercury  cups,  the  current  traversing  the  platinum  wire  renders  it 
incandescent,  which  fires  the  fuse  ;  and  thus  the  ignition  is  communicated 
to  the  charge  in  which  it  is  placed. 

The  heating  effect  depends  more  on  the  size  than  on  the  number  of  the 
plates  of  a  battery,  for  the  resistance  in  the  connecting  wires  is  small  (825). 
An  iron  wire  may  be  melted  by  a  single  Wollaston's  element,  the  zinc  of 
which  is  8  inches  by  6.  Hare's  battery  (805)  received  its  name  deflagrator 
on  account  of  its  greater  heating  effect,  produced  by  the  great  surface  of  its 
plates. 

When  any  circuit  is  closed,  a  definite  amount  of  heat,  H,  is  produced 
throughout  the  entire  circuit ;  and  the  amount  of  heat,  h,  produced  in  any 
particular  part  of  the  circuit  bears  to  the  total  heat,  H,  the  same  ratio  which 
the  resistance,  r,  of  this  part  bears  to  R,  that  of  the  entire  circuit.  Hence, 
in  firing  mines,  the  wire  to  be  hea'.ed  should  be  of  as  small  section  and  of  as 
small  conductivity  as  practicable.  These  conditions  are  well  satisfied  by 
platinum,  which  has  over  iron  the  advantage  of  being  less  brittle  and  of  not 
being  liable  to  rust.  Platinum  too  has  a  low  specific  heat,  and  is  thus  raised 
to  a  higher  temperature,  by  the  same  amount  of  heat,  than  a  wire  of  greater 
specific  heat.  On  the  other  hand,  the  conducting  wires  should  present  as 
small  a  resistance  as  possible,  a  condition  satisfied  by  a  stout  copper  wire  ; 
and  again,  as  the  heating  effect  of  any  circuit  is  proportional  to  the  square 
of  the  electromotive  force,  and  inversely  as  the  resistance,  a  battery  with  a 
high  electromotive  force  and  small  resistance,  such  as  Grove's  or  Bunsen's, 
should  be  selected. 

Another  application  of  the  heating  effect  is  to  what  are  called  safety  catches. 
These  are  lengths  of  lead  wire  or  strips  interposed  in  the  circuit  of  the 
powerful  currents  used  for  electrical  lighting  and  the  like.  Their  dimensions 
are  so  calculated  that  when  the  current  attains  a  certain  strength,  the  heat 
generated  is  sufficient  to  melt  them  and  thus  break  the  continuity  of  the 
circuit.  As  this  can  be  arranged  with  great  accuracy,  it  is  possible  so  to 
regulate  the  circuit  that  it  shall  not  exceed  a  certain  limit. 

By  means  of  a  heated  platinum  wire,  parts  of  the  body  may  be  safely 
cauterised  which  could  not  be  got  at  by  a  red-hot  iron  ;  the  removal  ot 
tumours  and  the  like  may  be  effected  by  drawing  a  loop  of  cold  platinum 
wire  round  their  base,  which  is  then  made  hot  by  pressing  the  button  of  a 
contact  arrangement,  and  gradually  pulled  together.  It  has  been  observed 
that  when  the  temperature  of  the  wire  is  about  600°  C,  the  combustion  of  the 
tissues  is  so  complete  that  there  is  no  haemorrhage;  while  at  1500°  the  action 
of  the  wire  is  like  that  of  a  sharp  knife.  For  other  purposes  of  this  galvajiic 
cauterisaiioiiy  platinum  wire  coiled  in  grooves  cut  in  a  porcelain  rod  is  used. 

830.  Xiaws  of  heatlng^  effects.  Calvanothermometer. — Although  the 
thermal  effects  are  most  obvious  in  the  case  of  thin  wires,  they  are  by  no 
means  limited  to  them.  The  laws  of  the  heating  effect  were  investigated  by 
Lenz,  by  means  of  an  apparatus  called  the  Galvanothcrmojiieter  (fig.  772). 
A  wide-mouthed  stoppered  bottle  was  fixed  upside  down,  with  its  stopper,  b^ 
in  a  wooden  box  ;  the  stopper  was  perforated  so  as  to  give  passage  to  two 
thick  platinum  wires,  connected  at  one  end  with  binding  screws,  ss,  while 
their  free  ends  were  provided  with  platinum  cones  by  which  the  wires  under 


8o8 


Dynamical  Electricity 


[830- 


investigation  could  be  readily  affixed ;  the  vessel  contained  alcohol,  the  tem- 
perature of  which  was  indicated  by  a  thermometer  fitted  in  a  cork  inserted 
in  a  hole  made  in  the  bottom  of  the  vessel.  The  current  is  passed  through 
the  platinum  wires,  and  its  strength  measured  by  means  of  a  tangent 
compass  interposed  in  the  circuit.  By  observing  the  increase  of  tempera- 
ture in  the  thermometer  in  a  given  time,  and 
knowing  the  weight  of  the  alcohol,  the  mass 
of  the  wire,  the  specific  heat,  and  the  calori- 
metric  values  (453)  of  the  vessel,  and  of  the 
thermometer,  compared  with  alcohol,  the  heat- 
ing effect  which  is  produced  by  the  current  in 
a  given  time  can  be  calculated. 

By  apparatus  of  this  kind  the  truth  of  the 
following  law  may  be  established. 

Tlic  heat  disengaged  in  a  given  time,  t,  is 
directly   proportional    to    the    square    of   the 
stre?tgth  of  the  current,  and  to  the  resistance. 
This  is  known  as  Joule's  law  (831),  and 

is    expressed    in    the   formula    H  =  C-R/  =  -— - 

R 

=  EC/.  If  the  values  E,  C,  R  are  expressed  in 
ergs,  we  get  the  value  H  in  water-gramme  de- 
grees if  we  divide  by  the  mechanical  equivalent  of  a  water-gramme  degree, 
that  is  by  4-16  x  10".  If  the  values  are  expressed  in  practical  units — volt, 
ohm,  ampere  (964) — we  get  the  value  in  the  same  unit  by  dividing  by  10^.   . 

If  the  current  passes  through  a  chain  of  platinum  and  silver  wire  of  equal 
sizes,  the  platinum  becomes  more  heated  than  the  silver  from  its  greater  re- 
sistance ;  and  with  a  suitable  current  the  platinum  may  become  incandescent 
while  the  silver  remains  dark.     This  experiment  was  devised  by  Children. 

If  a  long  thin  platinum  wire  be  raised  to  dull  redness  by  passing  a  voltaic 
current  through  it,  and  if  part  of  it  be  cooled  down  by  ice,  the  resistance  of 
the  cooled  part  is  diminished,  the  strength  of  the  current  increases,  and  the 
rest  of  the  wire  becomes  brighter  than  before.  If,  on  the  contrary,  a  part 
of  the  feebly  incandescent  wire  be  heated  by  a  spirit-lamp,  the  resistance  of 
the  heated  part  increases  ;  the  effect  is  the  same  as  that  of  introducing 
fresh  resistance,  the  strength  of  the  current  diminishes,  and  the  wire  ceases 
to  be  incandescent  in  the  non-heated  part. 

The  cooling  by  the  surrounding  medium  exercises  an  important  influence 
on  the  phenomenon  of  ignition.  A  round  wire  is  more  heated  by  the  same 
current  than  the  same  wire  which  has  been  beaten  out  flat  :  for  the  latter 
with  the  same  section  pffers  a  greater  surface  to  the  cooling  medium  than  the 
other.  For  the  same  reason,  when  a  wire  is  stretched  in  a  glass  tube  on 
which  two  brass  caps  are  fitted  airtight,  and  the  wire  is  raised  to  dull  in- 
candescence by  the  passage  of  a  current,  the  incandescence  is  more  vivid 
w  hen  the  air  has  been  pumped  out  of  the  tube,  because  it  now  simply  loses 
heat  by  radiation,  and  not  by  communication  to  the  surrounding  medium. 

Similarly,  a  current  which  will  melt  a  wire  in  air  will  only  raise  it  to  dull 
redness  in  ether,  and  in  oil  or  in  water  will  not  heat  it  to  redness  at  all,  for 
the  liquids  conduct  heat  away  more  readily  than  air  does. 


-831J       Relation  of  Heating  Effect  to  IVor/c  of  a  Battery.         809 

From  the  above  laws  it  follows  that  the  heating  effect  is  the  same  in  awn-e 
whatever  be  its  length,  provided  the  current  is  constant ;  but  it  must  be  remem- 
bered that  by  increasing  the  length  of  the  wire  we  increase  the  resistance, 
and  consequently  diminish  the  current  ;  further,  in  a  long  wire  there  is  a 
greater  surface,  and  hence  more  heat  is  lost  by  radiation  and  by  conduction. 

It  must  be  added  that  Joule's  law  only  holds  provided  the  current  does 
no  external  work,  such  as  acting  on  adjacent  conductors,  or  magnets — that, 
in  short,  the  thermal  is  the  only  action  of  the  current. 

831.  Graphical  representation  of  the  heating:  effects  in  a  circuit. — 
The  law  representing  the  production  of  heat  in  a  circuit  in  the  unit  of  time 
is  very  well  seen  by  the  following  geometrical  construction,  due  to  Professor 
Foster. 

The  heat  H  produced  in  a  circuit  in  the  unit  of  time  is  proportional  to 
the  square  of  the  strength  of  the  current  C,  and  to  the  resistance  R  (830), 

that  is  H  =  C-R  ;  but  since  C  =  ^  (825),  we  have  H  =  "I'. 
R  -R 

Draw  a  straight  line  DAB  (fig.  ITZ)-,  and  from  any  point  A  in  it  draw  a 
line  AC,  at  right  angles  to  DAB,  and  of  a  length  proportional  to  the  electro- 
motive force  of 
the  cell.  Lay 
off  a  length  AB 
proportional  to 
K  "^..^^  the     resistance 

^"^-^..^^^  of    the    circuit. 

^\  Join  CB,  and  at 

^""^  C    draw  a  line 

^"""--..^^^       at  right  angles 

^ -^ ~ -^^  to  BC,  and  let 

Fig.  773.  ^  I)  l^e  the  point 

where  this  line 

cuts  the  line  DAB.    Then  the  length  AD  is  proportional  to  the  heat  produced 

in  the  whole  circuit  in  unit  time.    For  the  triangles  ADC  and  ACB  are  similar, 

and  therefore  AD :  AC  =  AC :  AB  ;  that  is,  AD  =  ^^  ■  that  is,  H  =  ^\ 

AB  R     _ 

By  drawing  figures  similar  to  the  above  it  will  be  found  that  for  a  given 
electromotive  force  the  heat  is  inversely  proportional  to  the  resistance,  and  for 
a  given  resistance  directly  proportional  to  the  square  of  the  electromotive 
force.  That  is,  if  the  resistance  is  doubled,  the  heat  is  reduced  to  one-half  ;  if 
the  electromotive  force  is  doubled  the  heat  is  quadrupled. 

S32.  Relation  of  heating^  effect  to  work  of  a  battery. — In  every 
closed  circuit  chemical  action  is  continuously  going  on  ;  in  ordinary  cir- 
cuits, the  most  common  action  is  the  solution  of  zinc  in  sulphuric  acid,  which 
may  be  regarded  as  an  oxidation  of  the  zinc  to  form  oxide  of  zinc,  and 
a  combination  of  this  oxide  of  zinc  with  sulphuric  acid  to  form  water  and 
zinc  sulphate.  It  is  a  true  combustion  of  zinc,  and  this  combustion  serves  to 
maintain  all  the  actions  which  the  circuit  can  produce,  just  as  all  the  work 
which  a  steam-engine  can  effect  has  its  origin  in  the  combustion  of  fuel  (473). 

By  independent  experiments  it  has  been  found  that,  when  a  given  weight 
of  zinc  is  dissolved  in  sulphuric  acid,  a  certain  definite  measurable  quantity 


8io  Dynamical  Electricity.  [832- 

of  heat  is  produced,  which,  as  in  all  cases  of  chemical  action,  is  the  same, 
whatever  be  the  rapidity  with  which  this  solution  is  effected.  If  this  solution 
takes  place  while  the  zinc  is  associated  with  another  metal  so  as  to  form  a 
voltaic  couple,  the  rapidity  of  the  solution  will  be  altered  and  the  whole  cir- 
cuit will  become  heated — the  liquid,  the  plates,  the  containing  vessel  as  well 
as  the  connecting  wire.  But  although  the  distribution  of  the  heat  is  thus 
altered,  its  quantity  is  not.  If  the  values  of  all  the  several  heating  effects  in 
the  various  parts  of  the  circuit  be  determined,  it  will  still  be  found  that, 
however  the  resistance  of  the  connecting  wire  be  varied,  this  sum  is  exactly 
equivalent  to  that  produced  by  the  solution  of  a  certain  weight  of  zinc. 

If  the  couple  be  made  to  do  external  mechanical  work  the  case  is  dif- 
ferent. Joule  made  the  following  remarkable  experiment  : — A  small  zinc 
and  copper  couple  was  arranged  in  a  calorimeter,  and  the  amount  of  heat 
determined  while  the  couple  was  closed  for  a  certain  length  of  time  by  a 
short  thick  wire.  The  couple  still  contained  in  the  calorimeter  was  next 
connected  with  a  minute  electromagnetic  engine  (899),  by  which  a  weight  was 
raised.  It  was  thus  found  that  the  heat  produced  in  the  calorimeter  in  a 
given  time — while,  therefore,  a  certain  amount  of  zinc  was  dissolved — was 
less  while  the  couple  was  doing  work  than  when  it  was  not  ;  and  the 
amount  of  this  diminution  was  the  exact  thermal  equivalent  of  the  work 
performed  in  raising  the  weight  (497). 

That  the  whole  of  the  chemical  work  and  disengagement  of  heat  in  the 
circuit  of  an  ordinary  cell  has  its  origin  in  the  solution  of  zinc  in  acid  is  con- 
firmed by  the  following  experiment,  due  to  Favre  : — 

In  the  muffle  of  his  calorimeter  (456),  five  small  zinc  platinum  elements 
were  introduced  ;  the  other  muffle  contained  a  voltameter.  Now  when  the 
element  was  closed  until  one  equivalent  of  zinc  was  dissolved  in  the  whole  of 
the  cells,  \  of  an  equivalent  of  water  should  be  decomposed  in  the  voltameter 
(846),  which  was  found  to  be  the  case.  In  one  case  the  current  of  the 
battery  was  closed  without  inserting  the  voltameter,  and  the  heat  disengaged 
during  the  solution  of  one  equivalent  of  zinc  was  found  to  be  18,796  thermal 
units  ;  when,  however,  the  voltameter  was  introduced,  the  quantity  disengaged 
was  only  1 1,769  thermal  units.  Now  the  diftcrence,  7,027,  is  represented  by 
the  chemical  work  of  decomposing  \  of  an  equivalent  of  water  :  this  agrees 

very  well  with  the  number,  6,892  --^  34>4_r.^  which  represents  the  heat  disen- 
gaged during  the  formation  of  \  of  an  equivalent  of  water. 

However  complicated  may  be  a  voltaic  combination  the  total  heat  pro- 
duced in  it  is  the  sum  of  the  quantities  of  heat  which  are  produced  and  absorbed 
in  the  various  chemical  processes  which  take  place  in  it. 

We  may  illustrate  this  important  principle  by  reference  to  the  element 
of  l)e  la  Rue  and  Muller  (812),  the  chemical  actions  in  which  are  perhaps 
the  simplest  of  all  constant  elements.  The  normal  action  is  that,  when  the 
clement  is  closed,  zinc  decomposes  ammonium  chloride  with  the  formation 
of  zinc  chloride,  while  the  liberated  ammonium  unites  with  the  chlorine  of 
the  silver  chloride,  re-forming  ammonium  chloride  and  dcjxisiting  silver. 
The  heat  of  decomposition  and  of  re-formation  of  the  ammonium  chloride 
compensate  one  another,  and  the  net  result  is  the  formation  of  zinc  chloride, 
and  the  decomposition  of  silver  chloride.     Now  the  heat  produced  in  the 


-833]  Ljcminoiis  Effects.  8 1 1 

formation  of  a  molecule  ot  zinc  chloride  (ZnCl.,)  is  112,840  gramme  units, 
and  that  of  the  equivalent  silver  chloride  (2Ag  CI)  is  58,760.  The  difference 
is  54,800,  which  is  less  than  58,360,  the  heat  required  to  decompose  a  mole- 
cule of  water.  Hence  it  is  that  one  such  element  will  not  effect  a  continuous 
decomposition  of  water,  but  at  least  two  are  required  for  the  purpose.  In 
like  manner  the  heat  disposable  in  one  Daniell's  cell  is  represented  by  47,300, 
and  accordingly  at  least  two  of  these  elements  are  also  required. 

In  some  cases,  however,  the  current  of  a  single  cell  does  produce  a  feeble 
but  continuous  decomposition  of  water.  This  arises  from  the  fact  that  the 
water  of  the  voltameter  contains  air  in  solution,  and  the  hydrogen  as  it  is 
liberated  unites  with  the  dissolved  oxygen.  This  process  is  known  as 
electrolytic  convection. 

833.  Xinmlnous  effects. — Luminous  effects  are  obtained  when  the  battery 
is  sufficiently  powerful,  by  bringing  the  two  electrodes  very  nearly  in  contact  ; 
a  succession  of  bright  sparks  springs  sometimes  across  the  interval,  which 
follow  each  other  with  such  rapidity  as  to  produce  continuous  light.  Although 
the  quantity  of  electricity  put  in  motion  by  the  voltaic  current  is  very  great, 
the  distance  across  which  the  spark  passes  is  very  small.  Jacobi  found  that 
with  a  battery  of  12  Grove's  elements  the  electrodes  could  be  approached 
v.'ithin  0-0013  nim.  before  the  spark  passed. 

When  one  terminal  of  a  battery  of  a  few  elements  is  connected  with  a 
pile,  and  an  iron  wire  connected  with  the  other  is  moved  over  the  pile,  a 
stream  of  brilliant  luminous  sparks  is  obtained,  which  obviously  arises  from 
a  combustion. 

The  most  beautiful  effect  of  the  electric  light  is  obtained  when  two  pencils 
of  charcoal  are  connected  with  the  terminals  of  the  battery  in  the  manner 
represented  in  fig.  774. 
The  charcoal  b  is  fixed, 
while  the  charcoal  a  can 
be  raised  and  lowered  by 
means  of  a  rack  and  pinion 
motion,  c.  The  two  char- 
coals being  placed  in  con- 
tact, the  current  passes, 
and  their  ends  soon  be- 
come incandescent.  If 
they  are  then  removed  to 
a  distance  of  about  the 
tenth  of  an  inch,  accord- 
ing to  the  strength  of  the 
current,  a  luininous  arc 
extends  between  the  two 
points,  which  has  an  ex- 
ceedingly brilliant  lustre, 
and  is  called  the  voltaic 
arc.  _     _  

The  length  of  this  arc  ^ 

varies  with   the  force  of  '°  ''"*" 

the  current.     In  air  it  may  exceed  2;^inches,  with  a  batteiy  of  600  elements, 


8i2  Dynamical  Electricity.  [833- 

arranged  in  six  series  of  loo  each,  provided  the  positive  pole  is  uppermost, 
as  represented  in  the  figure  ;  if  it  is  undermost,  the  arc  is  about  one-third 
shorter.  In  a  partial  vacuum  the  distance  of  the  charcoals  may  be  greater 
than  in  air  ;  in  fact,  as  the  electricity  meets  with  no  resistance,  it  springs 
between  the  two  charcoals,  even  before  they  are  in  contact.  The  voltaic  arc 
can  also  be  produced  in  liquids,  but  it  is  then  much  shorter,  and  its  brilliancy 
is  greatly  diminished. 

The  voltaic  arc  has  the  property  that  it  is  attracted  when  a  magnet  is  pre- 
sented to  it — a  case  of  the  action  on  magnets  on  currents  (865). 

The  voltaic  arc  may  be  considered  as  formed  of  a  very  rapid  succession 
of  bright  sparks.  Its  colour  and  shape  depend  on  the  nature  of  the  conduc- 
tors between  which  it  is  formed,  and  it  is  probably  due  to  the  incandescent 
particles  of  the  conductor,  which  are  volatilised  and  transported  in  the  direc- 
tion of  the  current  ;  that  is,  from  the  positive  to  the  negative  pole.  The 
more  easily  the  electrodes  are  disintegrated  by  the  current,  the  greater  is 
the  distance  at  which  the  electrodes  can  be  placed.  Charcoal,  which  is  a 
very  friable  substance,  is  one  of  the  bodies  which  give  the  largest  luminous 
arc. 

Davy  first  made  the  experiment  of  the  electric  light,  in  1801,  by  means  of 
a  battery  of  2,000  plates,  each  four  inches  square.  He  used  charcoal  points 
made  of  light  wood  charcoal  which  had  been  heated  to  redness,  and  im- 
mersed in  a  mercury  bath  ;  the  mercury  penetrating  into  the  pores  of  the 
charcoal  increased  its  conductivity.  When  any  substance  was  introduced 
into  the  voltaic  arc  produced  by  this  battery,  it  became  incandescent  ;  pla- 
tinum melted  like  wax  in  the  flame  of  a  candle  ;  sapphire,  magnesia,  lime, 
and  most  refractory  substances  were  fused.  Fragments  of  diamond,  of 
charcoal,  and  of  graphite  rapidly  disappeared  without  undergoing  any 
previous  fusion. 

As  charcoal  rapidly  burns  in  air,  it  was  necessary  to  operate  in  vacuo, 
and  hence  the  experiment  was  for  a  long  time  made  by  fitting  the  two  points 
in  an  electric  egg,  like  that  represented  in  fig.  722.  At  present  the  electrodes 
are  made  of  gas  graphite,  a  modification  of  charcoal  deposited  in  gas  retorts  ; 
this  is  hard  and  compact,  and  only  burns  slowly  in  air  ;  hence  it  is  unneces- 
sary to  operate  in  vacuo.  When  the  experiment  is  made  in  vacuo,  there  is 
no  combustion,  but  the  charcoal  wears  away  at  the  positive  pole,  while  it  is 
somewhat  increased  on  the  negative  pole,  indicating  that  there  is  a  transport 
of  solid  matter  from  the  positive  to  the  negative  pole. 

It  appears  from  the  researches  of  Edlund  that  the  disintegration  of  the 
electrodes  which  takes  place  when  the  voltaic  arc  is  formed  gives  rise  to  a 
counter-electromotive  force  which  is  analogous  to  the  polarisation  which  takes 
place  in  the  decomposition  of  water  (806),  and  the  existence  of  which  can  be 
demonstrated  by  similar  experiments.  The  magnitude  of  this  force  varies 
with  the  nature  of  the  electrodes  ;  it  is  greatest  with  carbon,  amounting  to 
35  volts  ;  with  iron  it  is  25  ;  copper,  24  ;  zinc,  19  ;  and  cadmium  10  volts. 

The  resistance  of  the  arc  itself,  due  to  the  medium,  increases  like  other 
resistances  with  the  distance  of  the  terminals  ;  it  diminishes  as  the  strength 
of  the  current  increases,  for  then  the  temperature  increases.  Working 
with  carbon  electrodes,  it  was  found  to  amount  lo  \T)  ohm  for  each  mm.  of 
distance. 


-835]  Regulator  of  the  Electric  Light.  813 

This  counter-electromotive  force  explains  how  it  is  that  a  continuous  arc 
can  only  be  obtained  with  a  current  of  considerable  electromotive  force. 

834.  Foucault's  experiment. — This  consists  in  projecting  on  a  screen 
the  image  of  the  charcoal  points  produced  in  the  camera  obscura  at  the 
moment  at  which  the  electric  light  is  formed  (fig.  775).     By  means  of  this 


Fig-  775. 


experiment,  which  is  made  by  the  photo-electric  microscope  already  de- 
scribed (fig.  573),  the  two  charcoals  can  be  readily  distinguished,  and  the 
positive  charcoal  is  seen  to  become  somewhat  hollow  and  diminished,  while 
the  other  increases.  The  globules  represented  on  the  two  charcoals  arise 
from  the  fusion  of  a  small  quantity  of  silica  contained  in  the  charcoal.  When 
the  current  begins  to  pass,  the  negative  charcoal  first  becomes  luminous, 
but  the  light  of  the  positive  charcoal  is  the  brightest  ;  as  it  also  wears  away 
about  twice  as  rapidly  as  the  negative  electrode  it  ought  to  be  rather  the 
larger. 

835.  Regrulator  of  the  electric  light. — When  the  electric  light  is  to  be 
used  for  illumination,  it  must  be  as  continuous  as  other  modes  of  lighting. 
For  this  purpose,  not  only  must  the  current  be  constant,  but  the  distance  of 
the  charcoals  must  not  alter,  which  necessitates  the  use  of  some  arrange- 
ment for  bringing  them  nearer  together  in  proportion  as  they  wear  away. 
One  of  the  best  modes  of  effecting  this  is  by  an  apparatus  invented  by 
Duboscq. 

In  this  regulator  the  two  charcoals  are  movable,  but  with  unequal  veloci- 
ties, which  are  virtually  proportional  to  their  waste.  The  motion  is  trans- 
mitted by  a  drum  placed  on  the  axis  xy  (fig.  776).  This  turns,  in  the  direc- 
tion of  the  arrows,  two  wheels,  a  and  b.,  the  diameters  of  which  are  as  i  :  2, 
and  which  respectively  transmit  their  motion  to  two  rackworks,  C  and  C. 
C  lowers  the  positive  charcoal,  /,  by  means  of  a  rod  sliding  in  the  tube 
H,  while  the  other  C  raises  the  negative  charcoal,  ;/,  half  as  rapidly.  By 
means  of  the  milled  head  y  the  drum  can  be  wound  up,  and  at  the  same 
time  the  positive  charcoal  moved  by  the  hand  ;  the  milled  head  x  moves  the 


8i4 


Dynamical  Electricity, 


[835- 


negative  charcoal  also  by  the  hand,  and  independently^ of  the  first.  For  this 
purpose  the  axis,  xy^  consists  of  two  parts  pressing  against  each  other  with 
some  force,  so  that,  holding  the  milled  head  x  between  the  fingers,  the  other, 
_y,  may  be  moved,  and  by  holding  the  latter  the  former  can  be  moved.  But 
the  friction  is  sufficient  when  the  drum  works  to  move  the  two  wheels  a  and 
h  and  the  two  rackworks. 

The  two  charcoals  being  placed  in  contact,  the  current  of  a  powerful 
battery  of  40  to  50  elements  reaches  the  apparatus  by  means  of  the  wires  E 
and  E'.  The  current  rising  in  H  descends  by  the  positive  charcoal,  then  by 
the  negative  charcoal,  and  reaches  the  apparatus  •  but  without  passing  into 
the  rackwork  C,  or  into  the  part  on  the  right  of  the  plate  N  ;  these  pieces 

being  insulated  by  ivory 
discs  placed  at  their  lower 
part.  The  current  ultimately 
reaches  the  bobbin  B,  which 
forms  the  foot  of  the  regu- 
lator, and  passes  into  the 
wire  E'.  Inside  the  bobbin 
is  a  bar  of  soft  iron,  which 
is  magnetised  as  long  as  the 
current  passes  in  the  bobbin, 
and  demagnetised  when  it 
does  not  pass,  and  this  tem- 
porary magnet  is  the  regu- 
lator. For  this  purpose  it 
acts  attractively  on  an  arma- 
ture of  soft  iron.  A,  open  in 
the  centre  so  as  to  allow  the 
rackwork  C  to  pass,  and 
fixed  at  the  end  of  a  lever, 
which  works  on  two  points, 
;//;//,  and  transmits  a  slight 
oscillation  to  a  rod,  d^  which, 
by  means  of  a  catch,  /,  seizes 
the  wheel  z,  as  is  seen  on  a 
larger  scale  in  fig.  il"].  By 
an  endless  screw,  and  a  series 
of  toothed  wheels,  the  stop  is 
transmitted  to  the  drum,  and 
the  rackwork  being  fixed,  the 
same  is  the  case  with  the 
carbons.  This  is  what  takes 
place  so  long  as  the  mag- 
netisation in  the  bobbin  is 
strong  enough  to  keep  down 
the  armature  A  ;  but  in  pro- 
])ortion  as  the  carbons  wear  away,  the  current  becomes  feebler,  though  the 
voltaic  arc  continues,  so  that  ultimately  the  attraction  of  the  magnet  no 
longer  counterbalances  a  spring  r,  which  continually  tcinis  to  raise  the  arma- 


FlR    776 


-836] 


Brozvnincc's  Rcsrulator. 


815 


ture.     It  then  ascends,  the  piece  d  disengages  the  stop  z,  the  drum  works, 

and  the  carbons  come  nearer  ;  they  do  not,  however,  touch,  because  the 

strength  of  the  current  gains  the  upper 

hand,  the  armature  A  is  attracted,  and 

the   carbons   remain  fixed.      As  their 

distance  only  varies  within  very  narrow 

Hmits,  a  regular  and  continuous  light 

is  obtained  with  this  apparatus    until 

the  carbons  are  quite  used. 

By  means  of  a  regulator,  Duboscq 
illuminates  the  photogenic  apparatus 
represented  in  fig.  573,  by  which  all 
the  optical  experiments  may  be  per- 
formed for  which  sunlight  was  formerly 
necessary. 

836.  Browning's  reg'ulator. — -A 
much  simpler  apparatus,  represented 
in  fig.  778,  has  been  devised  by  Brown- 
ing, which  is  less  costly  than  the  other 
lamps,  and  also  requires  a  smaller 
number  of  elements  to  work  it.  The 
current  enters  the  lamp  by  a  wire  at- 
tached to  a  binding  screw  on  the  base 
of  the  instrument,  passing  up  the  pillar  _-__ 

by  the  small  electro-magnet  to  the  :i"lr^ 
centre  pillar  along  the  top  of  the  hori-  "— ==§ 
zontal   bar,   down    the   left-hand    bar  ~~ 

through  the  two  carbons,  and  away  by 
a  wire  attached  to  a  binding  screw  on 

the  left  hand.  A  tube  holding  the  upper  carbon  slides  freely 
up  and  down  a  tube  at  the  end  of  the  cross-piece,  and  would  by 
its  own  weight  rest  on  the  lower  carbon,  but  the  electromagnet 
is  provided  with  a  keeper,  to  which  is  attached  a  rest  that  en- 
circles the  carbon  tube  and  grasps  it.  When  the  electro-magnet 
works  and  attracts  the  keeper,  the  rest  tightens,  and  thereby 
prevents  the  descent  of  the  carbon.  When  the  keeper  is  not 
attracted  the  rest  loosens,  and  the  carbon-holder  descends. 

When  the  two  carbons  are  at  rest,  on  making  contact  with 
a  battery  the  current  traverses  both  carbons  and  no  light  is 
produced.  But  if  the  upper  carbon  be  raised  ever  so  little,  a 
brilliant  light  is  emitted.  When  the  lamp  is  thus  once  set  to 
work,  the  rod  attached  to  the  upper  carbon  may  be  let  go,  and 
the  magnet  will  afterwards  keep  the  lamp  at  work.  For  when 
some  of  the  carbon  is  consumed,  and  the  interval  between  the 
two  is  too  great  for  the  current  to  pass,  the  magnet  loses  some 
of  its  power,  the  keeper  loosens  its  hold  on  the  carbon,  and  this 
descends  by  its  own  weight.  When  they  are  sufficiently  near, 
but  before  they  are  in  contact,  the  current  is  re-established ; 
the  magnet  again  draws  on  the  keeper,  and  the  keeper  again  checks  the 


Fig.  77S. 


/ 


i---i^- 


Fig.  779. 


8i6  Dynamical  Electricity.  [836- 

descent  of  the  carbon,  and  so  forth.     Thus  the  points  are  retained  at  the 
right  distances  apart,  and  the  hght  is  continuous  and  brilhant. 

Stohrer  has  devised  a  regulator  for  the  electrical  light  which  is  very 
simple  in  principle,  and  which  also  only  requires  a  few  elements.  Its  essen- 
tial features  are  represented  in  fig.  779,  in  which  ^  is  a  cylinder  containmg 
vaseline  and  surrounded  by  the  wire  of  the  circuit  _/I  In  this  is  a  hollow 
cylindrical  floater  a.,  nearly  as  wide  as  the  vessel  ;  at  its  top  is  a  copper 
tube  r,  in  which  the  carbon  point  d  can  be  fixed.  A  stout  copper  wire  fixed 
to  the  bottom  of  the  float  dips  in  an  iron  tube  filled  with  mercury,  with 
which  is  connected  one  pole  of  the  battery  ;  the  other  pole  is  connected  with 
the  carbon  d\  which  is  supported  in  a  suitable  manner.  The  size  of  the  float 
is  such  that  it  moves  slowly  upwards,  so  that  the  carbon  d  presses  with  but 
very  slight  force  against  d'.  This  can  be  regulated  by  placing  small  weights 
in  the  collar  on  c.  An  insulated  wire  forming  part  of  the  circuit  is  coiled  in 
a  spiral  k  round  the  cylinder,  and  aids  the  regulation. 

837.  Properties  and  intensity  of  the  electric  Ilgrht. — The  electric 
light  has  similar  chemical  properties  to  solar  light  ;  it  effects  the  combina- 
tion of  chlorine  and  hydrogen,  acts  chemically  on  chloride  of  silver,  and 
can  be  applied  in  photography,  though  not  for  taking  portraits,  as  it  fatigues 
the  sight  too  greatly. 

Passed  through  a  prism,  the  electric  light,  like  that  of  the  sun,  is  decom- 
posed and  gives  a  spectrum.  WoUaston,  and  more  especially  Fraunhofer, 
found  that  the  spectrum  of  the  electric  light  differs  from  that  of  other  lights, 
and  of  sunlight,  by  the  presence  of  several  very  bright  lines,  as  has  been 
already  stated  (578).  Wheatstone  was  the  first  to  observe  that  by  using 
•electrodes  of  different  metals,  the  spectrum  and  the  lines  are  modified. 

Masson,  who  experimented  upon  the  light  of  the  electric  machine,  that  of 
voltaic  arc,  and  that  of  Ruhmkorff's  coil,  found  the  same  colours  in  the 
•electric  spectrum  as  in  the  solar  spectrum,  but  traversed  by  very  brilliant 
luminous  bands  of  the  same  shades  as  that  of  the  colour  in  which  they  occur. 
The  number  and  position  of  these  bands  do  not  depend  on  the  intensity  of 
the  light,  but,  as  we  have  seen  (833),  upon  the  substances  between  which 
the  voltaic  arc  is  formed. 

With  carbon  the  lines  are  remarkable  for  their  number  and  brilliancy  ; 
with  zinc  the  spectrum  is  characterised  by  a  very  marked  apple-green  tint, 
silver  produces  a  very  intense  green  ;  with  lead  a  violet  tint  predominates, 
and  so  on  with  other  metals. 

Bunsen.in  experimenting  with  48  couples,  and  removing  the  charcoals  to 
a  distance  of  a  quarter  of  an  inch,  found  that  the  intensity  of  the  electric 
light  is  equal  to  that  of  572  candles. 

Fizcau  and  Foucault  compared  the  chemical  effects  of  the  solar  and  the 
electric  lights  by  investigating  their  action  on  iodised  silver  plates.  Re- 
jiresenting  the  intensity  of  the  sun's  light  at  midday  at  1,000,  these  physicists 
found  that  the  light  from  a  battery  of  46  Bunsen's  elements  was  235,  while 
that  from  one  of  80  elements  was  only  238.  It  follows  that  the  intensity  does 
not  increase  to  any  material  extent  with  the  numl)er  of  the  couples  ;  but  ex- 
])criment  shows  that  it  increases  considerably  with  their  surface.  For  with 
a  battery  of  46  elements,  each  consisting  of  three  elements,  with  their  zinc 
and  copper  respectively  united  so  as  to  form  one  element  of  triple  surface 


-838J 


Electric  LigJiti7ig. 


817 


(82 5),  the  intensity  was  385,  the  battery  working  for  an  hour  ;  that  is  to  say, 
more  than  a  third  of  the  intensity  of  the  solar  light. 

Too  great  precautions  cannot  be  taken  against  the  effects  of  the  electric 
light  when  they  attain  a  certain  intensity.  The  light  of  100  couples  may 
produce  very  painful  affections  of  the  eyes.  With  600,  a  single  moment's 
exposure  to  the  light  is  sufficient  to  produce  very  violent  headaches  and 
pains  in  the  eye,  and  the  whole  frame  is  affected  as  by  a  powerful  sunstroke. 

838.  Electric  llgrbtingr. — Great  progress  has  of  late  been  made  in  the 
application  of  the  electric  light  to  purposes  of  ordinary  illumination.  This 
progress  has  been  mainly  due  to  the  improvements  which  have  been  made 
in  the  means  of  generating  electricity,  for  which  some  form  of  magneto  or 


6 


Fig.  780. 


Fig.  781. 


dynamo-electrical  machine  (916),  driven  by  steam  or  water  power  or  by  gas 
engines  (476),  is  used.  So  long  as  the  electricity  from  the  voltaic  battery 
was  alone  available  for  the  production  of  the  electric  light,  no  great  exten- 
sion was  possible,  for  the  cost  and  inconvenience  were  far  too  great  to 
permit  it  to  be  used  for  anything  more  than  lecture  purposes  and  occasional 
scenic  illumination. 

Veiy  considerable  improvements  have  also  been  made  in  the  lamps,  which 
are  ordinarily  divided  '\n\.o  arc  lamps,  in  which  the  light  is  produced  between 
carbon  points  automatically  kept  at  a  constant  distance  by  the  action  of  the 
current  itself,  and  incandescent  lamps,  in  which  the  light  is  produced  by  the 

3  O 


8i8  Dynamical  Electricity.  [838- 

incandescence  of  a  thin  continuous  solid  conductor.  To  this  may  be  added 
the  electrical  candles,  of  which  the  best  known  is  \\\&  JablochkoJ^  candle.  It 
consists  (fig.  780)  of  two  rods  of  gas  carbon,  a  and  b,  from  2  to  4  mm.  in 
diameter,  separated  by  a  layer  of  kaolin  or  Chinese  clay  about  2  mm.  thick, 
fixed  respectively  in  the  supports,  to  which  the  positive  and  negative 
electrodes  A  B  are  respectively  attached.  The  rods  are  insulated  from  each 
other  by  the  whole  being  bound  by  some  insulating  material. 

The  current  is  started  by  a  small  piece  of  carbon,  n,  placed  across  the 
top.  As  the  arc  passes,  the  kaolin  melts  away,  and  the  arrangement  may 
therefore  fitly  be  called  a  candle.  The  positive  electrode  wears  away  twice 
as  fast  as  the  negative,  which  would  soon  destroy  the  arc,  but  by  using  alter- 
nalin^  currents  the  unecjual  waste  of  the  carbons  is  prevented. 

Fig.  775,  which  represents  one  of  the  forms  of  an  arc  lamp,  may  be  taken 
as  an  example  of  the  manner  in  which  the  regulation  of  the  arc  is  effected. 

Regmc7^s  electric  lamp,  fig.  781,  consists  of  a  rectangular  copper  rod,  B, 
moving  in  a  copper  tube  A,  guided  by  four  pulleys,  «,  of  which  only  two  are 
shown  ;  to  B  is  fixed  a  cross-piece  holding  a  thin  carbon  pencil,  «,  the  lower 
part  of  which  passes  through  a  silver  guide,  and  its  end  presses,  but  not 
quite  over  the  centre,  against  a  carbon  disc,  w,  which  moves  about  a  hori- 
zontal axis.  The  piece  supporting  this  is  insulated  from  A,  but  is  connected 
with  the  negative  pole  by  a  wire,  b.  The  positive  current,  entering  by  A, 
passes  by  C  to  a  small  block  of  carbon,  o,  which  presses  against  the  pencil. 
Thus  the  current  only  passes  through  a  very  small  portion  of  this  pencil, 
and  it  is  this  small  portion  which  becomes  incandescent  and  forms  the  arc. 
The  rod,  as  it  burns  away  and  sinks  by  its  own  weight,  rotates  the  disc  in 
slowly,  and  prevents  its  being  irregularly  worn  away. 

When  either  of  the  carbon  electrodes  which  produce  the  electric  light  is 
increased  in  size  its  increase  of  temperature  is  lessened,  while  that  of  the 
other  is  greater.  When  the  negative  electrode  is  large  the  light  of  the 
positive  electrode  is  very  bright.  This  is  seen  in  Werder mannas  electric 
lamp,  which  consists  essentially  of  a  carbon  disc  about  2  inches  in  diameter 
and  an  inch  in  thickness,  which  is  connected  with  the  negative  pole  of  the 
battery  ;  the  positive  pole  is  a  rod  of  carbon  about  3  cm.  in  diameter,  of  any 
suitable  length  ;  it  slides  vertically  in  a  copper  tube,  which  serves  both  as  a 
guide  and  as  a  contact  for  it  ;  this  is  pressed  upwards  against  the  centre  by 
a  weight  passing  over  a  pulley.  The  current  can  be  passed  abreast  through 
as  many  as  ten  of  such  lamps,  though  it  seems  that  the  total  illuminating 
power  of  this  arrangement  is  not  so  great  as  when  only  two  parallel  lights 
are  employed. 

The  electrical  arc  has  had  a  very  useful  application  to  the  tcclding  or 
autogenous  soldering  of  metals,  that  is  to  say,  joining  them  without  the  use  of 
a  solder  ;  a  method  which  is  of  great  service  in  the  case  of  iron.  The  two 
plates  to  be  joined  are  placed  in  contact,  and  having  been  connected  with 
the  negative  pole,  the  positive  carbon  fixed  in  a  suitable  holder  is  held  at 
such  distance  that  the  arc  passes,  which  then  melts  one  plate  on  the  other. 
In  other  cases  the  two  pieces  of  metal  are  pressed  against  each  other,  and 
the  current  passed  through  the  line  of  contact. 

For  these  operations  accumulators  (849)  are  used  charged  by  dynamos, 
whi(  li  )ield  very  powerful  currents  ;  by  means  of  a  commutator  the  electro- 


-838] 


Electric  Lii'iitinc. 


819 

in  \ciy  wide 


Fig.  782. 


motive  force  and  the  strength  of  the  current  can  be  varied  w  i 
limits  at  the  will  of  the  operator. 

\'on  Hefner's  differential  lamp  is  represented  in  fig.  782  ;  the  current 
arriving  by  A  divides  at  /  (961)  ;  one  portion  passing  through  a  fine  wire 
coil,  R,  offering  a  large  resistance,  and  the  other  through  a  short  thick  coil  r, 
whence  it  passes  to  a  lever  which 
turns  about  d  ;  to  this  is  connected 
at  one  end,  w,  a  soft  iron  core  which 
plays  in  the  two  coils,  and  at  the 
other  end  is  the  positive  carbon  C,. 

When  the  carbons  are  apart  a 
great  resistance  is  presented,  and 
the  current  passes  chiefly  through 
R,  so  that  the  core  is  drawn  within 
R,  and  the  lever,  and  with  it  the 
carbon  C^  falls  ;  the  fastening  in  the 
holder  is  such  that  at  a  certain 
angle  the  carbon  C,  slips  in  the 
holder  a,  and,  touching  the  lower 
one,  the  current  now  passes  by 
rdQ^  C,  B  ;  the  iron  core  is  then  drawn  down,  but  the  holder  a  moves  up, 
grips  the  carbon,  which  it  moves  with  it,  and  the  arc  is  reproduced  ;  when 
its  normal  length  is  attained  its  resistance  increases  to  an  amount  such  that 
the  currents  passing  through  the  two  coils  now  balance  themselves,  and 
their  attraction  on  the  iron  being  equal  the  core  is  stationary.  Several  such 
lamps  may  be  arranged  in  a  circuit,  and  if  one  of  them  is  extinguished  it 
does  not  affect  the  others. 

Schwendler  has  devised  a  new  unit  of  luminous  intensity,  which  he 
calls  the  platinum  light  standard,  specially  for  use  with  the  electric  light. 
It  is  the  incandescence  produced  by  a  current  of  known  strength  passing- 
through  a  U-shaped  strip  of  platinum-foil  36-28  mm.  in  length,  2  mm.  in 
breadth,  and  0-017  mm.  in  thickness.  The  circuit  contains  a  rheostat  and  a 
galvanometer,  by  which  the  constancy  of  the  current  can  be  ensured  and 
observed.  When  the  strength  of  the  current  is  constant  the  intensity  of  the 
light,  radiated  by  the  platinum,  is  constant  also,  and  fulfils  all  the  conditions 
of  a  standard  measure  of  light,  as  it  can  always  be  reproduced  in  exactly  the 
same  form  from  pure  platinum. 

The  standard  of  light  adopted  by  the  International  Congress  of  Electri- 
cians in  1884  is  the  light  emitted  by  a  square  centimetre  of  melted  platinum 
when  on  the  point  of  solidifying. 

According  to  Rosetti  the  temperature  of  the  positive  carbon  is  between 
2400°  and  3900°  C.  ;  it  is  higher  the  smaller  is  the  radiating  surface.  The 
temperature  of  the  negative  electrode  lies  between  2138°  and  2530°. 

The  resistance  of  the  heated  air  in  the  arc  is  from  i  to  12  ohms  (834). 

Incandescent  lamps,  though  not  so  economical  as  arc  lights,  lend  them- 
selves best  to  the  distribution  of  the  electric  light.  We  have  seen  that  when 
a  strong  current  of  electricity  is  passed  through  a  wire  of  small  conductivity 
(829),  its  temperature  is  raised  to  incandescence  ;  if  the  strength  of  the 
current  is  increased,  the  brightness  of  the  light  increases,  but  in  a  greater 

3  G  2 


820 


Dynavi ical  Electricity 


[838- 


ratio  than  the  strength  of  the  current.  Unfortunately,  at  such  high  tempera- 
tures, wires  even  of  the  most  difficultly  fusible  metals  fuse  or  are  disinte- 
grated ;  and  the  only  material  which  does  not  fuse  at  the  highest  temperature 
is  carbon.  The  first  lamps  in  which  this  was  applied  were  constructed  inde- 
pendently by  Edison  in  America  and  Swan  in  this  country.  Fig.  783  is  a 
representation  oi Siuaiis  lamp.  Inside  the  globular  glass  \essel  with  a  neck, 
and  fused  to  it,  is  a  glass  rod,  through  which  pass  two  platinum  wires,  bent 

outside  in  loops.  These  loops 
can  be  easily  fitted  in  the  two 
bent  wires  in  the  holder  (fig. 
784),  which  are  in  contact  with 
the  binding  screws,  and  thus 
allow  a  current  to  be  transmitted. 
The  spring  wire  exerts  an  up- 
ward pressure,  so  as  to  always 
ensure  good  contact.  To  the 
other  ends  of  the  platinum  are 
fixed  the  characteristic  part,  the 
carbon  filament ;  this  is  about 
0-25  mm.  in  diameter,  and  is 
bent  in  the  form  of  a  double  loop. 
It  is  prepared  by  immersing 
crochet  cotton  in  sulphuric  acid 
of  a  certain  strength,  by  which 
it    is     converted    into   what   is 


Fig.  783- 


Fig.  784. 


known  as  vegetable  parchment.  This  is  then  carbonised  by  heating  it  to  a 
high  temperature  in  closed  vessels.  Before  sealing  the  bulb  it  is  exhausted 
of  air  by  means  of  a  Sprengel  pump,  and  the  vacuum  is  so  perfect  that  elec- 
tricity does  not  pass  in  it.  The  carbon  of  such  a  lamp,  which  is  a  thread 
about  127  cm.  in  length,  and  0-013  cm.  in  diameter,  has  a  resistance  of  143 
ohms  in  its  normal  incandescence. 

In  Edison's  lamp  the  carbon  filament  is  made  of  a  special  kind  of 
bamboo  carbonised  at  high  temperatures  in  closed  nickel  moulds.  In 
the  Maxim  lamp,  and  in  that  of  Lane  Fox,  the  carbon  filaments,  after 
being  carbonised  and  mounted,  are  heated  by  the  current  itself  in  an  atmo- 
sphere of  coal  gas  or  the  vapour  of  a  hydrocarbon  ;  in  this  way  carbon  is 
deposited  on  the  filament,  by  which  it  is  rendered  more  uniform  and  durable. 

If  we  surround  an  electric  light  in  one  case  by  an  opaque  calorimeter, 
which  therefore  absorbs  the  entire  radiation,  and  then  by  a  transparent  one, 
which  allows  the  light  to  pass,  it  will  be  found  that  the  luminous  radiation 
is  about  10  per.  cent,  in  the  case  of  arc  lamps  and  5  in  incandescent  lamps. 

The  lighting  power  varies  in  different  lamps  according  to  the  strength 
of  the  currents.  Edison's  lamp,  giving  i6-candle  power,  requires  a  current  of 
0-6  amperes  ;  taking  its  resistance  when  hot  at  170  ohms,  the  potential  dif- 
ference at  the  connections  would  be  from  Ohm's  law  (S25)  o-6  x  170=  102 
volts.  For  the  same  standard  of  light.  Swan's  lamp  requires  a  current  of 
1-28  amperes,  its  resistance  is  40,  and  hence  the  potential  difference  is  52 
volts. 

The  electric  effect  \'A,  dividctl  by  the  liL;lu  expressed  in  candles,  gives 


-839]  Mechanical  Effect  of  the  Battery.  82 1 

the  electric  effect  required  for  one  candle,  and  the  number  746,  divided  by 
the  number  thus  obtained,  gives  the  number  of  candles  which  can  be  obtained 
from  one  electrical  horse  power.  In  the  above  cases  these  are  198  and  180 
respectively.  Lamps  are  usually  classed  according  to  the  number  of  volts 
they  require.  Whatever  care  may  be  exerted  in  their  manufacture,  the 
carbons  at  last  give  way  ;  their  life,  however,  ought  to  be  from  1,000  to  2,000 
hours. 

839.  Mechanical  effects  of  the  battery. — Under  this  head  may  be  in- 
cluded the  motion  of  solids  and  liquids  effected  by  the  current.  An  example 
of  the  former  is  found  in  the  voltaic  arc,  in  which  there  is  a  passage  of  the 
molecules  of  carbon  from  the  positive  to  the  negative  pole  (834). 

The  mechanical  action  of  the  current  may  be  shown  by  means  of  the 
following  experiment  (fig.  785).  A  glass  tube,  AB,  bent  at  the  two  ends,  about 
50  cm.  in  length  and  i  cm.  in  diameter,  is  almost  filled  with  dilute  sulphuric 
acid,  and  a  globule  of  mercury,  ;;/,  is  introduced.  The  whole  is  fixed  in  a 
support,  and  the  level  of  the  tube  can  be  adjusted  by  the  screw  n,  the  drop 
of  mercury  itself  serving  as  index. 

When  the  two  poles  of  a  batteiy  of  4  or  5  cells  are  introduced  into  the  two 
ends,  the  globule  of  mercuiy  elongates  and  moves  towards  the  negative  pole 
with  a  velocity  which  increases  with  the  number  of  elements.  With  24,  a 
long  column  of  mercury  can  be  moved  through  a  tube  a  metre  in  length  ; 
with  50,  the  velocity  is  greater  and  the  mercury  divides  into  globules,  all 
moving  in  the  same  direc- 
tion. If  the  direction  of  the 
current  is  reversed,  the  mer- 
cury first  remains  stationary, 
and  then  moves  in  the  oppo- 
site direction. 

If  the  tube  is  gently  in- 
clined towards  the  positive 
pole,  the  mercury  is  still 
moved  with  the  current  ;  and 
a  moment  is  at  length  reached 
at  which  there  is  equilibrium 
between  the  force  of  the 
current  and  the  weight  of  the 
mercury.  The  component  of 
this  weight  parallel  to  the  plane  may  then  be  taken  as  representing  the 
mechanical  action  of  the  current  which  traverses  the  globule  of  mercury. 

A  similar  phenomenon,  known  as  electrical  endosniose,  is  observed  in  the 
following  experiment,  due  to  Porrett.  Having  divided  a  glass  vessel  into  two 
compartments  by  a  porous  diaphragm,  he  poured  water  into  the  two  com- 
partments to  the  same  height,  and  immersed  two  platinum  electrodes  in 
connection  with  a  battery  of  80  elements.  As  the  water  became  decomposed, 
part  of  the  liquid  was  carried  in  the  direction  of  the  current  through  the 
diaphragm,  from  the  positive  to  the  negative  compartment,  where  the  level 
rose  above  that  in  the  other  compartment.  A  solution  of  copper  sulphate  is 
best  for  these  experiments,  because  then  the  disturbing  influence  of  the  dis- 
engagement of  gas  at  the  negative  electrode  is  avoided. 


822  Dynmnical  Electricity.  [839- 

A  porous  vessel  is  necessary,  for  otherwise  the  transport  by  the  Hquid 
would  be  at  once  hydrostatically  equalised. 

According  to  Zollner  earth  currents  (894)  are  analogous  to  diaphragm 
currents  ;  there  are  currents  in  the  liquid  mass  in  the  interior  of  the  earth,  and 
these  currents  coming  in  contact  with  the  solidified  masses  produce  electrical 
currents. 

The  converse  of  these  phenomena  is  observed  when  a  liquid  is  forced 
through  a  diaphragm  by  mechanical  means.  Such  currents,  which  were  dis- 
covered by  Quincke,  are  called  diaphragm  currents.  A  porous  diaphragm, 
p,  is  fixed  in  a  glass  tube  (fig.  786),  in  which  are  also  fused  two  platinum 
wires  terminating  in  platinum  electrodes,  a  and  b  ;  on  forcing  a  liquid 
through  the  diaphragm  the  existence  of  a  current  is  evidenced  by  a  galvano- 
meter with  which  the  wires  are  connected,  the  direction  of  which  is  that  of 
the  flow  of  the  liquid.  The  difference  of  potential  due  to  this  flow  is  pro- 
portional to  the  pressure. 

According  to  Zollner,  all  circulatory  motions  in  liquids,  especially  when 
they  take  place  in  partial  contact  with  solids,  are  accompanied  by  electrical 

currents,  which  have  generally 
the  same  direction  as  that  in 
which  the  current  flows. 

Wertheim  found  that  the 
elasticity  of  metal  wires  is  di- 
minished by  the  current,  and 
not  by  the  heat  alone,  but  by  the  electricity  ;  he  has  also  found  that  the 
cohesion  is  diminished  by  the  passage  of  a  current. 

To  the  mechanical  effects  of  the  current  may  be  assigned  the  sounds 
produced  in  soft  iron  when  submitted  to  the  magnetising  action  of  a  discon- 
tinuous current — a  phenomenon  which  will  be  subsequently  described. 

840.  Electrocapillary  phenomena. — If  a  drop  of  mercury  be  placed  in 
dilute  sulphuric  acid  containing  a  trace  of  chromic  acid,  and  the  end  of  a 
bright  iron  wire  be  so  fixed  that  it  dips  in  the  acid  and  just  touches  the  edge 
of  the  mercury,  the  latter  begins  a  series  of  regular  vibrations  which  may 
last  for  hours.  The  explanation  of  this  phenomenon,  which  was  first  ob- 
served by  Kiihne,  is  as  follows  : — When  the  iron  first  touches  the  mercury, 
an  iron-mercury  couple  is  formed,  in  consequence  of  which  the  surface  of  the 
mercury  is  polarised  by  the  deposition  of  an  invisible  layer  of  hydrogen  ; 
this  polarisation  (806)  increases  the  surface-tension  of  the  mercury  (138),  it 
becomes  rounder,  and  contact  with  the  iron  is  broken  ;  the  chromic  acid 
present  depolarises  the  mercury,  its  original  shape  is  restored,  the  couple  is 
again  formed,  and  the  process  repeats  itself  continuously. 

Lippmann  was  led  by  the  observation  of  this  phenomenon  to  a  series 
of  interesting  experimental  results,  which  have  demonstrated  a  relation 
between  capillary  and  electrical  phenomena.  Of  these  results  the  most 
important  is  the  construction  of  a  capillary  electrometer. 

A  glass  tube,  A  (fig.  787),  is  drawn  out  to  a  fine  point,  and  is  filled  with 

mercury  :  its  lower  end  dips  in  a  glass  vessel,  B,  containing  mercury  at  the 

bottom  and  dilute  sulphuric  acid  at  the  top.     Platinum  wires  are  fused  in  the 

tubes  A  and  B,  and  terminate  in  the  binding  screws  a  and  b  respectively. 

Now  at  the  beginning  of  the  experiment,  the  i)osition  of  the  mercury  in  the 


-841] 


Chemical  Effects. 


823 


drawn-out  tube  is  such  that  the  capillary  action  due  to  the  surface-tension 
at  the  plane  of  separation  of  the  mercury  in  the  tube  and  the  liquid  is  suffi- 
cient to  counterbalance  the  pressure  of  the  column  A.  This  position  is 
observed  by  means  of  a 
microscope,  the  focus  of 
which  is  at  the  fiducial 
mark  on  the  glass  at  which 
the  mercurj'  stops.  If 
now  a  difference  of  po- 
tential be  established,  by 
connecting  the  poles  of 
a  cell  with  the  wires  a 
and  b,  the  surface-tension 
is  increased,  the  mercury 
ascends  in  the  capillary 
tube,  and  in  order  to 
bring  the  meniscus  back 
to  its  foriiier  position  the 
pressure  on  A  must  be 
increased.  This  is  most 
simply  effected  by  means 
of  a  thick  caoutchouc 
tube,  T,  connected  with 
the  top  of  A,  and  with  a 
manometer,  H ;  and  which 
can  be  more  or  less  com- 
pressed by  means  of  a 
screw,  E.    The  difference 


Fig.  7S7. 


in  level  of  the  two  legs  of  the  manometer  is  thus  a  measure  of  the  increase 
of  the  surface-tension,  and  therewith  of  the  difference  of  potential.  Lipp- 
mann  found,  by  special  experiments,  that  this  increase  is  almost  directly 
proportional  to  the  electromotive  force,  up  to  about  0-9  of  a  Daniell's  ele- 
ment. Each  electrometer  requires  a  special  table  of  graduation,  but  when 
once  this  is  constructed  it  can  be  directly  used  for  determining  electromotive 
forces.  It  should  not  be  used  for  greater  electromotive  forces  than  o-6  of  a 
Daniell ;  but  it  can  estimate  the  one-thousandth  part  of  this  quantity,  and, 
as  its  electrical  capacity  is  very  small,  it  can  show  rapid  changes  of  potential, 
which  ordinary  electrometers  cannot  do.  For  very  small  electromotive 
forces,  the  pressure  is  kept  constant,  and  the  displacement  of  the  meniscus 
is  measured  by  the  microscope.  Its  use  is  especially  convenient  with  zero 
methods. 

841.  Cbemlcal  eflfecta.^The  first  decomposition  effected  by  electricity 
was  that  of  water,  in  1800,  by  Carlisle  and  Nicholson,  by  means  of  a  voltaic 
pile.  Water  is  rapidly  decomposed  by  4  or  5  Bunsen's  cells  ;  the  apparatus 
(fig.  788)  is  convenient  for  the  purpose.  It  consists  of  a  glass  vessel  fixed  on 
a  wooden  base.  In  the  bottom  of  the  vessel  two  platinum  electrodes,/  and 
71,  are  fitted,  communicating  by  means  of  copper  wires  with  the  binding 
screws.  The  activity  of  these  electrodes  is  increased  by  covering  them  with 
a  deposit  of  pulverulent  platinum  by  electrolysis.     The  vessel  is  filled  with 


824 


Dynamical  Electricity. 


[841- 


water  to  which  some  sulphuric  acid  has  been  added  to  increase  its  conduc- 
tivity, for  pure  water  is  a  very  imperfect  conductor  ;  two  glass  tubes  filled 
with  water  are  inverted  over  the  electrodes,  and  on  interposing  the  apparatus 
in  the  circuit  of  a  battery,  decomposition  is  rapidly  set  up,  and  gas  bubbles 

rise  from  the  surface  of  each  pole. 
The  volume  of  gas  liberated  at  the 
negative  pole  is  about  double  that 
at  the  positive,  and  on  examination 
the  former  gas  is  found  to  be  hy- 
drogen and  the  latter  gas  oxygen. 
This  experiment  accordingly  gives 
at  once  the  qualitative  and  quanti- 
tative analysis  of  water.  The  oxy- 
gen thus  obtained  has  the  peculiar 
and  penetrating  odour  observed 
when  an  electrical  machine  is 
worked  (793),  and  which  is  due  to 
ozone.  The  water  contains  at  the 
same  time  peroxide  of  hydrogen,  in  producing  which  some  oxygen  is  con- 
sumed. Moreover,  oxygen  is  somewhat  more  soluble  in  water  than  hydrogen. 
Owing  to  these  causes  the  volume  of  oxygen  is  less  than  that  required  by  the 
composition  of  water,  which  is  two  volumes  of  hydrogen  to  one  of  oxygen. 
Hence  voltametric  measurements  are  most  exact  when  the  hydrogen  alone 
is  determined,  and  when  this  is  liberated  at  the  surface  of  a  small  electrode. 
842.  electrolysis. — The  term  electrolyte  was  applied  to  those  substances 
which,  like  water,  are  resolved  into  their  elements  by  the  voltaic  current,  by 
Faraday,  to  whom  the  principal  discoveries  in  this  subject  and  the  nomen- 


clature are  due.  Electrolysis  is  the  decomposition  by  the  voltaic  battery  ; 
the  positive  electrode,  or  that  by  which  posili\c  electricity  enters,  was  by 
Faraday  called  the  a/iode,  and  the  negative  electrode  the  katliodc.  The 
|)roducts  of  decomposition  are  ions ;  kation,  that  which  appears  at  the 
kathode  ;  and  a/iio;i,  that  which  appears  at  the  anode. 

By  means  of  the  battery,  the  compound  nature  of  several  substances 
which  had  previously  been  considered  as  elements  has  been  determined.  By 
means  of  a  battery  of  250  couples,  Davy,  shortly  after  the  discovery  of  the 
decomposition  of  water,  succeeded  in  decomposing  the  alkalies  potass  and 
soda,  and  proved  that  they  were  the  oxides  of  the  hitherto  unknown  metals 


842] 


Electrolysis. 


825 


potassium  and  sodium.  The  decomposition  of  potass  may  be  demonstrated, 
with  the  aid  of  a  battery  of  4  to  6  elements,  in  the  following  manner  :  a 
small  cavity  is  made  in  a  piece  of  solid  caustic  potass,  which  is  moistened, 
and  a  drop  of  mercuiy  placed  in  it  (fig.  789).  The  potass  is  placed  on  a 
piece  of  platinum  connected  with  the  positive  pole  of  the  battery.  The 
mercury  is  then  touched  with  the  negative  pole.  When  the  current  passes, 
the  potass  is  decomposed,  oxygen  is  liberated  at  the  positive  pole,  while  the 
potassium  liberated  at  the  negative  pole  amalgamates  with  the  mercury.  On 
distilling  this  amalgam  out  of  contact  with  air,  the  mercury  passes  off, 
leaving  the  potassium. 

A  very  convenient  arrangement  for  the  preparation  of  metallic  magnesium 
and  some  of  the  rarer  metals  consists  of  an  ordinary  clay  tobacco  pipe  (fig.  790), 
in  the  stem  of  which  an  iron  wire  is  inserted  just  extending  to  the  bowl,  which 
is  nearly  filled  with  a  mixture  of  the  chlorides  of  potassium  and  magnesium. 
This  is  melted  by  a  Bunsen's  burner,  and  a  piece  of  graphite  connected  by  a 
wire  with  the  positive  pole  of  a  battery  is  dipped  in  it,  the  wire  in  the  stem 
forming  the  negative  pole.  When  the  current  passes,  chlorine  gas  is  libe- 
rated at  the  positive  pole,  while  metallic  magnesium  collects  about  the  end 
of  the  iron  wire  in  the  bowl. 

The  decomposition  of  binary  compounds — that  is,  bodies  containing  two 
elements — is  quite  analogous  to  that  of  water  and  of  potass  ;  one  of  the 
elements  goes  to  the  positive  and  the  other  to  the  negative  pole.  The  bodies 
separated  at  the  positive  pole  are  called  electronegative  elements,  because  at 
the  moment  of  separation  they  are  considered  to  be  charged  with  negative 
electricity,  while  those  separated  at  the  negative  pole  are  called  electro- 
positive elements.  One  and  the  same  body  may  be 
electronegative  or  electropositive,  according  to  the 
body  with  which  it  is  associated.  For  instance, 
sulphur  is  electronegative  towards  hydrogen,  but 
is  electropositive  towards  oxygen.  The  various 
elements  may  be  arranged  in  such  a  series  that  any 
one  in  combination  is  electronegative  to  any  fol- 
lowing, but  electropositive  towards  all  preceding 
ones.  This  is  called  the  electrochemical  series,  and 
begins  with  oxygen  as  the  most  electronegative 
element,  terminating  with  potassium  as  the  most 
electropositive. 

The  decomposition  of  hydrochloric  acid  into  its 
constituents,  chlorine  and  hydrogen,  may  be  shown 
by  means  of  the  apparatus  represented  in  fig.  791. 
Carbon  electrodes  must,  however,  be  substituted  for  those  of  platinum, 
which  is  attacked  by  the  liberated  chlorine  :  a  quantity  of  common  salt  also 
must  be  added  to  the  hydrochloric  acid,  in  order  to  diminish  the  solubility 
of  the  liberated  chlorine.  The  decomposition  of  potassium  iodide  may  be 
demonstrated  by  means  of  a  single  element.  For  this  purpose  a  piece  of 
bibulous  paper  is  soaked  with  a  solution  of  starch,  to  which  potassium 
iodide  has  been  added.  On  touching  this  paper  with  the  electrodes,  a  blue 
spot  is  produced  at  the  positive  pole,  due  to  the  action  of  the  liberated  iodine 
on  the  starch. 


826  Dynamical  Electricity.  [842- 

One  of  the  best  methods  of  determining  whether  a  body  is,  or  is  not,  an 
electrolyte,  is  to  place  it  between  the  two  platinum  electrodes  of  a  battery, 
and  then,  disengaging  the  electrodes  from  the  battery,  connect  it  with  a 
galvanometer,  and  observe  whether  a  reverse  current,  due  to  polarisation  of 
the  electrodes  (806),  passes  through  the  galvanometer.  Such  a  current,  being 
due  to  the  accumulation  of  different  substances  on  the  two  electrodes,  is  a 
proof  that  the  substance  has  been  electrolytically  decomposed  by  the  original 
current  from  the  battery.  This  method  can  often  be  applied  when  it  is  dif- 
ficult, by  direct  chemical  methods,  to  detect  the  presence  of  products  of 
decomposition  at  the  electrodes. 

843.  Decomposition  of  salts. — Ternary  salts  in  solution  are  decomposed 
by  the  battery,  and  then  present  effects  varying  with  the  chemical  affinities 
and  the  intensity  of  the  current.  In  all  cases  the  acid,  or  the  body  which  is 
chemically  equivalent  to  it,  is  electronegative  in  its  action  towards  the  other 
constituent.  The  decomposition  of  salts  may  be  readily  shown  by  means  of 
the  bent  tube  represented  in  fig.  791.  This  is  nearly  filled  with  a  saturated 
solution  of  a  salt,  say  sodium  sulphate,  coloured  with  syrup  of  violets. 
The  platinum  electrodes  of  a  battery  of  four  Bunsen's  elements  are  then 
placed  in  the  two  legs  of  the  tube.  After  a  few  minutes  the  liquid  in  the 
positive  leg.  A,  becomes  of  a  red,  and  that  in  the  negative  leg,  B,  of  a  green 
colour,  showing  that  the  salt  has  been  resolved  into  acid  which  has  passed 
to  the  positive,  and  into  a  base  which  has  gone  to  the  negative  pole,  for  these 
are  the  effects  which  a  free  acid  and  a  free  base  respectively  produce  on 
syrup  of  violets. 

In  a  solution  of  copper  sulphate,  free  acid  and  oxygen  gas  appear  at  the 
positive  electrode,  and  metallic  copper  is  deposited  at  the  negative  electrode. 
In  like  manner,  with  silver  nitrate,  metallic  silver  is  deposited  on  the  nega- 
tive, while  free  acid  and  oxygen  appear  at  the  positive  electrode. 

This  decomposition  of  salts  was  formerly  explained  by  saying  that  the 
acid  was  liberated  at  the  positive  electrode  and  the  base  at  the  negative.  Thus 
potassium  sulphate,  K,OS03,  was  considered  to  be  resolved  into  sulphuric 
acid,  SO.,,  and  potash,  K.,0.  This  view  regarded  salts  composed  of  three 
elements  as  different  in  their  constitution  from  binary  or  haloid  salts.  Their 
electrolytic  deportment  has  led  to  a  mode  of  regarding  the  constitution  of 
salts  which  brings  all  classes  of  them  under  one  category.  In  potassium 
sulphate,  for  instance,  the  electropositive  element  is  potassium,  while  the 
electronegative  element  is  a  complex  of  sulphur  and  oxygen,  which  is  regarded 
as  a  single  group,  SO,,  and  to  which  the  name  cjij-j'/^^/wi?/'/ may  be  assigned. 
The  formula  of  potassium  sulphate  would  thus  be  K,,SO„  and  its  decom- 
position would  be  quite  analogous  to  that  of  potassium  chloride,  KCl, 
lead  chloride,  PbCl^,  potassium  iodide,  KI.  The  electronegati\c  group 
SO,  corresponds  to  a  molecule  or  two  atoms  of  chlorine  or  iodine.  In  the 
decomposition  of  potassium  sulphate,  the  potassium  liberated  at  the  negative 
pole  decomposes  water,  forming  potash  and  liberating  hydrogen.  In  like 
manner  the  electronegative  constituent  SO,,  which  cannot  exist  in  the  free 
state,  decomposes  into  oxygen  g'as,  which  is  liberated,  and  into  anhydrous 
sulphuric  acid,  SO3,  which  immediately  combines  with  water  to  form  ordi- 
nary sulphuric  acid,  H.,S04.  ^"  ^'^^^^  where  the  action  of  the  battery  is 
strong,  these  gases  are  liberated  at  the  corresponding  poles  ;  in  other  cases 


-845]  Grothilss's  Hypothesis.  827 

they  combine  in  the  Hquid  itself,  reproducing  water.  The  constitution  of 
copper  sulphate,  CuSO^,  and  of  silver  nitrate,  AgNOg,  and  their  decom- 
position, will  be  readily  understood  from  these  examples. 

844.  Transmissions  efiTected  by  the  current. — In  chemical  decompo- 
sitions effected  by  the  battery  there  is  not  merely  a  separation  of  the  elements, 
but  a  passage  of  the  one  to  the  positive  and  of  the  other  to  the  negative 
electrode.  This  phenomenon 
was  demonstrated  by  Davy  by 
means  of  several  experiments, 
of  which  the  two  following  are 
examples  : — 

i.  He  placed  solution  of  so- 
dium sulphate  in  two  capsules 
connected  by  a  thread  of  as- 
bestos moistened  with  the  same 
solution,     and     immersed     the 

positiv'-e  electrode  in  one  of  the  capsules,  and  the  negative  electrode  in  the 
other.  The  salt  was  decomposed,  and  at  the  expiration  of  some  time  all  the 
sulphuric  acid  was  found  in  the  first  capsule,  and  the  soda  in  the  second. 

ii.  Having  taken  three  glasses.  A,  B,  and  C  (fig  792),  he  poured  into  the 
first  solution  of  sodium  sulphate,  into  the  second  dilute  syrup  of  violets, 
and  into  the  third  pure  water,  and  connected  them  by  moistened  threads 
of  asbestos.  The  current  was  then  passed  in  the  direction  from  C  to  A. 
The  sulphate  in  the  vessel  A  was  decomposed,  and  in  the  course  of  time 
there  was  nothing  but  soda  in  this  glass,  which  formed  the  negative  end, 
while  all  the  acid  had  been  transported  to  the  glass  C,  which  was  positive, 
B  containing  only  pure  water.  If,  on  the  contrary,  the  current  passed  from 
A  to  C,  the  soda  w^as  found  in  C,  while  all  the  acid  remained  in  A  ;  but  in 
both  cases  the  remarkable  phenomenon  was  seen  that  the  syrup  of  violets  in 
B  neither  became  red  nor  green  by  the  passage  of  the  acid  or  base  through 
its  mass,  a  phenomenon  the  explanation  of  which  is  based  on  the  hypothesis 
enunciated  in  the  following  paragraph. 

845.  Grottaiiss's  liypotbesis. — Grothiiss  has  given  the  following  expla- 
nation of  the  chemical  decompositions  effected  by  the  battery.  Adopting  the 
hypothesis  that  in  every  binary  compound,  or  body  which  acts  as  such,  one 
of  the  elements  is  electropositive,  and  the  other  electronegative,  he  assumes 
that,  under  the  influence  of  the  contrary  electricities  of  the  electrodes,  there 
is  effected,  in  the  liquid  in  which  they  are  immersed,  a  series  of  successive 
decompositions  and  recompositions  from  one  pole  to  the  other,  Hence  it  is 
only  the  elements  of  the  terminal  molecules  which  do  not  recombine,  but, 
remaining  free,  appear  at  the  electrodes.  Water,  for  instance,  is  formed  of 
one  atom  of  oxygen  and  two  atoms  of  hydrogen  ;  the  first  gas  being  electro- 
negative, the  second  electropositive.  Hence  when  the  liquid  is  traversed  by 
a  sufficiently  powerful  current,  the  molecule  a  in  contact  with  the  positive 
pole  arranges  itself  as  shown  in  fig.  793 — that  is,  the  oxygen  is  attracted  and 
the  hydrogen  repelled.  The  oxygen  of  this  molecule  is  then  given  off  at  the 
positive  electrode,  the  liberated  hydrogen  immediately  unites  with  the  oxygen 
of  the  molecule  b,  the  hydrogen  of  this  with  the  oxygen  of  the  molecule  c, 
and  so  on,  to  the  negative   electrode,  where  the  last   atoms  of  hydrogen 


Ml 


Fig.  793- 


828  Dynamical  Electricity.  [845- 

become  free  and  appear  on  the  poles.      The  same   theory  appHes  to   the 
metallic  oxides,  to  the  acids  and  salts,  and  explains  why  in  the  experiment 

mentioned  in  the  preceding  para- 
graph the  syrup  of  violets  in  the 
vessel  B  becomes  neither  red  nor 
green.  The  reason  why,  in  the 
fundamental  experiment,  the  hy- 
'  drogen  is  gi\en  off  at  the  negative 
pole  when  the  circuit  is  closed  will 
be  readily  understood  from  a  consideration  of  this  hypothesis. 

Clausius  objected  that,  according  to  this  theory,  a  very  great  force  must 
be  required  for  overcoming  the  affinity  for  each  other  of  the  oppositely 
electrolysed  particles  of  the  compound  ;  and  that  below  a  certain  minimum 
strength  of  current  no  decomposition  could  occur.  Now  Buff  has  shown  that 
the  action  of  even  the  feeblest  currents  continued  for  a  long  time  can  pro- 
duce decomposition.  Again,  when  the  necessary  strength  of  the  current  is 
obtained,  it  should  be  sudden  and  complete  ;  whereas  we  know  it  to  be  pro- 
portional to  the  strength  of  the  current. 

To  overcome  this  difficulty  Clausius  applies  the  theory  now  generally 
admitted  of  the  constitution  of  liquids  (292).  The  particles  of  a  compound 
liquid  have  not  the  rigid  unalterable  condition  of  a  solid  body  ;  they  are  in  a 
perpetual  state  of  separation  and  reunion,  so  that  we  must  suppose  compound 
bodies  and  their  elementary  constituents  to  coexist  with  each  other  in  a  liquid. 
Water,  for  instance,  contains  particles  of  water,  together  with  particles  of 
oxygen  and  of  hydrogen  ;  the  former  are  being  continually  decomposed  and 
the  latter  continually  reunited.  When  the  voltaic  current  passes,  it  acts  on 
the  motion  of  the  molecules  in  such  a  manner  that  the  negatively  electrical 
particles  of  oxygen  pass  to  the  positive  electrode,  and  the  positive  electrical 
particles  of  hydrogen  to  the  negative  electrode,  and  so  prevents  their  re- 
combination. Hence  the  current  does  not  bring  about  the  decomposition, 
but  utilises  it,  to  give  definite  direction  to  the  particles  which  arc  already, 
separated. 

These  considerations  explain  why  the  conductivity  of  a  liquid  increases 
with  the  temperature  (95S)  ;  for  the  velocity  of  the  molecules  (294)  and  the 
number  of  the  partial  molecules  are  thereby  increased.  It  also  shows  that  the 
conductivity  should  increase  with  the  concentration  of  the  liquid,  seeing  that 
a  great  number  of  decomposable  molecules  must  be  favoural^le  to  the  move- 
ment of  electricity.  On  the  other  hand,  an  increase  in  the  number  must 
be  owing  to  the  increased  number  of  collisions  ;  hence  it  is  that,  though 
the  conductivity  increases  with  the  concentration,  it  does  so  more  slowly 
than  in  direct  ratio,  and  it  is  not  diftlcult  to  understand  that  for  some  liquids 
a  maximum  concentration  corresponds  to  a  maximum  conductivity. 

This  also  explains  why  solid  chemical  compounds,  such  as  water  and  pure 
acids,  which  within  the  ordinary  range  of  temperatures  are  not  subject  to 
dissociation  (389),  are  not  electrolysed,  and  therefore  not  decomposed,  while 
mixtures  of  acids  and  water,  and  solutions  of  salts,  which  may  be  regarded 
as  chemical  compounds  in  a  slate  of  dissociation,  are  easily  electrolysed 
and  conduct  well. 

In  dealing  with  iiiolccular  maj^nitudcs,  theoretical  investigations  make  it 


-846J  Laivs  of  Electrolysis.  829 

probable  that  the  electrolytic  resistance,  which  the  molecules  experience  in 
their  being  moved  by  the  current,  is  of  the  same  order  of  magnitude  as  the 
capillary  resistance  which  results  from  their  friction  in  the  liquid  (147). 
Nothing  is  opposed  to  the  idea  that  electrolysis  is  a  purely  mechanical  pro- 
cess. Decomposition  occurs  in  the  first  place  by  dissociation ;  the  differ- 
ence of  potential  is  the  force  in  virtue  of  which  the  previously  united  mole- 
cules are  urged  in  contrary  directions.  The  moving  molecules  are  the 
carriers  of  the  motion  of  electricity  and  produce  the  current  ;  the  resistance 
which  they  thereby  experience  is  the  electrical  resistance  of  the  liquid.  This, 
therefore,  is  the  cause  of  the  development  of  heat  in  the  circuit. 

846.  Xiaws  of  electrolysis. — The  laws  of  electrolysis  were  discovered 
by  Faraday  ;  the  most  important  of  them  are  as  follows  : — 

I.  Elecfrolysis  cantiot  take  place  unless  the  electrolyte  is  a  co7iductor. 
Hence  ice  is  not  decomposed  by  the  battery,  because  it  is  a  bad  conductor. 
Other  bodies,  such  as  lead  oxide,  silver  chloride,  &c.,  are  only  electrolysed 
in  a  fused  state — that  is,  when  they  can  conduct  the  current.  The  converse 
of  this  is  true  ;  if  a  liquid  transmits  a  current  it  must  be  an  electrolyte.  From 
the  fact  that  he  was  able  to  obtain  a  current  in  liquids  which  deflected  a 
galvanometer  without  producing  any  visible  decomposition,  Faraday  inferred 
that  liquids  had  a  slight  conductivity  like  that  of  metals  independently  of 
their  electrolytic  conductivity.  This  apparent  conductivity  is  however  to  be 
assigned  to  electrical  convectioji  (832). 

II.  The  energy  of  the  electrolytic  action  of  the  current  is  the  same  in  all 
its  parts. 

For  if  a  number  of  voltameters  V,  V,  V"  {vide  st/p.),  are  arranged  in 
series  so  that  they  are  all  traversed  by  the  same  current  (fig.  794),  it  is  found 
that  the  weight  of  hy- 
drogen in  each  of  them 
in  the  same  time  is  the 
same,  whatever  may  be 
the  nature  and  distance 
of  the  electrodes,  the 
proportion  and  nature  of 
the  acid. 

If  the  current  from  the  battery  divides  at  A  into  two  branches  (fig.  795), 
in  which  are  two  equal  voltameters  Vj  and  ¥„,  then  the  quantities  of  gas 
liberated  in  V  and  V" 
will  still  be  equal  to  each 
other ;  and  the  quantities 
in  Vj  and  Vn  will  be  equal 
to  each  other,  but  each 
will  only  have  half  the 
quantity  which  passes  in 
either  of  the  voltameters  V  and  V". 

III.  The  same  quantity  of  electricity — that  is,  the  same  electric  current — 
decomposes  chemically  equivalent  quantities  of  all  the  bodies  which  it  tra- 
verses ;  from  which  it  follows,  that  the  weights  of  elements  separated  in  these 
electrolytes  are  to  each  other  as  their  cJiemical  equivale7its. 

In  a  circuit  containing  a  voltameter,  V,  Faraday  introduced  a  tube,  AB, 


830 


D  vnaiii  ical  Electric  it  j '. 


[846 


containing  tin  chloride  kept  in  a  state  of  fusion  by  the  Jieat  of  a  spirit 
lamp  (fig.  796).  In  the  bottom  of  this  the  negative  pole  was  fused,  while  the 
positive  electrode  consisted  of  a  rod  of  a  graphite  ;  when  the  current  passed 
chlorine  was  liberated  at  the  positive,  while  tin  collected  at  the  negative 
pole  ;  in  like  manner  lead  oxide  was  electrolysed  and  yielded  lead  at  the 
negative  and  oxygen  at  the  positive  pole.  Comparing  the  quantities  of 
substances   liberated,  they  are   found   to  be  in  a  certain  definite  relation. 

B 


Fig.  796. 

Thus  for  every  18  parts  of  water  decomposed  in  the  voltameter  there  will 
be  liberated  2  parts  of  hydrogen,  207  parts  of  lead,  and  117  of  tin  at  the 
respective  negative  electrodes,  and  16  parts  of  oxygen  and  71  (or  2  x  35-5) 
parts  of  chlorine  at  the  corresponding  positive  electrodes.  Now  these  num- 
bers are  exactly  as  the  equivalents  (not  as  the  atomic  weights)  of  the  bodies. 

It  will  further  be  found  that  in  each  of 
the  cells  of  the  battery  65  parts  by  weight 
of  zinc  have  been  dissolved  for  every  two 
parts  by  weight  of  hydrogen  liberated  ; 
that  is,  that  for  every  equivalent  of  a  sub- 
stance decomposed  in  the  circuit  one  equi- 
valent of  zinc  is  dissolved.  This  is  the 
case  whatever  be  the  number  of  cells.  An 
increase  in  the  number  only  has  the  effect 
of  overcoming  the  great  resistance  which 
many  electrolytes  offer,  and  of  accelerating 
the  decomposition.  It  does  not  increase 
the  quantity  of  electrolyte  decomposed.  If 
in  any  of  the  cells  more  than  65  parts  of 
zinc  arc  dissolved  for  every  two  parts  of 
hydrogen  liberated,  this  arises  from  a  dis- 
advantageous local  action  ;  and  the  more 
perfect  the  battery,  the  more  nearly  does 
it  approach  this  ratio. 
Kiy.  7yj,_  Chemistry  takes  account  of  the  valency 

of  an  element,  and  divides  them  into 
vi07iads^  dyads,  triads,  and  tetrads — a  classification  based  on  their  equiva- 
lence to  and  their  power  of  replacing  other  elements  ;  thus  one  atom  of  the 


-846] 


Silver   Voltameter. 


831 


monad  hydrogen  (H  =  i),  the  basis  of  this  classification,  or  one  atom  of 
silver  (Ag=  108),  would  combine  with  one  atom  of  chlorine  (€1  =  35-5)  oi'  one 
atom  of  iodine  (I  =  127).  One  atom  of  oxygen  (O  =  16)  unites  with  two  atoms 
of  hydrogen  to  form  water,  or  with  two  atoms  of  silver  to  form  silver  oxide  ; 
one  atom  of  the  dyad  zinc  (Zn  =  65)  unites  with  one  atom  of  the  dyad  oxygen  or 
of  the  dyad  sulphur  (S  =  32).  Again,  gold  is  a  triad,  and  one  atom  (Au  =  196) 
can  combine  with  three  atoms  of  chlorine,  and,  accordingly,  one  monad  is 
equivalent  to  one-third  of  the  atom  of  the  triad.  Now  electrolysis  proceeds 
according  to  the  equivalence  ;  that  is,  the  same  quality  of  electricity  which 
liberates  one  atom  of  a  monad  liberates  half  a  one  of  a  dyad,  and  a  third  of 
a  triad.  This  remark  applies  to  the  compound  groups  such  as  NO3,  which 
is  a  monad,  and  SO.,,  which  is  a  dyad. 

IV.  It  follows  from  the  above  law,  that  the  quantity  of  a  body  decomposea 
in  a  given  time  is  proportional  to  tJie  strength  of  the  ciin'ent.  On  this  is 
founded  the  use  of  Faraday's  voltameter^  in  which  the  intensity  of  a  current 
is  ascertained  from  the  quantity  of  water  which  it  decomposes  in  a  given  time. 

A  convenient  form  of  this  instrument  is  that  represented  in  fig.  797.  The 
vessel  a  is  that  in  which  the  water  is  decomposed,  and  contains  two  platinum 
plates,  and  is  in  connection  with  the  flask  b,  which  contains  water.  In  this 
is  a  lateral  dehvery  tube,  c,  which  is  inclined  until  the  level  of  the  liquid  in 
it  is  the  same  as  in  the  funnel  tube  n.  The  air  is  then  under  the  same  pres- 
sure as  the  atmosphere.  When  the  battery  is  connected  with  the  decom- 
posing cell  a,  the  gases  disengaged  expel  a  corresponding  volume  of  water 
through  the  delivery  tube  c  ;  at  the  conclusion  of  the  experiment,  this  tube 
is  inclined  until  the  liquid  is  at  the  same  level  as  in  the  tube  n  and  in  the 
flask.  The  weight  of  the  liquid  expelled 
is  then  a  direct  measure  of  the  volume  of 
the  disengaged  gases. 

The  use  of  this  voltameter  appears 
simple  and  convenient  ;  and  hence  some 
physicists  have  proposed  as  unit  of  the 
strength  of  current,  that  current  which 
in  one  viitiute  yields  a  cubic  centimetre  of 
mixed  gas  reduced  to  the  temperature  0° 
and  the  pressure  760  mm.  This  isfacobPs 
unit.  It  is  equal  to  0-09567  ampere.  Yet, 
for  reasons  mentioned  before  (841),  the 
measurements  should  be  based  on  the 
volume  of  hydrogen  liberated. 

Poggendorft's  silver  voltai/ieter,  fig. 
798,  is  an  instrument  for  measuring  the 
strength  of  the  current.  A  solution  of 
silver  nitrate  of  known  strength  is  placed 
in  a  platinum  dish  which  rests  on  a  brass -^ 
plate  that  can  be  connected  with  the 
negati\e  pole  of  the  battery  by  means  of 
the  binding   screw  b.      In    this   solution  ^'^'  ^'^^' 

dips  the  positive  pole,  which  consists  of  a  rod  of  silver  wrapped  round  with 
muslin,  and  suspended  to  an  adjustable  support.    When  the  current  passes. 


832  Dynavtical  Electricity.  [846- 

silver  separates  at  the  negative  pole,  and  is  washed,  dried,  and  weighed  ; 
and  the  weii^dit  thus  produced  in  a  given  time  is  a  very  accurate  measure 
of  the  strength  of  the  current.  Some  silver  particles  which  are  apt  to 
become  detached  from  the  positive  pole  are  retained  in  the  muslin. 

It  has  been  found  by  experiment  that,  when  water  is  decomposed,  a 
current  of  i  ampere  liberates  0-000010386  gramme  or  o-ii68  cc.  of  hydrogen 
in  a  second;  this,  then,  is  the  electrochemical  equivalent  of  hydrogefi^  and 
from  this  we  can  deduce  the  weight  of  any  element  liberated  in  the  same 
time  by  unit  current,  if  we  multiply  it  by  the  equivalent  weight  of  the  element 
referred  to  hydrogen.  The  equivalent  of  silver  is  usually  taken  at  108  ; 
hence,  if  any  of  its  salts  are  decomposed,  the  weight  of  silver  liberated  by 
an  ampere  in  a  second  is  0-0011217  gramme  ;  this  is  the  electrochemical 
equivalent  of  silver,  and  similarly  that  of  copper  is  0-0003281. 

The  quantity  of  electricity  which  passes  through  a  conductor  with  a 
current  of  one  ampere  is  called  a  coulomb  {!]Z'S)i  ^.nd  thus  we  may  say  that  a 
coulomb  of  electricity,  in  traversing  an  electrolyte,  carries  with  it  a  weight 
of  a  metal  which  is  represented  by  its  electrochemical  equivalent. 

The  current  from  the  electrical  machine,  which  is  of  very  high  potential, 
is  capable  of  traversing  any  electrolyte,  but  the  quantity  which  it  can  decom- 
pose is  extremely  small  as  compared  with  even  the  smallest  voltaic  apparatus, 
and  the  quantity  of  electricity  developed  by  the  frictional  machine  is  very 
small  as  compared  with  that  developed  by  chemical  action.  It  has  been 
calculated  by  Weber  that  if  the  quantity  of  positive  electricity  required  to 
decompose  a  grain  of  water  were  accumulated  on  a  cloud  at  a  distance  of 
3,000  feet  from  the  earth's  surface,  it  would  exert  an  attractive  force  upon 
the  earth  of  upwards  of  1,500  tons. 

846^;.  IWigration  of  the  Ions. — From  what  has  been  said,  it  would  seem 
that  when  a  solution  of  copper  sulphate  is  electrolysed  between  copper  elec- 
trodes, for  every  equivalent  of  copper  deposited  at  the  negative  electrode 
an  equivalent  weight  should  be  dissolved  at  the  positive,  and,  the  transfer 
taking  place  as  described,  the  concentration  of  the  solution  should  remain 
unchanged.  This,  however,  is  not  the  case  ;  when  the  operation  takes 
place  without  any  agitation  of  the  solution,  the  liquid  about  the  negative 
pole  becomes  lighter  in  colour,  indicating  that  the  solution  there  is  weaker. 

This  phenomenon,  which  was  investigated  by  Hittorf,  is  ascribed  by  him 
to  the  fact  that  in  electrolysis  both  electricities,  together  with  their  ions  or 
products  of  electrolytical  decomposition,  travel  in  the  liquid  towards  their 
respective  electrodes,  but  with  unequal  velocities,  and  this  transference  is 
called  the  migration  of  the  ions.  Each  ion  has  a  special  velocity  in  the  liquid 
independently  of  the  compound  of  which  it  forms  part  ;  thus  in  the  same 
time  S04  travels  twice  as  fast  as  Cu. 

The  number  which  expresses  this  rate  of  travel  is  called  «,  and  has  this 
meaning  :  let  us  conceive  a  vertical  layer  in  the  liquid  the  concentration  of 
which  remains  unchanged  by  what  takes  place  on  each  side  ;  then,  if  after 
electrolysis  we  determine  the  quantity  of  the  constituents  on  each  side,  there 
is  an  increase  of  the  positive  on  one  side  and  of  the  negative  on  the  other. 
These  increases  correspond  to  the  iiuantitics  of  the  two  constituents  which 
have  been  driven  through. 

The  number  //  expresses  the  ratio  of  the  luunber  of  molecules  of  the 


-847] 


Tangent  Galvanometer  and   Voltameter. 


anion  which  passes  through  the  imaginary  layer  in  a  given  time  to  that  of 
the  electrolyte  decomposed. 

If  X-    is    the   velocity    of    the   kation,    and    a   that    of  the    anion,    then 
a  .  k  \  -n      k 


k  +  a 


k  +  a 


Hittorfif  has  shown  that  n  is  a  constant  independent  of  the  strength  of  the 
current,  but  which  varies  with  the  concentration  of  the  licjuid. 

S47.  Comparison  between  tbe  tangent  gralvanometer  and  the  volta- 
xneter. — There  are  several  objections  to  the  use  of  the  voltameter.  In  the 
first  place,  it  does  not  indicate  the  strength  at  any  given  moment,  for  in  order 
to  obtain  measurable  quantities  of  gas  the  current  must  be  continued  for  some 
time.  Again,  the  voltameter  gives  no  indications  of  the  changes  which  take 
place  in  this  time,  but  only  the  mean  intensity.  It  offers  also  great  resistance, 
and  can  thus  only  be  used  in  the  case  of  strong  currents  ;  for  weak  currents 
either  do  not  decompose  water,  or  only  yield  quantities  too  small  for  accurate 
measurement.  In  addition  to  this,  the  indications  of  the  voltameter  depend 
not  only  on  the  strength  of  the  current,  but  on  the  acidity  of  the  water,  and 
on  the  distance  and  size  of  the  electrodes.  But  although  it  does  not  measure 
the  strength  of  the  current  at  any  one  time,  it  does,  apart  from  accidental 
influences,  give  a  measure  of  the  total  quantity  of  electricity  that  has  passed 
within  the  period  of  observation. 

The  magnetic  measurements  are  preferable  to  the  chemical  ones.  Not 
only  are  they  more  delicate  and  offer  less  resistance,  but  they  give  the 
strength  at  any  moment.  On  the  other  hand,  indications  furnished  by  the 
tangent  galvanometer  hold  only  for  one  special  instrument.  They  vary 
with  the  diameter  of  the  ring  and  the  number  of  turns  ;  moreover,  one 
and  the  same  instrument  will  give  different  indications  on  different  places, 
seeing  that  the  force  of  the  earth's  magnetism  varies  from  one  place  to 
another  (701). 

The  indications  of  the  two  instruments  may,  however,  be  readily  com- 
pared with  one  another.  For  this  purpose  the  voltameter  and  the  tangent 
galvanometer  are  simultaneously  inserted  in  the  circuit  of  a  battery,  and  the 
deflection  of  the  needle  and  the  amount  of  gas  liberated  in  a  given  time  are 
noted.     In  one  set  of  experiments  the  following  results  were  obtained  : — 


Number  of  elements 

Deflection 

Gas  liberated  in  three  minutes 

12 

28-5° 

125  cc. 

8 

24-8 

106 

6 

22-0 

93 

3 

1375 

56 

2 

6-9 

24 

If  we  divide  the  tangents  of  the  angles  into  the  corresponding  volumes  of 
gas  liberated  in  one  minute,  we  should  obtain  a  constant  magnitude  which 
represents  how  much  gas  is  developed  in  a  minute  by  a  current  which  could 
produce  on  the  tangent  galvanometer  the  deflection  45°,  for  tang.  45°  =  i. 
Making  this  calculation  with  the  above  obsei-vations,  we  obtain  a  set  of 
closely  agreeing  numbers  the  mean  of  which  is  76-5.    The  gas  was  measured 

3H 


834  Dy}iamical  Electricity.  [847- 

under  a  pressure  of  "jy]  mm.  and  at  a  temperature  of  15°,  and  therefore 
under  normal  conditions  (332)  its  volume  would  be  70  cubic  centimetres. 
That  is  to  say,  this  is  the  volume  of  gas  which  corresponds  to  a  deflection 
of  45°.  Hence  in  chemical  measure  the  strength  C  of  a  current  which  pro- 
duces in  this  particular  tangent  galvanometer  a  deflectron  of  ^°  is 

C  =  70  tang.  0. 

For  instance,  supposing  a  current  produced  in  this  tangent  galvanometer 
a  deflection  of  54°,  this  current,  if  it  passed  through  a  voltameter,  would 
liberate  in  a  minute  70  x  tang.  54°  =  7ox  1*376  =  96*32  cubic  centimetres  of 
^as. 

If  once  the  reduction  factor  for  a  tangent  galvanometer  has  been  deter- 
mined, the  strength  of  any  current  may  be  readily  calculated  in  chemical 
measure  by  a  simple  reading  of  the  angle  of  deflection.  This  reduction  factor 
of  course  only  holds  for  one  special  instrument,  and  for  experiments  in  the 
same  place,  seeing  that  the  force  of  the  earth's  magnetism  varies  in  different 
places. 

The  indications  of  the  sine-compass  may  be  compared  with  those  of  the 
galvanometer  in  a  similar  manner. 

848.  Polarisation. — When  the  platinum  electrodes,  which  have  been 
used  in  decomposing  water,  are  disconnected  from  the  battery,  and  connected 
with  a  galvanometer,  the  existence  of  a  current  is  indicated  which  has  the 
opposite  direction  to  that  which  had  previously  passed.  This  phenomenon 
is  explained  by  the  fact  that  oxygen  has  been  condensed  on  the  surface  of  the 
positive  plate,  and  hydrogen  on  the  surface  of  the  negative  plate,  analogous 
to  what  has  been  already  seen  in  the  case  of  the  nonconstant  batteries  (806). 
The  effect  of  this  is  to  produce  two  different  electromotors,  which  produce  a 
current  opposed  in  direction  to  the  original  one,  and  which,  therefore,  must 
weaken  it.  As  the  two  electrodes  thus  become  the  poles  of  a  new  current, 
they  are  said  to  \>q.  polarised.,7\x\^  the  current  is  called  2l  polarisation  current. 
The  polarisation  is  not  instantaneous,  but  may  increase  continuously  from 
zero  to  a  certain  maximum  limit  which  may  be  considerable  ;  it  increases 
with  the  strength  of  the  current,  attaining  the  force  of  2*6  volts  with  platinum 
plates  in  dilute  sulphuric  acid.  It  constitutes  a  negative  electromotive  force, 
and  must  be  allowed  for  in*  Ohm's  formula. 

The  quantity  of  electricity  required  to  produce  a  given  state  of  polarisa- 
tion depends  on  the  condition  and  dimensions  of  the  plate,  and  is  often 
called  the  capacity  oj polar isatioti  relative  to  the  gi\-en  system. 

849.  Secondary  batteries.  Accumulators. — Ritter  was  the  first  to  show 
that  on  this  principle  batteries  might  l)e  constructed  of  pieces  of  metal  of 
the  same  kind — for  instance,  platinum — which  otherwise  give  no  current. 
A  piece  of  moistened  cloth  is  interposed  between  each  pair,  and  each  end  of 
this  system  is  connected  with  the  poles  of  a  battery.  After  some  time  the 
apparatus  has  received  a  charge,  and  if  separated  from  the  battery  can  itself 
produce  all  the  effects  of  a  voltaic  battery.  Such  batteries  are  called  second- 
ary batteries  or,  also,  accumulators.  Their  action  depends  on  an  alteration 
of  the  surface  of  the  metal  produced  by  the  electric  current,  the  constituents 
of  the  liquid  with  which  the  cloth  is  moistened  having  become  accumulated 
on  the  opposite  plates  of  the  circuit. 


-849] 


Secondary  Batteries. 


835 


Fig.  799. 


Plante  first  showed  the  practical  importance  of  these  batteries.  His  ele- 
ment (fig.  799)  is  constructed  as  follows  :  A  broad  strip  of  sheet  lead  with  a 
tongue  is  laid  upon  a  second 
similar  sheet,  contact  being 
prevented  by  narrow  strips 
of  felt  ;  and  two  similar 
strips  having  been  laid  on 
the  upper  piece,  the  sheets 
are  rolled  together  so  as  to 
form  a  compact  cylinder. 
This  is  placed  in  a  vessel 
containing  dilute  sulphuric 
acid,  and,  being  connected 
by  wires  attached  to  the 
tongues  with  a  battery  of  two  Grove's  cells,  a  current  is  passed  through  it. 
The  effect  of  this  is  that  water  is  decomposed,  oxygen  being  liberated  at 
the  anode,  or  plate,  which  serves  as  positive  pole,  and  there  unites  with 
the  lead,  forming  peroxide  of  lead,  while  hydrogen  is  accumulated  at  the 
other  plate.  If  now  the  plates  are  detached  from  the  charging  battery  and 
are  connected  with  each  other,  a  powerful  polarisation  current  is  produced 
in  the  opposite  direction  to  the  primary  ;  the  oxygen  of  the  peroxide  at  the 
anode  decomposes  the  dilute  acid,  combining  with  its  hydrogen,  and  so 
travels  through  to  the  other  plate,  where  it  combines  with  the  lead.  When 
these  operations  are  repeated  several  times  the  activity  of  the  element  in- 
creases, owing  in  great  measure  to  the  alteration  in  the  surfaces  which  is 
thereby  produced.  The  element  does,  in  fact,  require  some  time  and  energy 
to  charge  or  form  it.  Faure  has  made  a  great  improvement  in  this  direction. 
It  consists  in  coating  the  lead  plates  with  a  thick  paste  of  red  lead,  Pb^O,, 
so  as  to  have  about  one  gramme  to  the  square  centi- 
metre. This  is  kept  in  its  place  by  a  sheet  of  parch- 
ment paper  and  slips  of  felt,  and  is  then  coiled  up  as 
in  Plante's  (fig.  799).  When  the  current  is  passed, 
the  ultimate  effect  is  that  the  red  lead  at  the  one  elec- 
trode is  oxidised  to  Pb.jOj,  and  that  at  the  other  into 
metallic  lead  in  the  form  of  a  sponge,  which  therefore 
exposes  a  greater  surface. 

In  accumulators  it  is  important  to  increase  the 
surface  while  diminishing  the  weight,  as  well  as  to 
make  the  oxide  adhere  more  firmly  ;  this  is  promoted 
by  constructing  the  plates  of  gratings,  or  by  making 
the  surface  ribbed. 

The  inverse  electromotive  force  of  such  a  couple 
is  about  2i  times  that  of  a  Daniell's  cell,  so  that  three 
DanielFs  or  two  Grove's  cells  are  required  to  charge 
it.  In  charging,  a  considerable  number  of  elements 
are  joined  together  by  their  similar  poles,  and  connected  with  the  respective 
electrodes  of  the  charging  battery  ;  the  effect  is  the  same  as  that  of  using  a 
single  element  of  a  surface  equal  to  the  sum  of  the  surfaces  of  all  the 
elements.     By  means  of  a    specially  contrived  commutator  they  may  be 

3H  2 


S^6  Dytiamical  Electricity.  [849- 

arranged  tandem,  and  then  discharged,  and  in  this  way  very  high  potentials 
can  be  obtained.  So  long  as  such  batteries  could  be  charged  only  from  a 
voltaic  battery  they  could  never  be  economical ;  but  the  fact  that  after  having 
been  once  charged  they  retain  the  charge  for  a  considerable  time,  has  led 
to  their  use  in  what  is  called  '  storing  electricity,'  produced  by  mechanical 
power  through  the  agency  of  dynamo-  and  magneto-electrical  machines. 
What  they  do  is  to  store  the  products  of  chemical  decomposition,  and  that 
in  a  form  in  which  they  are  immediately  available  for  electrical  effects. 

An  accumulator  of  great  capacity  is  obtained  by  placing  a  plate  of  zinc 
plate  in  a  solution  of  zincate  of  potass  or  soda,  and  a  porous  plate  of  copper 
obtained  by  compression.  During  the  charge  the  zinc  in  the  solution  is  pre- 
cipitated on  the  zinc  plate,  and  the  copper  absorbs  an  equivalent  quantity,  of 
oxygen.  During  the  discharge  the  copper  is  reduced  and  the  zinc  redissolves. 
This  accumulator,  however,  does  not  retain  its  charge,  and  is  only  suitable 
for  cases  in  which  the  discharge  rapidly  succeeds  the  charge. 

During  the  charge  the  E.M.F.  of  a  secondary  battery  at  first  rises  rapidly 
until  it  is  about  2-3  volts,  and  then  remains  constant  until  the  charge  is 
complete,  which  is  known  by  the  disengagement  of  gas.  In  discharging 
the  potential  sinks  rapidly  the  first  few  minutes,  and  then  remains  constant 
at  about  2  volts  until  towards  the  end  of  the  charge,  when  it  again  sinks. 

An  accumulator  gradually  loses  its  charge  by  leakage  ;  the  excellence  of 
an  accumulator  depends  on  its  power  of  retaining  its  charge,  on  its  capacity, 
and  on  its  efficiency.  By  this  latter  is  meant  the  ratio  of  the  electrical  work 
which  is  accumulated  in  order  to  charge  it,  to  that  which  it  gives  out  in 
sinking  to  its  initial  condition. 

The  following  experiments,  which  are  the  earliest  of  their  kind,  will  give 
a  fair  idea  of  the  results  produced  by  their  means.  A  battery  of  thirty-five 
cells,  each  weighing  nearly  437  kilog.,  was  connected  with  a  Siemens  dynamo 
machine  (918),  in  working  which  one  horse-power  was  employed  during 
thirty-five  hours.  When  this  was  discharged  through  eleven  Maxim's  lamps, 
these  were  kept  lighted  for  10  hours  40  minutes.  The  measured  work 
transmitted  to  the  dynamo  machine  in  that  time  was  9,570,000  kilogram- 
metres  (61).  This  accumulated  in  the  battery  an  amount  of  electric  energy 
of  6,382,000  kgm.,  or  66  per  cent.  While  the  battery  was  being  discharged 
it  yielded  3,809,000,  or  60  per  cent,  of  the  work  stored  in  the  form  of  elec- 
tricity, which  is  therefore  equivalent  to  40  per  cent,  of  the  work  transmitted 
to  the  dynamo  machine. 

It  thus  appears  that  each  kilogramme  weight  of  battery — that  is,  the 
weight  of  the  lead  and  coating,  together  with  the  acid — requires  a  work  of 
6,257  kilogrammetres  to  charge  it,  and  yields  2,500  kgm.  in  the  form  of 
electricity.  Each  of  the  above  lamps  gave  a  light  equal  to  i'4  Carrel  lamps 
— a  standard  lamp  much  used  in  France  and  equal  to  7*4  standard  candles 
(509).  This,  therefore,  is  ecjual  to  1,215  candles  for  one  hour;  hence  this 
represents  3,135  kgm.  per  hour  per  candle,  which  is  equal  to  o-oii6  of  a 
horse-power,  or,  if  an  amount  of  energy  equal  to  one  horse-power  were 
stored  in  the  accumulator,  it  would  produce  86  candles  ;  but  as  only  40  per 
cent,  of  the  power  transmitted  to  the  dynamo  appears  as  light,  one  horse- 
power in  the  engine  is  equivalent  to  the  production  of  2,2)  candles  wheil 
worked  through  a  battery  of  this  kind. 


-850] 


Grove's  Gas  Battery. 


S37 


The  capacity  of  an  accumulator  is  the  quantity  of  electricity  which  can 
be  stored  for  unit  weight  ;  this  quantity  may  be  expressed  in  ampere  hours, 
that  is  to  say,  a  current  of  one  ampere  maintained  for  one  hour  or  3,600 
coulombs.  The  whole  charge  which  can  be  imparted  to  an  accumulator 
cannot  be  utilised,  for  it  is  found  to  injure  the  accumulator  if  this  is  done, 
and  in  practice  the  charge  is  only  allowed  to  run  down  until  the  potential  is 
10  per  cent,  less  than  at  the  outset.  A  good  accumulator,  such  as  those  of 
the  Electric  Power  Storage  Company,  will  take  a  utilisable  charge  which 
may  be  represented  at  4,250  kilogrammetres  for  one  kilo,  of  battery  ;  suffi- 
cient therefore  to  raise  the  battery  through  a  height  of  4,250  metres,  and  of 
this  85  to  90  per  cent,  can  be  utilised  as  electricity  ;  this  being  its  efficiency. 

In  accumulators  which  are  to  be  used  as  motors  in  such  cases  as 
tramcars,  electrical  boats,  the  capacity  is  of  first  importance,  while  with 
the  use  of  stationary  accumulators,  as  in  electric  lighting,  the  efficiency  is 
the  chief  point. 

jNIany  instructive  comparisons  may  be  made  between  a  secondary  bat- 
tery and  a  charged  Leyden  jar.  Thus,  for  instance,  when  the  poles  of  a 
secondary  battery  have  been  connected  until  no  current  passes,  and  are 
then  disconnected  for  a  while,  a  current  in  the  same  direction  as  the  first  is 
obtained  on  again  connecting  them  ;  this  is  the  residual  discharge.  The 
capacity  of  a  secondary  battery  depends  on  the  area  of  the  electrodes,  on 
their  nature,  and  on  that  of  the  interposed  liquid,  but  not  on  the  distance 
between  them.  The  energy  of  the  Leyden  jar  is  stored  in  that  state  of  strain 
which  is  called  polarisation  of  the  dielectric  ;  in  the  secondary  battery  the 
energy  consists  in  the  products  which  are  stored  up  on  the  surface  of  the 
electrodes  in  a  state  ranging  from  chemical  combination  to  mechanical 
adherence  or  simple  juxtaposition. 

A  dry  pile  which  has  become  inactive  may  be  used  as  a  secondary 
battery.  When  a  current  is  passed  through  it,  in  a  direction  contrary  to 
that  which  the  active  battery  yields,  it  then  regains  its  activity. 

850.  Grove's  gras  battery. — On  the  property,  which  metals  have,  of  con- 
densing gases 
on  their  sur- 
faces, Grove 
constructed  his 
gas  battery,  fig. 
Soi.  A  single 
cell  consists  of 
two  glass  tubes. 
B  and  A,  in 
each  of  whicli 
is  fused  a  plati- 
num electrode, 
provided  on 
the  outside 
with  binding 
screws.  These 
electrodes  are 
made  more  efficient  by  being  covered  with  finely  divided  platinum.     One  of 


g.  801 


838  Dynamical  Electricity.  [850- 

the  tubes  is  partially  filled  with  hydrogen,  and  the  other  partially  with 
oxygen,  and  they  are  inverted  over  dilute  sulphuric  acid,  so  that  half  the 
platinum  is  in  the  liquid  and  half  in  gas.  On  connecting  the  electrodes 
with  a  galvanometer,  the  existence  of  a  current  is  indicated  whose  direction 
in  the  connecting  wire  is  from  the  platinum  in  oxygen  to  that  in  hydrogen  • 
so  that  the  latter  is  negative  towards  the  former,  As  the  current  passes 
through  water  this  is  decomposed  :  oxygen  is  separated  at  the  positive  plate 
and  hydrogen  at  the  other.  These  gases  unite  with  the  gases  condensed  on 
their  surface,  so  that  the  volume  of  gas  in  the  tubes  gradually  diminishes, 
but  in  the  ratio  of  one  volume  of  oxygen  to  two  volumes  of  hydrogen.  These 
elements  can  be  formed  into  a  battery  (fig.  767)  by  joining  the  dissimilar 
plates  with  one  another  just  as  they  are  joined  in  an  ordinary  battery.  One 
element  of  such  a  battery  is  sufficient  to  decompose  potassium  iodide,  and 
four  will  decompose  water. 

851.  Passive  state  of  iron. — With  polarisation  is  probably  connected  a 
very  remarkable  chemical  phenomenon,  which  many  metals  exhibit,  but  more 
especially  iron.  When  this  is  immersed  in  concentrated  nitric  acid  it  is 
unattacked.  This  condition  of  iron  is  called  the  passive  state,  and  upon  it 
depends  the  possibility  of  the  zinc-iron  battery  (810).  It  is  probable  that  in 
this  experiment  a  thin  superficial  layer  of  protosesquioxide  of  iron  is  formed  ; 
on  the  one  hand  this  protects  the  iron  from  further  attack,  and  on  the  other  it 
acts  as  an  electromotor,  like  the  layer  of  peroxide  of  lead  in  Plante's  element 
(849).  The  position  of  passive  iron  in  the  electromotive  series  is  near  that 
of  platinum. 

852.  iTobili's  ring's. — When  a  drop  of  acetate  of  copper  is  placed  on  a 
silver  plate,  and  the  silver  is  touched  in  the  middle  of  a  drop  with  a  piece 
of  zinc,  there  are  formed  around  the  point  of  contact  a  series  of  copper  rings 
alternately  dark  and  light.  These  are  N'obilfs  coloured  rings.  They  may 
be  obtained  in  beautiful  iridescent  colours  by  the  following  process  :  A  solu- 
tion of  lead  oxide  in  potash  is  obtained  by  boiling  finely  powdered  litharge 
in  a  solution  of  potash.  In  this  solution  is  immersed  a  polished  plate  of 
silver  or  of  German  silver,  which  is  connected  with  the  positive  electrode  of 
a  battery  of  eight  Bunsen's  elements.  With  the  negative  pole  is  connected 
a  fine  platinum  wire  fused  in  glass,  so  that  only  its  point  projects  ;  and  this 
is  placed  in  the  liquid  at  a  small  distance  from  the  plate.  Around  this  point 
binoxide  of  lead  is  separated  on  the  plate  in  very  thin  concentric  layers,  the 
thickness  of  which  decreases  from  the  middle.  They  show  the  same  series 
of  colours  as  Newton's  coloured  rings  in  transmitted  light  (650).  The  bin- 
oxide  of  lead  owes  its  origin  to  a  secondary  decomposition  ;  by  the  passage 
of  the  current  some  lead  oxide  is  decomposed  into  metallic  lead,  which  is 
deposited  at  the  negative  pole,  and  o.xygen  which  is  liberated  at  the  positive ; 
and  this  oxygen  combines  with  some  oxide  of  lead  to  form  bioxide,  which 
is  deposited  on  the  positive  pole  as  the  decomposition  proceeds.  This 
process  is  used  for  the  metallic  coloration  of  objects  of  domestic  use  and 
ornamentation. 

The  effects  are  also  well  seen  if  a  solution  of  copper  sulphate  is  placed 
on  a  silver  plate,  which  is  touched  with  a  zinc  rod,  the  point  of  which  is 
in  the  solution  ;  for  then  a  current  is  formed  liy  these  metals  and  the 
liquid. 


-853]      Arbor  Satiirni,  or  Lead  Tree.     Arbor  Diamv.  839 

853.  Arbor  Saturni,  or  lead  tree.  Arbor  Bianse. — When  in  a  solu- 
tion of  a  salt  is  immersed  a  metal  which  is  more  oxidisable  than  the  metal 
of  the  salt,  the  latter  is  precipitated  by  the  former,  while  the  immersed  metal 
is  substituted,  equivalent  for  equivalent,  for  the  metal  of  the  salt.  This  pre- 
cipitation of  one  metal  by  another  is  partly  attributable  to  the  difference 
in  their  affinities,  and  partly  to  the  action  of  a  current  which  is  set  up  as 
soon  as  a  portion  of  the  less  oxidisable  metal  has  been  deposited.  The 
action  is  promoted  by  the  presence  of  a  slight  excess  of  acid  in  the  solu- 
tion. 

A  remarkable  instance  of  the  precipitation  of  one  metal  by  another  is 
the  Arbor  Sahirni.  This  name  is  given  to  a  series  of  brilliant  ramified 
crystallisations  obtained  by  zinc  in  solutions  of  lead  acetate.  A  glass  flask 
is  filled  with  a  clear  solution  of  this  salt,  and  the  vessel  closed  with  a  cork, 
to  which  is  fixed  a  piece  of  zinc  in  contact  with  some  copper  wire.  The 
flask,  being  closed,  is  left  to  itself  The  copper  wire  at  once  begins  to  be 
covered  with  a  moss-like  growth  of  metallic  lead,  out  of  which  brilliant 
crystallised  lamina?  of  the  same  metal  continue  to  form  ;  the  whole  pheno- 
menon has  great  resemblance  to  the  growth  of  vegetation,  from  which  indeed 
the  old  alchemical  name  is  derived.  For  the  same  reason  the  name  arbor 
Diancv  has  been  given  to  the  metallic  deposit  produced  in  a  similar  manner 
by  mercury  in  a  solution  of  silver  nitrate. 

If  a  rod  of  zinc  be  dipped  in  an  acid  solution  of  stannous  chloride 
crystallised  tin  is  formed  upon  it  ;  the  experiment  is  more  beautiful  by 
dipping  the  platinum  electrodes  of  a  battery  in  the  solution  ;  if  the  poles 
are  reversed  the  crystallised  lamiucE  disappear  at  one  pole  to  reappear  at 
the  other. 


840  Dynamical  Electricity.  [854- 


ELECTROMETALLURGY, 

854.  Electrometallurgy. — The  decomposition  of  salts  by  the  battery- 
has  received  a  most  important  application  in  electrometallurgy,  or  galvano- 
plnsttcs,  or  the  art  of  precipitating  certain  metals  from  their  solutions  by  the 
slow  action  of  a  galvanic  current,  by  which  means  the  salts  of  certain  metals 
are  decomposed,  the  metal  being  deposited  on  the  negative  pole,  while  the 
acid  is  liberated  at  the  positive.  The  art  was  discovered  independently  by 
Spencer  in  England  and  by  Jacobi  in  St.  Petersburg. 

In  order  to  obtain  a  galvanoplastic  reproduction  of  a  medal  or  any  other 
object,  a  mould  must  first  be  made,  on  which  the  layer  of  metal  is  deposited 
by  the  electric  current. 

For  this  purpose  several  substances  are  in  use,  and  one  or  the  other 
is  preferred  according  to  circumstances.  For  medals  and  similar  objects 
which  can  be  submitted  to  pressure,  gutta-percha  may  be  used  with  advan- 
tage. The  gutta-percha  is  softened  in  hot  water,  pressed  against  the  object 
to  be  copied,  and  allowed  to  cool,  when  it  can  be  detached  without  difficulty. 
For  the  reproduction  of  engraved  woodblocks  or  type,  wax  moulds  are  now 
commonly  used.  They  are  prepared  by  pouring  into  a  narrow  flat  pan  a 
suitable  mixture  of  wax,  tallow,  and  Venice  turpentine,  which  is  allowed  to 
set,  and  is  then  carefully  brushed  over. with  very  finely  powdered  graphite. 
While  this  composition  is  still  somewhat  soft,  the  woodblock  or  type  is 
pressed  upon  it  either  by  a  screw  press,  or,  still  better,  by  hydraulic  pressure. 
If  plaster  of  Paris  moulds  are  to  be  made  use  of,  it  is  essential  that  they  be 
first  thoroughly  saturated  with  wax  or  tallow  so  as  to  become  impervious  to 
water. 

In  all  cases,  whether  the  moulds  be  of  gutta-percha  or  wax,  or  any  non- 
conducting substance,  it  is  of  the  highest  importance  that  the  surface  be 
brushed  over  very  carefully  with  graphite,  and  so  made  a  good  conductor. 
The  conducting-  surface  thus  prepared  must  also  be  in  metallic  contact  with 
a  wire  or  a  strip  of  copper  by  which  it  is  connected  with  the  negative  elec- 
trode. Sometimes  the  moulds  are  made  of  a  fusible  alloy  (340),  which  may 
consist  of  5  parts  of  lead,  8  of  busmuth,  and  3  of  tin.  Some  of  the  melted 
alloy  is  poured  into  a  shallow  box,  and  just  as  it  begins  to  solidify,  the  medal 
is  placed  horizontally  on  it  in  a  fixed  position.  When  the  alloy  has  become 
cool,  a  slight  shock  is  sufficient  to  detach  the  medal.  A  copper  wire  is  then 
bound  round  the  edge  of  the  mould,  by  which  it  can  be  connected  with 
the  negative  electrode  of  the  battery,  and  then  the  edge  and  the  back  are 
covered  with  a  thin  non-conducting  layer  of  wax,  so  that  the  deposit  is  only 
formed  on  the  mould  itself 

The  most  suitable  arrangement  for  producing  an  electro-deposit  of  copper 
consists  of  a  trough  of  glass,  slate,  or  of  wood,  lined  with  india-rubber  or 
coated  with  marine  glue  (fig.  802).  This  contains  an  acid  solution  of  copper 
sulphate,  and  across  it  are  stretched  copper  rods,  B  and  D,  connected  re- 
spectively with  the  negative  and  positive  poles  of  a  battery.  By  their  copper 
conductors  the  moulds,  ;//,  are  suspended  in  the  liquid  from  the  negative 
rod  B,  whilst  a  sheet  of  copper,  C,  presenting  a  surface  about  ci|ual  to  that 


-854] 


Elcttrovietallu  rgy. 


841 


Fig. 


of  the  moulds  to  be  covered,  is  suspended  from  the  positive  rod  D,  at  the 
distance  of  about  2  inches,  directly  opposite  to  them. 

The  battery  employed  for  the  electric  deposition  of  metals  ought  to  be 
one  of  great  constancy,  and  Daniell's  and  Smee's  are  mostly  in  use.  The  cur- 
rents of  electricity  furnished  by  magneto-electrical  machines  of  a  special 
construction  are 
also  used  in 
large  establish- 
ments (913)  ; 
they  furnish  a 
current  which 
has  small  ;E. 
]\I.F.,  but  great 
quantity. 

The  density 
of  a  current  is 
the  strength  di- 
vided by  the 
surface  of  the 
electrodes,  or  the  number  of  amperes  per  square  decimetre. 

The  copper  plate  suspended  from  the  positive  pole  acts  not  only  as  elec- 
tricity, but  it  keeps  the  solution  in  a  state  of  concentration,  for  the  acid 
liberated  at  the  positive  pole  dissolves  the  copper,  and  reproduces  a  quantity 
of  copper  sulphate  equal  to  that  decomposed  by  the  current. 

Another,  and  veiy  simple,  process  for  producing  the  electric  deposit  of 
copper  consists  in  making  use  of  what  is  in  effect  a  Daniell's  cell.  A  porous 
pot,  or  a  glass  cylinder  covered  at  the  bottom  with  bladder  or  with  vegetable 
parchment,  is  immersed  in  a  vessel  of  larger  capacity  containing  a  concen- 
trated solution  of  copper  sulphate.  The  porous  vessel  contains  acidulated 
water,  and  in  it  is  suspended  a  piece  of  amalgamated  zinc  of  suitable  form, 
and  having  a  surface  about  equal  to  that  of  the  mould.  The  latter  is  attached 
to  an  insulated  wire  connected  with  the  zinc,  and  is  immersed  in  the  solution 
of  copper  sulphate  in  such  a  position  that  it  is  directly  opposite  to  the 
diaphragm.  The  action  commences  by  the  mould  becoming  covered  with 
copper,  commencing  at  the  point  of  contact  with  the  conductor,  and  gradually 
increasing  in  thickness  in  proportion  to  the  action  of  the  Daniell's  element 
thus  formed.  It  is,  of  course,  essential  in  the  process  to  keep  the  solution  of 
copper  sulphate  at  a  uniform  strength,  which  is  done  by  suspending  in  it 
muslin  bags  filled  with  crystals  of  this  salt.  How  great  is  the  delicacy  which 
such  electric  deposits  can  attain  appears  from  the  fact  that  galvanoplastic 
copies  can  be  made  of  daguerreotypes,  which  are  of  the  greatest  accuracy. 

An  important  industrial  application  is  made  of  electrolysis  in  \\\&  refining 
of  copper.  The  metal  is  extracted  by  the  ordinary  chemical  processes  so  as 
to  obtain  plates  with  95  per  cent,  of  pure  copper.  These  plates  are  used  as 
positive  electrodes  in  a  bath  of  copper  sulphate,  and  the  metal  is  deposited 
in  a  state  of  perfect  purity  on  thin  sheets  which  form  the  negative  electrode, 
while  the  impurities  fall  to  the  bottom.  As  the  electrodes  are  practically 
identical,  there  is  no  polarisation  (848),  and  the  work  of  the  current  is  solely 
emi)loyed  in  overcoming  the  resistance  of  the  baths. 


842  Dynamical  Electricity.  [855- 

855.  Blectrogilding. — The  old  method  of  gilding  was  by  means  of 
mercury.  It  was  effected  by  an  amalgam  of  gold  and  mercury,  which  was 
applied  on  the  metal  to  be  gilt.  The  objects  thus  covered  were  heated  in  a 
furnace,  the  mercury  volatilised,  and  the  gold  remained  in  a  very  thin  layer 
on  the  objects.  The  same  process  was  used  for  silvering  ;  but  they  were 
expensive  and  unhealthy  methods,  and  have  now  been  entirely  replaced  by 
electrogilding  and  electrosilvering.  Electrogilding  only  differs  from  the 
process  described  in  the  previous  paragraph  in  that  the  layer  is  thinner  and 
adheres  more  firmly.  Brugnatelli,  a  pupil  of  Volta,  appears  to  have  been 
the  first,  in  1803,  to  observe  that  a  body  could  be  gilded  by  means  of  the 
battery  and  an  alkaline  solution  of  gold  ;  but  De  la  Rive  was  the  first  who 
really  used  the  battery  in  gilding.  The  methods  both  of  gilding  and  silver- 
ing owe  their  present  high  state  of  perfection  principally  to  the  improve- 
ments of  Elkington,  Ruolz,  and  others. 

The  pieces  to  be  gilt  have  to  undergo  three  processes  before  gilding. 

The  first  consists  in  heating  them  so  as  to  remove  the  fatty  matter  which 
has  adhered  to  them  in  previous  processes. 

As  the  objects  to  be  gilt  are  usually  of  what  is  called  gilding  iiietal  or  red 
brass,  which  is  a  special  kind  of  brass  rich  in  copper,  and  their  surface 
during  the  operation  of  heating  becomes  covered  with  a  layer  of  cupric  or 
cuprous  oxide,  this  Is  removed  by  the  second  operation.  For  this  purpose 
the  objects,  while  still  hot,  are  immersed  in  very  dilute  nitric  acid,  where 
they  remain  until  the  oxide  is  removed.  They  are  then  rubbed  with  a  hard 
brush,  washed  iji  distilled  water,  and  dried  in  gently  heated  sawdust. 

To  remove  all  spots  they  must  undergo  the  third  process,  which  consists 
in  rapidly  immersing  them  in  ordinary  nitric  acid,  and  then  in  a  mixture  of 
nitric  acid,  bay-salt,  and  soot. 

When  thus  prepared  the  objects  are  attached  to  the  negative  pole  of  a 
battery,  consisting  of  three  or  four  Bunsen's  or  Daniell's  elements.  They  are 
then  immersed  in  a  bath  of  gold,  as  previously  described.  They  remain  in 
the  bath  for  a  time  which  depends  on  the  thickness  of  the  desired  deposit. 
There  is  a  great  difference  in  the  composition  of  the  baths.  That  most  in 
use  consists  of  i  part  of  gold  chloride  and  10  parts  of  potassium  cyanide, 
dissolved  in  200  parts  of  water.  In  order  to  keep  the  bath  in  a  state  of  con- 
centration, a  piece  of  gold  is  suspended  from  the  positive  electrode,  which 
dissolves  in  proportion  as  the  gold  dissolved  in  the  bath  is  deposited  on  the 
objects  attached  to  the  negative  pole. 

The  method  which  has  just  been  described  can  also  be  used  for  silver, 
bronze,  German  silver,  &c.  But  other  metals,  such  as  iron,  steel,  zinc,  tin, 
and  lead,  are  very  difficult  to  gild  well.  To  obtain  a  good  coating,  they  must 
first  be  covered  with  a  layer  of  copper,  by  means  of  the  battery  and  a  bath 
of  copper  sulphate  ;  the  copper  with  which  they  are  coated  is  then  gilded, 
as  in  the  previous  case. 

The  tint  of  the  deposit  is  modified  by  adding  solutions  of  copper  or  of 
silver  to  the  gold  bath ;  the  former  gives  a  reddish  and  the  latter  a  greenish 
tint. 

856.  Electrosllverlngr. — What  has  been  said  about  gilding  applies  exactlj^ 
to  the  process  of  electrosilvering.  The  difference  is  in  the  composition  of 
the  bath,  which  consists  of  2  parts  of  silver  cyanide  and  2  parts  of  potas- 


-857J  Electric  Deposition  of  Iron  and  Nickel.  843 

sium  cyanide,  dissohed  in  250  parts  of  water.  To  the  positive  electrode  is 
suspended  a  plate  of  siher,  which  prevents  the  bath  from  becoming  poorer  ; 
the  pieces  to  be  silvered,  which  must  be  well  cleaned,  are  attached  to  the 
negative  pole.  It  may  here  be  observed  that  these  processes  succeed  best 
with  hot  solutions,  and  when  the  baths  are  old. 

Knowing  the  weight  of  any  given  metal  which  is  transported  by  unit  of 
electricity  (846),  it  is  easy  to  calculate  the  weight  deposited  in  a  given  time 
Ij)-  a  current  of  known  strength.  A  deposit  of  one  ounce  of  silver  on  a  square 
foot  of  surface  gives  a  good  coating  ;  its  thickness,  g|j  inch  or  0'03  mm.,  is 
about  that  of  thin  writing  paper. 

857.  Electric  deposition  of  Iron  and  nickel. — One  of  the  most  valuable 
applications  of  the  electric  deposition  of  metals  is  to  what  is  called  the 
steeling  {acierage)  of  engra\ed  copper  plates.  The  bath  required  for  this 
purpose  is  obtained  by  suspending  a  large  sheet  of  iron,  connected  with  the 
positive  pole  of  a  battery,  in  a  trough  filled  with  a  saturated  solution  of  sal- 
ammoniac  ;  whilst  a  thin  strip  of  iron,  also  immersed,  is  connected  with  the 
negative  pole.  By  this  means  iron  from  the  large  plate  is  dissolved  in  the 
sal-ammoniac,  while  hydrogen  is  given  off  on  the  surface  of  the  small  one. 
When  the  bath  has  thus  taken  up  a  sufficient  quantity  of  iron,  an  engraved 
copper  plate  is  substituted  for  the  small  negative  strip.  A  bright  deposit  of 
iron  begins  to  form  on  it  at  once,  and  the  plate  assumes  the  colour  of  a 
polished  steel  plate.  The  deposit  thus  obtained  in  the  course  of  half  an  hour 
is  exceedingly  thin,  and  an  impression  of  the  plate  thus  covered  does  not 
seem  different  from  an  uncovered  plate  ;  it  possesses,  however,  an  extraordi- 
nary degree  of  hardness,  so  that  a  very  large  number  of  impressions  can  be 
taken  from  such  a  plate  before  the  thin  coating  of  iron  is  worn  off.  When, 
however,  this  is  the  case,  the  film  of  iron  is  dissolved  off  by  dilute  nitric  acid, 
and  the  plate  is  again  covered  with  the  deposit  of  iron. 

An  indefinite  number  of  perfect  impressions  may,  by  this  means,  be 
obtained  from  one  copper  plate,  without  altering  the  original  sharp  condition 
of  the  engraving. 

The  covering  of  metals  by  a  deposit  of  nickel  has  of  late  come  into  use. 
The  process  is  essentially  the  same  as  that  just  described.  The  bath  used 
for  the  purpose  can,  however,  be  made  more  directly  by  mixing,  in  suitable 
proportions,  salts  of  nickel  with  those  of  ammonia.  The  positive  pole  con- 
sists of  a  plate  of  pure  nickel.  A  special  difficulty  is  met  with  in  the  electric 
deposition  of  nickel,  owing  to  the  tendency  of  this  metal  to  deposit  in  an  un- 
even manner,  and  then  to  become  detached.  This  is  got  over  by  frequently 
removing  the  articles  from  the  bath,  and  submitting  them  to  a  polishing 
process. 

Objects  coated  with  nickel  show  a  highly  polished  surface  of  the  charac- 
teristic bright  colour  of  this  metal  ;  this  is  moreover  very  hard  and  durable, 
and  is  not  affected  either  by  the  atmosphere  or  even  by  sulphuretted  hydro- 
gen. A  deposit  of  2  grammes  of  nickel  on  the  square  decimetre  represents  a 
coating  0-023  n^iri.  in  thickness. 


844 


Dynamical  Electricity. 


[858- 


CHAPTER    IV. 


ELECTRODYNAMICS.      ATTRACTION   AND   REPULSION   OF   CURRENTS   BY 
CURRENTS. 


858.  Electrodynamics. — By  the  term  electrodynamics  is  understood  the 
laws  of  electricity  in  a  state  of  motion,  or  the  action  of  electric  currents  upon 
each  other  and  upon  magnets,  while  electrostatics  deals  with  the  laws  of  elec- 
tricity in  a  state  of  rest. 

The  action  of  one  electrical  current  upon  another  was  first  investigated 
by  Ampere,  shortly  after  the  discovery  of  Oersted's  celebrated  fundamental 


Fig.  803. 

experiment  (820).     All  the  phenomena,  even  the  most  complicated,  folloVv 
from  two  simple  laws,  which  are — 

I.  Tiuo  currents  which  arc  parallel,  and  in  the  same  direction,  attract  one 
another. 

II.  Two  currents  parallel,  hut  in  contrary  directions,  repel  one  another. 
In  order  to  demonstrate  these  laws,  the  circuit  which  the  current  traverses 

must  consist  of  two  parts,  one  fixed  and  the  other  movable.   This  is  effected 


-859] 


Kogefs    Vibrating  Spiral. 


845 


Fig. 


by  the  apparatus  (fig.  803),  which  is  a  modified  and  improved  form  of  one 
©riginally  devised  by  Ampere, 

It  consists  of  two  brass  columns,  A  and  D,  between  which  is  a  shorter 
one.  The  column  D  is  provided  with  a  multiplier  (821)  of  20  turns,  MN  (fig 
805),  which  greatly  increases  the  sensitiveness  of  the  instrument.  This  can 
be  adjusted  at  any  height,  and  in  any  position,  by  means  of  a  universal  screw 
clamp  (see  figs.  805-807). 

The  short  column  is  hollow,  and  in  its  interior  slides  a  brass  tube  termi- 
nating in  a  mercury  cup,  c,  which  can  be  raised  or  lowered*.  On  the  column 
A  is  another  mercury  cup  represented  in  section  at 
fig.  804  in  its  natural  size.  In  the  bottom  is  a 
capillary  aperture  through  which  passes  the  point 
of  a  sewing-needle  fixed  to  a  small  copper  ball. 
This  point  extends  as  far  as  the  mercury,  and  turns 
freely  in  the  hole.  The  movable  part  of  the  circuit 
consists  of  a  copper  wire  proceeding  from  a  small 
ball,  and  turning  in  the  direction  of  the  arrows 
from  the  cup  a  to  the  cup  c.  The  two  lower  branches  are  fixed  to  a  thin 
strip  of  wood,  and  the  whole  system  is  balanced  by  two  copper  balls, 
suspended  to  the  ends. 

These  details  being  known,  the  current  of  a  Bunsen's  battery  of  4  or  5  cells 
ascending  by  the  column 
A  (fig.  805)  to  the  cup  a, 
traverses  the  circuit  BC, 
reaches  the  cup  c^  descends 
the  central  column,  and 
thence  passes  by  a  wire, 
P,  to  the  multiplier  MN, 
whence  it  returns  to  the  bat- 
teiy  by  the  wire  Q.  Now  if, 
before  the  current  passes, 
the  movable  circuit  has 
been  arranged  in  the  plane 
of  the  multiplier,  with  the 
sides  B  and  M  opposite 
each  other,  when  the  cur- 
rent passes,  the  side  B  is  re- 
pelled, which  demonstrates 
the  second  law  ;  for  in  the  branches  B  and  M  the  currents,  as  indicated 
by  the  arrows,  are  proceeding  in  opposite  directions. 

To  demonstrate  the  first  law  the  experiment  is  arranged  as  in  fig.  807 
— that  is,  the  multiplier  is  reversed  ;  the  current  is  then  in  the  same  direc- 
tion both  in  the  multiplier  and  in  the  movable  part  ;  and  when  the  latter  is 
removed  out  of  the  plane  of  the  multiplier,  so  long  as  the  current  passes 
it  tends  to  return  to  it,  proving  that  there  is  attraction  between  the  two 
parts. 

859.  Kogret's  vibrating-  spiral. — The  attraction  of  parallel  currents  may 
also  be  shown  by  an  experiment  known  as  that  of  Rogcfs  vibrating  sptj-al. 
A  copper  wire  about  07  mm.  in  diameter  is  coiled  in  a  spiral  of  about  30 


Fig.  80s. 


846 


Dynamical  lilcciricity. 


[859- 


coils  of  25  mm.  in  diameter.  At  one  end  it  is  hung  vertically  from  a  binding- 
screw,  while  the  other  just  dips  in  a  mercury  cup.  On  passing  the  current 
of  a  battery  of  3  to  5  (drove's  cells  through  the  spiral  by  means  of  the  mer- 
cury cup  and  the  binding  screw,  its  coils  are  traversed  by  parallel  currents  ; 
they  therefore  attract  one  another,  and  rise,  and  thus  the  contact  with  the 
mercury  is  broken.  The  current  having  thus  ceased,  the  coils  no  longer 
attract  each  other,  they  fall  by  their  own  weight,  contact  with  the  mercury 
is  re-established,  and  the  series  of  phenomena  are  indefinitely  produced. 
The  experiment  is  still  more  striking  if  a  magnetised  rod  the  thickness  of  a 
pencil  is  introduced  into  the  interior.  This  will  be  intelligible  if  we  consider 
the  action  between  the  parallel  Amp^rian  currents  of  the  magnet  and  of  the 
helix. 

860.  Xiaws  of  angrular  currents. — I.  Two  rectilinear  crcrrents^  the  direc- 
tions of  which  form  an  angle  with  each  other,  attract  one  another  when  both 
approach  or  recede  from  the  apex  of  the  angle. 

II.  They  repel  one  another,  if  one  approaches  and  the  other  recedes  from 
the  apex  of  the  angle. 

These  two  laws  may  be  demonstrated  by  means  of  the  apparatus  above 

described,  replac- 
ing the  movable 
circuit  by  the  cir- 
cuit BC.  If  then 
the  multiplier  is 
placed  horizontally, 
so  that  its  current 
is  in  the  same  direc- 
tion as  in  the  mov- 
able current,  on  re- 
moving the  latter  it 
quickly  approaches 
the  multiplier, 

which  verifies  the 
first  law. 

To     prove     the 

second  law,  the  multiplier  is  turned  so  that  the  currents  are  in  opposite  direc- 
tions, and  then  repulsion  ensues  (fig.  805). 

/;/  a  rectilinear  current  each  clement  of  the  current  repels  the  succeeding 
one,  and  is  itself  repelled. 

This  is  an  im])ortant  consequence  of  Ampere's  law,  and  may  be  experi- 
mentally demonstrated  by  the  following  arrangement,  which  was  devised 
by  Faraday.  A  U-shaped  jiiece  of  copper  wire,  whose  ends  dip  in  two 
separate  deep  mercury  cups,  is  suspended  from  one  end  of  a  delicate  balance 
and  suitably  equipoised.  When  the  mercury  cups  are  connected  with  the 
two  poles  of  a  Ijattery,  the  wire  rises  very  appreciably,  and  sinks  again 
to  its  original  position  when  the  current  ceases  to  pass.  The  current  passes 
into  the  mercury  and  into  the  wire  ;  but  from  the  construction  of  the  appa- 
ratus the  former  is  fixed,  while  the  latter  is  movable,  and  is  accordingly^ 
repelled. 


Kig.  806. 


862] 


Action  of  an  Infinite  Current. 


847 


861.  Xiaws  of  sinuous  currents. —  The  action  of  a  sinuous  current 
is  equal  to  tliat  oj  a  rectilinear  current  of  the  same  length  in  projection. 
This  principle  is  demon- 
strated by  arranging  the 
multiplier  vertically  and 
placing  near  it  a  movable 
circuit  of  insulated  wire 
half  sinuous  and  half 
rectilinear  (fig.  807).  It 
will  be  seen  that  there 
is  neither  attraction  nor 
repulsion,  showing  that 
the  action  of  the  sinuous 
portion  ?ii?i  is  equalled 
by  that  of  the  rectilinear 
portion. 

An  application  of  this 
principle  will  presently  be 
met  with  in  the  appara- 
tus called  solenoids  (874), 
which  are  formed  of  the  combination  of  a  sinuous  with  a  rectilinear  current. 

862.  Action  of  an  infinite  current  on  a  current  perpendicular  to  its 
direction. — From  the  action  exerted  between  two  angular  currents  (860)  the 
action  of  a  fixed  and  infinite  rectilinear  current,  PQ  (fig.  808),  on  a  movable 
current,  KH,  perpendicular  to  its  direction  can  be  determined.  Let  OK  be 
the  perpendicular  common  to  KH  and  PQ,  which  is  null  if  the  two  lines  PQ 


Fig.  807. 


/A- 


.--r 


0 

Fig.  808. 


ig.  809. 


and  KH  meet.  The  current  PQ  flowing  from  Q  to  P  in  the  direction  of  the 
arrows,  let  us  first  consider  the  case  in  which  the  current  KH  approaches  the 
current  QP.  From  the  first  law  of  angular  currents  (860)  the  portion  OQ  of 
the  current  PQ  attracts  the  current  KH,  because  they  both  flow  towards  the 
summit  of  the  angle  formed  by  their  directions.  The  portion  PO,  on  the  con- 
trar)?^,  will  repel  the  current  KH,  for  here  the  two  currents  are  in  opposite 
directions  at  the  summit  of  the  angle.  If  then  mq  and  mp  stand  for  the  two 
forces,  one  attractive  and  the  other  repulsive,  which  act  on  the  current  KH, 
and  which  are  necessarily  of  the  same  intensity,  since  they  are  symmetrically 
arranged  in  reference  to  the  two  sides  of  the  point  O,  these  two  forces  may 
be  resolved  into  a  single  force,  w//,  which  tends  to  move  the  current  KH 
parallel  to  the  current  QP,  but  in  a  contrary  direction. 


848 


Dj  ni  a  in  zeal  Electricity. 


[862- 


A  little  consideration  will  show  that  when  the  current  KH  is  below  the 
current  PQ,  its  action  will  be  the  opposite  of  what  it  is  when  above. 

On  considering  the  case  in  which  the  current  KH  moves  away  from  PQ 
(fig.  809),  it  will  be  readily  seen  from  similar  considerations  that  it  moves 
parallel  to  this  current,  but  in  the  same  direction. 

Hence  follows  this  general  principle.  A  finite  movable  current  which 
approaches  a  fixed  infiiiite  current  is  acted  on  so  as  to  move  in  a  directio7t 
parallel  and  opposite  to  that  oj  the  fixed  current ;  if  the  movable  current 
tends  from  the  fixed  current,  it  is  acted  on  so  as  to  move  pa7-allel  to  the 
curreiit  and  in  the  same  direction. 

It  follows  from  this,  that  if  a  vertical  current  is  movable  about  an  axis, 
XY,  parallel  to  its  direction  (figs.  810  and  811),  any  horizontal  current  PQ 


Fig.  810.  Fig.  811. 

will  have  the  eftect  of  turning  the  movable  current  about  its  axis,  until  the 
plane  of  the  axis  and  of  the  current  have  become  parallel  to  PQ  ;  the  vertical 
current  stopping,  in  reference  to  its  axis,  on  the  side  frojn  which  the  current 
PQ  comes  (fig.  810),  or  07i  the  side  towards  which  it  is  directed  (fig.  811), 
according  as  the  vertical  cu7'rent  desce7ids  or  asce7ids — that  is,  according"  as  it 
approaches  or  moves  from  the  horizontal  axis. 

It  also  follows  from  this  principle  that  a  system  of  two  vertical  currents 

rotating  about  a 
Xi  vertical    axis 

(figs.  812  and 
813)  is  directed 
by  a  horizontal 
current,  PQ,  in 
a  plane  parallel 
to  this  current 
when  one  of 
the  vertical  cur- 
rents is  ascend- 


Fig.  S12. 


Fig.  S13. 


ing  and  the  other  descending  (fig.  812)  ;  but  that  if  they  are  both  ascending 
or  both  descending  (fig.  813),  they  arc  not  directed. 

863.  Action  of  an  Infinite  rectilinear  current  on  a  rectangrular  or 
circular  current. —  It  is  easy  to  see  that  a  horizontal  infinite  current  exer- 
cises the  same  directive  action  on  a  rectangular  current  movable  about  a 
vertical  axis  (fig.  814)  as  what  has  been  above  stated.  For  from  the  direction  of 
the  currents  indicated  by  the  arrows,  the  part  QY  acts  by  attraction  not 
only  on  the  horizontal  portion  YD  (law  of  a/igula/-  curre7its),  but  also  on  the 
vertical  portion  AD   {/aw   of  pc7pcndicular  ci/iTC/its).      The    same  action 


-864]  Rotation  of  a  Finite  Horico?ital  Current.  849 

evidently  takes  place  between  the  part  PY  and  the  parts  CY  and  BC. 
Hence,  the  fixed  current  VQ  tends  to  direct  the  movable  rectangular  current 
A  BCD  into  a  position  parallel  to  PQ,  and  such 
that  itt  the  wires  CD  and  PQ  the  direction  of  the 
two  currents  is  the  sa7ne. 

This  principle  is  readily  demonstrated  by 
placing  the  circuit  ABCD  on  the  apparatus  with 
two  supports  (fig.  814),  so  that  at  first  it  makes 
an  angle  with  the  plane  of  the  supports.  On 
passing  a  somewhat  powerful  current  below  the 
circuit  in  the  same  plane  as  the  supports,  the 
movable  part  passes  into  that  plane.  It  is  best 
to  use  the  circuit  in  fig.  822,  which  is  astatic,  while 
that  of  fig.  814  is  not. 

What   has   been   said  about   the  rectangular  '  '*'  ""*■ 

current  in  fig.  814  applies  also  to  circular  currents,  and  is  demonstrated  by 
the  same  experiments. 

864.  Rotation  of  a  finite  horizontal  current  by  an  infinite  horizontal 
rectilinear   current. — The   attractions   and   repulsions  which    rectangular 
currents    exert   on   one  another 
may     readily     be     transformed 
into   a  continuous  circular   mo- 
tion.     Let   OA  (fig.  815)   be   a 
current     movable     about      the 
point    O  in  a  horizontal   plane, 
and  let  PQ  be  a  fixed   infinite 
current     also     horizontal.      As    !L 
these  two   currents  flow   in  the 
direction  of  the   arrows,  it   fol- 


Fig. 


lows  that  in  the  position  OA  the  movable  current  is  attracted  by  the  current 
PQ,  for  they  are  in  the  same  direction.  Having  reached  the  position  OA', 
the  movable  current  is  attracted  by  the  part  NQ  of  the  fixed  current,  and 
repelled  by  the  part  PN.  Similarly  in  the  position  OA",  it  is  attracted  by 
MQ  and  repelled  by  PM,  and  so  on  ;  from  which  follows  a  continuous  rota- 
tory motion  in  the  direction  AA'A"A"'.  If  the  movable  current,  instead  of 
being  directed  from  O  towards  A,  were  directed  from  A  towards  O,  it  is 
easy  to  see  that  the  rotation  would  take  place  in  the  contrar}^  direction. 
Hence,  by  the  action  of  a  fixed  infinite  current,  PQ,  the  movable  current 
OA  tends  to  a  continuous  motion  in  a  direction  opposite  to  that  of  the  fixed 
currefit. 

If,  both  currents  being  horizontal,  the  fixed  current  were  circular  instead 
of  being  rectilinear,  its  effect  would  still  be  to  produce  a  continuous  circular 
motion.  For,  let  ABC  (fig.  816)  be  a  fixed  circular  current,  and  w;;  a  rec- 
tilinear current  movable  about  the  axis  ;/,  both  currents  being  horizontal. 
These  currents,  flowing  in  the  direction  of  the  arrows,  would  attract  one 
another  in  the  angle  «AC,  for  they  both  flow  towards  the  summit  (860).  In 
the  angle  7zAB,  on  the  contrary,  they  repel  one  another,  for  one  goes  towards 
the  summit  and  the  other  moves  from  it.  Both  effects  coincide  in  moving 
the  wire  jnn  in  the  same  direction  .\CR. 

31 


b^O 


Dynamical  Electricity. 


865- 


'fffl'Tr'r^""''*  igBffiSiif 


865.  Rotation  of  a  vertical  current  by  a  horizontal  circular  current. 

A  horizontal  circular  current,  acting  on  a  rectilinear  vertical,  also  imparts  to 
it  a  continuous  rotatory  motion.  In  order  to  show  this,  the  apparatus  repre- 
sented in  fig.  817  is  used. 

It  consists  of  a  brass  vessel,  round  which  are  rolled  several  coils  of  in- 
sulated copper  wire,  through  which  a  current  passes.  In  the  centre  of  the 
vessel  is  a  brass  support,  a,  terminated  by  a  small  cup  containing  mercury. 
In  this  dips  a  pivot  supporting  a  copper  wire,  bb^  bent  at  its  ends  in  two  ver- 
tical branches,  which  are  soldered  to  a  very  light  copper  ring  immersed  in 
acidulated  water  contained  in  the  vessel.  A  current  entering  through  the 
wire  wz,  reaches  the  wire  A,  and  having  made  several  circuits,  terminates 
at  B,  which  is  connected  by  a  wire  underneath  with  the  lower  part  of 
the    column    a.     Ascending  in  this  column,  it  passes  by  the  wires  bb  into 

the  copper  ring, 
into  the  acidu- 
lated water,  and 
into  the  sides 
of  the  vessel, 
whence  it  re- 
turns to  the 
battery  by  the 
strip  D.  The 
current  being 
thus  closed,  the 
circuit    bh    and 

the  iiUj,  tend  to  turn  m  a  dnection  contiary  to  th  it  of  the  fixed  current,  a 
motion  due  to  the  action  of  the  circular  current  on  the  current  in  the  vertical 
branches  bb  ;  for,  as  follows  from  the  two  laws  of  angular  currents,  the 
branch  b  on  the  right  is  attracted  by  the  portion  A  of  the  fixed  current,  and 
the  branch  b  on  the  left  is  attracted  in  the  contrary  direction  by  the  opposite 
part,  and  these  two  motions  coincide  in  giving  the  ring  a  continuous  rotatory 
motion  in  the  same  direction.  The  action  of  the  circular  current  on  the 
horizontal  part  of  the  circuit  bb  would  tend  to  turn  it  in  the  same  direction  ; 
but  from  its  distance  it  may  evidently  be  neglected. 

866.  Rotation  of  mag-nets  by  currents. — Faraday  proved  that  currents 
impart  the  same  rotatory  motions  to  magnets  which  they  do  to  currents.  This 
may  be  shown  by  means  of  the  apparatus  represented  in  fig.  818.  It  consists 
of  a  large  glass  vessel,  almost  filled  with  mercury.  In  the  centre  of  this  is 
immersed  a  magnet,  A,  about  eight  inches  in  length,  which  projects  a  little 
al)ove  the  surface  of  the  mercury,  and  is  loaded  at  the  bottom  with  a  pla- 
tinum cylinder.  At  the  top  of  the  magnet  is  a  small  cavity  containing 
mercury  ;  the  current  ascending  the  column  ;//  passes  into  this  cavity 
hy  the  rod  C.  Yxom.  the  magnet  it  passes  by  the  mercury  to  a  copper 
ring,  G,  whence  it  emerges  by  the  column  //.  When  this  takes  place  the 
magnet  begins  to  rotate  round  its  own  axis  with  a  velocity  depending  on  its 
magnetic  power  and  on  the  intensity  of  the  current. 

Instead  of  making  the  magnet  rotate  on  its  a.xis,  it  may  be  caused  to^ 
rotate  round  a  line  parallel  to  its  axis  byarrani;ing  the  experiment  as  shown 
in  fijj-.  822. 


866] 


Rotation  of  Magnets  by  Currents. 


851 


Fig.  819. 


This  rotatory  motion  is  readily  intelligible  on  Ampere's  theory~of  mag- 
netism (879),  according  to  which,  magnets  are  traversed  on  their  surface 
by  an  infinity  of  circular  currents  in  the  same  direction,  in  planes  perpendi- 
cular to  the  axis  of  the  magnet.  At  the  moment  at  which  the  current 
passes  from  the 
magnet  into  the 
mercury,  it  di- 
vides on  the 
surface  of  the 
mercury  into  an 
infinity  of  rec- 
tilinear currents 
proceeding  from 
the  axis  of  the 
magnet  to  the 
circumference  of 
the  glass.  Figs. 
820  and  8: 
which  corre- 
spond respec- 
tively to  figs. 
818     and     819, 

give  on  a  larger  scale,  and  on  a  horizontal  plane  passing  through  the  surface 
of  the  mercury,  the  direction  of  the  currents  to  which  the  rotation  is  due.  In 
fig.  820  the  north  pole  being  at  the  top,  the  Amperian  currents  pass  round 
the  magnet  in  the  reverse  direction  to  that  of  the  hands  of  a  watch,  as  indi- 
cated by  the  arrow  i 
(879),  while  the  cur- 
rents which  radiate 
from  the  rod  C 
towards  the  metal 
ring  GG',  have 
the  directiom  CD, 
CE.  Thus  (860) 
any  given  element 
c  of  the  magnetic 
current  of  the  bar 
A  is  attracted  by 
the  current  CE 
and  repelled  by  the  current  CD  ;  hence  results  a  rotation  of  the  bar  about 
its  axis  in  the  same  direction  as  the  hands  of  a  watch. 

In  fig.  821  the  currents  CD,  CF  being  in  the  opposite  direction  to  those 
of  the  bar  would  repel  the  latter,  which  would  be  attracted  by  the  currents 
CE,  CH.  Hence  the  bar  rotates  in  a  circular  direction,  shown  by  the  arrow 
J-,  about  the  vertical  axis  which  passes  through  the  rod  C. 

If  the  north  pole  is  below,  or  if  the  direction  of  the  current  be  altered,  the 
rotation  of  the  magnet  is  in  the  opposite  direction. 


Fig.  820. 


Fig.  821. 


3  12 


852 


Dynamical  Electricity. 


[867- 


ACTION  OF  THE  EARTH  AND  OF  MAGNETS  ON  CURRENTS. 

867.  Directive  action  of  mag-nets  on  currents. — Not  only  do  currents 
act  upon  magnets,  but  magnets  also  act  upon  currents.  In  Oersted's  funda- 
mental experiment  (fig.  757),  the  magnet  being  movable  while  the  current  is 
fixed,  the  former  is  directed  and  sets  at  right  angles  with  the  current.  If, 
on  the  contrary,  the  magnet  is  fixed  and  the  current  movable,  the  latter  is 
directed  and  sets  across  the  direction  of  the  magnet.  This  may  be  illus- 
trated by  the  apparatus  represented  in  fig.  822.  This  is  the  original  form 
of  Ampere's  stand,  and  is  frequently  used  in  experimental  demonstration. 
It  needs  no  explanation.  The  circuit  which  the  current  traverses  is  movable, 
and  below  its  lower  branch  a  powerful  bar  magnet  is  placed  ;  the  circuit 
immediately  begins  to  turn,  and  stops  after  some  oscillations  in  a  plane 
perpendicular  to  the  axis  of  the  magnet. 


Fig.  S23. 


For  demonstratmg  the  action  of  magnets  upon  currents,  De  la  Rive's 
floating  battery  (fig.  823)  is  well  adapted.  It  consists  of  plates  of  zinc  and 
copper  which^are  immersed  in  dilute  sulphuric  acid  contained  in  a  gl.iss 
iKilb  slightly  loaded  with  mercury  to  keep  it  upright,  and  which  can  float 
freely  on  water.  With  the  plates  can  be  connected  either  circular  or  rect- 
angular wires,  coils,  or  solenoids  ;  they  are  then  traversed  by  a  current,  and 
can  be  subjected  to  the  action  either  of  magnets  or  of  currents. 

868.  Rotation  of  currents  by  mapnets.— Not  merely  can  currents 
be  directed  by  magnets,  but  they  may  also  be  made  to  rotate,  as  is  seen 
from  the  following  experiment,  devised  by  Faraday  (fig.  824).  On  a  base 
with  levelling  screws,  and  resting  on  an  ivory  support,  is  a  copper  rod,  BD. 
It  is  surrounded  in  part  of  its  length  by  a  bundle  of  magnetised  wires,  AB; 
;uk1  at  the  top  is  a  mercury  cup.     A  copper  circuit,  EF,  balanced  on  a  steel 


-869]  Electrodynamic  and  Electromagnetic  Rotation  of  Liquids.  853 

point,  rests  in  the  cup,  and  the  other  ends  of  the  circuit,  which  terminate 
in  steel  points,  dip  in  an  annular  trough  full  of  mercury. 

The  apparatus  being  thus  arranged,  the  current  from  4  or  5  Bunsen's 
elements  enters  at  the  binding  screw  b  ;  it 
thence  rises  in  the  rod  D,  descends  by  the 
two  branches,  reaches  the  mercury  by  the 
steel  points,  whence  it  passes  by  the  frame- 
work, which  is  of  copper,  to  the  battery  by 
the  binding  screw  a.  If  now  the  magnetised 
bundle  be  raised,  the  circuit  EF  rotates, 
either  in  one  direction  or  the  other,  according 
to  the  pole  by  which  it  is  influenced.  This 
rotation  is  due  to  currents  assumed  to  circu- 
late round  magnets  ;  currents  which  act  on 
the  vertical  branches  EF  in  the  same  way  as 
the  circular  current  on  the  branches  bb  in 
fig.  817. 

In  this  experiment  the  magnetised  bundle 
may  be  replaced  by  a  solenoid  (874)  or  by 
an  electromagnet,  in  which  case  the  two 
binding  screws  in  the  base  of  the  apparatus 
on  the  left  give  entrance  to  the  current 
which  is  to  traverse  the  solenoid  or  electro- 
magnet. 

S69.  Electrodynamic  and  electromagr- 
netic  rotation  of  liquids. — The  condition 
of  a  linear  current  assumed  in  the  previous 
experiments  is  not  necessary.  Fig.  825 
represents  an  apparatus  devised  by  Bertin 
to  show  the  electrodynamic  and  electromag-  Fig.  824. 

netic  rotation  of  liquids.      This   apparatus 

consists  of  an  annular  earthen  vessel,  VV  ;  that  is  to  say,  it  is  open  in  the 
centre  so  as  to  be  traversed  by  a  coil,  H.  It  rests  on  a  board  which  can  be 
raised  along  two  columns,  E  and  I,  and  which  are  fixed  by  means  of  the 
screws  KK.  Round  the  vessel  VV  is  a  second  larger  coil,  G,  fixed  on  the 
columns  SS'.  The  vessel  VV  rests  on  the  lower  plane.  In  the  centre  of 
the  coil  is  a  bar  of  soft  iron,  x^  which  makes  an  electromagnet. 

The  vessel  VV  contains  acidulated  water,  and  in  the  liquid  are  two 
cylindrical  copper  plates  e  and  i,  soldered  to  copper  wires,  e'  and  i\  which 
convey  the  current  of  a  battery  of  four  cells  through  the  rods  E  and  I.  The 
whole  system  is  arranged  on  a  larger  base,  on  the  left  of  which  is  a  commu- 
tator represented  afterwards  on  a  larger  scale  (fig,  826).  With  the  base  of 
the  columns  E,  I,  S  and  S'  are  connected  four  copper  strips,  three  of  which 
lead  to  the  commutator  and  the  fourth  to  the  binding  screw  A,  which 
receives  the  wire  from  the  positive  pole. 

The  following  three  effects  may  be  obtained  with  this  apparatus  :— (i),  the 
action  of  the  coil  G  alone  ;  (2),  the  action  of  the  electromagnet  H  alone  ; 
(3),  the  simultaneous  action  of  the  coil  and  of  the  electromagnet. 

I.  Fig.  824  represents  the  apparatus  arranged  for  the  first  effect.     The 


854 


Dynamical  Electricity. 


[869 


current  coming  by  the  bindin.i;  screw  A  attains  the  column  S',  which  leads  it 
to  the  coil  (},  with  regard  to  which  it  is  left — that  is,  in  a  contrary  direction 
to  the  hands  of  a  watch.     Then  descending  by  the  column  S,  it  reaches  the 

c  o  m  m  u  t  a  t  o  r, 
which  leads  it 
by  the  plate 
marked  centri- 
pete  to  the 
column  E  and 
to  the  electrode 
e'.  The  current 
here  traverses 
the  licjuid  from 
the  circumfer- 
ence to  the 
centre,  attains 
the  electrode  z, 
the  column  I, 
and  by  the  inter- 
\ention  'of  the 
plate  cefitrifuge 
the  central  piece 
of  the  com- 
mutator. This 
transmits  it  finally  to  the  negative  binding  screw,  which  leads  it  to  the  battery. 
The  liquid  then  commences  a  direct  rotatory  motion — that  is  to  say,  in  the 
same  direction  as  the  coil.  If  the  direction  of  the  current  in  the  liquid  is 
centrifugal — that  is,  proceeds  from  the  centre  to  the  circumference — the 
rotation  is  inverse ;  that  is,  in  the  opposite  direction  to  that  of  the  coil. 
In  both  cases  the  rotations  may  be  shown  to  those  at  a  distance  by  means 
of  small  flags,  f  f^  fixed  on  discs  of  cork  which  float  on  the  liquid,  and 
which  are  coated  with  lampblack  to  prevent  adherence  by  capillary  attraction 
between  the  discs  and  the  electrodes  e  and  /. 

II.  To  experiment  with  the  electromagnet  alone,  the  positive  wire  of  the 
battery  is  connected  with  the  binding  screw  C,  and  the  binding  screws  D  and 
B  are  joined  by  a  copper  wire.  The  current  first  passes  into  the  electromagnet 
H,  then,  reaching  the  commutator  by  the  binding  screw  B,  passes  into  the 
centripetal  plate,  whence  it  rises  in  the  column  E,  traverses  the  liquid  in  the 
same  direction  as  at  first,  reascends  by  the  column  I,  and  from  thence  to 
the  centre  of  the  commutator  and  the  negative  binding  screw,  which  leads  it 
to  the  battery.  If  the  north  pole  of  the  electromagnet  is  at  the  same  height 
as  the  glass  vessel,  as  in  the  figure,  the  Ampcrian  currents  move  in  the 
opposite  direction  to  the  hands  of  a  watch,  and  the  floats  then  move  in  the 
same  direction  as  above  ;  and  if  the  electromagnet  is  raised  until  the  neutral 
line  is  at  the  same  heij^ht  as  the  vessel,  the  floats  stop  ;  if  it  is  above  ihcm, 
the  floats  move  again,  but  in  the  opposite  direction. 

III.  To  cause  the  coil  and  the  electromagnet  to  act  simultaneously,  the. 
positive  wire  of  the  battery  is  attached  at  C,  and  the  binding  screws  D  and 
A  are  connected  by  a  conductor.     Hence,  after  having  traversed  the  coil  H, 


-871]     Directive  Actio?i  of  tlie  Earth  on  Vertical  Currents.     855 

the  current  arrives  from  D,  and  the  binding  screw  A,  whence  it  traverses 
exactly  the  same  circuit  as  in  the  first  experiments.  The  effects  are  the 
same,  though  more  intense  ;  the  action  of  the  coil  and  the  electromagnet 
being  in  the  same  direction. 

A  simpler  form  of  this  experiment  was  devised  by  Clerk  Maxwell.  At 
the  bottom  of  a  small  beaker,  a  copper  disc  is  placed  with  an  insulated 
tongue  bent  at  right  angles,  and  connected  with  a  similar  zinc  disc  supported 
about  an  inch  above  the  copper.  Dilute  acid  is  placed  so  as  to  cover  both 
discs,  and  some  fine  sawdust  having  been  added  to  the  liquid  the  whole  is 
placed  on  the  pole  of  an  electromagnet.  The  rotation  of  the  liquid  is  then 
shown  by  that  of  the  sawdust. 

S70.  Bertln's  commutator. — Commutators  are  apparatus  by  which  the 
direction  of  currents  may  be  changed  at  pleasure,  or  by  which  they  may  be 
open  or  closed.  Bertin's  has  the  advantage  of  at  once  showing  the  direc- 
tion of  the  current.  It  consists  of  a  small  base  of  hard  wood  on  which  is  an 
ebonite  plate,  which,  by  means  of  the  handle  in  (fig.  826),  is  turned  about  a 
central  axis,  between  two  stops,  c  and  c'.  On  the  disc  are  fixed  two  copper 
plates,  one  of  which,  c,  is  always  positive,  being  connected  by  the  axis  and 
by  a  plate,  +  ,  with  the  binding  screw  P,  which  receives  the  positive  electrode 
of  the  battery  ;  the  other,  zV,  bent  in  the  form  of  a  horseshoe,  is  in  metallic 
connection  with  a  plate  below  the  disc  against  which  it  moves  with  friction  ; 
this  plate  is  in  connection  with  the  negative  electrode  N.  On  the  opposite 
side  of  the  board  are  two  binding  screws,  b  and  b' ,  to  which  are  adapted  two 
elastic  metal  plates,  r  and  r'. 

These  details  being 
premised,  the  disc  being 
turned  as  shown  in  the 
figure,  the  current  coming 
by  the  binding  screw  P 
passes  into  the  piece  ^, 
the  plate  r  and  the  bind- 
ing screw  ^,  which  by  a 
second  plate,  or  by  a  cop- 
per wire,  leads  it  to  the 
apparatus  shown  in  fig. 
825,  or  any  other.     Then  Fijr.  826. 

returning  to  the  binding 

screw  b\  the  current  attains  the  plate  /■',  the  piece  i  e,  and  ultimately  the 
binding  screw  N,  which  returns  it  to  the  battery. 

If  the  disc  is  turned  so  that  the  handle  is  halfway  between  c  and  c',  the 
pieces  o  and  i  e  being  no  longer  in  contact  with  the  plates  r  and  ;■',  the  cur- 
rent does  not  pass.  If  w  is  turned  as  far  as  c,  the  plate  0  touches  r',  and  r 
touches  c  ;  the  current  thus  passes  first  to  b'  and  returns  by  iJ ;  it  is  therefore 
reversed. 

871.  Directive  action  of  tbe  earth  on  vertical  currents. — The  earth, 
which  exercises  a  directive  action  on  magnets  (690),  acts  also  upon  currents, 
giving  them  in  some  cases  a  fixed  direction,  in  others  a  continuous  rotatoiy 
motion. 

The  first  of  these  two  actions  may  be  thus  enunciated  :  Every  vertical 


856 


Dynainical  Electricity. 


[871- 


currcnt  movable  about  an  axis  parallel  to  itself  ,  places  itself  under  the  direc- 
tive action  of  the  earth  in  a  plane  through  this  axis  perpendicular  to  the 
7nagnctic  meridian,  and  stops  after  some  oscillations,  07i  the  east  of  its  axis 
of  rotatio7i  wheii  it  is  descending,  and  on  the  west  when  it  is  ascending. 

This  may  be  demonstrated  by  means  of  the  apparatus  represented  in  fig. 
828,  which  consists  of  two  brass  vessels  of  somewhat  different  diameters. 
The  larger,  a,  about  13  inches  in  diameter,  has  an  aperture  in  the  centre, 
through  which  passes  a  brass  support,  b,  insulated  from  the  vessel  a,  but 
communicating  with  the  vessel  K.     This  column  terminates  in  a  small  cup. 


Fig.  828. 

in  which  a  light  wooden  rod  rests  on  a  pivot.  At  one  end  of  this  rod  a  fine 
wire  is  coiled,  each  end  of  which  dips  in  acidulated  water,  with  which  the 
two  vessels  are  respectively  filled. 

The  current  arriving  by  the  wire  m  passes  to  a  strip  of  copper,  which  is 
connected  underneath  the  base  of  the  apparatus  with  the  bottom  of  the 
column  b.  Ascending  in  this  column,  the  current  reaches  the  vessel  K,  and 
the  acidulated  water  which  it  contains  ;  it  ascends  from  thence  in  the  wire 
c,  redescends  by  the  wire  e,  and,  traversing  the  acidulated  water,  it  reaches 
the  sides  of  the  vessel  a,  and  so  back  to  the  battery  through  the  wire  n. 

The  current  being  thus  closed,  the  wire  e  moves  round  the  column  b,  and 
stops  to  the  east  of  it,  when  it  descends,  as  is  the  case  in  the  figure  ;  but  if 
it  ascends,  which  is  eflTected  by  transmitting  the  current  by  the  wire  «,  the 
wire  e  stops  to  the  west  of  the  column  b,  in  a  position  directly  opposite  to 
that  which  it  assumes  when  it  is  descending. 

If  the  rod  with  a  single  wire,  in  fig.  82S,  be  replaced  by  one  with  two  wires 
as  in  fig.  S29,  the  rod  will  not  move,  for  as  each  wire  tends  to  place  itself  on 
the  east  of  the  column  a,  two  equal  and  conlraiy  effects  are  produced,  which 
counterbalance  one  another. 

872.   Action  of  the  earth  on  horizontal  currents  movable  about  a 
vertical  axis. — The  action  of  the  earth  on  horizontal  currents  is  not  direc- 
tive, but  gives  them  a  continuous  rotatoiy  motion  from  the  east  to  the  wcsty  " 
whcfi  the  horizontal  current  moves  away  from  the  axis  of  rotation,  and  from 
the  west  to  the  east  when  it  is  directed  towards  this  axis. 


-874] 


Structure  of  a  Solenoid. 


857 


This  may  be  illustrated  by  means  of  the  apparatus  represented  in  fig.  829, 
which  only  differs  from  that  of  fig.  828  in  having  but  one  vessel.  The 
current  ascending  by  the 
column  rt,  traverses  the 
two  wires  cc,  and  de- 
scends by  the  wires  bb, 
from  which  it  regains 
the  pile  ;  the  circuit  bccb 
then  begins  a  continuous 
rotation  either  from  the 
east  to  the  west,  or  from 
the  west  to  the  east,  ac- 
cording as  in  the  wires 

cc  the  current  goes  from  the  centre,  as  is  the  case  in  the  figure,  or  goes 
towards  it,  which  is  the  case  when  the  current  enters  by  the  wire  ///  instead 
of  by  ;/.  But  we  have  seen  (871)  that  the  action  of  the  earth  on  the  vertical 
wires  bb  is  destroyed  ;  hence  the  rotation  is  that  produced  by  the  action  on 
the  horizontal  branches  cc.  This  rotatory  action  of  the  terrestrial  current 
on  horizontal  currents  is  an  instance  of  the  rotation  of  a  finite  horizontal  by 
an  infinite  horizontal  current  (S64). 

873.  Directive  action  of  the  earth  on  closed  currents  movable  about 
a  vertical  axis. — If  the  current  on  which  the  earth  acts  is  closed,  whether 
it  be  rectangular  or  circular,  the  result  is  not  a  continuous  rotation,  but  a 
directive  action,  as  in  the  case  of  vertical  currents  (871),  in  virtue  of  which 
the  current  places  itself  in  a  plane  perpe7idi- 
cular  to  the  magftetic  meridia?i,  so  that  it  is 
ascending  on  the  east  of  its  axis  of  rotation, 
and  descefiding  on  the  west. 

This  property,  which  can  be  shown  by 
means  of  the  apparatus  represented  in  fig. 
830,  is  a  consequence  of  what  has  been  said 
about  horizontal  and  vertical  currents.  For 
in  the  closed  circuit  BA,  the  current  in  the 
upper  and  lower  parts  tends  to  turn  in  oppo- 
site directions,  from  the  law  of  horizontal 
currents  (872),  and  hence  is  in  equilibrium  ; 
while  in  the  lateral  parts  the  current  on  the 
one  side  tends  towards  the  east,  and  on  the 
other  side  to  the  west,  from  the  law  of  vertical  currents. 

From  the  directive  action  which  the  earth  exerts  on 
sary,  in  many  experiments,  to  neutralise  this  action, 
arranging  the  movable  circuit  symmetrically  about  its  axis  of  rotation,  so 
that  the  directive  action  of  the  earth  tends  to  turn  the  two  branches  in 
opposite  directions,  and  hence  destroys  them.  This  condition  is  fulfilled  in 
the  circuit  in  fig.  822.     Such  circuits  are  hence  called  astatic  circuits. 

874.  Structure  of  a  solenoid. — A  solenoid  is  a  system  of  equal  and 
parallel  circular  currents  formed  of  the  same  piece  of  covered  copper  wire 
and  coiled  in  the  fomi  of  a  helix  or  spiral,  as  represented  in  fig.  831.  A  sole- 
noid, however,  is  only  complete  when  part  of  the  wire  BC  passes  in  the 


currents,  it  is  neces- 
This  is  effected  by 


858 


Dynamical  Electricity. 


874- 


direction  of  the  axis  in  the  interior  of  the  heHx.  With  this  arrangement, 
when  the  circuit  is  traversed  by  a  current,  it  follows  from  what  has  been 
said  about  sinuous  currents  (86 1)  that  the  action  of  a  solenoid  in  a  longi- 
tudinal direction,  AB,  is  counterbalanced  by  that  of  the  rectilinear  current 
BC.  This  action  is  accordingly  null  in  the 
A^^^^^Xpv-NTV'y-v'^r^v^ir-ir^jr^-N         direction  of  the  length,  and  the  actioti  of 

(.  ^ Q  A-A  y  y  A  IfrruVlYPCr  ^      '^  solenoid  in  a  direction  perpendicular  to 

^  its  axis  is  exactly  eqiiivatent  to  that  of  a 

'^'  "^^*  series  of  equal  parallel  curretits. 

875.  Action  of  currents  on  solenoids. — What  has  been  said  of  the 
action  of  fixed  rectilinear  currents  on  finite  rectangular,  or  circular  currents 

(864),  applies  evidently  to 
each  of  the  circuits  of  a  sole- 
noid, and  hence  a  rectilinear 
current  must  tend  to  direct 
these  circuits  parallel  to 
itself.  To  demonstrate  this 
fact  experimentally,  a  sole- 
noid is  constructed  as  shown 
in  fig.  832,  so  that  it  can  be 
suspended  by  two  pivots  in 
the  cups  a  and  c  of  the  appa- 
ratus represented  in  fig.  830. 
The  solenoid  is  then  mov- 
able about  a  vertical  axis, 
and  if  a  rectilinear  current 
QP  be  passed  beneath  it,  which  at  the  same  time  traverses  the  wires  of 
the  solenoid,  the  latter  is  seen  to  turn  and  set  at  right  angles  to  the  lower 
current — that  is,  in  such  a  position  that  its  circuits  are  pai-allel  to  the  fixed 
current  ;  and,  further,  the  current  in  the  lower  part  of  each  of  the  circuits  is 
in  the  same  direction  as  in  the  rectilinear  wire. 

If,  instead  of  passing  a  rectilinear  current  below  the  solenoid,  it  is  passed 
vertically  on  the  side,  an  attraction  or  repulsion  will  take  place,  according 
as  the  two  currents  in  the  vertical  wire,  and  in  the  nearest  part  of  the 
solenoid,  are  in  the  same  or  in  contrary  directions. 

876.  Directive  action  of  the  earth  on  solenoids. — If  a  solenoid  be 
suspended  in  the  two  cups  (fig.  833),  not  in  the  direction  of  the  magnetic 
meridian,  and  a  current  be  passed  through  tlie  solenoid,  the  latter  will 
begin  to  move,  and  will  finally  set  in  such  a  position  that  its  axis  is  in  the 
direction  of  the  magnetic  meridian.  If  the  solenoid  be  removed,  it  will, 
after  a  few  oscillations,  return,  so  that  its  axis  is  in  the  magnetic  meridian. 
Further,  it  will  be  found  that  in  the  lower  half  of  the  coils  of  which  the 
solenoid  consists,  the  direction  of  the  current  is  from  east  to  west ;  in  other 
words,  the  current  is  descending  on  that  side  of  the  coil  turned  towards  the 
cast  and  asce7tding  on  the  Mcst.  The  directive  action  of  the  earth  on 
solenoids  is  accordingly  a  consequence  of  that  which  it  exerts  on  circular 
currents.  In  this  experiment  the  solenoid  is  directed  like  a  magnetic  needle, 
and  the  nortJi  pole,  as  in  magnets,  is  that  end  which  points  towards  the 
north,  and  the  south  pole  that  whicli  jioints  towards  tlie  south.     This  cxperi- 


Fig.  832. 


-879J 


Ampere's  TJieory  of  Magnetism. 


859 


ment  may  be  made  by  means  of  a  solenoid  fitted  on  a  De  la  Rive's  floating 
battery  (867), 


Fig.  S33. 

877.  Mutual  action  of  magnets  and  solenoids. — Exactly  the  same 
phenomena  of  attraction  and  repulsion  exist  between  solenoids  and  magnets 
as  between  magnets  themselves.  For  if  one  of  the  poles  of  a  magnet  be  pre- 
sented to  a  movable  solenoid,  traversed  by  a  current,  attraction  or  repulsion 
will  take  place,  according  as  the  poles  of  the  magnet  and  of  the  solenoid  are 
of  contrary  or  of  the  same  name.  The  same  phenomenon  takes  place 
when  a  solenoid  traversed  by  a  current  and  held  in  the  hand  is  presented  to 
a  movable  magnetic  needle.  If  one  pole  of  a  long  bar  magnet  be  presented 
to  the  centre  of  the  floating  coil  (fig.  823),  then  if  the  direction  of  the  current 
in  the  coil  is  the  same  as  that  of  the  amperian  current  (879)  in  that  pole  of  the 
magnet,  the  coil  will  be  attracted  to  the  magnet,  and,  encircling  it,  will  move 
towards  the  middle,  where  it  is  stationary  ;  if  the  currents  are  opposite,  then  the 
coil  will  first  of  all  be  repelled,  it  will  then  turn  round,  and  proceed  as  before. 

878.  ivzutual  action  of  solenoids. — When  two  solenoids  traversed  by  a 
powerful  current  are  allowed  to  act  on  each  other,  one  of  them  being  held 
in  the  hand  and  the  other  being  movable  about  a  vertical  axis,  as  shown 
in  fig.  833,  attraction  and  repulsion  will  take  place  just  as  in  the  case  of  two 
magnets.  These  phenomena  are  readily  explained  by  reference  to  what  has 
been  said  about  the  mutual  action  of  the  currents,  bearing  in  mind  the  direc- 
tion of  the  currents  in  the  extremities  presented  to  each  other. 

879.  iimpere's  theory  of  mag-netism. — Ampere  propounded  a  theory, 
based  on  the  analogy  between  solenoids  and  magnets,  by  which  all  magnetic 
phenomena  may  be  referred  to  electrodynamical  principles. 

Instead  of  attributing  magnetic  phenomena  to  the  existence  of  two  fluids. 
Ampere  assumed  that  each  individual  molecule  of  a  magnetic  substance  is 
traversed  by  a  closed  electric  current,  and  further  that  these  molecular  cur- 
rents are  free  to  move  about  their  centres.  The  coercive  force,  however, 
which  is  little  or  nothing  in  soft  iron,  but  considerable  in  steel,  opposes  this 
motion,  and  tends  to  keep  them  in  any  position  in  which  they  happen  to  be. 
When  the  magnetic  substance  is  not  magnetised,  these  molecular  currents, 
under  the  influence  of  their  mutual  attractions,  occupy  such  positions  that 
their  total  action  on  any  external  substance  is  nil.  Magnetisation  consists 
in  giving  to  these  molecular  currents  a  parallel  direction,  and  the  stronger 


Fig.  834. 


860  Dynaniicixl  Rlectvicity.  [879- 

the  magnetising  force  the  more  perfect  the  paralleHsm.     The  limit  of  mag- 
netisation is  attained  when  the  currents  are  completely  parallel. 

The  resultant  of  the  actions  of  all  the  molecular  currents  is  equivalent  to 
that  of  a  single  current  which  traverses  the  outside  of  a  magnet.     For  by 

inspection  of  fig.  834,  in  which 
the  molecular  currents  are  re- 
presented by  a  series  of  small 
internal  circles  in  the  two  ends 
of  a  cylindrical  bar,  it  will  be 
seen  that  the  adjacent  parts  of 
the  currents  oppose  one  another 
and  cannot  exercise  any  external 
electrodynamic  action.  This  is 
not  the  case  with  the  surface  ; 
there  the  molecular  currents  at 
ab  are  not  neutralised  by  other 
currents,  and  as  the  points  abc 
are  infinitely  near,  they  form  a  series  of  elements  in  the  same  direction 
situated  in  planes  perpendicular  to  the  axis  of  the  magnet,  and  which  con- 
stitute a  true  solenoid 

The  direction  of  these  currents  in  magnets  can  be  ascertained  by  con- 
sidering the  suspended  solenoid  (fig.  832).  If  we  supposed  it  traversed  by  a 
current,  and  in  equilibrium  in  the  magnetic  meridian,  it  will  set  in  such  a 
position  that  in  the  lower  half  of  each  coil  the  current  flows  from  east  to 
west.  We  have  then  the  following  rule  : — When  the  7iorth  pole  of  a  magnet 
is  looked  at,  the  direction  of  tJie  amperian  currents  is  opposite  to  that  of  the 
hands  of  a  watch ;  and  wJien  the  south  pole  is  looked  at,  the  direction  is  the 
same  as  that  of  the  Iiands. 

880.  Terrestrial  current. — In  order  to  explain  terrestrial  magnetic 
effects  on  this  supposition,  the  existence  of  electrical  currents  is  assumed, 
which  continually  circulate  round  our  globe  from  east  to  west  perpendicular 
to  the  magnetic  meridian.  The  resultant  of  their  action  is  a  single  current 
traversing  the  magnetic  equator  from  east  to  west.  They  are  supposed  by 
some  to  be  thermo-electric  currents  due  to  the  variations  of  temperature 
caused  by  the  successive  influence  of  the  sun  on  the  difterent  parts  of  the 
globe  from  east  to  west. 

These  currents  direct  magnetic  needles  ;  for  a  suspended  magnetic 
needle  comes  to  rest  when  the  molecular  currents  on  its  under-surface  are 
parallel  and  in  the  same  direction  as  the  terrestrial  currents.  As  the 
molecular  currents  are  at  right  angles  to  the  direction  of  its  length,  the 
needle  places  its  greatest  length  at  right  angles  to  east  and  west,  or  north 
and  south.  Natural  magnetisation  is  probably  imparted  in  the  same  way  to 
iron  minerals. 

88  r.  Kail's  experiment. — In  the  action  of  magnets  on  currents  which 
has  been  described  in  the  foregoing  sections,  we  have  been  concerned  with 
the  action  of  the  magnet  on  the  body  which  conveys  the  current. 

Professor  Hall  of  Baltimore  has  made  the  following  experiment  to 
determine  whether  the  path  of  a  current  itself  in  the  body  of  a  conductor  is 
or  is  not  deflected  when  it  is  exposed  to  the  direct  action  of  a  magnetic  field. 


-881]  HalFs  Experiment.  86 1 

A  strip  of  gold  leaf  AB,  9  centimetres  in  length  by  2  centimetres  broad  (fig. 

835),  was  fastened  on  a  glass  plate,  which  was  placed  between  the  poles  of 

an  electromagnet  in  such  a  manner  that  the  plane  of  the  strip  was  at  right 

angles  to  the  lines  of  force  of  the  magnetic  field.     The  ends  of  this  strip  A 

and  B  were  in  connection  with  the  poles 

of  a  Bunsen's  cell.     Two  wires  leading  to 

a  Thomson's  galvanometer  a  and  b  were 

connected  with  two  equipotential  points 

at  the  opposite  edges  of  the  strip  ;  that 

is  to  say,  in  two  points,  found  by  trial, 

in    which    there    was    no    deflection    of  /     5I 

the  galvanometer  (738).     When  now  the  -5^'  X, 

electromagnet  was  excited  by  passing  a 

current  through  it,  a  distinct  deflection  "'     ^' 

was  produced  in  the  galvanometer,  showing  that  the  path  of  the  current  in 

the  conducting  strip  had  been  deflected.     This  deflection  was  permanent, 

and  could  not  therefore  be  due  to  induction,  and  its  direction  was  reversed 

when  the  current  in  the  magnet  was  reversed. 

The  magnetic  field  acts  thus  upon  the  current  in  the  gold  leaf  in  such  a 
manner  as  to  displace  it  from  one  edge  towards  the  other,  and  to  cause  a 
small  portion  to  pass  through  the  circuit  of  the  galvanometer. 

The  electricity  is  displaced  in  the  direction  of  the  electromagnetic  force 
T,  that  is,  from  a\.o  b  through  the  galvanometer  in  the  case  of  iron,  zinc,  and 
cobalt,  but  from  b  \.o  a  through  the  galvanometer,  with  nickel,  gold,  and 
bismuth.  ~0f  all  metals,  bismuth  shows  the  phenomenon  in  the  highest 
degree. 


862  Dynamical  Electricity.  [882- 


CHAPTER   V.      . 

MAGNETISATION  BY  CURRENTS.      ELECTROMAGNETS. 
ELECTRIC  TELEGRAPHS. 

882.  Magrnetisation  by  currents. — From  the  influence  which  currents 
exert  upon  magnets,  turning  the  north  pole  to  the  left  and  the  south  pole  to 
the  right,  it  is  natural  to  think  that  by  acting  upon  magnetic  substances  in 
the  natural  state  the  currents  would  tend  to  separate  the  two  magnetisms. 
In  fact,  when  a  wire  traversed  by  a  current  is  immersed  in  iron  filings,  they 
adhere  to  it  in  large  quantities  (fig.  836),  each  particle  sets  particularly  to  the 


wire  ;  they  become  detached  as  soon  as  the  current  ceases,  and  there  is  no 
action  on  any  non-magnetic  metal. 

In  like  manner  an  iron  or  steel  bar  is  magnetised  when  placed  at  right 
angles,  and  near  to  a  current  ;  the  effect  is  increased  by  coiling  an  insulated 
copper  wire  round  a  glass  tube,  in  which  there  is  an  unmagnetised  steel  bar. 
If  a  current  be  passed  through  the  wire,  even  for  a  short  time,  the  bar  be- 
comes strongly  magnetised. 

If,  as  we  have  already  seen  (791),  the  discharge  of  a  Leydenjar  be  trans- 
mitted through  the  wire,  by  connecting  one  end  with  the  outer  coating,  and 
the  other  with  the  inner  coating,  the  bar  is  also  magnetised.  This  is  a 
convenient  way  of  illustrating  the  identity  between  frictional  and  voltaic 
electricity. 

If  in  this  experiment  the  wire  be  coiled  on  the  tube  in  such  a  manner 
that  when  it  is  held  vertically  the  downward  direction  of  the  coils  is  from 
right  to  left  on  the  side  next  the  observer,  this  constitutes  a  riglit-handcd  or 
dcxtrorsal  spiral  or   Iiclix  (fig.  837),  of   which  the  ordinary  screw  is  an 


Eig.  837- 

example.     In  a  Icft-iutiidcd  ox  si /i isi rorsal  /w/ix  ihc  coiling  is  in  the  opposite 
direction,  that  is,  from  left  to  right  (fig.  83S). 

In  a  right-handed  spiral  the  north  pole  is  at  the  end  at  which  the  current 
emerges,  and  the  south  pole  at  the  end  at  which  it  enters  ;  the  reverse  is  the 
case  in  a  left-handed  spiral.  But  whatever  the  direction  of  the  coiling,  the 
polarity  is  easily  found  by  the  following  rule  :  1/ a  person  s7(.'ii/uiiifio  iti  tlic 


-883] 


Electromagnets. 


863 


cuniiil  look  (if  the  axis  of  the  spiral^  the  north  pole  is  always  on  his  left.  If 
the  wire  be  not  coiled  regularly,  but  if  its  direction  be  reversed,  at  each 
change  of  direction  a  consequent  pole  (681)  is  formed  in  the  magnet.     The 


^^^m^^^i^i^i^^s^^;^^^ 


simplest  method  of  remembering  the  polarity  produced  is  as  follows  :  What- 
ever be  the  nature  of  the  helix,  either  right  or  left  handed,  if  the  end  facing 
the  observer  has  the  current  flowing  in  the  direction  of  the  handsof  a  watch, 
it  is  a  south  pole,  and  vice  versa.  The  same  polarity  is  produced  whether 
or  not  there  is  an  iron  core  with  the  helix. 

The  nature  of  the  tube  on  which  the  helix  is  coiled  is  not  without  influence. 
Wood  and  glass  have  no  effect,  but  a  thick  cylinder  of  copper  may  greatly 
affect  the  action  of  the  current  unless  the  copper  be  slit  longitudinally.  This 
action  will  be  subsequently  explained.  The  same  is  the  case  with  iron, 
silver,  and  tin. 

In  order  to  magnetise  a  steel  bar  by  means  of  electricity,  it  need  not  be 
placed  in  a  tube,  as  shown  in  figs.  837  and  838.  It  is  sufficient  to  coil  round 
it  a  copper  wire,  covered  with  silk, 
cotton,  or  gutta-percha,  in  order  to  in- 
sulate the  circuits  from  one  another. 
The  action  of  the  current  is  thus  mul- 
tiplied, and  a  feeble  current  is  suffi- 
cient to  produce  a  powerful  magneti- 
sing effect. 

8S3.  Electromag'nets.  — -  IClcctro- 
jiiao/iets  arc  bars  of  soft  iron  which, 
under  the  influence  of  a  voltaic  current, 
become  magnets  ;  this  magnetism  is 
only  temporary,  for  the  coercive  force 
of  perfectly  soft  iron  is  ////,  and  as  soon 
as  the  current  ceases  to  pass  through 
the  wire,  the  bar  reverts  to  its  normal 
magnetic,  but  unmagnetised  state.  If, 
liowever,  the  iron  is  not  quite  pure  it 
retains  more  or  less  traces  of  magneti- 
sation. Electromagnets  have  the 
horse-shoe  form,  as  shown  in  fig.  839, 
and  a  copper  wire,  co\ered  with  silk  or 
cotton,  is  rolled  several  times  rounil 
them   on  the  two  branches  so  as    to 

form  two  bobbins,  A  and  B.     In  order  _  ^^ 

that   the  two  ends  of  the  horse-shoe  i^-  kv„u  u  _ 

may  be  of  opposite  polarity,  the  wind-  ^  '■^"  "'" 

ing  on  the  two  limbs  A  and  B  must  be  such  that  if  the  horse-shoe  were 
straightened  out,  it  would  be  in  the  same  direction.  Such  an  arrangement 
as  this  is  called  a  magnetising  spiral. 


'^'f'tllUljiJ* 


864  Dynamical  Electricity.  [883- 

Electromagnets,  instead  of  being  made  in  one  piece,  are  constructed  of 
two  cylinders  firmly  screwed  to  a  stout  piece  of  the  same  metal.  Such  are 
the  electromagnets  in  Morse's  telegraph  (889)  and  the  electromagnetic  motor 
(899).  The  helices  on  them  must  be  such  that  the  current  shall  flow  in  the 
same  direction  as  the  hands  of  a  watch  as  seen  from  the  south  pole,  and 
against  the  hands  of  a  watch  as  seen  from  the  north  pole. 

The  most  powerful  permanent  magnets  are  obtained  by  means  of  electro- 
magnets. For  this  purpose  the  steel  bar  is  placed  in  a  ring  consisting  of  several 
turns  of  insulated  wire  through  which  a  strong  current  is  passed,  and  the  bar 
is  moved  backwards  and  forwards  in  the  coil,  finishing  where  it  had  begun 
in  the  middle  of  the  bar  ;  the  current  is  then  opened.  Or  starting  with  the 
middle,  one  half  of  the  bar  is  moved  15  or  20  times  over  one  pole  of  an  elec- 
tromagnet such  as  fig.  839,  and  the  other  half  is  passed  in  the  same  way  over 
the  other  limb. 

The  following  are  the  principal  results  which  have  been  obtained  in  refer- 
ence to  electromagnets  : — 

The  magtietising  force  of  a  spiral  is  proportional  to  the  product  of  the 
number  of  turns  of  the  wire  into  the  strength  of  the  current  which  traverses 
it.  With  a  given  battery,  the  greatest  magnetising  power  is  obtained  when 
the  resistance  in  the  magnetising  spiral  is  equal  to  the  sum  of  the  other  re- 
sistances in  the  circuit,  those  of  the  battery  included,  and  the  length  and  dia- 
meter of  the  wire  must  be  so  arranged  as  to  satisfy  these  conditions. 

Provided  the  bar  projects  sufficiently  at  each  end  of  the  spiral,  the  width 
of  the  coils  has  no  influence  on  the  magnetism  produced. 

Taking  into  account  the  resistance,  the  electromagnetic  force  is  indepen- 
dent of  the  nature  and  thickness  of  the  wire.  Thus  the  strength  of  the  cur- 
rent, and  the  number  of  coils  being  the  same,  thick  and  thin  wires  produce 
the  same  effect. 

The  relation  between  the  strength  of  the  magnetism  developed  in  soft 
iron  and  the  strength  of  the  current  cannot  be  expressed  in  a  simple  manner. 
At  first  the  electromagnetism  increases  somewhat  more  rapidly  than  in  pro- 
portion to  the  strength  of  the  current,  but  the  rate  becomes  less  until  it 
reaches  a  maximum  which  is  not  exceeded  however  strong  be  the  current. 
The  existence  of  this  maximum,  which  varies  for  each  bar,  is  a  support  for 
the  theory  of  molecular  magnets,  or  molecular  currents  which  have  been  laid 
down  (879).  The  maximum  is  attained  when  all  the  currents  in  the  magnets 
have  set  in  their  final  position. 

Soft  iron  and  steel  differ  greatly  as  to  their  retention  of  magnetisation  ; 
thus  for  the  same  strength  of  current  the  temporary  magnetisation  (or  that 
observed  while  the  current  lasts)  was  0*499  in  the  case  of  soft  iron,  0-248  for 
steel,  and  0-246  for  cast  iron  ;  while  that  remaining  after  the  current  ceased 
was  o,  0T58,  and  o'Oi7  respectively.  In  other  words,  soft  iron  retained  none 
of  the  magnetisation,  and  cast  iron  7  per  cent.  ;  while  steel  retained  64  per 
cent,  of  that  which  had  been  evoked  in  it. 

The  magnetism  which  a  magnet  retains  after  the  current  ceases  to  act  is 
called  ihc  pcriiuvtc/if  or  rcDiaiicnt  magnetism.  The  latter  term  is  frequently 
employed  to  denote  the  small  quantity  left  in  soft  iron  in  which  its  presence 
is  undesirable.     The  term  residual  is  also  used  in  this  sense. 

The   limiting   value  of  the  magnetism  which  can  be  imparted  to  the 


-883]  Electromagnets.  865 

strongest  magnets  is  40  C.G.S.  units  per  gramme,  according  to  \^'eber  ;  with 
sewing  needles  as  much  as  85  and  with  thin  knitting-  needles  as  much  as  106 
have  been  obtained.  With  ordinary  bar  magnets  the  value  is  usually  much 
less  than  40. 

During  magnetisation  the  \-olume  of  a  magnet  does  not  vary.  This  has 
been  established  by  placing  the  bar  to  be  magnetised  with  its  helix  in  a  sort 
of  water  thermometer,  consisting  of  a  flask  provided  with  a  capillary  tube. 
On  magnetising,  no  alteration  in  the  position  of  the  water  is  observed.  But 
the  dimensions  vary  ;  the  diameter  is  somewhat  lessened,  and  the  length 
increased  :  according  to  Joule  to  the  extent  of  about  075000 j  i^  the  bar  is 
magnetised  to  saturation.  Bidwell  has  shown  that  if  the  magnetisation  is 
carried  beyond  the  point  at  which  the  magnetic  elongation  of  the  rod  reaches 
a  maximum,  the  length  of  the  rod,  instead  of  remaining  unchanged,  steadily 
diminishes,  the  curve  expressing  the  relation  between  the  length  and  the 
magnetising  force  descending  in  a  straight  line  which  shows  no  tendency  to 
become  horizontal. 

The  iron  used  for  an  electromagnet  must  be  pure,  and  be  made  as  soft  as 
possible  by  being  reheated  and  cooled  a  great  many  times  ;  it  is  polished  by 
means  of  a  file,  so  as  to  avoid  twisting.  If  this  is  not  the  case,  the  bar  re- 
tains, after  the  passage  of  the  current,  a  quantity  of  residual  magnetism.  A 
bundle  of  soft  iron  wires  loses  its  magnetism  more  rapidly  than  a  massive 
bar  of  the  same  size.  According  to  Stone,  iron  wires  may  be  materially 
improved  for  electromagnetic  experiments  by  forming  them  into  bundles 
by  tying  them  round  with  wire  ;  these  bundles  are  then  dipped  in  melted 
parafifine  and  set  fire  to. 

Remanent  magnetism  is  greater  in  long  magnets — those,  that  is  to  say,  in 
which  the  diameter  is  small  in  proportion  to  the  length.  It  is  decidedly 
greater  in  soft  iron  when  the  magnetising  current  is  not  opened  suddenly,  as 
is  usually  the  case,  but  is  gradually  brought  to  zero  by  inserting  successively 
greater  resistances.  By  suddenly  opening  the  current  it  has  occasionally 
been  found  with  thick  rods  of  very  soft  iron  that  a  reversed  remanent  mag- 
netism is  met  with,  which  is  called  abttornial  magnetisation. 

This  is  easily  understood  from  the  tendency  of  molecular  magnets  to  re- 
vert to  this  primitive  condition  (879).  In  doing  this  they  experience  a  certain 
friction  or  resistance,  and  when  the  magnetisation  gradually  diminishes  this 
hinders  the  complete  reversal  of  the  molecules  ;  but  with  a  sudden  cessation 
the  molecules,  from  the  greater  vis  viva  of  their  reversal,  will  sooner  come 
back  to  their  original  position,  or  even  pass  it,  and  come  to  rest  on  the 
opposite  side. 

The  weight  attached  to  the  keeper  which  a  magnet  can  support  is  known 
as  its  lifting  ox  portative  force.  If  the  armature  is  prevented  from  coming 
in  contact  with  the  magnet  by  interposing  a  non-magnetic  substance  an  attrac- 
tion is  excited  ;  this  is  proportional  to  the  square  of  the  cm-rent  strength  so 
long  as  the  magnetic  moment  does  not  attain  its  maximum.  Two  unequally 
strong  electromagnets  attract  each  other  with  a  force  proportional  to  the 
square  of  the  sum  of  both  currents. 

The  relation  between  the  portative  and  the  magnetising  force  is  not  so 
simple  ;  according  to  the  researches  of  Bidwell  it  seems  that  for  small 
magnetisation  the   portative  force  increases  less  rapidly  than  the  current 

3  K 


866  Dynamical  Electricity.  [883- 

strcngth  up  to  a  certain  point,  when  the  strength  of  the  field  was  about  270- 
units  and  the  weight  supported  was  ) 0,800  grammes  per  square  centimetre. 
P'rom  this  point  the  magnetising  current  and  the  load  increased  in  exactly 
ihe  same  proportion.  When  the  field  had  an  intensity  of  1,074  C.G.S.  units 
the  greatest  weight  supported  was  15,100  grammes  per  square  centimetre^ 
or  52  pounds  per  square  inch. 

If  the  current  be  broken  while  the  electromagnet  is  supporting  even  a 
heavy  weight  attached  to  the  keeper,  it  frequently  happens  that  the  keeper 
does  not  become  at  once  detached  ;  if  now  the  magnet  is  gently  tapped  so  as 
to  set  the  molecules  in  vibration,  the  keeper  at  once  falls  ;  this  phenomenon  is 
due  to  what  is  called  magnetic  hysteresis. 

If  a  bar  magnet  be  suspended  by  a  string  so  that  its  axis  is  in  the  prolon- 
gation of  that  of  a  spiral,  and  a  current  be  now  passed,  it  will  be  seen  that 
the  magnet  will  be  attracted  or  repelled  according  as  the  direction  of  the 
supposed  current  in  the  magnet  is  the  same  as  that  of  the  current  in  the 
spiral  or  not.  In  the  case  of  the  attraction,  and  if  the  magnet  be  not  too- 
bng  and  be  sufficiently  free  to  move,  it  will  be  drawn  within  the  spiral.  The 
force  with  which  the  magnet  is  drawn  in  is  nearly  proportional  to  the  strength 
of  the  current  and  to  the  number  of  turns  of  the  wire. 

If  the  experiment  be  made  with  a  bar  of  soft  iron,  it  is  drawn  in,  and  there 
is  a  remarkable  difference  in  the  strength,  which  is  proportional  to  the  square 
of  the  magnetising  force  of  the  spiral. 

Magnetism  is  not  uniformly  distributed  in  the  section  of  electromagnets  ; 
the  external  layer  exhibits  a  stronger  magnetisation  than  the  inner  ones^ 
and  with  feeble  forces  there  is  only  a  magnetic  excitation  in  the  outer  layer. 
The  magnetism  in  solid  and  in  hollow  cylinders  of  the  same  diameters  is 
the  same,  provided  in  the  latter  case  there  is  sufficient  thickness  of  iron  for 
the  development  of  the  magnetisation.  With  currents  below  a  certain 
strength,  wide  tubes  of  sheet-iron  are  far  more  powerfully  magnetised  than 
solid  rods  of  the  same  length  and  weight  ;  but  with  more  powerful  currents 
the  magnetism  of  the  latter  preponderates. 

This  may  be  illustrated  by  the  following  experiment  :  Two  identical 
magnetising  spirals  are  joined  by  a  wire  and  placed  vertically  a  little  dis- 
tance apart  ;  from  one  end  of  the  beam  of  an  ordinary  balance  a  solid  soft 
iron  rod  is  suspended  so  that  it  is  half  way  within  the  spiral,  and  this  is 
counterpoised  by  a  sheet-iron  cylinder  of  the  same  length  and  weight  but 
of  greater  diameter,  which  is  also  halfway  within  the  other  spiral. 

If  now  the  same  weak  current  is  transmitted  through  both  spirals  the 
cylinder  is  drawn  down,  but  if  a  stronger  one  is  passed  it  is  the  rod  which 
is  sucked  in. 

884.  Vibratory  motion  and  sounds  produced  by  currents. — When  a 
rod  of  soft  iron  is  magnetised  by  a  strong  electric  current,  it  gives  a  very 
distinct  sound,  which,  however,  is  only  produced  at  the  moment  of  closing 
or  opening  the  current.  This  phenomenon,  first  observed  by  Page  in 
.America,  and  by  Delezenne  in  France,  was  ]xirticularly  investigated  by 
l)e  la  Rive,  who  attributed  it  to  a  vibratory  motion  of  the  molecules  of 
iron  in  consequence  of  a  rapid  succession  of  magnetisations  and  demag- 
netisations. 

Wiicn  the  current  is  broken  and  closed  at  very  short  intervals,  Dela  Rive 


-885]  Reis's  Telephone.  867 

observed  tliat,  whatever  be  the  shape  or  magnitude  of  the  iron  bars,  two 
sounds  may  always  be  distinguished  ;  one,  which  is  musical,  corresponds  to 
that  which  the  rod  would  give  by  vibrating  transversely  ;  the  other,  which 
consists  of  a  series  of  harsh  sounds,  corresponding  to  the  interruptions  of 
the  current,  was  compared  by  De  la  Rive  to  the  noise  of  rain  falling  on  a 
metal  roof  The  most  marked  sound  is  that  obtained  by  stretching,  on  a 
sounding-board,  pieces  of  soft  iron  wire,  well  annealed,  from  i  to  2  mm.  in 
diameter  and  i  to  2  yards  long.  These  wires,  being  placed  in  the  axis  of  one 
or  more  bobbins  traversed  by  powerful  currents,  send  forth  a  number  of 
sounds,  which  produce  a  surprising  effect,  and  much  resemble  that  of  a 
number  of  church  bells  heard  at  a  distance.  Rods  of  zinc,  copper,  or  brass 
give  no  note  even  with  strong  currents. 

Wertheim  obtained  the  same  sounds  by  passing  a  discontinuous  cur- 
rent, not  through  the  bobbins  surrounding  the  iron  wires,  but  through  the 
wires  themselves.  The  musical  sound  is  then  stronger  and  more  sonorous 
in  general  than  in  the  previous  experiment.  The  hypothesis  of  a  molecular 
movement  in  the  iron  wires  at  the  moment  of  their  magnetisation,  and  of 
their  demagnetisation,  is  confirmed  by  the  researches  of  Wertheim,  who 
found  that  their  elasticity  is  then  diminished. 

885.  Rels's  telephone. — The  essential  features  of  this  instrument  (fig. 

840)  are  a  sort  of  box,  B,  one  side  of  which  is  closed  by  a  membrane  C, 

while    there    is 

a     mouthpiece,  ,''  Z7nt 

A,    in     another  T°--j 

side.       On    the      ^;Jj       ^ 

membrane  is  a     a_,       b 

piece     of     thin  jl 

metal-foil        C, 

which     is     con-  :=; 

nected    with    a 

wire  leading  to 

one  pole  of  the 

battery    G,   the  _.     „ 

,        "^        ,  r  f^'S-  840. 

other     pole     of 

which  is  put  to  earth.  Just  above  the  foil,  and  almost  touching  it,  is  a  metal 
point  D,  which  is  connected  by  the  line  wire  (886)  with  one  end  of  a  coil  of 
insulated  wire  surrounding  an  iron  wire,  the  other  end  of  which  is  put  to  earth. 
When  the  mouthpiece  is  spoken  or  sung  into  the  sounds  set  the  mem- 
brane in  vibration  ;  this  alternately  opens  and  closes  the  current,  and  these 
makes  and  breaks  being  transmitted  through  the  circuit  to  the  electromagnet 
F,  produce  the  corresponding  sounds. 


a 


3  K  2 


868  Dynamical  Electricity.  [886- 


ELECTRIC   TELEGRAPH. 

886.  Electric  telegraphs. — These  are  apparatus  by  which  signals  can  be 
transmitted  to  considerable  distances  by  means  of  voltaic  currents  propa- 
gated in  metallic  wires.  Towards  the  end  of  the  last  century,  and  at  the 
beginning  of  the  present,  many  philosophers  proposed  to  correspond  at  a 
distance  by  means  of  the  effects  produced  by  electrical  machines  when  pro- 
pagated in  insulated  conducting  wires.  In  i8ii,  Soemmering  invented  a 
telegraph,  in  which  he  used  the  decomposition  of  water  for  giving  signals. 
In  1820,  at  a  time  when  the  electromagnet  was  unknown,  Ampere  proposed 
to  correspond  by  means  of  magnetic  needles,  above  which  a  current  w^as  sent, 
as  many  wires  and  needles  being  used  as  letters  were  required.  In  1834, 
Gauss  and  Weber  constructed  an  electromagnetic  telegraph,  in  which  a  voltaic 
current  transmitted  by  a  wire  acted  on  a  magnetised  bar  the  oscillations  of 
which  under  its  influence  were  observed  by  a  telescope.  They  succeeded  in 
thus  sending  signals  from  the  Observatory  to  the  Physical  Cabinet  in  Got- 
tingen,  a  distance  of  a  mile  and  a  quarter,  and  to  them  belongs  the  honour  of 
having  first  demonstrated  experimentally  the  possibility  of  electrical  com- 
munication at  a  considerable  distance.  In  1837,  Steinheil  in  Munich,  and 
Wheatstone  in  London,  constructed  telegraphs  in  which  several  wires  each 
acted  on  a  single  needle  ;  the  current  in  the  first  case  being  produced  by  an 
electromagnetic  machine,  and  in  the  second  by  a  constant  battery. 

Every  electric  telegraph  consists  essentially  of  three  parts  :  i,  a  circuit 
consisting  of  a  metallic  connection  between  two  places,  and  an  electromotor 
for  producing  the  current  ;  2,  a  coinmiinicator  for  sending  the  signals  from 
the  one  station  ;  and,  3,  an  indicator  for  receiving  them  at  the  other  station. 
The  manner  in  which  these  objects,  more  especially  the  last  two,  are  effected 
can  be  greatly  varied,  and  we  shall  limit  ourselves  to  a  description  of  the 
three  principal  methods. 

One  form  of  electromotor  still  sometimes  used  in  England  is  a  modifica- 
tion of  Wollaston's  battery.  It  consists  of  a  trough  divided  into  compart- 
ments in  each  of  which  is  an  amalga- 
mated zinc  plate  and  a  copper  plate  ; 
these  plates  are  usually  about  4^,  inches 
in  height  by  3!  in  breadth.  The  com- 
partments are  filled  with  sand,  which  is 
moistened  with  dilute  sulphuric  acid. 
This  battery  is  inexpensive  and  easily 
worked,  only    requiring   from    time    to 

time  the  addition  of  a  little   acid  ;  but 

it  has  very  low  electromotive  force  and 

consideiable  resistance,  and  when  it  has 

^  '  been  at  work  for  some  time  the  effects 

' '^-  '''•  of  polarisation    begin    to   be    perceived. 

On  the  telegraphs  of  the    South-Eastern  Railway,  the  platinised  graphite. 

(811)  battery,  invented  l^y  Mr.  C.  V,  Walker,  has  been  used  with  success. 

On  circuits  on  which  there  is  constant  work  some  form  of  Daniell's  battery 


-887]  Wheatstone  and  Cooke's  TekgrapJi.  869 

Is  used,  and  for  other  circuits  Leclanche's  cell  is  coming  into  more  extended 
use.     In  France,  Daniell's  battery  is  used  for  telegraphic  purposes. 

The  connection  between  two  stations  is  made  by  means  of  galvanised  iron 
wire  suspended  by  porcelain  supports  (fig.  841),  which  insulate  and  protect 
them  against  the  rain,  either  on  posts  or  against  the  sides  of  buildings.  In 
England  and  other  moist  climates  special  attention  is  required  to  be  paid  to 
the  perfection  of  the  insulation.  In  towns,  wires  covered  with  gutta-percha 
are  placed  in  tubes  laid  in  the  ground.  Submarine  cables,  where  great 
strength  is  required  combined  with  lightness  and  high  conducting  power, 
are  formed  on  the  general  type  of  one  of  the  Atlantic  cables,  a  longitudinal 
view  of  which  is  given  in  fig.  842,  while  fig.  843  represents  a  cross  section. 


Fig.  S4.'.  Fig.  843. 

In  the  centre  is  the  core,^\i\<^  is  the  conductor  ;  it  consists  of  seven  copper 
wires,  each  i  mm.  in  diameter,  twisted  in  a  spiral  strand  and  covered  with 
several  layers  of  gutta-percha,  between  each  of  which  is  a  coating  of  Chat- 
tertoiis  compound — a  mixture  of  tar,  resin,  and  gutta-percha.  This  forms 
the  insulator  proper,  and  it  should  have  great  resistance  to  the  passage  of 
electricity,  combined  with  low  specific  inductive  capacity  (748).  Round  the 
insulator  is  a  coating  of  hemp,  and  on  the  outside  is  wound  spirally  a  pro- 
tecting sheath  of  steel  wire,  spun  round  with  hemp. 

At  the  station  which  sends  the  despatch,  the  line  is  connected  with  the 
positive  pole  of  a  battery,  the  current  passes  by  the  line  to  the  other  station, 
and  if  there  were  a  second  return  line,  it  would  traverse  it  in  the  opposite 
direction  to  return  to  the  negative  pole.  In  1837,  Steinheil  made  the  very 
important  discovery  that  the  earth  might  be  used  for  the  return  conductor, 
thereby  saving  the  expense  of  the  second  line.  For  this  purpose  the  end  of 
the  conductor  at  the  one  station,  and  the  negative  pole  of  the  battery  at  the 
other,  are  connected  with  large  copper  plates,  which  are  sunk  to  some  depth 
in  the  ground.  The  action  is  then  the  same  as  if  the  earth  acted  as  a 
return  wire.  The  earth  is,  indeed,  far  superior  to  a  return  wire  ;  for  the 
added  resistance  of  such  a  wire  would  be  considerable,  whereas  the  resist- 
ance of  the  earth  beyond  a  short  distance  is  absolutely  7iil.  The  earth  really 
dissipates  the  electricity,  and  does  not  actually  return  the  same  current  to 
the  battery. 

8S7.  "Wbeatstone  and  Cooke's  sing^le  needle  telegrraph. — This  con- 
sists essentially  of  a  vertical  multiplier  (821)  with  an  astatic  needle,  the 
arrangement  of  which  is  seen  in  fig.  845,  while  fig.  844  gives  a  front  view 
of  the  case  in  which  the  apparatus  is  placed.  A  (fig.  845)  is  the  bobbin, 
consisting  of  about  400  feet  of  fine  copper  wire,  wound  in  a  frame  in  two 
connected  coils.  Instead  of  an  astatic  needle,  Mr.  Walter  has  found  it  ad- 
vantageous to  use  a  single  needle  formed  of  several  pieces  of  very  thin  steel 


870 


Dynamical  Electricity. 


[887- 


strongly  magnetised  ;  it  works  with  the  bobbin,  and  a  light  index  joined  to 
it  by  a  horizontal  axis  indicates  the  motion  of  the  needle  on  the  dial. 

The  signs  are  made  by  transmitting  the  current  in  different  directions 
through  the  multiplier,  by  which  the  needle  is  deflected  either  to  the  right 
or  left,  according  to  the  will  of  the  operator.  The  instrument  by  which  this 
is  effected  is  a  commutator  or  key,  G,  fig.  846  ;  its  action  is  shown  in  fig.  847, 
while  fig.  846  shows  on  a  large  scale  how  two  stations  are  connected.  It 
consists  of  a  cylinder  of  boxwood  with  a  handle,  which  projects  in  front  of 
the  case  (fig.  844).  On  its  circumference  parallel  to  the  axis  are  seven  brass 
strips  (fig.  846),  the  spaces  between  which   are  insulated  by    ivory ;  these 


strips  are  connected  at  the  end  by  metallic  wires,  also  insulated  from  each 
other,  in  the  following  manner  :  a  with  b  and  f,/with  d.,  and  c  with  g.  Four 
springs  press  against  the  cylinder  ;  x  and  y  arc  connected  with  the  poles  of 
the  battery,  ;;/,  with  the  earth  plate,  and  //  witli  one  end  of  the  multiplier,  N. 
When  not  at  work  the  cylinder  and  the  handle  are  in  a  vertical  position, 
as  seen  on  the  left  of  the  diagram.  The  circuit  is  thus  open,  for  the  pole 
springs,  x  and/,  are  not  connected  with  the  metal  of  the  commutator.  But 
if,  as  in  the  figure  on  tlie  right,  the  key  is  turned  to  the  right,  the  battery 
is  brouglit  into  the  circuit,  and  the  current  passes  in  the  following  direc- 
tion :  +  r^o\Q,  x'a'b'fi'Wq"i^,  conductor  y/M//^/t7//E/,  earth /'E'wV'^>', -- 
pole.     The  coils  N  and  N'  are  so  arranged  that  by  the  action  of  the  current 


-888] 


Dial  Telegraphs. 


871 


the  motion  of  the  needle  corresponds  to  the  motion  of  the  handle.  By 
turning  the  handle  to  the  left  the  current  would  have  the  following  direction  : 
+  pole  x'df  in'E'p',  c:ivth  p'E//ical>/iM^,  conductor /'^'MV/'^^'c?/', -pole,  and 
thus  the  needle  would  be  deflected  in  the  opposite  direction. 

The  signs  are  given  by  differently  combined  deflections  of  the  needle 
as  represented  in  tlic  alphaljct  on  tlic  dial  (fig.  844).    \  denotes  a  deflection 


Fig.  S46. 

of  the  upper  end  of  the  needle  to  the  left,  and /a  deflection  to  the  right  ; 
I,  for  instance,  is" indicated  by  two  deflections  to  the  left,  and  M  by  two  to 
the  right.    D  is  expressed  by  right-left-left,  and  C  by  right-left-right-left,  tS:c. 


require   great   practice 


These  signs  are  somewhat  complicated  and 
usually  not  more  than  12  to  20  words  can  be  sent 
in  a  minute.  The  single-needle  telegraph  was  for- 
merly sometimes  replaced  by  the  double-needle 
one,  which  is  constructed  on  the  same  principle, 
but  there  are  two  needles  and  two  wires  instead 
of  one. 

888.  Dial  telegrrapbs. — Of  these  many  kinds 
e.xist.  Figs.  848  and  849  represent  a  lecture- 
model  of  one  form,  constructed  by  Froment,  and 
which  will  serve  to  illustrate  the  principle.  It 
consists  of  two  parts — the  Xtj  for  transmitting 
signals  (fig.  848),  and  the  indicator  (fig.  849)  for 
receiving  them.  The  first  apparatus  is  connected 
with  a  battery,  Q,  and  the  two  apparatus  are 
in  communication  by  means  of  metal  wires,  one  of  which,  AOD  (fig.  848), 
goes  from  the  departure  to  the  arrival  station,  and  the  other,  HKLI  (fig. 


Fig.-  847- 


8/2 


Dynamical  Electricity 


[888- 


849),  from  the  arrival  to  the  departure.      In  practice,  the  latter  is  replaced 
by  the  earth  circuit.     Each  apparatus  is  furnished  with  a  dial  with  25    of 


the  letters  of  the  alphabet,  on  which  a  noodle  iinnos.     Tlie  needle  at  the 
departure  station  is  moved  by  hand,  that  of  the  ani\al  by  olcclricit)-. 


-888]  Dial  Telegraph.  873 

The  path  of  the  current  and  its  effects  are  as  follows  :  from  the  battery  it 
passes  through  a  copper  wire,  A  (fig.  848),  into  a  brass  spring,  N,  which 
presses  against  a  metal  wheel,  R,  then  by  a  second  spring,  M,  into  the  wire 
O,  which  joins  the  other  station.  Thence  the  current  passes  into  the  bobbin 
of  an  electromagnet,  b,  not  fully  shown  in  fig.  849,  but  of  which  fig.  847 
represents  a  section,  showing  the  front  of  the  apparatus.  This  electromagnet 
is  fixed  horizontally  at  one  end,  and  at  the  other  it  attracts  an  armature  of 
soft  iron,  a,  which  forms  part  of  a  bent  lever,  movable  about  its  axis,  <?,  while 
a  spring,  r,  attracts  the  lever  in  the  opposite  direction. 

When  the  current  passes,  the  electromagnet  attracts  the  lever  ci;C,  which 
by  a  rod,  z,  acts  on  a  second  lever,  d,  fixed  to  a  horizontal  axis,  itself  con- 
nected with  a  fork,  F.  When  the  current  is  broken  the  spring  r  draws  the 
lever  r^C,  and  therewith  all  the  connected  pieces  ;  a  backward-and-forward 
motion  is  produced,  which  is  communicated  to  the  fork  F  ;  this  transmits 
it  to  a  toothed  wheel,  G,  on  the  axis  of  which  is  the  needle.  From  the 
arrangement  of  its  teeth,  the  wheel  G  is  always  moved  in  the  same  direction 
by  the  fork. 

To  explain  the  intermittent  action  of  the  magnet,  we  must  refer  to  fig. 
848.  The  toothed  wheel,  R,  has  26  teeth,  of  which  25  correspond  to  letters 
of  the  alphabet,  and  the  last  to  the  interval  reserved  between  the  letters  Z 
and  A.  When  holding  the  knob  P  in  the  hand  the  wheel  R  is  turned,  the  end 
of  the  plate  >N  from  its  curvature  is  always  in  contact  with  the  teeth  ;  the 
plate  M,  on  the  contrary,  terminates  in  a  catch  cut  so  that  contact  is  alter- 
nately made  and  broken.  Hence,  the  connections  with  the  battery  having 
been  made,  if  the  needle  P  is  advanced  through  four  letters,  for  example,  the 
current  passes  four  times  in  N  and  M,  and  is  four  times  broken.  The  electro- 
magnet of  the  arrival  station  will  then  have  attracted  four  times,  and  have 
ceased  to  do  so  four  times.  Lastly,  the  wheel  G  will  have  turned  by  four 
teeth,  and  as  each  tooth  corresponds  to  a  letter,  the  needle  of  the  arrival 
station  will  have  passed  through  exactly  the  same  number  of  letters  as  that 
of  the  departure  station.  The  piece  S,  represented  in  the  two  figures,  is  a 
copper  plate,  mo\able  on  a  hinge,  which  serves  to  make  or  to  break  the 
current  at  will. 

From  this  explanation  it  will  be  readily  intelligible  how  communications 
are  made  between  different  places.  Suppose,  for  example,  that  the  first  ap- 
paratus being  at  London  and  the  second  at  Brighton,  there  being  metallic 
connection  between  the  two  towns,  it  is  desired  to  send  the  word  signal  to 
the  latter  town  :  as  the  needles  correspond  on  each  apparatus  to  the  interval 
retained  between  Z  and  A,  the  person  sending  the  despatch  moves  the 
needle  P  to  the  letter  S,  where  it  stops  for  a  very  short  time  ;  as  the  needle 
in  Brighton  accurately  reproduces  the  motion  of  the  London  needle,  it  stops 
at  the  same  letter,  and  the  person  who  receives  the  despatch  notes  this  letter. 
The  one  at  London,  always  continuing  to  turn  in  the  same  direction,  stops 
at  the  letter  I,  the  second  needle  immediately  stops  at  the  same  letter  ;  and 
continuing  in  the  same  manner  with  the  letters  G,  N,  A,  L,  all  the  word  is 
soon  transmitted  to  Brighton.  The  attention  of  the  observer  at  the  arrival 
station  is  attracted  by  means  of  an  electric  alarum.  Each  station  must 
further  be  provided  with  the  two  apparatus  (figs.  848  and  849),  without  which 
it  would  be  impossible  to  answer. 


•874 


Dynamical  Electricity. 


[889- 


889. — Morse's  telegrapb. — The  telegraphs  hitherto  described  leave  no 
trace  of  the  despatches  sent,  and  if  any  errors  have  been  made  in  copying 
the  signals  there  is  no  means  of  remedying  them.  These  inconveniences 
are  now  met  with  in  the  case  of  the  writing  telegraphs.,  in  which  the  signs 
themselves  are  printed  on  a  strip  of  paper  at  the  time  at  which  they  are 
transmitted. 

Of  the  numerous  printing  and  writing  telegraphs  which  have  been  devised, 
that  of  Morse,  first  brought  into  use  in  North  America,  is  best  known.  It 
has  been  almost  universally  adopted  on  the  Continent.  In  this  instrument 
there  are  three  distinct  parts  :  the  receiver.,  the  sender.,  and  the  relay  ;  figs. 
850,  851,  852,  and  853  represent  these  apparatus. 

Receiver.  We  will  first  describe  the  receiver  (fig.  850),  leaving  out  of  sight 
for  the  moment  the  accessory  pieces,  G  and  T,  placed  on  the  right  of  the 
figure.  The  current  which  enters  the  indicator  by  the  wire,  C,  passes  into  an 
electromagnet,  E,  which  when  the  current  is  closed  attracts  an  armature  of 
soft  iron.  A,  fixed  at  the  end  of  a  horizontal  lever  movable  about  an  axis,  x ; 
when  the  current  is  open  the  lever  is  raised  by  a  spring  r.  By  means  of  two 
screws,  m  and  v,  the  amplitude  of  the  oscillations  is  regulated.  At  the  other 
end  of  the  lever  there  is  a  pencil,  <?,  which  writes  the  signals.  For  this 
purpose  a  long  band  of  strong  paper,  ///,  rolled  round  a  drum,  R,  passes 


i'"ii;.  £50. 

between  two  copper  rollers  with  a  rough  surface,  //■,  and  turning  in  contrary 
directions.  Drawn  in  the  direction  of  the  arrows,  the  band  of  paper  becomes 
•i*elled  on  a  second  drum,  Q,  which  is  turned  by  hand.  A  clockwork  motion 
placed  in  the  box,  HI),  works  the  rollers,  between  which  the  band  of  paper 
passes. 


-889] 


Morse's  TelegrapJi. 


875 


The  paper  being  thus  set  in  motion,  whenever  the  electromagnet  works, 
the  point  o  strikes  the  paper,  and,  without  perforating  it,  produces  an  inden- 
tation the  shape  of  which  depends  on  the  time  during  which  the  point  is  in 
contact  with  the  paper.  If  it  only  strikes  it  instantaneously,  it  makes  a  dot 
(-)  or  short  stroke  ;  but  if  the  contact  has  any  duration,  a  dash  ( — )  of  corre- 
sponding length  is  produced.  Hence,  by  varying  the  length  of  contact  of 
the  transmitting  key  at  one  station,  a  combination  of  dots  and  dashes  may 
be  produced  at  another  station,  and  it  is  only  necessary  to  give  a  definite 
meaning  to  these  combinations. 

In  order  to  make  an  indentation  a  considerable  pressure  is  required,  which 
necessitates  the  employment  of  a  strong  current,  and  the  newer  instruments 
(fig.  851)  are  based  on  the  use  of  ink-wriic7's.  The  paper  band  passes 
close  to,  but  not  touching,  a  metal  disc  with  a  fine  edge,  r,  which  turns 
against  a  small  ink-roller^  a,  all  being  rotated  by  the  same  mechanism. 
When  the  end  A  is  attracted,  the  bent  plate  at  the  other  end  presses  the 
paper  against  the  disc  which  is  inked  by  contact  with  the  ink-roller,  and 
thus  produces  a  mark  on  the  paper,  which  is  either  short  or  long  according 
to  the  duration 
of  the  contact. 
The  signs  are 
thus  more  le- 
gible, and  are 
produced  by 
far  weaker  cur- 
rents. 

The  same 
telegraphic  al- 
phabet is  now 
u  n  i  \-  e  r  s  a  1 1  y 
used     wherever 

telegraphic  communication  exists  ;  and  the  signals  for  the  single-needle  instru- 
ment (fig.  844)  as  well  as  those  used  for  printing  have  been  modified,  so  that 
they  now  correspond  to  each  other.  Thus  a  beat  of  the  top  of  the  needle  to 
the  left  \  is  equixalent  to  a  dot :  and  a  beat  to  the  right  /  to  a  dash.  The 
figure  on  the  next  page  gives  the  alphabet. 

The  Jlag  signals  used  in  military  operations  are  similarly  used.  A  swing 
of  the  flag  from  its  upright  vertical  position  to  the  right  or  left  has  the  same 
meaning  as  the  corresponding  motion  of  the  top  end  of  the  needle.  So  too 
long  or  short  obscurations  of  the  limelight  used  in  signalling  by  night,  or 
of  the  heliograph  (523),  correspond  to  dashes  and  dots. 

Sender  or  key.  This  consists  of  a  small  mahogany  base,  which  acts  as 
support  for  a  metal  lever  ab  (fig.  852),  movable  about  a  horizontal  axis  which 
passes  through  its  middle.  The  extremity  a  of  this  lever  is  always  pressed 
upwards  by  a  spring  beneath,  so  that  it  is  only  by  pressing  with  the  finger 
on  the  key  B  that  the  lever  sinks  and  strikes  the  button  x.  Round  the  base 
are  three  binding  screws,  one  connected  with  the  wire  P,  which  comes  from 
the  positi^•e  pole  of  the  battery  ;  the  second  connected  with  L,  the  line  wire  ; 
and  the  third  with  the  wire  A,  which  passes  to  the  indicator,  for  of  course 


8/6 


Dynamical  Electricity. 


[889- 


two  places  in  communication  are  each  provided  with  an  indicator  and  com- 
municator. 

These  details  known,  there  are  two  cases  to  be  considered,     i.  The  key 


SCs'GLE 

SLVGia; 

PRINTIKG. 

-VEEDLE. 

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/Av 

arranged    so   as    to    receive   a   message   from   a    distant    station  ;    the  end 
b   is    then    down,  as  represented  in    the  figure,  so  that  the  current  which 

arri\es  by  the  line  wire  L, 
►B  and  ascends   in  the   me- 

tallic piece  m,  descends 
in  the  wire  A,  which  leads 
it  to  the  indicator  of  the 
station  at  which  the  ap- 
l^aratus  is  placed.  i.  A 
message  is  to  be  trans- 
milted  ;  in  this  case  the 
1.  !■  key  B  is  pressed  so  that 

1  .^.    tj.  tlie  lever  comes  in  contact 

with  the  button  x.  The 
current  of  the  local  battery,  which  comes  by  the  wire  P,  ascending  then  in 
the  lever,  descends  by  in  and  joins  the  wire  L,  which  conducts  it  to  the 
station  to  which  the  despatch  is  addressed.  According  to  the  length  of  time 
during  which  B  is  pressed,  a  dot  or  a  line  is  ])r()duccd  in  the  recei\er  to 
wliich  the  current  proceeds. 

Relay.  In  describing  the  receiver  wc  have  assumed  that  the  current  of 
the  line  coming  by  the  wire  C  (fig.  850)  entered  directly  into  the  electro- 
magnet, and  worked  the  armature  A,  producing  a  despatch  ;  but  when  the 


-889] 


Morse's   Telegraph. 


S77 


current  has  traversed  a  distance  of  a  few  miles  its  strength  has  diminished 
so  greatly  that  it  cannot  act  upon  the  electromagnet  with  sufficient  force  to 
print  a  despatch.  Hence  it  is  necessary  to  have  recourse  to  a  relay — that  is, 
to  an  auxiliary  electromagnet  which  is  still  tra\ersed  by  the  current  of  the 
line,  but  which  serves  to  introduce  into  the  communicator  the  current  of  a 
local  battery  of  four  or  five  elements  placed  at  the  station,  and  which  is  only  used 
to  print  the  signals  transmitted  by  the  wire. 

For  this  purpose  the  current  entering  the  relay  by  the  binding  screw,  L 
(fig.  8 53),  passes  into  an  electromagnet,  E,  whence  it  passes  into  the  earth 
by  the  binding  screw  T.  Now,  each  time  that  the  current  of  the  line  passes 
into  the  relay,  the  electromagnet  attracts  an  armature,  A,  fixed  at  the  bottom 
of  a  vertical  lever,  ^z^,  which  oscillates  about  a  horizontal  axis. 

At  each  oscillation  the  top  of  the  lever  p  strikes  against  a  button  ;;, 
and  at  this  moment  the  current  of  the  local  battery  which  enters  by  the  bind- 
ing screw  c^  ascends  the  column ;«,  passes  into  the  lever/,  descends  by  the  rod 
o,  which  transmits  it  to  the  screw  Z  :  thence  it  enters  the  electromagnet  of  the 
indicator,  whence  it  emerges  by  the  wire  Z,  to  return  to  the  local  battery  from 
which  it  started.  Then,  when  the  current  of  the  line  is  open,  the  electro- 
magnet of  the  relay  does  not  act,  and  the  le"\er/,  drawn  by  a  spring  r,  leax^es 
the  button  ;/,  as  shown  in  the  drawing,  and  the  local  current  no  longer 
passes.  Thus  the  relay  transmits  to  the  indicator  exactly  the  same  phases  of 
passage  and  intermittence  as  those  effected  by  the  manipulator  in  the  station 
which  sends  the  despatch. 

With  a  general  battery  of  25  Daniell's  elements  the  current  is  usually 
strong  enough  at  upwards  of  90  miles  from  its  starting-point  to  work  a  relay. 
For  a  longer  distance  a  new  current  must  be  taken,  as  will  be  seen  in  the 
paragraph  on  the  change  of  current  {vide  infra). 

Wo7idng  of  the  three  apparatus.  The  three  principal  pieces  of  Morse's 
apparatus  being  thus  known,  the  following  is  the  actual  path  of  the  current. 

The  current  of 
the  line  coming  by 
the  wire  L(fig.  850) 
passes  at  first  to 
the  piece  T  intended 
to  serve  as  light- 
ning -  conductor, 
when,  from  the  in- 
fluence of  atmos- 
pheric electricity  in 
time  of  storm,  the 
conducting  wires 
become  charged 
with  so  much  elec- 
tricity as  to  give 
dangerous    sparks. 

This  apparatus  consists  of  two  copper  discs,  rt'and/  provided  with  teeth  on 
the  sides  opposite  each  other,  but  not  touching.  The  disc  d  is  connected 
with  the  earth  by  a  metal  plate  at  the  back  of  the  stand  which  supports  this 
lightning  conductor,  while  tlic  disc/ is  in  the  current.    The  latter  coming  by 


8/8  Dynamical  Electricity.  [889- 

the  line  L  enters  the  lightning-conductor  by  the  binding  screw  fixed  at  the 
lower  part  of  the  stand  on  the  left  ;  then  rises  to  a  commutator, ;?,  which  con- 
ducts it  to  a  button,  r,  whence  it  reaches  the  disc /by  a  metal  plate  at  the 
back  of  the  stand  ;  in  case  a  lightning  discharge  should  pass  along  the  wire, 
it  would  now  act  inductively  on  the  disc  ^,  and  emerge  by  the  points  without 
danger  to  those  about  the  apparatus.  Moreover,  from  the  disc/,  the  current 
passes  into  a  very  fine  wire  insulated  on  a  tube,  e.  As  the  wire  is  melted 
when  the  discharge  is  too  strong,  the  electricity  does  not  pass  into  the 
apparatus,  which  still  further  removes  any  danger. 

Lastly,  the  current  proceeds  from  the  foot  of  the  support  to  a  screw  on 
the  right,  which  conducts  it  to  a  small  galvanometer,  G,  serving  to  indicate 
by  the  deflection  of  the  needle  whether  the  current  passes.  From  this 
galvanometer  the  current  passes  to  a  key  (fig.  852),  which  it  enters  at  L, 
emerging  at  A  to  go  to  the  relay  (fig.  853).  Entering  this  at  L,  it  works 
the  electromagnet,  and  establishes  the  communication  necessary  for  the 
passage  of  the  current  of  the  local  battery,  as  has  been  said  in  speaking  of 
the  relay. 

Change  of  ciirrejit.  To  complete  this  description  of  Morse's  apparatus  it 
must  be  observed  that  in  general  the  current  which  arrives  at  L,  after  having 
traversed  several  miles,  has  not  sufficient  force  to  register  the  despatch,  nor 
to  proceed  to  a  new  distant  point.  Hence  in  each  telegraphic  station  a 
new  current  must  be  taken,  that  of  the  postal  battery.,  which  consists  of  20  to 
30  Daniell's  elements,  and  is  not  identical  with  the  local  battery. 

This  new  current  enters  at  P  (fig.  850),  reaches  a  binding  screw  which 
conducts  it  to  the  column  H,  and  thence  only  proceeds  further  when  the 
armature  A  sinks.  A  small  contact  placed  under  the  lever  then  touches  the 
button  V  :  the  current  proceeds  from  the  column  H  to  the  metallic  mass 
BD,  whence  by  a  binding  screw  and  a  wire,  not  represented  in  the  figure,  it 
reaches,  lastly,  the  wire  of  the  line,  which  sends  it  to  the  following  post,  and 
so  on  from  one  point  to  another. 

890.  Cowper's  writing-  telegraph. — This  very  remarkable  invention  is 
a  true  telegraph,  in  that  it  faithfully  reproduces  at  a  distance  an  exact  fac- 
simile of  a  person's  handwriting.  The  following  is  a  general  idea  of  the 
principle  of  the  instrument. 

Two  line  wires  are  required,  which  are  severally  connected  at  the  re- 
ceiving station  with  two  galvanometers,  whose  coils  are  at  right  angles  to 
each  other.  At  the  sending  station  is  a  vertical  pencil  with  two  light  rods, 
jointed  to  it  at  right  angles  to  each  other.  One  of  these  contact  rods  guides 
a  contact  piece  which  is  connected  by  a  wire  with  one  pole  of  a  battery,  the 
other  pole  of  which  is  to  earth.  This  contact  piece  slides  over  the  edges  of 
a  series  of  contact  plates  insulated  from  each  other,  between<^ach  of  which 
a  special  resistance  is  interposed,  and  the  last  of  the  contact  pimp's  is  con- 
nected with  one  line  wire.  The  other  contact  piece  slides  over  a  second 
series  of  such  plates  connected  with  the  other  line  wire. 

Let  us  consider  one  contact  alone  ;  as  it  moves  over  the  contact  plates  in 
one  direction  or  the  other,  it  l)rings  less  or  more  resistance  into  the  circuit, 
and  thercljy  alters  the  strength  of  the  current.  The  effect  of  this  is  that  the 
needle  of  the  corresponding  galvanometer  is  less  or  more  deflected.  Now  the 
end  of  this  needle  is  connected  by  a  light  thread  with  a  receiving  pen,  which 


-891]  Induction  in   Telegraph  Cables.  879 

is  a  capillary  tube  full  of  ink.  An  oscillation  of  the  needle  would  produce  an 
up-and-down  motion  of  the  pen,  and  if  simultaneously  a  band  of  paper  passed 
under  the  pen,  being  moved  regularly  by  clockwork,  there  would  be  produced 
on  it  a  series  of  up-and-down  strokes.  A  corresponding  effect  would  be  pro- 
duced by  the  action  of  the  needle  of  the  other  galvanometer,  except  that  its 
strokes  would  be  backwards  and  forwards  instead  of  up  and  down. 

Now  the  action  of  the  writing  pen  is  that  it  varies  simultaneously  the 
strengths  of  the  two  currents,  and  they  produce  a  motion  of  the  receiving 
pen  which  is  compounded  of  the  two  movements  described  above,  and 
which  is  an  exact  reproduction,  on  a  smaller  scale,  of  the  original  motion. 
The  following  line  is  a  facsimile. 

Both  the  paper  written  in  pencil  at  the  sending  station  and  that  written 
in  ink  at  the  receiving  station  move  along  as  the  writing  proceeds,  and  the 
messages  have  only  to  be  cut  off  from  time  to  time. 

Experiments  made  with  this  instrument  show  that  it  will  write  through 
resistances  equal  to  36  miles. 

891.  Induction  inteleg:rapb  cables. — In  the  earliest  experiments  on  the 
use  of  insulated  subterranean  wires  for  telegraphic  communication  it  was 
found  that  difficulties  occurred  in  their  use  which  were  not  experienced  with 
overhead  wires.  This  did  not  arise  from  defective  insulation,  for  the  better 
the  insulation  the  greater  the  difficulty.  It  was  suspected  by  Siemens  and 
others  that  the  retardation  was  due  to  statical  induction,  taking  place  be- 
tween the  inner  wire  through  the  insulator  and  the  external  moisture  ;  and 
Faraday  proved  that  this  was  the  case  by  the  following  experiments  among 
others.  A  length  of  about  100  miles  of  gutta-percha-covered  copper  wire 
was  immersed  in  water,  the  ends  being  led  into  the  chamber  of  observation. 
When  the  pole  of  a  battery  containing  a  large  number  of  cells  was  momen- 
tarily connected  with  one  end  of  the  wire,  the  other  end  being  insulated,  and 
a  person  simultaneously  touched  the  wire  and  the  earth  contact,  he  obtained 
a  violent  shock. 

When  the  wire,  after  being  in  momentary  contact  with  the  battery,  was 
placed  in  connection  with  a  galvanometer,  a  considerable  deflection  was 
observed  ;  there  was  a  feebler  one  3  or  4  minutes  after,  and  even  as  long  as 
20  or  30  minutes  afterwards. 

When  the  insulated  galvanometer  was  permanently  connected  with  one 
end  of  the  wire,  and  then  the  free  end  of  the  galvanometer  wire  joined  to  the 
pole  of  the  battery,  a  rush  of  electricity  through  the  galvanometer  into  the 
wire  was  perceived.  This  speedily  diminished  and  the  needle  ultimately 
came  to  rest.  When  the  galvanometer  was  detached  from  the  battery  and 
put  to  earth,  the  electricity  flowed  as  rapidly  out  of  the  wire,  and  the  needle 
was  momentarily  deflected  in  the  opposite  direction. 

These  phenomena  are  not  difficult  to  explain.  The  wire  with  its  thin 
insulating  coating  of  gutta-percha  becomes  statically  charged  with  electricity 
from  the  batter)'.  The  coating  of  gutta-percha  through  which  the  inductive 
action  takes  place  is  only  yV  of  an  inch  in  thickness,  and  the  extent  of  the 
coatings  is  very  great.     The  surface  of  the  copper  wire  amounts  to  8,300 


88o  Dynamical  Electricity.  [891- 

square  feet,  and  that  of  the  outside  coating  is  four  times  as  much.  The 
potential  can  only  be  as  great  as  that  of  the  battery,  but  from  the  enormous 
surface  the  capacity,  and  therefore  the  quantity,  is  very  great.  Thus  the 
wires,  after  being  detached  from  the  battery,  showed  all  the  actions  of  a 
powerful  electric  battery.  These  effects  take  place  but  to  a  less  extent  with 
wires  in  air  ;  the  external  coating  is  here  the  earth,  which  is  so  distant  that 
induction  and  charge  are  very  small,  more  especially  in  the  long  lines. 

Hence  the  difficulty  in  submarine  telegraphy.  The  electricity  which 
enters  the  insulating  wire  must  first  be  used  in  charging  the  large  Leyden 
jar  which  it  constitutes,  and  only  after  this  has  happened  can  the  current 
reach  the  distant  end  of  the  circuit.  The  current  begins  later  at  the  distant 
end,  and  ceases  sooner.  The  electricity  is  not  projected  like  the  bullet  from 
a  gun,  but  rather  like  a  quantity  of  water  flowing  from  a  large  reservoir  into 
a  canal  in  connection  with  large  basins  which  it  has  to  fill  as  well  as  itself 
If  the  electrical  currents  follow  too  rapidly,  an  uninterrupted  current  will 
appear  at  the  other  end,  which  indicates  small  differences  in  strength,  but 
not  with  sufficient  clearness  differences  in  duration  or  direction.  Hence  in 
submarine  wires  the  signals  must  be  slower  than  in  air  wires  to  obtain  clear 
indications.  By  the  use  of  alternating  currents — that  is,  of  currents  which 
are  alternately  positive  and  negative — these  disturbing  influences  may  be 
materially  lessened,  and  communication  be  accelerated  and  made  more 
certain,  iDut  they  can  never  be  entirely  obviated. 

In  the  Atlantic  Cable,  instruments  on  the  principle  of  Thomson's  reflect- 
ing galvanometer  (822)  are  used  for  the  reception  of  signals  ;  the  motions  of 
the  spot  of  light  to  the  right  and  left  forming  the  basis  of  the  alphabet. 

892.  Syphon  recorder — Sir  W.  Thomson  has  invented  an  extremely 
ingenious  instrument  called  the  syphon  recorder,  by  which  the  very  feeble 

signals  transmitted  through  long 
lengths  of  submarine  cables  are  ob- 
served and  also  recorded. 

A  light  rectangular  coil  of  iron  .$• 
(fig.  854),  connected  with  the  line  wire 
by  the  screws^  and  q,  hangs  by  a  bi- 
polar suspension  between  the  two  poles 
of  a  powerful  electromagnet  AB,  so 
that  its  plane  is  in  the  right  line  joining 
l'/'\  ''     i    I  'v       '  '"Z^^^^        '•'^^  poles.     The  space  inside  the  coil 

'    '  11,  is  occupied  by  a  mass  of  soft  iron  /, 

by  which  the  strength  of  the  fluid  is 
greatly  increased.  When  a  current 
is  passed  this  coil  thereby  becomes 
a  magnet,  and  is  deflected  cither  to 
the  right  or  the  left  according  to  the 
direction  of  the  current  ;  its  move- 
ments are  almost  deadbeat,  as  the 
damping  is  considerable. 

A  veiy  light  capillary  tube  c  dips 
with  its  short  end  in  a  reservoir  of  ink,  while  the  other  end  is  in  front  of  a 
jjajjcr  riI)bon  which  is  moved  along  at  a  uniform  rate  like  the  ribbon  in  a 


Fi-.  85 


-893] 


Duplex  TelegrapJiy. 


88i 

Morse's  recorder.  In  order  to  get  rid  of  friction  against  the  paper,  this  ink 
is  electrified,  and  spurts  out  in  a  continuous  series  of  fine  drops  against  the 
paper,  marking  on  it  a  straight  line  so  long  as  no  current  passes  in  the  coil. 
This  syphon  is,  however,  connected  by  a  system  of  silk  threads  with  the  coil, 
and  according  as  this  is  deflected  either  to  the  right  or  the  left  the  end  of 
the  syphon  is  deflected  too,  and  accordingly  traces  a  wavy  line  (fig.  85 5)  on 


\rXr^f\T-yKr-^f' — 

op         q         r       s         t       n       V       7v      x      y  z 

Fig.  855. 

the  paper,  which  represents  deflections  right  or  left  of  the  central  line,  that 
are,  in  short,  the  Morse  signals  (889). 

The  electrification  of  the  ink  is  effected  by  a  small  electrostatic  induction 
machine  ;  this  is  worked  by  clockwork,  which  at  the  same  time  pays  out  the 
paper  ribbon. 

893.  Duplex  telegraphy — By  this  is  meant  a  system  of  telegraphy  by 
which  messages  maybe  simultaneously  sent  in  opposite  directions  on  one  and 
the  same  wire,  whereby  the  working  capacity  of  a  line  is  practically  doubled. 

Several  plans  have  been  devised  for  accomplishing  this  very  important 
improvement ;  no  more  can  here  be  attempted  than  to  give  a  general  account 
of  the  principle  of  the  method  in  one  or  two  cases. 

Let  m  (fig.  856)  represent  the  electromagnet  of  a  Morse's  instrument 
which  is  wound  round  with  two  equal  coils  in  opposite  directions  ;  these  coils 
are  represented  by  the  full  and  dotted  lines,  and  one  of  them,  which  may  be 
called  the  li7ie  coil,  is  joined  to  the  line  LL',  which  connects  the  two  stations. 
The  other  coil, 
that  repre- 

sented by  the 
dotted  line, 
which  may  be 
called  the 

equating  coil, 
is  in  connec- 
tion with  the 
earth  at  E  by 
means  of  an 
adjustable  re- 
sistance, or  ar- 
tificial line,  R. 
By  this  means 
the  resistance 
of  the   branch  Fig.  856. 

rtRE  may  be  made  equal  to  that  of  the  branch  a'LL'a.  The  battery  b  has 
one  pole  to  earth  at  E,  and  the  other  pole,  by  means  of  a  make-and-break 
key,  c,  can  be  connected  at  a,  where  the  two  oppositely  wound  coils  bifurcate. 
The  back  contact  of  the  key  is  also  connected  with  earth. 

3  L 


882  Dynamical  Electricity.  [893- 

The  station  at  B  is  arranged  in  a  similar  manner,  as  is  represented  by 
corresponding  letters  with  affixes. 

Now  when  B  depresses  his  key  and  sends  a  current  into  the  line,  inasmuch 
as  the  electromagnet  of  his  instrument  is  wound  with  equal  coils  in  opposite 
directions,  the  armature  is  not  attracted,  for  the  core  is  not  magnetised  because 
the  currents  in  the  two  coils  counteract  one  another.  Thus,  although  a 
current  passes  from  B,  there  is  no  indication  of  it  in  his  own  instrument — a 
condition  essential  in  all  systems  of  duplex. telegraphy. 

But  with  regard  to  the  effect  on  A,  there  are  two  cases,  according  as  he 
is  or  is  not  sending  a  message  at  the  same  time.  If  A's  key  is  not  down, 
then  the  current  will  circulate  round  the  core  of  the  electromagnet  and  will 
reach  the  earth  by  the  path  Lrt^-E  ;  the  core  will  therefore  become  magnet- 
ised, the  armature  attracted,  and  a  signal  produced  in  the  ordinaiy  way. 

If,  however,  at  the  moment  at  which  B  has  his  key  down,  A  also  depresses 
his,  then  it  will  be  seen  that,  as  currents  are  sent  in  opposite  directions  from 
both  A  and  B,  they  neutralise  one  another,  no  current  passes  in  the  line 
a\AJa' :  it  is,  as  it  were,  blocked.  But  though  no  current  passes  in  the  line 
coil,  a  current  does  pass  at  each  station  to  earth,  through  the  equating  coil, 
which,  being  no  longer  counterbalanced  by  any  opposite  current  in  the  line 
coil,  magnetises  the  core  of  the  electromagnet,  which  thus  attracts  the  arma- 
ture and  produces  a  signal. 

We  have  here  supposed  that  A  and  B  both  send,  for  instance,  the  same 
currents  to  line  :  the  final  effect  is  not  different  if  they  send  opposite  currents 
at  the  same  time.  For  then,  as  they  neutralise  each  other  in  the  line  LL', 
the  effect  is  the  same  as  if  the  resistance  of  the  line  were  diminished.  More 
electricity  flows  at  line  from  each  station  through  the  line  coil  being  no  longer 
balanced  by  the  equating  coil  ;  the  current  of  the  line  coil  preponderates  and 
then  works  the  electromagnet. 

Hence,  in  both  these  cases,  each  station,  so  to  speak,  produces  the  signal 
which  the  other  one  wishes  to  selid. 

Another  method  is  based  on  the  principle  of  Wheatstone's  bridge  (955). 
At  each  station  is  a  battery  P  (fig.  857),  one  pole  of  which  is  to  earth  while 
the  other  is  connected  with  the  key  M. 
The  wire  from  M  bifurcates  at  A  into  the 
two  branches  B  and  C,  between  which  is 
connected  the  galvanometer  ttr  the  receiv- 
ing instrument.  The  branch  ,AB  goes  to 
line  and  AC  to  earth.  There  arc  exactly 
corresponding  parts  at  the  other  station. 
Now,  from  the  principle  of  the  bridge,  the 
resistances  AB  and  AC  may  be  adjusted 
n  such  a  manner  that  the  potentials  at 
the  points  B  and  C  are  equal  when  the 
key  is  depressed  and  the  current  sent  ; 
accordingly  no  current  passes  in  the  bridge, 
and  the  galvanometer  is  at  rest ;  but  the  current  from  A  passing  to  line 
bifurcates  at  B',  traversing  the  galvanometer  and  going  to  earth  ;  hence  a 
signal  is  received  at  that  station. 

Other   methods  of   duplex    telegraphy  arc    based    on    the  principle    of 


\\>s^\VaV^\V;<;\<\\v 


Fig.  857. 


-896]  The  Sounder.  883 

leakage  ;  but  for  these,  as  well  as  for  quad ruplex  telegraphy,  special  manuals 
must  be  consulted. 

894.  Earth  currents. —  In  long  telegraph  circuits  more  or  less  powerful 
currents  are  produced,  even  \\hcn  the  battery  is  not  at  work.  This  arises 
from  a  difference  of  potential  being  established  in  the  earth  at  the  two  places 
between  which  the  communication  is  established.  These  currents  are  some- 
times in  one  direction  and  sometimes  in  another,  and  are  at  times  so  power- 
ful and  irregular  as  quite  to  interfere  with  the  working  of  the  lines.  Lines 
running  NE  and  SW  are  most  frequently  affected  ;  lines  running  NW  and 
SE  are  less  so,  and  the  currents  are  far  weaker.  Their  strength  often 
amounts  to  as  much  as  40  millamperes,  which  is  a  stronger  current  than  is 
required  for  working  ordinary  telegraph  instruments. 

These  currents  do  not  seem  to  be  due  to  atmospheric  electricity,  for  they 
cease  if  a  wire  be  disconnected  at  one  of  its  ends,  and  they  appear  in  under- 
ground wires. 

According  to  Wild,  they  are  the  prime  cause  of  magnetic  storms,  but  not 
of  the  periodical  variations  in  the  magnetic  elements. 

895.  Bain's  electrochemical  teleg^raph. — If  a  strip  of  paper  be  soaked 
in  a  solution  of  ferrocyanide  of  potassium  and  be  placed  on  a  metal  surface 
connected  with  the  negative  pole  of  a  battery,  on  touching  the  paper  with  a 
steel  pointer  connected  with  the  positive  pole,  a  blue  mark  due  to  the  forma- 
tion of  some  Prussian  blue  will  be  formed  about  the  iron,  so  long  as  the  current 
passes.  The  first  telegraph  based  on  this  principle  was  invented  by  Bain. 
The  alphabet  is  the  same  as  Morse's,  but  the  despatch  is  first  composed  at 
the  departure  station  on  a  long  strip  of  ordinary  paper.  It  is  perforated 
successively  by  small  round  and  elongated  holes,  which  correspond  respec- 
tively to  the  dots  and  marks.  This  strip  of  paper  is  interposed  between  a 
small  metal  wheel  and  a  metal  spring,  both  forming  part  of  the  circuit.  The 
wheel,  in  turning,  carries  with  it  the  paper  strip,  all  parts  of  which  pass 
successively  between  the  wheel  and  the  plate.  If  the  strip  were  not  per- 
forated, it  would,  not  being  a  conductor,  constantly  offer  a  resistance  to  the 
passage  of  the  current ;  but,  in  consequence  of  the  holes,  eveiy  time  one  of 
them  passes,  there  is  contact  between  the  wheel  and  the  plate.  Thus  the 
current  works  the  relay  of  the  station  to  which  it  is  sent,  and  traces  in  blue, 
on  a  paper  disc,  impregnated  with  ferrocyanide  of  potassium,  the  same  series 
of  points  and  marks  as  those  on  the  perforated  paper. 

896.  The  sounder. — The  sound  produced  when  the  armature  of  the  elec- 
tromagnet in  a  Morse's  instrument  is  attracted  by  the  passage  of  the  current 
is  so  distinct  and  clear  that  many  telegraph  operators  have  been  in  the 
habit  of  reading  the  messages  by  the  sounds  thus  produced,  and  at  most  of 
checking  their  reading  by  comparison  with  the  signs  produced  on  the  paper. 

Based  on  this  fact  a  form  of  instrument  invented  in  America  has  come 
into  use  for  the  purpose  of  reading  by  sound.  The  sounder,  as  it  is  called, 
is  essentially  a  small  electromagnet  on  an  ebonite  base,  resembling  the  relay 
in  fig.  853.  The  armature  is  attached  to  one  end  of  a  lever,  and  is  kept  at 
a  certain  distance  from  the  electromagnet  by  a  spring.  When  the  current 
passes,  the  armature  is  attracted  against  the  electromagnet  with  a  sharp 
click,  and  when  the  current  ceases  it  is  withdrawn  by  the  spring.  Hence  the 
interval  between  the  sounds  is  of  longer  or  shorter  duration  according  to  the 

31-2 


884 


Dynamical  Electricity. 


[896- 


will  of  the  sender,  and  thus  in  effect  a  series  of  short  or  long  intervals  which 
represent  short  and  long  sounds  can  be  produced  which  correspond  to  the 
dots  and  dashes  of  the  Morse  alphabet.  Such  instruments  are  simple,  easily- 
adjusted,  and  portable,  not  occupying  more  space  than  an  ordinary  field-glass. 
They  are  coming  into  extended  use,  especially  for  military  telegraph  work. 

897.  Electric  alarum. — One  form  of  these  instruments  is  represented  in 
fig.  858.  On  a  wooden  board  arranged  vertically  is  fixed  an  electromagnet, 
E ;  the  line  wire  is  connected  with  the  bind- 
ing screw,  w,  with  which  is  also  connected 
one  end  of  the  wire  of  the  electromagnet ; 
the  other  end  is  connected  with  a  spring,  r, 
to  which  is  attached  the  armature,  a  ;  this 
again  is  pressed  against  by  a  spring,  C,  which 
in  turn  is  connected  with  the  binding  screw 
n,  from  which  the  wire  leads  to  earth. 

Whenever  the  current  passes,  the  arma- 
ture a  is  attracted,  carrying  with  it  a  hammer, 
P,  which  strikes  against  the  bell  T  and  makes 
it  sound.  The  moment  this  takes  place,  con- 
tact is  broken  between  the  armature  a  and 
the  spring  C,  and  the  current  bemg  stopped 
the  electromagnet  does  not  act  ;  the  spring 
r,  however,  in  virtue  of  its  elasticity,  brings 
the  armature  in  contact  with  the  spring  C, 
the  current  again  passes,  and  so  on  as  long 
as  the  current  continues  to  pass. 

898.  Electrical  clocks.  —  Electrical 
clocks  are  clockwork  machines,  in  which  an 
eiectromagnet  is  both  the  motor  and  the  regulator,  by  means  of  an  electric 
current  regularly  interrupted,  in  a  manner  resembling  that  described  in  the 
preceding  paragraph.  Fig.  859  represents  the  face  of  such  a  clock,  and  fig. 
860  the  mechanism  which  works  the  needles. 

An  electromagnet,  B,  attracts  an  armature  of  soft  iron,  P,  movable  on  a 
pivot,  rt.  The  armature  P  transmits  its  oscillating  motion  to  a  lever,  s,  which 
by  means  of  a  ratchet,  ;/,  turns  the  wheel  A.  This,  by  the  pinion,  D,  turns 
the  wheel  C,  which  by  a  series  of  wheels  and  pinions  moves  the  hands.  The 
small  one  marks  the  hours,  the  large  one  the  minutes  ;  but  as  the  latter  does 
not  move  regularly,  but  by  sudden  starts  from  second  to  second,  it  follows 
that  it  may  also  be  used  to  indicate  the  seconds. 

It  is  obvious  that  the  regularity  of  the  motion  of  the  hands  depends  on 
the  regularity  of  the  oscillations  of  the  piece  P.  For  this  purpose,  the  oscil- 
lations of  the  current,  before  passing  into  the  electromagnet  B,  are  regulated 
by  a  standard  clock,  which  itself  has  been  previously  regulated  by  a  seconds 
pendulum.  At  each  oscillation  of  the  pendulum  there  is  an  arrangement  by 
which  it  opens  and  closes  the  current,  and  thus  the  armature  P  beats  seconds 
exactly. 

To  illustrate  the  use  of  these  electrical  clocks,  suppose  that  on  the  railway - 
from  London  to  Birmingham  each  station  has  an  electric  clock,  and  that 
from  the  London  station  a  conducting  wire  passes  to  all  the  clocks  on  the 


-899] 


Electromagnetic  Machines. 


line  as  far  as  Birmingham.  When  the  current  passes  in  this  wire  all  the 
clocks  will  simultaneously  indicate  the  same  hour,  the  same  minute,  and  the 
same  second  ;  for  electricity  takes  an  inappreciable  time  to  go  from  London 
to  Birmingham. 


Fig.  859. 


899.  Electromag'netic  machines.— Numerous  attempts  have  been  made 
to  apply  electromagnetism  as  a  motive  power  in  machinery.  Fig.  861  repre- 
sents an  engine  of  this  kind  constructed  by  Froment.  It  consists  of  four 
powerful  electromagnets,  ABCD,  fixed  on  an  iron  frame,  X.  Between  these 
electromagnets  is  a  system  of  two  iron  wheels  movable  on  the  same  hori- 
zontal axis,  with  eight  soft  iron  armatures,  M,  on  their  circumference. 

The  current  arrives  at  K,  ascends  in  the  wire  E,  and  reaches  a  metallic 
arc,  O,  which  serves  to  pass  the  current  successively  into  each  electromagnet, 
so  that  the  attractions  exerted  on  the  armatures  M  shall  always  be  in  the 
same  direction.  Now  this  can  only  be  the  case  provided  the  current  is 
broken  in  each  electromagnet  just  when  an  armature  comes  in  front  of  the 
axis  of  the  bobbin.  To  produce  this  interruption  the  arc  O  has  three  branches 
c,  each  terminating  with  a  steel  spring,  to  which  a  small  sheave  is  attached. 
Two  of  these  establish  the  communication  respectively  with  one  electro- 
magnet, and  the  third  with  two.  On  a  central  wheel,  a,  there  are  cogs,  on 
which  the  sheaves  alternately  rest.  Whenever  one  of  them  rests  on  a  cog, 
the  current  passes  into  the  corresponding  electromagnet,  but  ceases  to  pass 
when  there  is  no  longer  contact.  On  emerging  from  the  electromagnets  the 
current  passes  to  the  negative  pole  of  the  battery  by  the  wire  H. 

In  this  manner,  the  armatures  M  being  successively  attracted  by  the  four 
electromagnets,  the  system  of  wheels  which  carries  them  assumes  a  rapid 
rotatoiy  motion,  which  by  the  wheel  P  and  an  endless  band  is  transmitted  to  a 
sheave,  Q,  which  sends  it  finally  to  any  machine,  a  grinding-mill  for  example. 

In  his  workshops  Froment  had  an  electromotive  engine  of  one-horse 
power.  But,  though  an  interesting  application  of  the  transformation  of 
energy,  these  machines  will  never  be  practically  applied  in  manufactures, 


Dynamical  Electricity. 


[899- 


for  the  expense  of  the  acids  and  the  zinc  which  they  use  veiy  far  exceeds 
that  of  the  coal  in  steam-engines  of  the  same  force. 

Thus  a  machine  devised  by  Kravogl  produces  about  1 7  per  cent,  of  the 
useful  effect  due  to  the  chemical  combination  of  the  zinc  with  the  acid  in  the 
battery,  and  therefore  in  utilising  this  force  they  are  about  equal  to  the  best 
steam-engines.  But  a  pound  of  coal  yields  7,200  thermal  units,  and  a  pound 
of  zinc  only  1,200  (484) ;  and  as  zinc  is  ten  times  as  dear  as  coal,  engines 


worked  by  electricity,  independently  of  any  question  as  to  the  cost  of  con- 
struction, or  of  the  cost  of  the  acids,  are  sixty  times  as  dear  to  work  as 
steam-engines. 

The  energy  of  the  electrical  current  may  be  compared  with  the  I'is  viva 
of  a  small  mass  which  moves  with  very  great  velocity.  Hence  it  can  be 
understood  that  at  present  the  most  advantageous  employment  of  electricity 
is  to  be  found,  not  so  much  in  the  transformation  of  its  vis  viva  into  the 
relatively  slow  movement  of  large  masses,  as  in  the  rapid  transmission  of  a 
small  power  to  great  distances,  as  in  the  electric  telegraph. 


900] 


Induction  by  Currents. 


887 


CHAPTER'  VI. 

VOLTAIC   INDUCTION. 

900.  Induction  by  currents. — We  have  already  seen  (744)  that  by 
induction  is  meant  the  action  which  electrified  bodies  exert  at  a  distance 
on  bodies  in  the  natural  state.  Hitherto  we  have  only  had  to  deal  with 
electrostatical  induction  ;  we  shall  now  see  that  dynamical  electricity  pro- 
duces analogous  effects. 

Faraday  discovered  this  class  of  phenomena  in  1832,  and  he  gave  the 
name  of  currents  of  induction  or  induced  currc7its  to  instantaneous  currents 
developed  in  conductors  under  the  influence  of  metallic  conductors  traversed 
by  electric  currents,  or  by  the  influence  of  powerful  magnets,  or  even  by 
the  magnetic  action  of  the  earth  ;  and  the  currents  which  give  rise  to  them 
he  called  inducing  currents. 

The  inductive  action  of  a  current  at  the  moment  of  opening  or  closing 
may  be  shown  by  means  of  a  bobbin  with  X.\\o  wires.    This  consists  (fig.  862) 


of  a  cylinder  of  wood  or  of  cardboard,  on  which  a  quantity  of  silk-covered 
No.  16  copper  wire  is  coiled  ;  on  this  is  coiled  a  considerably  greater  length 
of  fine  copper  wire,  about  No.  35,  also  insulated  by  being  covered  with  silk. 
This  latter  coil,  which  is  called  the  secondary  coil,  is  connected  by  its  ends 
with  two  binding  screws,  «,  b,  from  which  wires  pass  to  a  galvanometer, 
while  the  thicker  wire,  \.\v&  prima fy  coil,  is  connected  by  its  extremities  with 
two  binding  screws,  c  and  d.  One  of  these,  d,  being  connected  with  one  pole 
of  a  batteiy,  when  a  wire  from  the  other  pole  is  connected  with  c,  the  current 
passes  in  the  primary  coil,  and  in  this  alone.  The  following  phenomena  are 
then  observed  : — 


888 


Dynamical  Electricity, 


[900- 


i.  At  the  moment  at  which  the  thick  wire  is  traversed  by  the  current, 
the  galvanometer,  by  the  deflection  of  the  needle,  indicates  the  existence  in 
the  secondary  coil  of  a  current  invei'se  to  that  in  the  primaiy  coil,  that  is, 
in  the  contrary  direction  ;  this  is  only  instantaneous,  for  the  needle  imme- 
diately reverts  to  zero,  and  remains  so  as  long  as  the  inducing  current  passes 
through  cd. 

ii.  At  the  moment  at  which  the  current  is  opened — that  is,  when  the  wire 
cd  ceases  to  be  traversed  by  a  current — there  is  again  produced  in  the  wire 
ab  an  induced  current  instantaneous  like  the  first,  but  direct^  that  is,  in  the 
same  direction  as  the  inducing  current. 

901.  Production  of  induced  currents  toy  continuous  ones. — Induced 
currents  are  also  produced  when  a  primary  coil  traversed  by  a  current  is 
approached  to  or  removed  from  a  secondary  one  ;  this  may  be  shown  by  the 
following  apparatus  (fig.  863),  in  which  B  is  a  hollow  coil  consisting  of  a 


^ 


great  length  of  fine  wire,  and  A  a  coil  consisting  of  a  shorter  and  thicker 
wire,  and  of  such  dimensions  that  it  can  be  placed  in  the  secondary  coil. 
The  coil  A  being  traversed  by  a  current,  if  it  is  suddenly  placed  in  the  coil 
B,  a  galvanometer  connected  with  the  latter  indicates  by  the  direction  of  its 
deflection  the  existence  in  it  of  an  inverse  current ;  this  is  only  instantaneous ; 
the  needle  rapidly  returns  to  zero,  and  remains  so  as  long  as  the  small 
bobbin  is  in  the  large  one.  If  it  is  rapidly  withdrawn,  the  galvanometer 
shows  that  the  wire  is  traversed  by  a  direct  current.  If,  instead  of  rapidly 
introducing  or  replacing  the  primaiy  coil,  this  is  done  slowly,  the  galvano- 
meter only  indicates  a  weak  current,  which  is  the  feebler  the  slower  the 
motion. 

If,  instead  of  varying  the  distance  of  the  inducing  current,  its  intensity 
Ije  varied  that  is,  cither  increased  by  bringing  additional  batteiy  power  into 


-903]  Inductive  Action  of  the  Ley  den  Discharge.  889 

the  circuit,  or  diminished  by  increasing  the  resistance,  an  induced  current 
is  produced  in  the  secondary  wire,  which  is  inverse  if  the  intensity  of  the 
inducing  current  increases,  and  direct  if  it  diminishes. 

902.  Conditions  of  induction.  Iienz's  law. — P'rom  the  experiments 
which  have  been  described  in  the  previous  paragraphs  the  following  prin- 
ciples may  be  deduced  : — 

I.  The  distance  remaining  the  same,  a  co7itinuoiis  a?id  constant  curreitt 
docs  not  induce  any  current  in  an  adjacent  conductor. 

W.  A  current,  at  the  moment  of  being  closed,  produces  in  an  adjacent  con- 
ductor an  inverse  current. 

III.  A  current,  at  the  moment  it  ceases, produces  a  direct  current. 

IV.  A  current  which  is  removed,  or  whose  strength  dimittishes,  gives 
rise  to  a  direct  induced' current. 

V.  A  current  which  is  approached,  or  whose  strength  increases,  gives  rise 
to  aft  ifiverse  induced  current. 

VI.  On  the  induction  produced  between  a  closed  circuit  and  a  current  in 
activity,  when  their  relative  distance  varies,  Lenz  has  based  the  following 
law,  which  is  known  as  Lenz's  law  : — 

If  the  relative  position  of  two  conductors  A  and  B  be  changed,  of  which 
A  is  traversed  by  a  curretit,  a  current  is  induced  in  B  in  such  a  direction 
that,  by  its  electrodynamic  actioji  on  the  curretit  in  A,  it  wotdd  have  imparted 
to  the  conductors  a  motion  of  the  contraty  kind  to  that  by  which  the  inducing 
action  was  produced. 

Thus,  for  instance,  in  V.,  when  a  current  is  approached  to  a  conductor,  an 
inverse  current  is  produced  ;  but  two  conductors  traversed  by  currents  in 
opposite  directions  repel  one  another,  according  to  the  received  laws  of 
electrodynamics  (858).  Conversely  when  a  current  is  moved  away  from  a 
conductor,  a  current  of  the  same  direction  is  produced  ;  now  two  currents  in 
the  same  direction  attract  one  another. 

On  bringing  the  inducing  wire  near  the  induced  as  well  as  in  removing  it 
away,  work  is  required  ;  hence  a  quantity  of  heat  proportional  to  the  work 
consumed  must  result,  as  Edlund's  investigations  have  shown.  On  the 
other  hand,  when  induction  results  from  the  opening  and  closing  of  the  cir- 
cuit (II.  and  III.)  no  work  is  lost,  but  the  inducing  current  loses  as  much 
heat  as  is  produced  in  the  induced  circuit. 

903.  Inductive  action  of  the  Iieyden  discliargre. — Figure  864  represents 
an  apparatus  devised  by  Matteucci,  which  is  very  well  adapted  for  showing 
the  development  of  induced  currents  produced  either  by  the  discharge  of  a 
Leyden  jar  or  by  the  passage  of  a  voltaic  current. 

It  consists  of  two  glass  plates  about  12  inches  in  diameter,  fixed  vertically 
on  the  two  supports  A  and  B.  These  supports  are  on  movable  feet,  and 
can  either  be  approached  or  removed  at  will.  On  the  anterior  face  of  the 
plate  A  are  coiled  about  30  yards  of  copper  wire  C,  a  millimetre  in  diameter. 
The  two  ends  of  this  wire  pass  through  the  plate,  one  in  the  centre,  the  other 
near  the  edge,  terminating  in  two  binding  screws,  like  those  represented  in 
;;/  and  7i  on  the  plate  B.  To  these  binding  screws  are  attached  two  copper 
wires,  c  and  d,  through  which  the  inducing  current  is  passed. 

On  the  face  of  the  plate  B,  which  is  towards  A,  is  enrolled  a  spiral  of 
finer  copper  wire  than  the  wire  C.     Its  extremities  terminate  in  the  binding 


890 


Dynamical  Electt  icity. 


[903- 


screws  m  and  «,  on  which  are  fixed  two  wires,  h  and  z,  intended  to  transmit 
the  induced  current.  The  two  wires  on  the  plates  are  not  only  covered  with 
silk,  but  each  circuit  is  insulated  from  the  next  one  by  a  thick  layer  of  shellac 
varnish. 

In  order  to  show  the  production  of  the  induced  current  by  the  discharge 
of  a  Leyden  jar,  one  end  of  the  wire  C  is  connected  with  the  outer  coating, 
and  the  other  end  with  the  knob  of  the  Leyden  jar,  as  shown  in  the  figure. 
When  the  spark  passes,  the  electricity  traversing  the  wire  C  acts  by  induc- 
tion on  the  wire  on  the  plate  B,  and  produces  an  instantaneous  current 
in  this  wire.  A  person  holding  two  copper  handles  connected  with  the 
wire  i  and  h  receives  a  shock,  the  intensity  of  which  is  greater  in  pro- 
portion as  the  plates  A  and  B  are  nearer. 


JUJJAHUIN  i  - 
Fig.  864. 

The  experiment  may  also  be  made  by  simply  twisting  together  two 
lengths  of  a  few  feet  of  gutta-percha-covered  copper  wire.  The  ends  of  one 
length  being  held  in  the  hand,  an  electric  discharge  is  passed  through  the 
other  length. 

The  above  apparatus  can  also  be  used  to  show  the  production  of  induced 
currents  by  the  influence  of  voltaic  currents.  For  this  purpose  the  current 
of  a  battery  is  passed  through  the  inducing  wire  C,  while  the  ends  of  the 
other  wire,  h  and  z,  are  connected  with  a  galvanometer.  At  the  moment  at 
which  the  current  commences  or  finishes,  or  when  the  distance  of  the  two 
conductors  is  varied,  the  same  phenomena  are  observed  as  in  the  case  of  the 
apparatus  represented  in  fig.  863. 

904.  Induction  by  magrnets. — It  has  been  seen  that  the  influence  of  a 
current  magnetises  a  steel  bar  ;  in  like  manner  a  magnet  can  produce  induced 
currents  in  metal  circuits,  Faraday  showed  this  by  means  of  a  coil  with  a 
single  wire  of  200  to  300  yards  in  length.  The  two  ends  of  the  wire  being 
connected  with  a  galvanometer,  as  shown  in  fig.  865,  a  strongly  magnetised 
bar  is  suddenly  inserted  in  the  bobbin,  and  the  following  phenomena  are 
observed  : — 

i.  At  the  moment  at  which  the  magnet  is  introduced,  the  galvanometer 
indicates  in  the  wire  the  existence  of  a  current,  the  direction  of  which  isr 
opposed  to  that  which  circulates  round  the  magnet,  considering  the  latter  as 
a  solenoid  on  Ampere's  theory  (87Q). 


-905]     Inductive  Action  of  Magnets  on  Bodies  in  Motion.     891 

ii.  When  the  magnet  is  withdrawn,  the  needle  of  the  galvanometer,  which 
has  returned  to  zero,  indicates  the  existence  of  a  direct  current. 

The  inductive  action  of  magnets  may  also  be  illustrated  by  the  follow- 
ing experiment  :  a  bar  of  soft  iron  is  placed  in  the  above  bobbin  and  a  strong- 
magnet  suddenly  brought  in  contact  with  it  ;  the  needle  of  the  galvanometer 
is  deflected,  but  returns  to  zero  when  the  magnet  is  stationary,  and  is  de- 
flected in  the  opposite  direction  when  it  is  removed.  The  induction  is  here 
pi^oduced  by  the  magnetisation  of  the  soft  iron  bar  in  the  interior  of  the 
bobbin  under  the  influence  of  the  magnet. 

The  same  inductive  effects  are  produced  in  the  wires  of  an  electromagnet, 
if  a  strong  magnet  be  made  to  rotate  rapidly  in  front  of  the  extremities  of 


the  wire  in  such  a  manner  that  its  poles  act  successively  by  influence  on  the 
two  branches  of  the  electromagnet ;  or  also  by  forming  two  coils  round  a 
horseshoe  magnet,  and  passing  a  plate  of  soft  iron  rapidly  in  front  of  the 
poles  of  the  magnet  ;  the  soft  iron  becoming  magnetic  reacts  by  influence  on 
the  magnet,  and  induced  currents  are  produced  in  the  wire  alternately  in 
different  directions. 

The  inductive  action  of  magnets  is  a  confirmation  of  Ampere's  theory 
of  magnetism.  For  as,  on  this  theory,  magnets  are  solenoids,  all  the  ex- 
periments which  have  been  mentioned  may  be  explained  by  the  inductive 
action  of  currents  which  traverse  the  surface  of  magnets  ;  the  induction  of 
magnets  is,  in  short,  an  induction  of  currents.  And  it  is  a  useful  exercise 
to  see  how  on  this  view  the  inductive  action  of  magnets  falls  under  Lenz's 
law  (902). 

905.  Inductive  action  of  magrnets  on  bodies  in  motion. — Arago  was 
the  first  to  observe,  in  1824,  that  the  number  of  oscillations  which  a  mag- 
netised needle  makes  in  a  given  time,  under  the  influence  of  the  earth's 
magnetism,  is  very  much  lessened  by  the  proximity  of  certain  metallic 
masses,  and  especially  of  copper,  which  may  reduce  the  number  in  a  given 
time  from  300  to  4.     This  observation  led  Arago  in  1825  to  the  discovery  of 


892  Dynamical  Electricity.  [905- 

an   equally  unexpected   fact — that  of  the   rotative  action  which  a  plate  of 
copper  in  motion  exercises  on  a  magnet. 

This  phenomenon  may  be  shown  by  means  of  the  apparatus  represented 
in  fig.  866.  It  consists  of  a  copper  disc,  M,  movable  about  a  vertical  axis. 
On  this  axis  is  a  sheave,  B,  round  which  is  coiled  an  endless  cord,  passing 
also  round  the  sheave  A.  By  turning  this  with  the  hand,  the  disc  M  may 
be  rotated  with  great  rapidity.     Above  the  disc  is  a  glass  plate,  on  which  is 


Fig.  866. 

a  small  pivot  supporting  a  magnetic  needle,  ab.  If  the  disc  be  now  rotated 
with  a  slow  and  uniform  velocity,  the  needle  is  deflected  in  the  direction  of 
the  motion,  and  stops  at  an  angle  of  from  20°  to  30°  with  the  direction  of  the 
magnetic  meridian,  according  to  the  velocity  of  the  rotation  of  the  disc. 
But  if  this  velocity  increases,  the  needle  is  ultimately  deflected  more  than 
90°  ;  it  is  then  carried  along,  describes  an  entire  revolution,  and  follows  the 
motion  of  the  disc  until  this  stops. 

Babbage  and  Herschel  modified  Arago's  experiment  by  causing  a  horse- 
shoe magnet  placed  vertically  to  rotate  below  a  copper  disc  suspended  on 
silk  threads  without  torsion  ;  the  disc  rotated  in  the  same  direction  as  the 
magnets.  The  effect  decreases  with  the  distance  of  the  disc,  and  varies 
with  its  nature.  The  maximum  effect  is  produced  with  metals  ;  with  wood, 
glass,  water,  &c.,  it  disappears.  Babbage  and  Herschel  found  that,  represent- 
ing this  action  on  copper  at  100,  the  action  on  other  metals  is  as  follows  : 
zinc  95,  tin  46,  lead  25,  antimony  9,  bismuth  2.  Lastly,  the  effect  is  enfeebled 
if  there  are  non-conducting  breaks  in  the  disc,  especially  in  the  direction  of 
the  radii  ;  but  it  is  the  same  if  these  breaks  arc  soldered  with  any  metal. 

Faraday  made  an  experiment  the  reverse  of  Arago's  first  obser\ation  ; 
since  the  presence  of  a  metal  at  rest  stops  the  oscillations  of  a  magnetic 
needle,  the  neighbourhood  of  a  magnet  at  rest  ought  to  stop  the  motion  of  a 
rotating  mass  of  metal.  Faraday  suspended  a  cube  of  copper  to  a  twisted 
thread,  which  was  placed  between  the  poles  of  a  powerful  electromagnet. 
When  the  thread  was  left  to  itself,  it  began  to  spin  round  with  great  velocity,, 
but  sto])ped  the  moment  a  powerful  current  passed  through  the  electromagnet. 

Faratlay  was  the  first  to  give  an  explanation  of  all  these  phenomena  of 


-906]  Induction  by  the  Action  of  the  EartJi.  893 

magnetism  by  rotation.  They  depend  on  the  circumstances  that  a  magnet 
or  a  solenoid  can  induce  currents  in  a  solid  mass  of  metal.  In  the  above  case 
the  magnet  induces  currents  in  the  disc  when  the  latter  is  rotated  ;  and  con- 
\-ersely  when  the  magnet  is  rotated  while  the  disc  is  primarily  at  rest.  Now 
these  induced  currents,  by  their  electrodynamic  action,  tend  to  destroy  the 
motion  which  gave  rise  to  them  ;  they  are  simple  illustrations  of  Lenz's  law  ; 
they  act  in  the  same  way  as  friction  would  do. 

i.  For  instance,  let  AB  (fig.  867)  be  a  needle  oscillating  over  a  copper 
disc,  and  suppose  that  in  one  of  its  oscillations  it  goes  in  the  direction  of  the 
arrows  from  N  to  M.  In  approaching  the  point  M,  for 
instance,  it  develops  there  a  current  in  the  opposite 
direction,  and  which  therefore  repels  it  ;  in  moving  away 
from  N  it  produces  currents  which  are  of  the  same  kind, 
and  which  therefore  attract,  and  both  these  actions 
concur  in  bringing  it  to  rest. 

ii.  Suppose  the  metallic  mass  turns  from  N  towards 
M,  and  that  the  magnet  is  fixed  ;  the  magnet  Avill  repel 
by  induction  points  such  as  N  which  are  approaching  A,  .  ^' 

and  will  attract  M  which  is  moving  away  ;  hence  the  motion  of  the  metal 
stops,  as  in  Faraday's  experiment. 

iii.  If  in  Arago's  experiment  the  disc  is  moving  from  N  to  M,  N  ap- 
proaches A  and  repels  it,  while  M,  moving  away,  attracts  it ;  hence  the  needle 
moves  in  the  same  direction  as  the  disc. 

If  this  explanation  is  true,  all  circumstances  which  favour  induction  will 
increase  the  dynamic  action  ;  and  those  which  diminish  the  former  will 
also  lessen  the  latter.  We  know  that  induction  is  greater  in  good  conductors, 
and  that  it  does  not  take  place  in  insulating  substances  ;  but  we  have  seen 
that  the  needle  is  moved  with  a  force  which  is  less,  the  less  the  conducting 
power  of  the  disc,  and  it  is  not  moved  when  the  disc  is  of  glass.  Dove  found 
that  there  is  no  induction  on  a  tube  split  lengthwise  in  which  a  coil  is 
introduced. 

906.  Induction  by  the  action  of  the  earth. — Faraday  discovered  that 
terrestrial  magnetism  can  develop  induced  currents  in  metallic  bodies  in 
motion,  acting  like  a  powerful  magnet  placed  in  the  interior  of  the  earth  in 
the  direction  of  the  dipping  needle,  or,  according  to  the  theoiy  of  Ampere, 
like  a  series  of  electrical  currents  directed  from  east  to  west  parallel  to  the 
magnetic  equator.  He  first  proved  this  by  placing  a  long  helix  of  copper 
wire  covered  with  silk  (such  as  A,  fig.  863)  in  the  plane  of  the  magnetic 
meridian  parallel  to  the  dipping  needle  ;  by  turning  this  helix  180°  about  an 
axis  perpendicular  to  its  length  in  its  middle,  he  observed  that  at  each  turn 
a  gahanom.eter  connected  with  the  two  ends  of  the  helix  was  deflected.  The 
apparatus  depicted  in  fig.  868,  and  known  as  DelezeiuK^s  circle^  serves  for 
showing  the  currents  produced  by  the  inductive  action  of  the  earth.  It 
consists  of  a  wooden  ring,  RS,  about  two  feet  in  diameter,  fixed  to  an  axis, 
oa,  about  which  it  can  be  turned  by  means  of  a  handle,  M.  The  axis  oa  is 
itself  fixed  in  a  frame  PQ,  movable  about  a  horizontal  axis.  By  pointers 
fixed  to  these  two  axes  the  inclination  towards  the  horizon  of  the  frame  PQ, 
and  therefore  of  the  axis  oa,  is  indicated  on  a  dial,  b,  while  a  second  dial,  c, 
gives  the  angular  displacement  of  the  ring.   This  ring  has  a  groove  in  which 


894 


Dynamical  Electricity. 


[906- 


is  coiled  a  great  length  of  insulated  copper  wire.  The  two  ends  of  the  wire 
terminate  in  a  commutator  analogous  to  that  in  Clarke's  apparatus  (912),  the 
object  of  which  is  to  pass  the  current  always  in  the  same  sense,  although  its 
direction,  SR,  changes  at  each  half-turn  of  the  ring.  On  each  of  the  rings 
of  the  commutator  are  two  brass  plates,  which  transmit  the  current  to  two 
wires  in  contact  with  the  galvanometer.  Suppose  that  the  ends  of  the 
wire  on  the  coil  are  directly  connected  with  wires  leading  to  a  galvanometer 
at  some  distance,  and  the  apparatus  so  placed  that  its  axis  of  rotation  oa 
is  at  right  angles  to  the  magnetic  meridian,  and  the  plane  of  the  ring,  RS, 
at  right  angles  to  the  hne  of  dip.  If,  now,  the  frame  be  quickly  turned 
through  180°,  the  needle  will  be  momentarily  deflected,  to  the  right  for 
instance  ;  if,  while  the  needle  on  its  return  is  just  passing  its  position  of 


rest,  the  frame  is  rapidly  turned  to  its  original  position,  it  will  be  deflected 
to  the  left  to  a  greater  angle  than  at  first,  for  the  needle  is  already  in  motion  ; 
by  repeating  the  operation,  that  is,  reversing  the  swing  when  the  needle  is 
passing  its  position  of  rest,  the  deflections  will  increase  to  a  maximum,  which 
is  a  measure  of  the  earth's  magnetism.  This  method  of  amplifying  an 
originally  small  motion  is  known  as  the  method  of  multiplication. 

If  the  axis  of  rotation,  oa.,  is  vertical  and  the  ring  is  rotated  as  above 
described,  only  the  horizontal  component  of  the  earth's  magnetism  can  act, 
and  the  angular  deflection  is  then  a  measure  of  the  horizontal  component  H. 
Similarly,  if  the  axis  is  horizontal  and  in  the  plane  of  the  magnetic  meridian, 
and  if  the  rotation  is  made  through  180°  from  the  horizontal  position,  only 
the  vertical  component  V  acts,  and  is  thus  measured  by  the  deflection. 

Hence,  from  two  such  sets  of  observations  wc  may  determine  the  inclina- 


tion in  any  place,  for  tan  i  = 


H 

To  experiment  with  the  currents  produced  by  continuous  rotation  the 
wires  are  connected  with  the  commutator. 

907.  Current  of  self-induction.  Extra  current. —  If  a  closed  circuit 
traversed  by  a  \c)Itaic  current  \)e  broken,  a  scarcely  perceptible  spark  is  ob- 


907] 


Currejit  of  Self-induction.     Extra  Curretit. 


895 


tained  if  the  wire  joining  the  two  poles  be  short.  Further,  if  the  obsei-ver 
himself  form  part  of  the  circuit  by  holding  a  pole  in  each  hand,  no  shock  is 
perceived  unless  the  current  is  very  strong.  If,  on  the  contrary,  the  wire  is 
long,  and  especially  if  it  makes  a  great  number  of  turns  so  as  to  form  a 
coil  with  very  close  folds,  and  still  more  if  a  soft  iron  bar  be  inserted  in  the 
coil,  the  spark,  which  is  inappreciable  when  the  current  is  closed,  acquires  a 
great  intensity  when  it  is  opened,  and  an  observer  in  the  circuit  receives  a 
shock  which  is  the  stronger  the  greater  the  number  of  turns. 

Faraday  referred  this  strengthening  of  the  current  when  it  is  broken  to 
an  inductive  action  which  the  current  in  each  winding  exerts  upon  the  others  : 
an  action  in  virtue  of  which  there  is  produced  in  the  bobbin  a  direct  current 
q{  self-induction — that  is,  one  in  the  same  direction  as  the  principal  one.  This 
is  known  as  the  extra  current,  or  curre?it  of  self-induction. 

To  show  the  existence  of  this  current  on  breaking,  Faraday  arranged  the 
experiment  as  seen  in  fig.  869.  Two  wires  from  the  poles  E  E'  of  a  battery 
are  connected  with  two  binding  screws,  D  and  F,  with  which  are  also  con- 
nected the  two  ends  of  a  coil  B,  with  a  long  fine  wire.     On  the  path  of  the 


wires  at  the  points  A  and  C  are  two  other  wires,  which  are  connected  with  a 
galvanometer,  G.  Hence  the  current  from  the  pole  E  branches  at  A  into 
two  currents,  one  which  traverses  the  galvanometer,  the  other  the  bobbin, 
and  both  joining  the  negative  pole  E'. 

The  needle  of  the  galvanometer  being  then  deflected  from  G  to  a'  by  the 
current  which  goes  from  A  to  C,  it  is  brought  back  to  zero,  and  kept  there  by 
an  obstacle  which  prevents  it  from  turning  in  the  direction  Qa\  but  leaves  it 
free  in  the  opposite  direction.  On  breaking  contact  at  E,  it  is  seen  that  the 
moment  the  circuit  is  open  the  needle  is  deflected  in  the  direction  Qa  ; 
showing  a  current  contrary  to  that  which  passed  during  the  existence  of  the 
current — that  is,  showing  the  current  from  C  to  A.  But  the  battery  current 
having  ceased,  the  only  remaining  one  is  the  current  AFBDCA  ;  and  since 
in  the  part  C  A  the  current  goes  from  C  to  A,  it  must  traverse  the  entire  circuit 
in  the  direction  AFBDC — that  is,  the  same  as  the  principal  current.     This 


896  Dynamical  Electricity.  [907- 

currcnt,  which  thus  appears  when  the  circuit  is  made,  is  the  extra  current 
or  ciirre7it  of  self-induction. 

908.  Extra  current  on  opening-  and  on  closing-. — ^The  coils  of  the  spiral 
act  inductively  on  each  other,  not  merely  on  opening  but  also  on  closing 
the  current.  Hence,  in  accordance  -with  the  general  law  of  induction,  each 
spiral,  acting  on  each  succeeding  one,  induces  a  current  in  the  opposite 
direction  to  its  own — that  is,  an  inverse  current  :  this,  which  is  the  extra 
current  on  closing.,  or  the  inverse  extra  current,  being  of  contrary  direction 
to  the  principal  one,  diminishes  its  intensity  and  lessens  or  suppresses  the 
spark  on  closing. 

When,  however,  the  current  is  opened,  each  turn  then  acts  inductively 
on  each  succeeding  one,  producing  a  current  in  the  same  direction  as  its  own, 
and  which  therefore  greatly  heightens  the  intensity  of  the  principal  current. 
This  is  the  extra  current  oji  opefiing,  or  direct  extra  current. 

To  observe  the  direct  extra  current,  the  conductor  on  which  its  effect  is 
to  be  traced  may  be  introduced  into  the  circuit,  by  being  connected  in  any 
suitable  manner  with  the  binding  screws  A  and  C  in  the  place  of  the  galvano- 
meter. It  can  thus  be  shown  that  the  direct  extra  current  gives  violent 
shocks  and  bright  sparks,  decomposes  water,  melts  platinum  wires,  and 
magnetises  steel  needles.  The  shock  produced  by  the  current  may  be 
tried  by  attaching  the  ends  of  the  wire  to  two  files,  which  are  held  in  the 
hands.  On  moving  the  point  of  one  file  over  the  teeth  of  the  other,  a 
series  of  shocks  is  obtained,  due  to  the  alternate  opening  and  closing  of  the 
current. 

The  above  effects  acquire  greater  intensity  when  a  bar  of  soft  iron  is 
introduced  into  the  bobbin,  or,  what  is  the  same  thing,  when  the  current  is 
passed  through  the  bobbin  of  an  electromagnet ;  and  still  more  is  this  the 
case  if  the  core,  instead  of  being  massive,  consists  of  a  bundle  of  insulated 
straight  wires.  Faraday  explained  this  strengthening  action  of  soft  iron  as 
follows  :  If  inside  the  spiral  there  is  an  iron  bar,  on  opening  the  circuit 
when  the  principal  current  disappears,  the  magnetism  which  it  evokes  in  the 
bar  disappears  too  ;  but  the  disappearance  of  this  magnetism  acts  like  the 
disappearance  of  the  electrical  current,  and  the  disappearing  magnetism  in- 
duces a  current  in  the  same  direction  as  the  disappearing  principal  current, 
the  effect  of  which  is  thus  heightened. 

In  the  experiments  just  described  the  effects  of  the  two  extra  currents 
accompany  those  of  the  principal  current.  Edlund  has  devised  an  in- 
genious arrangement  of  apparatus  by  which  the  action  of  the  principal  cur- 
rent on  the  measuring  instruments  can  be  completely  avoided,  so  that  only 
that  of  the  extra  current  remains. 

The  plan  of  this  experiment  is  represented  in  fig.  870,  in  which  A  is  a 
battery  the  poles  of  which  are  connected  with  b  and  c.  M  is  a  differential 
reflecting  galvanometer  the  exactly  equal  coils  of  which  terminate  in  cp  and 
fh.  Wires  connect  b  with  //  and/,  and  in  like  manner  c  is  connected  with 
e  and/  The  current  from  A  divides  at  c,  passing  round  the  galvanometer 
the  adjustment  of  the  resistances  is  such  that  the  primary  current  A  does  not 
deflect  the  needle  of  the  galvanometer.  This  current  is  denoted  by  the  un- 
feathered  arrow. 

A  coil  being  introduced  at  S,  and  an  equivalent  resistance  T  between  c 


-911] 


Properties  of  Induced  Currents. 


897 


and  c  ;  in  order  that  this  latter  might  have  no  self-induction,  it  was  coiled 
on  two  glass  rods  10  feet  apart. 

When  the  resistances  had  been  adjusted  so  that  they  were  equal,  and  the 
current  at  q  was  broken,  an  extra  current  was  produced  in  the  coil  S,  which, 
circulating  in  the  same  direction  round  both  windings  in 
the  galvanometer  as  represented  by  the  feathered  arrows, 
deflected  it.  When  the  current  was  closed,  the  extra  cur- 
rent passed  through  both  coils  in  the  same  direction, 
which  was  opposite  that  of  the  feathered  arrows,  and  as 
the  deflections  in  the  two  cases  were  the  same  it  followed 
that  the  currents  on  opening  and  closing  are  equal  and 
opposite. 

Edlund  also  showed  that  the  electromotive  force  of 
the  extra  current  is  proportional  to  the  strength  of  the 
primary  current. 

909.  Induced  currents  of  different  orders. — Spite 
of  their  instantaneous  character,  induced  currents  can 
themselves,  by  their  action  on  closed  circuits,  give  rise 
to  new  induced  currents,  these  again  to  others,  and  so 
on,  producing  induced  cin-7-cnts  of  different  orders. 

These  currents,  discovered  by  Henry,  may  be  ob- 
tained by  causing  to  act  on  each  other  a  series  of  bobbins, 
each  formed  of  a  copper  wire  covered  with  silk,  and 
coiled  spirally  in  one  plane,  like  that  represented  in 
plate  A,  fig.  864.  The  currents  thus  produced  are  alter- 
nately in  opposite  directions,  and  their  intensity  decreases 
in  proportion  as  they  are  of  a  higher  order. 

910.  Properties  of  induced  currents. — The  preced- 
ing experiments  that  induced  currents  have  all  the  pro- 
perties of  ordinary  currents.  They  produce  violent  physiological,  luminous, 
calorific,  and  chemical  efiects,  and  finally  give  rise  to  new  induced  currents. 
They  also  deflect  the  magnetic  needle,  and  magnetise  steel  bars  when 
they  are  passed  through  a  copper  wire  coiled  in  a  helix  round  the  bars. 

The  direct  induced  current  and  the  inverse  induced  current  have  been 
compared  as  to  their  chemical  action  ;  the  violence  of  the  shock  ;  the  deflec- 
tion of  the  galvanometer  ;  and  the  magnetising  action  on  steel  bars.  In  these 
respects  they  differ  greatly  :  they  are  equal  in  their  chemical  action  ;  they  are 
about  equal  in  their  action  on  the  galvanometer  ;  but  while  the  shock  of  the 
direct  current  is  very  powerful,  that  of  the  inverse  current  is  scarcely  percept- 
ible. The  same  difference  prevails  with  reference  to  the  magnetising  force. 
The  direct  current  magnetises  to  saturation,  while  the  inverse  current  does 
not  magnetise. 

911.  iviairneto-electrical  machine.— After  the  discovery  of  magneto- 
electrical  induction,  several  attem.pts  were  made  to  produce  an  uninterrupted 
series  of  sparks  by  means  of  a  magnet.  Apparatus  for  this  purpose  were 
devised  by  Pixii  and  Ritchie,  and  subsequently  by  Saxton,  Ettingshausen, 
and  Clarke.  Fig.  871  represents  that  invented  by  Clarke.  It  consists  of 
a  owerful  horseshoe  magnetic  batter}'.  A,  fixed  against  a  vertical  wooden 
support.     In  front  of  this  are  two  coils,  B  B',  movable   round  a  horizontal 

.3  M 


898 


Dynamical  Electricity. 


[911- 

ron  joined  at  one 


axis.     These  coils  are  wound  on  two  cylinders  of  soft 

end   by   a   plate    of  soft  iron,  V,  and  at  the    other  by   a    similar  plate  of 

brass.     These  two  plates   are   fixed    on  a  copper  axis,    terminated  at  one 

end  by  a  commutator,  qi,   and  at  the  other  by  a  pulley,  which  is  moved 

by  an  endless   band  passing  round  a  large  wheel,  which  is  turned  by  a 

handle. 

Each  coil  consists  of  about   1,500  turns  of  very  fine  copper  wire  covered 
with  silk.     One  end  of  the  wire  of  the  coil  B  is  connected  on  the  axis  of 


Fig.  871. 


rotation  with  one  end  of  the  wire  of  the  coil  15',  and  the  two  other  ends 
of  these  wires  terminate  in  a  copper  washer,  (^,  which  is  fixed  to  the  axis, 
but  is  insulated  by  a  cylindrical  envelope  of  ivory.  In  order  that  in  each 
wire  the  induced  current  may  be  in  the  same  direction,  it  is  coiled  on  the 
two  coils  in  different  directions— that  is,  one  is  right-handed,  the  other 
left-handed. 

When  now  the  electromagnet  turns,  its  two  branches  become  alternately 
magnetised  in  contrary  directions  under  the  influence  of  the  magnet  A,  and 
in  each  wire  an  induced  current  is  produced,  the  direction  of  which  changes 
at  each  half-turn. 

Let  us  follow  one  of  the  coils— 15,  for  instance— while  it  makes  a  com*' 
plcte  revolution  in  front  of  the  poles  a  and  b  of  the  magnet  ;  calling  the 
poles  of  the  electromagnet  successively  a'  and  b'.     Let  us  further  consider 


911] 


Magneto-electrical  Machine. 


899 


the  latter  when  it  passes  in  front  of  the  north  pole  of  the  magnetic  battery 
(fig.  871).  The  iron  has  then  a  south  pole,  in  which,  as  we  know,  the  Am- 
porian  currents  move  like  the  hands  of  a  watch.  The  contrary  seems  to  be 
represented  in  fig.  873,  but  it  must  be  remembered  that  the  coils  are  seen 
here  as  they  are  in  fig.  871  ;  and  hence,  when  viewed  at  the  end  which 
faces  the  magnet,  the  Amperian  currents  seem  to  turn  like  the  hands  of  a 
watch.  These  currents  act  inductively  on  the  wire  of  the  bobbin,  producing 
a  current  in  the  same  direction  (902,  iii.),  for  the  bobbin  moves  away  trom 
the  pole  <?,  its  soft  iron  is  demagnetised,  and  the  Amperian  currents  cease. 
The  intensity  of  the  induced  currents  in  the  coil  decreases,  until  the  right 


Fig.  873. 


Fig.  874 


Fig.  S75. 


Fig.  876. 


line  joining  the  axes  of  the  two  coils  is  perpendicular  to  that  which  joins  the 
poles  a  and  b  of  the  magnet.  There  is  now  no  magnetisation  in  the  bar, 
laut  quickly  approaching  the  pole  b^  its  soft  iron  is  then  magnetised  in  the 
opposite  direction — that  is,  becomes  a  north  pole  (fig.  874).  The  Amperian 
currents  are  then  in  the  direction  of  the  arrow  a' ;  and  as  they  are  com- 
mencing, they  develop  in  the  wire  of  the  bobbin  an  inverse  current  (901) 
which  is  in  the  same  direction  as  that  developed  in  the  first  quarter  of  the 
turn.  Moreover,  this  second  current  adds  itself  to  the  first  ;  for  while  the 
coil  moves  away  from  «,  it  approaches  b.  Hence,  during  the  lower  half- 
turn  from  a  to  b.,  the  wire  was  successively  traversed  by  two  induced  currents 
in  the  same  direction,  and  if  the  rotatory  motion  is  sufificiently  rapid,  we 

3  M  2 


900 


D)niamical  Electricity. 


[911- 


might  admit  during  this  half-turn  the  existence  of  a  single  current  in  the 
wire. 

The  same  reasoning  applied  to  the  figures  875  and  876  will  show  that 
during  the  upper  half-turn  the  wire  of  the  coil  B  is  still  traversed  by  a 
single  current,  but  in  the  opposite  direction  to  that  of  the  lower  half-turn. 
What  has  been  said  about  the  coil  B  applies  obviously  to  the  coil  B'  ;  yet, 
as  one  of  these  is  right-handed  and  the  other  left-handed,  the  currents  are 
constantly  in  the  same  direction  in  the  two  coils  during  each  upper  or  lower 
half-revolution.  At  each  successive  half-turn  they  both  change,  but  are  in 
the  same  direction  as  regards  each  other  ;  the  term  '  direction  '  having  here 
reference  to  figs.  873-876. 

912.  Commutator.— The  object  of  this  apparatus  (fig.  877),  of  which  fig. 
878  is  a  section,  is  to  bring  the  two  alternating  currents  always  in  the  same 
direction.  It  consists  of  an  insulating  cylinder  of  ivory  or  ebony,  J,  in  the 
axis  of  which  is  a  copper  cylinder,  k^  of  smaller  diameter,  fixed  to  the  arma- 
ture V,  and  turning  with  the  coils.  On  the  ivory  cylinder  is  first  a  brass 
ferrule,  q,  and  in  front  of  it  two  half-ferrules,  0  and  o\  also  of  brass,  and 
completely  insulated  from  one  another.  The  half-ferrule  o  is  connected  with 
the  ferrule  ^  by  a  tongue,  .i".  On  the  sides  of  a  block  of  wood,  M,  there  are 
two  brass  plates,  7;/,  ;z,  on  which  are  screwed  two  elastic  springs,  b  and  c^  which 
press  successively  on  the  half-ferrules  0  and  o\  when  rotation  takes  place. 

We  have  al- 
ready seen  that 
the  two  ends  of 
the  wire  of  the 
coil,  those  in 
the  same  direc- 
tion with  respect 
to  the  currents 
passmg  through 
them  at  any 
time,  which  will 
be  found  to  be 
tliose  farthest 
away  from  the 
armature  \',  ter- 
minate in  the 
metallic  axis  k, 
and  therefore  on 
the  half-ferrule 
o  ;  while  the 
'^"'S-  ^^^•  other  two  ends, 

both  in  the  same  direction  with  respect  to  the  current,  are  joined  to  the 
ferrule  i]^  and  therefore  to  the  half- ferrule  0.  It  follows  that  the  pieces 
0  o'  are  always  poles  of  alternating  currents  which  are  developed  in  the 
coils  :  and,  as  these  are  alternately  in  contrary  directions,  the  pieces  o. 
and  0'  are  alternately  positive  and  negative.  Now,  taking  the  case  in 
which  the  half-ferrule  0'  is  positive,  the  current  descends  by  the  spring  b, 
follows  the  plate  ///,  arrives  at  n  by  the  wire  /,  ascends  in  c,  and  is  closed 


-912] 


Covunutator. 


901 


by  contact  with  the  piece  0  ;  then  when,  in  consequence  of  rotation,  0 
takes  the  place  of  o\  the  current  retains  the  same  direction  ;  for,  as  it  is 
then  reversed  in  the  coils,  o  has  become  positive  and  0'  negative,  and  so 
forth,  as  long-  as  the  coil  is 
turned. 

With  the  two  springs  b 
and  c  alone,  the  opposite 
currents  from  the  two  pieces 
0  and  o'  could  not  unite 
when  ni  and ;/  are  not  joined  ; 
this  is  effected  by  means  of 
a  third  spring,  a  (fig.  880), 
and  of  two  appendices,  z", 
only  one  of  which  is  visible 
in  the  figure.  These  two 
pieces  are  insulated  from  one  F'g-  878. 

another  on  an  ivory  cylinder,  but  communicate  respectively  with  the  pieces 
0  and  o'.  As  often  as  the  spring  a  touches  one  of  these  pieces  it  is  con- 
nected with  the  spring  b^  and  the  current  is  closed,  for  it  passes  from  b 
to  a,  and  then  reaches  the  spring  c  by  the  plate  n.  On  the  contrary,  as 
long  as  the  spring  a  does  not  touch  one  of  these  appendices  the  current  is 
broken. 

For  physiological  effects  the  use  of  the  spring  a  greatly  increases  the 
intensity  of  the  shocks.  For  this  purpose  two  long  spirals  of  copper  wire 
with  handles,/  and/',  are  fixed  at  n  and  m.  Holding  the  handles  in  the 
hands,  so  long'  as  the  spring  a  does  not  touch  the  appendices  z,  the  current 
passes  through  the  body  of  the  experimenter,  but  without  appreciable  effect  ; 
while  each  time  that  the  plate  a  touches  one  of  the  appendices  z,  the  current, 
as  we  have  seen  above,  is  closed  by  the  pieces,  b,  a,  and  c,  and  ceasing  then 
to  pass  through  the  wires  >!p,  nip',  produces  in  this  and  through  the  body  a 
direct  extra  current  which  causes  a  violent  shock. 

This  is  renewed  at  each  half-turn  of  the  electromagnet,  and  its  intensity 
increases  with  the  velocity  of  the  rotation.     The  muscles  contract  with  such 
force  that  they  do  not  obey  the  will,  and  the  two  hands  cannot  be  detached. 
With  an  apparatus  of  large  dimen- 
sions a  continuance  of  the  shock 
is  unendurable. 

All  the  effects  of  voltaic  cur- 
rents may  be  produced  by  the  in- 
duced current  of  Clarke's  machine. 
Fig.  S72  shows  how  the  apparatus 
is  to  be  arranged  for  the  decom- 
position of  water.  The  spring  a 
is  suppressed,  the  current  being 
closed  by  the  two  wires  which  re- 
present the  electrodes. 

For  physiological  and  chemical  effects  the  wire  rolled  on  the  coils  is 
fine,  and  each  about  500  or  600  yards  in  length.  For  heating  effects,  on  the 
contrary',  the  wire  is  thick,  and  there  are  about  25  to  35  yards  on  each  coil. 


Fis.  S79. 


902  Dynamical  Electricity.  i_912~ 

Figs.  879  and  880  represent  the  arrangement  of  the  bobbins  and  the  com- 
mutator in  each  case.  The  first  represents  the  inflammation  of  ether,  and 
the  second  the  incandescence  of  a  wire,  c,  in  which  the  current  from  the 
plate  a  to  the  plate  c  always  passes  in  the  same  direction. 

Pixii's  and  Saxton's  electromagnetic  machine  differs  from  Clarke's  in 
having  the  electromagnet  fixed  while  the  magnet  rotates. 

Wheatstone  devised  a  compendious  form  of  the  mag'neto-electrical 
machine,  for  the  purpose  of  using  the  induced  spark  in  firing  mines  (794). 

Breguet's  apparatus  for  the  same  purpose  consists  of  a  powerful  horse- 
shoe magnetic  battery,  to  the  ends  of  which  are  screwed  soft  iron  cores, 
round  which  are  coils  of  fine  wires  ;  to  these  are  connected  the  wires  leading 
to  the  mine  to  be  fired.  The  ends  of  the  soft  cores  are  connected  by  a 
soft  iron  keeper ;  and  when,  by  a  suitable  mechanism,  this  is  suddenly 
detached  from  the  cores,  a  powerful  momentary  induction  current  is  pro- 
duced in  the  coils,  which  is  sufficient  to  fire  more  than  one  fuse,  through 
even  a  considerable  length  of  wire. 

913.  Magrneto-electrical  machine. — The  principle  of  Clarke's  apparatus 
has  received  in  the  last  few  years  a  remarkable  extension  in  large  magneto- 
electrical  machines,  by  means  of  which  mechanical  work  is  transformed  into 
powerful  electrical  currents  by  the  inductive  action  of  magnets  on  coils  in  mcftion. 

The  first  machine  of  this  kind  was  invented  by  Nollet,  in  Brussels,  in 
1850.  It  consists  (fig.  881)  of  a  cast-iron  frame,  5^  feet  in  height,  on  the 
circumference  of  which  eight  series  of  five  powerful  horseshoe  magnetic 
batteries,  A,  A,  A,  are  arranged  in  a  parallel  order  on  wooden  cross-pieces. 
These  batteries,  each  of  which  can  support  from  120  to  130  pounds,  are  so 
arranged  that  if  they  are  considered  either  parallel  to  the  axis  of  the  frame, 
or  in  a  plane  perpendicular  to  this  axis,  opposite  poles  always  face  one 
another.  In  each  series  the  outside  batteries  consist  of  three  magnetised 
plates,  while  the  three  middle  ones  have  six  plates,  because  they  act  by  both 
faces,  while  the  first  only  acts  by  one. 

On  a  horizontal  iron  axis  going  from  one  end  to  the  other  of  the  frame 
four  bronze  wheels  are  fixed,  each  correspondmg  to  the  intervals  between 
the  magnetic  batteries  of  two  vertical  series.  There  are  16  coils  on  the 
circumference  of  each  of  these — that  is,  as  many  as  there  are  magnetic  poles 
in  each  vertical  series  of  magnets.  These  coils,  represented  in  fig.  882,  differ 
from  those  of  Clarke's  apparatus  in  having  12  wires,  each  i  li  yards  in  length, 
instead  of  a  single  wire,  by  which  the  resistance  is  diminished.  The  wires 
of  these  coils  are  insulated  by  means  of  bitumen  dissolved  in  oil  of  turpentine. 
They  are  not  wound  upon  solid  cylinders  of  iron,  but  on  iron  tubes,  split 
longitudinally  ;  this  device  renders  the  magnetisation  and  demagnetisation 
more  rapid  when  the  coils  pass  in  front  of  the  poles  of  the  magnet.  Further, 
the  discs  of  copper  which  terminate  the  coils  are  slit  in  the  direction  of  the 
radius,  in  order  to  prevent  the  formation  of  induced  currents  in  these  discs. 
The  four  wheels  being  respectively  provided  with  16  coils  each,  there  are 
altogether  64  coils  arranged  in  16  horizontal  series  of  four,  as  seen  at  D  on 
the  left  of  the  frame.  The  Tength  of  the  wire  on  each  coil  being  12  times 
\\h  yards,  or  138  yards,  the  total  length  in  the  whole  apparatus  is  64  times* 
138  yards,  or  8,832  yards. 

The  wires  are  wound  on  all  the  coils  in  the  same  direction  ;  and  not  only 


-913] 


Magneto-electrical  MacJiine. 


903 


on  the  same  wheel,  but  on  all  four,  all  wires  are  connected  with  one  another. 
For  this  purpose  the  bobbins  are  joined,  as  shown  in  fig.  883  ;  on  the  first 
wheel  the  twelve  wires  of  the  first  coil,  x,  are  connected  on  a  piece  of 
mahogany  fixed  on  the  front  face  of  the  wheel  with  a  plate  of  copper,  in, 
connected  by  a  wire,  O,  with  the  centre  of  the  axis  which  supports  the 
wheels.     At  the  other  end,  on  the  other  face  of  the  wheel,  the  same  wires  are 

%i :ii,ii;!if;iv:i!:::,;"i":v,,i;3S 


m^"      \ 


i 


Fig.  881. 

soldered  to  a  plate  indicated  by  a  dotted  line  which  connects  them  with  the 
coilj/ ;  from  this  they  are  connected  with  the  coil  s'  by  a  plate,  /,  and  so  on, 
for  the  coils  /,  tt,  .  .  .  up  to  the  last,  v.  The  wires  of  this  coil  terminate  in 
a''plate,  11,  which  traverses  the  first  wheel,  and  is  soldered  to  the  wires  of  the 
first  coil  of  the  next  wheel,  on  which  the  same  series  of  connections  is  re- 
peated ;  these  wires  pass  to  the  third  wheel,  thence  to  the  fourth,  and  so  on 
to  the  end  of  the  axis. 


904 


Dynamical  Electi'icity. 


[913- 


The  coils  being-  thus  arranged,  one  after  another,  like  the  elements  of  a 
battery  connected  in  a  series  (825),  the  electricity  is  of  high  potential.  But 
they  may  also  be  arranged  by  connecting  the  plates  alternately,  not  with 
each  other,  but  with  two  metal  rings,  in  such  a  manner  that  all  the  ends  of 


Fig.  882.  Fig.  8S3. 

the  same  name  are  connected  with  the  same  ring-.  Each  of  these  rings 
is  then  a  pole,  and  this  arrangement  may  be  used  where  a  high  degree  of 
potential  is  not  required. 

From  these  explanations  it  will  be  easy  to  understand  the  manner  in 
which  electricity  is  produced  and  propagated  in  this  apparatus.  An  endless 
band,  receiving  its  motion  from  a  steam-engine,  passes  round  a  pulley  fixed 
at  the  end  of  the  axis  which  supports  the  wheels  and  the  coils,  and  moves 
the  whole  system  with  any  desired  rapidity.  Experience  has  shown  that  to 
obtain  the  greatest  degree  of  light  the  most  suitable  velocity  is  235  revolu- 
tions in  a  minute.  During  this  rotation,  if  we  at  first  consider  a  single 
coil,  the  tube  of  soft  iron  on  which  it  is  coiled,  in  passing  in  front  of  the 
poles  of  the  magnet,  undergoes  at  its  two  ends  an  opposite  induction,  the 
efifects  of  which  are  added,  but  change  from  one  pole  to  another.  As  these 
tubes,  during  one  rotation,  pass  successively  in  front  of  sixteen  poles 
alternately  of  different  names,  they  are  magnetised  eight  times  in  one 
direction  and  eight  times  in  the  opposite  direction.  In  the  same  time  there 
are  thus  produced  in  the  bobbin  eight  direct  induced  currents  and  eight 
inverse  induced  currents  ;  in  all,  sixteen  currents  in  each  revolution.  With 
a  velocity  of  235  turns  in  a  minute,  the  number  of  currents  in  the  same  time 
is  235  X  16  =  3,760  alternately  in  opposite  directions.  The  same  phe- 
nomenon is  produced  with  each  of  the  64  coils  ;  but  as  they  are  all  wound 
in  the  same  direction,  and  are  connected  with  each  other,  their  effects  accu- 
mulate, and  there  is  the  same  number  of  currents,  but  they  are  more  intense. 

To  utilise  these  currents  in  producing  the  electric  light,  the  connections 
are  made  as  shown  in  fig.  884.  On  the  posterior  side  the  last  coil,  x\  of 
the  fourth  wheel  terminates  by  a  wire,  G,  on  the  axis  MN,  which  supports 
the  wheels  :  the  current  thus  passes  to  the  axis,  and  thence  over  all  the 
machine,  so  that  it  can  be  taken  from  any  desired  point.  In  the  front 
the  first  coil,  x,  of  the  first  wheel  communicates,  by  the  wire  O,  not  with 
the  axis  itself  but  with  a  steel  cylinder,  <■,  fitted  in  the  axis,  from  which,  how- 
ever, it  is  insulated  by  an  ivory  collar.  The  screw  ^,  to  which  the  wire  Q 
is  attached,  is  likewise  insulated  by  a  piece  of  ivory.  From  the  cylinder  c 
the  current  passes  to  a  fixed  metal  piece,  K,  from  which  it  passes  to  the 


-914]  Siemens'  Armature.  905 

wire  H,  which  transmits  it  to  the  binding  screw  a  of  fig.  881.  The  binding 
screw  b  communicates  with  the  framework,  and  therefore  with  the  wire  of 
the  last  coil  x'  (fig.  S84).  From  the  two  binding  screws  a  and  h  the  current 
passes  by  two  copper  wires  to  two  carbons,  the  distance  of  which  is  regu- 
lated by  means  of  an  apparatus  analogous  in  principle  to  that  already 
described  (835). 

In  this  machine  the  currents  are  not  rectified  so  as  to  be  in  the  same 
direction^— it  produces  alternate  currents  ;  hence  each  carbon  is  alternately 


^1 


IMl 


w  "  iir'      'r  -^  ^ 


Fig.  SS4. 

positive  and  negative,  and  in  fact  they  are  consumed  with  equal  rapidity 
if  a  suitable  lamp  be  used  ;  but  when  they  are  to  be  used  for  electro-metal- 
lurgy, or  for  magnetising,  they  must  be  rectified,  which  is  effected  by  means 
of  a  suitable  commutator  (912). 

This  type  of  machine  may  claim  a  description  here  as  that  by  which 
magneto-electrical  currents  were  first  applied  on  a  large  scale  for  technical 
purposes.  Such  machines,  are,  however,  being  superseded  by  various  im- 
proved forms  of  machines,  which  for  the  same  power  are  simpler,  less  costly, 
and  occupy  a  smaller  space.  Of  the  newer  forms  of  magneto-electrical 
machine  that  of  Meriten's  is  stated  to  give  the  best  results. 

Q14.  Siemens'  armature. — Dr.  Siemens  devised  a  cylindrical  armature 
for  magneto-electrical  machines,  in  which  the  insulated  wire  is  wound  length- 
wise on  the  core,  instead  of  transversely,  as  is  usually  the  case. 

It  consists  of  a  soft  iron  rod  or  cylinder,  AB  (fig.  8S5),  from  one  foot  to 
three  feet  in  length.     A  deep  groove  is  cut  in  this  cylinder  and  on  the  ends, 


in  which  is  coiled  the  insulated  wire,  as  shown  in  section  in  fig.  887.  To 
the  two  ends  of  the  cylinder,  brass  discs,  E  and  D,  are  secured.  With  E  is 
connected  a  commutator  C,  consisting  of  two  pieces  of  steel  insulated  from 
each  other,  and  connected  respectively  with  the  two  ends  of  the  wire.  On 
the  other  disc  is  a  pulley,^,  round  which  passes  a  cord,  so  that  the  bobbin 
moves  veiy  rapidly  on  the  two  pivots. 


9o6  Dynamical  Electricity  [914- 

When  a  voltaic  current  circulates  in  the  wire,  the  two  cylindrical  seg- 
ments A  and  B  are  immediately  magnetised,  one  with  one  polarity  and  the 
other  with  the  opposite.  On  the  other  hand,  if  instead  of  passing  a  voltaic 
current  through  the  wire  of  the  coil,  the  coil  itself  be  made  to  rotate  rapidly 
between  the  opposite  poles  of  magnetised  masses,  as  the  segments  A  and 
B  become  alternately  magnetised  and  demagnetised,  their  induction  pro- 
duces in  the  wire  a  series  of  currents  alternately  positive  and  negative,  as  in 
Clarke's  apparatus  (910).  When  these  currents  are  collected  in  a  commutator 
which  adjusts  them  (912),  that  is,  sends  all  the  positive  currents  on  one 
spring  and  all  the  negative  on  another — these  springs  become  electrodes, 
from  one  of  which  positive  electricity  starts,  and  from  the  other  negative.  If 
these  springs  are  connected  by  a  conductor,  the  same  effects  are  obtained  as 
when  the  two  poles  of  a  voltaic  battery  are  united. 

This  armature  has  the  great  advantage  that  a  large  number  of  com- 
paratively small  magnets  may  be  used  instead  of  one  large  one.  As,  weight 
for  weight,  the  former  possess  greater  magnetic  force  than  the  latter,  they 
can  be  made  more  economically.  And  as  the  armature  is  enclosed  by  and 
is  very  near  the  magnets,  it  experiences  the  action  of  the  field  in  its  greatest 
strength. 

915.  "Wild's  magneto-electrical  luachine. — Mr.  Wild  constructed  a 
magneto-electrical  machine  in  which  Siemens'  armature  is  used  along  with 
a  new  principle— that  of  the  multiplication  of  tlie  current.  Instead  of  uti- 
lising directly  the  current  produced  by  the  introduction  of  a  magnet,  Mr.  Wild 
passes  It  into  an  electromagnet,  and  by  the  induction  of  this  latter  a  more 
energetic  current  is  obtained  ;  the  electromagnet  thus  excited  plays  the  part 
of  the  permanent  magnets,  but  is  more  powerful, 

This  machine  consists  first  of  a  battery  of  12  to  16  magnets,  P  (fig.  886), 
each  of  which  weighs  about  3  pounds,  and  can  support  about  20  pounds. 
Between  the  poles  of  the  magnets  two  soft  iron  keepers  CC  are  arranged, 
separated  by  a  brass  plate,  O.  These  three  pieces  are  joined  by  bolts,  and 
the  whole  compound  keeper  is  perforated  longitudinally  by  a  cylindrical 
cavity,  in  which  works  a  Siemens'  armature,  //,  about  2  inches  in  diameter. 
The  wire  of  this  armature  terminates  in  a  commutator,  which  leads  the 
positive  and  negative  currents  to  two  binding  screws,  a  and  b.  This  com- 
mutator is  represented  on  a  larger  scale  in  fig.  887.  At  the  other  end  is  a 
pulley  by  which  the  armature  can  be  turned  at  the  rate  of  25  turns  in  a 
second.     The  wire  on  the  armature  is  20  yards  long. 

Below  the  support  for  the  magnets  and  their  armatures  are  two  large 
electromagnets,  Bl>,  which  are  called  ihojictd  nuii^ncts,  since  to  them  is  due 
the  production  of  the  magnetic  field.  Each  consists  of  a  rectangular  soft 
iron  plate,  36  inches  in  length  by  26  in  breadth  and  i.^  inch  thick,  on  which 
arc  coiled  about  1,610  feet  of  insulated  copper  wire.  The  wires  of  these 
electromagnets  are  joined  at  one  end,  so  as  to  form  a  single  circuit  of  3,200 
feet.  One  of  the  other  ends  is  connected  with  the  binding  screw  a,  and  the 
other  with  b.  At  the  top  the  two  plates  arc  joined  hy  a  transverse  plate  of 
iron,  so  as  to  form  a  single  electromagnet. 

At  the  bottom  of  the  electromagnets  BB  are  two  iron  armatures,  scpanitcd- 
l)y  a  brass  plate,  0,and  in  the  entire  length  is  a  cylindrical  channel  in  which 
works  a  Siemens'  armature,  w,  as  above  :  this  armature,  however,  is  above  a 


-915J 


Jl'i/d's  Mao;neio-electrical  Machine. 


,07 


yard  in  length,  nearly  6  inches  in  diameter,  and  its  wire  is  100  feet  long. 
The  ends  are  connected  with  a  commutator,  from  which  the  adjusted  currents 
pass  to  two  wires,  r  and  s.  The  armatui'c  m  is  rotated  at  the  rate  of  1,700 
turns  in  a  minute. 


|inil|i|iV''«tr"^ 


111  II 


'*  »IL  »     «a^_ 


illl^Pt«V 


Fig.  886. 

•  Fig.  887  shows  on  a  larger  scale  a  cross  section  of  the  coil  of  the  armatures 
CC,  and  of  the  plates  AA,  on  which  the  wire  of  the  electro-magnets  BB  is 
coiled. 

These  details  being  premised,  the  following  is  the  working  of  the 
machine  : — When  the  armatures  n  and  m  are  rotated  by  means  of  a  steam- 
engine  with  the  velocity  mentioned,  the  magnets  produce  in  the  first  arma- 


9o8 


Dynamical  Elettricity, 


[915- 


ture  induced  currents,  which,  adjusted  by  the  commutator,  pass  into  the 
electromagnet  BB,  and  magnetise  it.  But  as  these  impart  to  the  lower 
armatures,  CC,  opposite  polarities^the  induction  of  these  latter  produces  in 
the  armature  ;;/  a  series  of  positive  and  negative  currents  far  more  powerful 


Fig. 


Fig. 


than  those  of  the  upper  armature  ;  so  that  when  these  are  adjusted  by  a 
commutator  and  directed  by  the  wires  ;-  and  s,  very  powerful  effects  are 
obtained. 

These  effects  are  still  further  intensified  if,  as  Mr.  Wild  has  done,  the 
adjusted  current  of  the  armature  ;//  is  passed  into  a  second  electromagnet, 
whose  armatures  surround  a  third  and  larger  Siemens'  armature  turning  with 
the  two  others.  Mr.  Wild  thus  produced  currents  of  a  strength  far  exceeding 
anything  which  up  to  that  time  had  been  attained  ;  he  was  able,  for  instance, 
to  melt  easily  an  iron  wire  a  foot  long  and  more  than  0'2  inch  in  diameter. 

916.  Bynamo-electrlcal  macbines. — A  great  advance  was  made  by  the 
discovery  of  the  principle  of  the  reaction  of  a  current  on  itself— a  discovery 
made  by  Dr.  Werner  Siemens  and  Sir  C.  Wheatstone  independently  of  each 
other,  and  almost  simultaneously.  If  a  momentary  voltaic  current  be  passed 
through  the  wires  of  the  rotating  armature  of  such  a  machine  as  the  above, 
a  trace  of  residual  magnetism  (715)  will  be  left  in  the  core.  The  rotation  of 
this  armature  induces  a  current  in  the  electromagnets  BB  ;  this  in  turn 
reacts  on  the  armature,  increases  its  magnetism,  which  again  increases  the 
strength  of  the  electromagnets,  and  so  forth.  We  have  in  this  an  analogy 
with  Holtz's  machine  (759),  in  which  the  electricity  of  the  plate  and  the  con- 
ductors reciprocally  strengthen  each  other.  It  is  not  even  necessary  to 
specially  magnetise  the  iron  at  the  outset  ;  the  trace  of  residual  magnetism 
always  present  in  iron  (715)  is  sufficient  to  start  the  apparatus,  which  then 
goes  on  increasing  with  the  velocity  of  the  rot;ition,  and  which  indeed  is 
only  limited  by  the  heating  of  the  wires  and  the  bearings,  and  by  the  diffi- 
culty of  properly  insulating  the  coils  when  such  powerful  currents  are  used. 

Apparatus  which  transform  mechanical  work  into  electricity  without  the 
use  of   permanent    magnets,  or  of  extraneous  electromagnets,  are  known 
as    dynamo-clcctrical  machitics  or  brief!)-  dyntuitos^  in  contradistinction  tor' 
ina_Q;nctfl-elccfrical  machines,  in  which  the  magnetism  is  not  furnished  by 
the  play  of  the  machine  itself,  but  is  got  from  permanent  magnets.     It  must 


-916] 


Dynamo-electrical  MacJiines. 


909 


not,  however,  be  supposed  that  in  the  one  the  electricity  is  produced  at  the 
expense  of  the  magnetism,  and  in  the  other  at  the  expense  of  the  work. 
There  is  really  no  distinction  of  this  kind  between  them  ;  in  both  kinds  of 
machine  electricity  is  produced  at  the  cost  of  work  ;  and  for  this  reason 
both  are  indeed  dynamo-electrical  machines,  and  the  distinction  of  the  two 
kinds  is  only  one  of  convenience. 

The  earliest  machine  of  this  kind  was  that  invented  by  Mr.  Ladd.  It  con- 
sists essentially  of  two  Siemens'  armatures,  rotating  with  great  velocity,  and 
of  two  iron  plates,  A  A  (fig.  889),  surrounded  by  an  insulated  copper  wire. 


r^i 


Fig.  889. 

The  electromagnets  BB  are  not  joined  so  as  to  form  a  single  one,  but 
are  two  distinct  electromagnets,  each  having  at  the  end  two  hollow  cylin- 
ders, CC,  in  which  are  fitted  two  Siemens'  armatures,  in  and  «  :  the  current 
of  the  armature  n  passing  round  the  electromagnets  reverts  to  itself.  The 
wire  of  the  armature  m  passes  into  the  apparatus  which  is  to  utilise  the 
current — for  instance,  two  carbon  points,  D. 

The  residual  magnetism  in  the  armature  plates  and  their  keepers  is  sufficient 
to  start  the  machine.  If,  then,  the  armatures  m  and  n  be  rotated  by  means  of 
two  bands  passing  round  a  common  drum,  the  magnetism  of  the  hollow  cylin- 
ders CC,  acting  upon  the  armature  ;/,  excites  induction  currents,  which,  ad- 
justed by  a  commutator,  pass  round  the  electromagnets  BB,  and  more  strongly 
magnetise  the  cylinders  or  shoes  CC.  These  in  their  turn  reacting  more 
powerfully  on  the  armature  ;/,  strengthen  the  current  ;  we  thus  see  that  n  and 
B  continually  and  mutually  strengthen  each  other  as  the  velocity  of  the  rota- 
tion increases.  Hence,  as  the  iron  of  the  armature  m  becomes  more  and 
more  strongly  magnetised  under  the  influence  of  the  electromagnets  BB,  a 


9IO 


Dynamical  Electricity 


[916- 


Fig. 


gradually  more  powerful  induced  current  is  developed  in  this  armature,  which 
is  directed,  commutated  or  not,  according  to  the  use  for  which  it  is  designed. 

In  a  machine  exhi- 
bited at  the  Paris  Exhi- 
bition of  1867  the  plates 
A  A  were  only  24  inches 
in  length  by  12  inches  in 
width.  With  these  small 
dimensions  the  current  is 
equal  to  that  of  25  to  30 
Bunsen's  cells.  It  can 
work  the  electric  light  and 
keep  incandescent  a  plati- 
num wire  a  metre  in  length 
and  0-5  mm.  in  diameter. 
The  above  form  of  the 
machine  is  worked  by 
steam  power.  Mr.  Ladd 
devised  a  more  compact 
form,  which  may  be 
worked  by  hand.  This 
is  represented  in  fig.  890. 
The  two  armatures  are 
fixed  end  to  end,  and  the 
coils  are  wound  on  it  at 
right  angles  to  each  other, 
as  shown  in  the  figure. 
The  current  from  this  can 
raise  to  white  heat  18 
in.  of  platinum  wire  o-oi 
in.  in  thickness,  and  with 
an  inductorium  (921)  con- 
taining 3  miles  of  second- 
ary wire  2-in.  sparks  can 
be  obtained. 

917.   Pacinotti's  ringr. 
Cramme's  magneto- 

electrical  maclilne. — .V 
remarkable  improvement 
in  magneto-  and  dynamo- 
electric  machines  is 
tlie  application  of  a  ling 
inductor.  This  was  in- 
vented by  Prof  Pacinotti 
in  186?,  and  is  known 
as  Paciiwtti's  7-i)ig.  It 
was  applied  by  him  to- 
an  electromagnetic  motor,  but  he  showed  that  it  could  be  used  as  a  mag- 
neto-electrical motor.      The  same   principle  was   discovered  several  years 


Fig.  891. 


-917j 


Paa'iiotti's  Rino;.     GTamine^s  Machine. 


911 


Fig.  392. 


later,  it  would  appear  quite   independently,   by   M.   Gramme,  and  utilised 

by  him  in   the  construction  of  a  new  form  of  magneto-electrical  machine. 

This  differed  from  all  previous  forms  in  giving  at  once  direct,  and   what  are 

practically    continuous    currents,    and 

which,  having  regard  to  the  size  of  the 

machine,  M^ere  more  powerful  than  any 

hitherto  obtained.      A  laboratory  form 

of  Gramme's  machine  is  represented  in 

fig.  891,  in  about  |  of  the  real  size.    On 

a  base  is  fixed  vertically   a    powerful 

Jamin's  magnetic  battery,  A  (fig.  891), 

constructed  of  24  steel  plates,  each  i  mm. 

in  thickness,  then  separately  magnetised 

to     saturation.        To    the     poles    are 

affixed  two  soft  iron  armatures  a  and  ^, 

between  which  an  axle  is  rotated   by 

means  of  a  wheel  and  rackwork.     On 

this  axle  is  a  ring  on  which  are  wound 

a  series  of  thirty  coils.      The  ring  or 

core  is  not  solid,  but  itself  consists  of  a  coil  of  a  number  of  turns  of  soft  iron 

wire,  as  seen  in  fig.  892,  and  in  this  way  the  changes  in  its  magnetisation 

which  take  place  are  far  more  rapid,  and  the  heating  effect  due  to  these 

rapid  changes  is  less  ;  the  wire  is  continuous,  and  the  two  ends  are  soldered 

together. 

On  this  core  are  wound  the  coils  BCD  ;  they  are  united  by  thin  brass 
knee-plates,  ;//;?,  to  each  of  which  are  soldered  the  copper  wires  of  two  suc- 
cessive coils,  so  as  to  form  a  continuous  whole.  The  plates  are  insulated 
from  each  other,  and  are  fixed  on  a  wooden  block  <?,  mounted  on  the  axis 
of  rotation.  The  branches  mn  of  the  knee-plates  form  a  sheath  about  this 
axis,  and  two  flat  brushes  of  copper  wire,  fixed  to  the  binding  screws  c  and  z, 
are  in  contact  with  the  upper  and  lower  parts  of  this 
sheath,  and  receive  the  currents  which  originate  in  the 
coils. 

In  order  to  understand  the  action  of  Gramme's  ma- 
chine, let  us  now  consider  the  condition  of  a  soft  iron 
ring  which  is  placed  between  the  two  opposite  poles  of 
a  powerful  permanent  magnet,  at  the  opposite  ends  of 
a  diameter  of  the  ring  (fig.  893).  The  parts  nearest  the 
magnet  will  be  of  the  opposite  polarity  to  that  of  the  in- 
ducing magnet.  We  may  consider  that  under  its  in- 
fluence each  half  of  the  ring  is  converted  into  a  magnet 
with  its  two  poles  and  neutral  line.  The  same  poles  of 
the  ring  face  each  other,  and  the  effect  is  not  altered  if 
the  ends  touch.  Let  us  now  suppose  the  ring  fixed, 
and  that  a  thin  coil  moves  round  it,  starting  from  the  neutral  line, 
nears  the  pole  j^,  a  current  on  approach  will  be  induced  in  the  coil 
opposite  direction  to  that  which,  on  Ampere's  hypothesis,  circulates  round 
the  end  of  the  pole  s  ;  as  it  passes  over  the  other  half  s,  a  leaving  current 
is  produced,  which  is  in  the  same  direction  as  that  Avhich  circulates  round  .\- ; 


912  Dynamical  Electricity.  [917- 

but  it  must  be  remembered  that  as  these  poles  face  one  another,  their 
Amperian  currents  are  in  opposite  directions,  the  result  of  which  is  that  the 
currents  induced  on  approaching  s  and  on  leaving  s  are  in  the  same  direc- 
tion ;  in  other  words,  as  the  coil  circulates  in  front  of  the  double  pole  it 
will  be  traversed  by  a  continuous  current  in  the  same  direction,  the  strength 
of  which  increases  from  the  neutral  point  till  it  comes  in  front  of  the  poles, 
and  then  diminishes  until  it  is  at  the  neutral  point  again.  The  same  process 
repeats  itself  in  the  coil  as  it  approaches  the  other  pole,  except  that  the 
current  is  negative,  so  that  if  the  collectors  are  adjusted  one  on  each  side  of 
the  neutral  point  they  will  collect  the  opposite  currents,  and  they  can  be 
utilised  in  an  external  circuit.  What  is  here  true  of  one  coil  is  true  of  all 
others  as  they  pass  in  front  of  the  poles  ;  and  as  they  are  all  connected 
together  we  get,  not  so  much  a  series  of  separate  impulses,  as  a  continuous 
series  of  currents.  This  continuous  character  of  the  currents  is  improved 
by  the  fact  that  the  collector  brushes  are  so  arranged  as  to  touch  more  than 
one  of  the  knee-pieces  at  once. 

The  ring  of  course  does  actually  rotate  with  the  coils,  and  the  polarity  of 
each  part  is  continually  changing ;  but  although  this  is  the  case,  the  position 
of  the  poles  remains  fixed  in  space,  and  the  effect  is  as  we  have  said.  It 
must  be  added  that  the  poles  of  the  magnet  also  act  directly  on  the  coils  ; 
and  if  we  consider  the  ring  as  non-magnetic,  and  only  the  direct  action  of 
the  poles  on  the  coils  to  operate,  it  will  be  seen  to  be  in  the  same  direction 
as  the  action  of  the  ring.  Both  effects  concur  then  in  increasing  the  strength 
and  also  continuity  of  the  currents. 

This  apparatus  is  very  powerful ;  the  smallest  size  made  can  decompose 
water,  and  heat  to  redness  an  iron  wire  20  centimetres  in  length  and  a 
millimetre  in  diameter.  Masc&rt  and  Angot  determined  the  electromotive 
force  of  different  Gramme's  machines  by  placing  in  the  circuit  of  the 
machine,  but  in  opposition  to  it,  a  number  of  Daniell's  elements.  The 
velocity  of  rotation  was  then  increased  until  a  galvanometer  in  the  circuit 
was  not  deflected.  When  this  was  the  case,  seeing  that  the  resistance 
traversed  by  the  opposing  currents  was  the  same,  it  is  clear  that  the  electro- 
motive force  due  to  the  machine  rotating  at  the  given  speed  is  exactly  equi- 
valent to  that  of  the  corresponding  number  of  elements.  Thus,  for  instance, 
the  current  from  3  Daniell's  cells  was  found  to  neutralise  that  of  a  particular 
hand  Gramme's  machine  rotating  with  a  velocity  of  10-2  turns  per  second. 
The  average  electromotive  force  due  to  this  machine  was  found  equal  to  0-27 
of  a  Daniell  for  a  velocity  of  i  turn  per  second.  With  another  the  ratio 
was  0-31,  and  with  others  again  as  much  as  o-8  of  a  Daniell. 

It  will  be  seen  from  the  description  that  the  action  of  the  ring  inductor  is 
not  inconsistent  with  the  application  of  the  dynamo-electrical  principle  ;  and 
in  the  larger  machines  it  is  applied,  and  the  rotation  effected,  by  steam  or 
gas  engines  or  by  water  power.  The  dimensions  and  details  of  the  construc- 
tion vary  with  the  purpose  for  which  the  machine  is  designed.  Thus  in  a 
machine  which  is  to  be  used  for  electrolysis,  the  coils  in  the  ring  inductor 
are  made  up  of  a  comparatively  short  length  of  insulated  upper  bands,  while 
for  the  electric  light  a  long  length  of  fine  insulated  wire  is  used. 

Gramme's  machine  is  reversible  ;  for  while  by  its  means  motion  is  con- 
verted into  electricity,  it  can  in  like  manner  convert  electricity  into  motion. 


-918] 


Siemens'  Dynamo-electrical  Machine. 


913 


This  may  be  seen  by  connecting  the  binding  screws  c  and  /  with  the  poles 
of  a  Grove's  battery.  This  iron  core  then  becomes  magnetised  by  the 
action  of  the  current  passing  through  the  coils  ;  the  whole  system  rotates 
rapidly  under  the  influence  of  the  magnetised  bundle. 

918.  Siemens'  dyoamo-electrlcal  machines. — Fig  894  represents  the 
essential  features  of  one  of  the  small-sized  vertical  machines  made  by 
Messrs.  Siemens.  A  character- 
istic is  the  cylindrical  or  drum 
armature,  which  may  be  re- 
garded as  an  extension  of  that 
already  described  (914).  The 
electromagnets  MM  and  M'M' 
with  double  poles  feed  the  mag- 
netism of  the  soft  iron  arma- 
tures NN,  which  are  bent  so 
as  to  almost  completely  encircle 
the  inductor  ;  they  are  in  de- 
tached pieces,  so  that  air  can 
freely  circulate  between  them, 
and  thereby  the  temperature  be 
kept  down. 

The  inductor  itself,  D,  con- 
sists of  a  drum-shaped  frame  of 
soft  iron  wire  covered  with  a 
layer  of  insulating  material,  and 
fixed  to  an  axle  which  rests  in  the  strong  upright  supports,  and  is  rotated  by 
means  of  power  transmitted  to  the  sheave  A.  The  wire  is  coiled  on  this  ; 
one  end  is  attached  to  a  plate  which  forms  part  of  the  collector,  as  in 
Gramme's  machine  ;  it  passes  lengthwise  round  the  drum  in  several  turns, 
and  the  other  end  is  attached  to  a  similar  piece  on  the  collector,  which  is 
diametrically  opposite  the  first.  The  wire  is  continuous,  the  connection  of 
the  individual  strands  being  effected  by  means  of  the  collector.  On  the 
collector  rest  two  pairs  of  brushes,  b  b,  and  b'  b' ;  they  are  connected  re- 
spectively with  insulated  binding  screws  ;  from  these  the  current  passes 
through  the  wires  of  the  electromagnet,  and  thence  to  the  terminals,/^', 
where  it  may  be  utilised  in  the  external  circuit. 

The  advantage  of  this  construction  is  that  from  the  length  of  the  inductor 
the  wires  are  moving  in  a  more  extended  field  ;  and  being  on  the  surface, 
and  quite  close  to  the  armature  of  the  field  magnets,  are  more  under  their 
influence. 

A  small  machine  of  this  kind,  which  does  not  occupy  a  space  of  more 
than  three  cubic  feet,  and  rotating  with  a  velocity  of  15  turns  in  a  second, 
which  is  effected  by  U  horse-power,  can  produce  a  light  of  1,400  candles. 
The  larger  sizes  produce  far  more  powerful  effects,  but  require  of  cb"urse 
greater  power  to  work  them. 

Machines  of  this  class  give  continuous  currents.  A  kind  is  constructed 
for  alternating  currents  ;  it  consists  of  a  combination  of  two  machines,  one 
of  which  is  on  the  dynamo  principle,  as  in  the  above  case,  while  the  other  is 
analogous  to  the  magneto-electrical  machine. 

3N 


914  Dynamical  Electricity.  [919- 

919.  Brush  dynamo-electrical  machine. — The  armature  of  this  ma- 
chine (fig.  895)  is  ring-shaped,  and  has  some  resemblance  to  Gramme's, 
but  the  coiling  is  different.     The  section  of  the  ring  is  rectangular  (fig.  896),. 


and  there  are  deep  rectangular  grooves  in  it,  in  which  are  the  coils  of  wire 
eight  in  number.  The  projecting  cheeks  thus  formed  between  the  coils  form 
polar  appendices,  which  are  intended  to  act  laterally  on  the  coils.  These 
cheeks  are  traversed  by  deep  horizontal  grooves,  and  also  by  a  large  and 
deep  vertical  groove,  which  almost  divides  the  ring  into  two  parts.     By  this 

means  the  formation  of  local  cur- 
rents is  hindered,  and  a  greater 
cooling  surface  is  obtained. 

The  ring  rotates  between  the 
four  poles  of  two  very  powerful 
electromagnets,  M  and  M',  whose 
soft  iron  armatures  are  prolonged 
in  pole  plates,  N  and  S,  double  poles 
*''«-^96.  Fig.  897.         being  adjacent.        " 

On  the  collector  are  four  rings  (fig.  897-.  Each  ring  consists  of  two  seg- 
ments, A  B,  separated  from  each  other  at  one  end  by  an  air  space,  while 
between  the  others  is  a  smaller  segment,  C,  called  the  '  insulator.'  During 
the  rotation  one  pair  of  coils  is  in  the  neutral  position,  in  which  no  electro- 
motive force  is  being  developed  in  it.  In  this  position  the  coils  only  repre- 
sent a  resistance,  and  their  presence  in  the  circuit  is  a  pure  loss.  The 
contacts  are  so  arranged  that  the  moment  the  pair  is  in  this  position,  which 
is  at  each  quarter  of  a  rotation,  one  of  the  brushes  touches  the  insulator, 
and  is  thus  not  only  removed  from  the  circuit,  but,  not  being  closed,  no 
current  can  circulate  in  it. 

One  end  of  each  coil  is  connected  with  one  end  of  the  coil  exactly 
opposite  it,  the  other  ends  being  connected  with  one  of  the  four  commutator 
rings  where  they  are  connected  to  isolated  segments.  From  these  segments 
the  current  of  the  two  coils  is  taken  off  by  brushes  arranged  horizontally  and 


-919a] 


Classification  of  Dvnaino  Machines. 


915 


in  connection  with  curved  spring  bands,  which  lead  it  to  the  binding  screws, 
from  which  it  passes  into  thd  external  circuit. 

In  a  machine  of  this  kind  which  gives  16  arc  lights  the  ring  is  half  a 
metre  in  diameter,  and  each  of  the  8  coils  contains  275  metres  of  cotton- 
covered  copper  wire  2  mm.  in  diameter,  and  weighing  10  kg.  Each  pair  of 
coils  has  a  resistance  of  ih  ohms,  and  the  electromagnets  have  a  resistance 
of  6  ohms^o  that  the  total  internal  resistance  is  12  ohms. 

In  any  such  machines,  the  strength  of  the  current  which  it  produces  is 
proportional  to  the  strength  of  the  magnetic  field,  and  with  a  given  armature 
to  the  speed  of  rotation,  or  to  the  number  of  lines  of  force  cut  in  a  given 
time  (826)  ;  and  is  inversely  as  the  resistance  of  the  circuit.  The  strength 
of  the  magnetic  field  in  a  magneto  machine  depends  on  the  strength  of  the 
permanent  magnets  which  form  the  field,  and  when  these  are  electromagnets 
and  are  separately  excited,  on  the  strength  of  the  magnets  by  which  they  are 
excited.  With  dynamo  machines  the  strength  of  the  field  magnets  is  a  func- 
tion of  the  current  which  it  itself  produces  in  the  coils  of  the  electromagnet, 
and  the  strength  of  this  current  depends  on  the  resistance  of  the  circuit,  the 
external  part  of  which  is  liable  to  frequent  variations  from  accidental  causes. 
Hence  dynamo  machines  are  more  irregular  in  their  action  than  magneto 
machines,  which  are  therefore  to  be  preferred  where  steadiness  is  required. 
With  both  classes  of  machines  the  most  favourable  results  are  obtained 
with  the  larger  sizes. 

919^?,  Classification  of  dynamo  machines. — The  principal  types  of 
dynamo  machines  arc  depicted  in  figs.  898-901.  Fig.  898  represents  a  machine 
in  which  the  wires  from  a  separate 
machine  excite  the  field  magnets,  and 
this  type  is  known  as  the  separately 
excited  machine  ;  Wild's  machine  (fig. 
886)  is  an  example  of  this  class. 

Fig.  899  represents  the  original 
form  of  the  dynamo  ;  the  current  from 
the  armature  passes  directh-  from  (ine 
brush  into  the  wire  of  the  field  magnet, 
from  thence  into  the  external  circuit, 
returning  to  the  armature  by  the  other 
brush  ;  such  machines  are  said  to  be 
series  wound.  This  mode  of  winding 
has  the  defect  that  variations  or  breaks 
in  the  external  resistance  ha\e  a  much  greater  effect  on  the  current  than  in 
magneto  machines  ;  for  the  E.M.F.  in  these  is  constant  for  a  given  speed  of 
rotation,  and  alterations  in  the  external  resistance  only  affect  the  current  in 
accordance  with  Ohm's  law.  With  the  series  machine  the  E.M.F.  itself 
is  lessened  if  the  external  resistance  is  doubled,  for  instance,  for  a  weaker 
current  now  circulates  in  the  field  magnets,  and  the  magnetic  field  in  which 
the  armature  rotates  is  thereby  \\eaker.  Accordingly  the  current  becomes 
much  less  than  half  what  it  was.  If,  further,  the  current  is  completely  stopped, 
the  field  magnets  almost  entirely  lose  their  magnetism,  and  a  considerable 
time  elapses  before  their  magnetism  is  again  excited.  Complete  stoppages 
also  reverse  the  polarity  of  the  magnets  in  consequence  of  the  production  of 

3  N  2 


Fig.  809. 


gi6 


Dynamical  Electricity. 


[919a- 


Fig.  900. 


Fig.  goi. 


polarisation  currents,  and  accordingly  when  a  steady  current  is  required  as 
in  electroplating,  or  in  charging  an  accumulator  (849),  such  machines  are 
not  used. 

A  third  type  is  that  represented  in  fig.  goo,  and  is  known  as  the  shmit 
wound  dynamo  ;  the  current  at  the  armature  divides  at  B,  one  portion  passes 

through  the  wire  of  the  field  magnet, 
which  is  long  and  thin,  and  the  other 
through  the  external  circuit — for  in- 
stance, an  electroplating  bath.  If  a 
total  break  occurs  in  this  circuit  the 
effect  is  that  a  more  powerful  current 
passes  through  the  field  magnets, 
which  are  thus  again  in  readiness  to 
act  when  the  circuit  is  restored.  An 
increase  in  the  resistance  of  the  ex- 
ternal circuit  has  but  small  effect  ;  for 
if  the  E.M.F.  remained  constant,  the 
current  would  only  diminish  in  accord- 
ance with  Ohm's  law,  and  as  a  rela- 
tively larger  proportion  now  goes  through  the  field  magnets,  the  latter  are 
more  strongly  excited,  and  the  current  again  increased  ;  the  latter  is,  in 
short,  lessened  in  a  smaller  degree  than  that  in  which  the  resistance  is 
increased.  Such  machines  are  used  for  electroplating  and  other  qlectrolytic 
work. 

The  <;^;;//(?z^/;^/ w^?/;/c/ dynamo  is  represented  in  fig.  901.  Consider  one 
wire  as  in  the  ordinary  series  wound  machine,  and  in  addition  to  this  a 
second  long  thin  wire  from  B  passing  round  the  field  magnets  to  the  other 
brush  at  B'.  This  machine  is  used  for  feeding  a  number  of  glow  lamps  which 
are  inserted  in  parallel,  and  for  which  it  is  essential  that  the  difference  of 
potential  is  constant.  If  now  a  number  of  these  lamps  are  removed  the  re- 
sistance in  the  circuit  of  the  stout  wire  is  increased,  and  the  current  would 
be  lessened,  partly  from  Ohm's  law  and  partly  from  the  weaker  magnetism, 
whereby  the  difference  of  potential  would  be  less,  and  possibly  to  such  an 
extent  that  the  lamps  would  not  glow  ;  but  with  the  compound  winding  a 
greater  proportion  of  the  current  now  passes  through  the  thin  wire,  and  thus 
acts  more  strongly  on  the  magnetism.  By  a  suitable  choice  of  the  resistances, 
and  the  relative  number  of  turns  of  the  wires,  the  increase  of  the  magnetisation 
can  be  made  so  great  that  the  diminution  in  the  difference  of  potential  is 
thereby  compensated. 

920.  Applications  of  magrneto  and  dynamo-electrical  macbines. — 
Magneto-electrical  machines  with  lonstant  currents  arc  a  triumph  of  modern 
times;  from  their  discovery,  together  with  that  of  the  dynamo  principle  (946), 
is  dated  the  introduction  of  electricity  for  industrial  purposes.  Great  improve- 
ments have  of  late  been  made  in  magneto-electrical  machines,  both  in  the 
economy  and  simplicity  of  their  construction,  and  also  in  their  power  ;  for 
details  on  these  matters  we  must  refer  to  special  technical  works. 

The  energy  of  any  electrical  current  or  |)ortion  of  an  electrical  current  is 
measured  by  the  product  of  the  electromotive  force,  E,  or  difference  of  poten- 
tials at  the  ends  of  the  portion  considered,  into  the  strength  of  the  current 


-920J         Applications  of  Dynamo-electrical  lilacJiines.  917 

itself.  The  magnitude  represented  by  an  electromotive  force  of  a  volt,  V, 
multiplied  by  a  current  strength  of  an  ampere,  A,  is  called  a  volt-ampere^ 
and  from  its  great  practical  utility  has  got  a  special  name,  that  of  Watt 
(964).  A  volt-ampere  is  equivalent  to  a  watt,  but  the  two  are  not  identical  ; 
the  former  is  the  measure  of  the  electrical,  and  the  latter  of  the  mechanical 
effect  which  can  result  from  the  electrical,  that  is,  can  be  transformed  into  it. 
A  horse-power  is  equal  to  746  watts,  or  a  watt  is  0-0134  of  a  horse-power. 
Hence,  if  we  know  the  number  of  watts  produced  in  any  circuit,  this  divided 
by  746  gives  at  once  the  equivalent  in  horse-power.  The  kilowatt  is  the 
Board  of  Trade  unit  of  electrical  energy  ;  it  is  1000  watts  or  i^  horse-power. 

A  magneto-electrical  machine  may  be  compared  to  a  pump  forcing  water 
through  a  pipe  against  friction  ;  the  electrical  current  corresponds  to  the 
volume  of  water  passing  in  a  second,  and  the  electromotive  force  corresponds 
to  the  difference  in  pressure  on  the  two  sides  of  the  pump.  Just  as  the 
power  of  a  pump  is  measured  by  the  product  of  the  pressure,  and  volume  of 
water  per  second,  so  the  product  of  the  electromotive  force  and  current  is 
power,  and  the  ratio  of  this  power  to  the  mechanical  power  expended  in 
driving  the  magneto-electrical  machine  is  the  efficie?icy  of  the  magneto- 
electrical  machine.  The  peculiarity  of  the  dynamo-electrical  machine  is 
this,  that  the  electromotive  force,  or  the  element  corresponding  to  difference 
of  pressure  in  the  case  of  a  pump,  depends  directly  on  the  current  passing. 
It  does  not  increase  indefinitely  with  increase  of  current,  but  increases  to  a 
certain  limit,  and  then  remains  constant. 

Dr.  Hopkinson  made  a  series  of  experiments  with  a  machine  of  Siemens' 
construction,  where  special  arrangements  were  made  for  determining  the 
speed  at  which  the  machine  was  driven,  the  driving  power,  the  resistances 
in  the  circuit,  and  the  difference  in  potential  between  the  two  ends  of  a  known 
resistance  in  the  circuit.  He  thus  found  that  to  drive  the  machine  in  open 
circuit  at  a  speed  of  720  rotations  required  an  expenditure  of  0-28  horse- 
power. Exclusive  of  friction,  the  efficiency  of  the  machine  was  found  to  be 
about  90  per  cent.,  so  that  in  this  respect  little  improvement  can  be  expected. 

If  the  relation  between  the  electromotive  force  measured  in  volts  (814), 
and  the  strength  of  the  current  measured  in  amperes  (814),  for  a  given  speed 
of  rotation  be  expressed  by  a  curve,  it  is  found  that  this  curve  has  the  form 
of  a  slanting  straight  line  starting  from  the  origin,  and  then  begins  to  bend 
away,  approaching  a  horizontal  line.  The  point  at  which  it  begins  to  bend 
away  is  when  the  electromotive  force  is  about  two-thirds  of  its  maximum, 
and  this  is  called  by  Hopkinson  the  criticat  current  :  it  has  this  physical 
meaning,  that  below  this  point  any  change  in  the  speed  of  rotation,  with  a 
steady  external  resistance,  or  any  change  in  the  external  resistance,  with  a 
constant  speed  of  rotation,  produces  considerable  changes  in  the  current. 

The  principal  application  which  has  been  made  of  the  currents  produced 
by  dynamo  machines  is  to  the  production  of  the  electrical  light  (837).  In 
this  respect  it  may  be  said  that  the  arrangements  for  producing  the  electricity 
are  more  perfect  than  those  for  producing  the  light ;  for  while  over  90  per 
cent,  of  the  mechanical  power  used  appears  in  the  form  of  current,  only  about 
half  of  that  which  is  transmitted  to  the  machine  appears  in  the  electrical  arc. 

For  electrodes  of  a  definite  material,  kept  at  a  definite  distance  apart, 
and  under  the  ordinary  atmospheric  pressure,  the  difference  of  potential  is 


91 8  Dynamical  Electricity.  [920- 

approximatcly  constant  tor  a  constant  speed  of  rotation.  The  product  of 
difference  of  potential  into  the  current  passing,  is  the  work  developed  in  the 
arc,  and  the  ratio  of  this,  to  the  mechanical  power  expended  in  driving  the 
machine,  is  the  efficiency  of  tJte  electrical  arc. 

Comparing  together  the  relative  costs  of  producing  a  certain  degree  of 
illumination— ci;,  by  means  of  gas  ;  b.,  by  the  electrical  arc  with  alternating- 
currents  ;  c,  by  one  with  continuous  currents,  the  machines  for  the  production 
of  the  last  two  being  worked  by  a  gas  engine — it  was  found  that  the  ratio 
was  as  ii6  :  62  :  15  ;  when  the  machine  was  heated  by  coal  instead  of  gas 
the  cost  was  as  116  :  50  :  10,  it  being  assumed  that  four  pounds  of  coal  pro- 
duced one  horse-power  per  hour.  The  actual  cost  of  lighting  the  British 
Museum  with  a  light  representing  18,800  candles  was  six  shillings  an  hour, 
of  which  the  carbons  cost  nearly  one-half. 

Hopkinson  gives  the  following  illustration  of  the  luminous  effect  produced 
by  converting  energy  into  heat  in  a  closed  space.  One  hundred  and  twenty 
feet  of  what  is  called  15-candle  gas  (509)  produce  a  light  of  360  standard  candles 
for  an  hour.  The  heat  produced  in  this  combustion  is  equivalent  to  about  60 
millions  of  foot-pounds  (484).  If  this  gas  be  burned  in  a  gas-engine  (476)  about 
8  million  foot-pounds  of  work  will  be  done  outside  the  engine,  or  4  horse- 
power for  an  hour  (472).  This  power  is  sufficient  to  drive  an  A  Gramme 
machine  for  an  hour  ;  the  amount  of  energy  which  is  converted  into  current 
is  6,400,000  foot-pounds,  of  which  about  one-half,  or  3,200,000,  appear  in  the 
form  of  energy  in  the  electric  arc.  Viewed  horizontally  this  radiates  a  light 
of  2,000  candles,  and  two  or  three  times  as  much  when  viewed  from  below. 
Hence  about  3  million  foot-pounds  changed  into  heat  in  the  electric  arc  will 
affect  our  eyes  six  times  as  powerfully  as  60  millions  changed  into  heat  in  a 
gas  burner. 

Both  for  arc  and  incandescent  lamps  the  relative  efficiency  is  greater  the 
higher  the  illuminating  power.  Thus  with  ;i  Swan  lamp  of  16  candles  the 
work  required  for  each  candle-power  is  272  candles  for  a  horse-power,  or 
about  2^^  watts,  while  with  a  32-canclle  lamp  the  number  of  candles  equiva- 
lent to  a  horse-power  is  415. 

Although  the  temperature  of  the  electric  arc  is  exceedingly  high'(838),  yet 
from  the  small  amount  of  racHating  surface  the  heating  effect  is  far  less  than 
that  produced  by  other  sources  of  equal  illumination.  Thus  Siemens  found 
that  an  electric  arc  light  of  4,000  candles  radiated  142-5  thermal  units  in  a 
minute,  while  to  produce  this  light  by  gas  would  require  200  Argand  burners, 
•which  would  emit  15,000  units,  or  over  a  hundred  times  as  much.  So  too  it 
has  been  found  that  incandescent  lamps  produce  less  than  five  per  cent,  of 
the  heat  from  other  sources  of  equal  intensity  as  regards  this  light. 

Siemens  made  a  series  of  experiments  on  the  influence  of  the  electrical 
light  on  vegetation.  The  light  was  produced  by  a  dynamo-electrical  machine 
of  his  construction,  and  was  equal  in  illuminating  powcrto  1,400  candles.  Of 
a  series  of  four  sets  of  quickly  growing  plants  in  pots,  one  set  was  left  in  the 
dark,  and  two  other  sets  were  exposed  to  the  action  of  the  daylight  and  of 
the  electric  light  separately;  while  the  fourth  was  exposed  to  the  joint  action 
of  the  two  lights.  The  first  set  sowed  withered  and  died  ;  those  exposed  to  . 
the  electric  light  grew  and  flourished,  but  not  so  vigorously  as  those  exposecf 
to  daylight  alone  ;  those,  however,  which  had  been  exposed  to  the  conjoint 


-920]  Applications  of  Dynamo  Machines.  gig 

action  of  both  lights,  showed  the  most  vigorous  growth.  Plants  did  not 
seem  to  require  a  period  of  repose,  but  made  increased  and  vigorous  pro- 
gress if  subjected  at  daytime  to  sunlight,  and  by  night  to  the  electric  light. 

The  electric  light  was  also  found  beneficial  in  promoting  the  formation  of 
aromatic  and  saccharine  substances  on  which  the  ripening  of  fruits  depends. 

Abney  found  that  the  luminosity  and  also  thj  actinic  action  of  the  light 
produced  by  the  electric  arc  increased  more  rapidly  than  in  direct  ratio  to 
the  velocity  of  rotation,  and  the  horse-power  required  to  produce  it.  This 
increase  was  slowest  for  red  light,  more  rapid  with  blue,  and  most  rapid 
of  all  with  tlie  actinic  action.  With  a  speed  of  565  rotations,  and  an  ex- 
penditure of  9  horse-power,  the  actinic  action  was  equal  to  that  of  1 1,000 
candles. 

Cohn  f  )und  that  the  electrical  light  is  more  favourable  for  the  pure  per- 
ception of  colour  than  any  other  light  of  equal  luminosity. 

Electrical  furnace. — It  is  probable  that  the  temperature  which  can  be 
produced  by  the  oxyhydrogen  flame  is  limited  and  has  been  already  reached, 
ani  that  we  must  look  to  the  electrical  arc  for  the  production  of  higher 
temperatures  than  those  at  which  carbonic  acid  and  water  are  decomposed.^ 
Direct  experiments  by  Siemens  with  the  electric  arc  show  not  only  that  it 
produces  a  very  high  temperature  withm  a  contracted  space,  but  also  that 
it  will  conveniently  and  economically  produce  such  larger  effects  as  will 
render  it  useful  for  many  purposes  in  the  arts,  like  the  fusion  of  platinum 
and  steel.  He  constructed  an  arrangement  by  which  the  electric  arc  was, 
formed  within  a  crucible  made  of  the  most  refractory  materials  ;  the  one 
electrode  passed  through  the  bottom  of  the  crucible  and  the  other  through 
the  lid,  and  there  was  an  arrangement  by  which  the  distance  of  the  elec- 
trodes could  be  automatically  regulated  ;  another  important  point  was  to 
constitute  the  positive  pole  of  the  material  to  be  fused,  as  it  is  at  this  pole 
that  the  heat  is  principally  developed,  the  arrangement  formed  in  short  an 
electrical  furnace.  A  dynamo  machine  capable  of  producing  a  current  of 
36  amperes,  and  which  produces  a  light  equal  to  6,000  candles,  fused  a 
kilogramme  of  steel  within  half  an  hour.  vSiemens  calcu  ated  that  the  heat 
in  his  furnace  represented  J  of  the  horse-power  expende.l  in  working  the 
machine  ;  and  as  a  good  engine  onl-/  utilises  about  ,'.  of  the  combustible 
value  of  the  coal  employed  m  working  it,  it  follows  that  the  electrical 
furnace  utilises  l^  of  the  energy  residing  in  the  fuel  under  the  engine.  The 
electrical  furnace  is  theoretically  more  economical  than  the  ordinary  air 
furnaces.  Not  only  is  the  furnace  thus  a  source  of  intense  heat,  but  in 
certain  operations  the  reducing  action  of  the  electrodes  plays  an  important 
part,  as  in  Cowle's  method  for  the  direct  production  of  aluminum  bronze. 
A  charge  of  35  kgr.  powdered  corundum,  an  aluminous  mineral  mixed  with 
powdered  charcoal  and  twice  its  weight  of  granulated  copper,  was  placed 
between  carbon  electrodes  in  a  suitable  vessel.  On  passing  a  powerful 
current  the  alumina  was  reduced  and  united  directly  with  the  copper  to 
form  aluminum  bronze.  The  current  actually  employed  was  one  of  5,000 
amperes  with  an  E.M.F.  of  50  volts,  or  with  a  power  of  500,000  watts- 
second.  The  current  was  continued  for  an  hour  and  a  half,  and  produced 
about  82  kgr.  of  the  alloy.  Each  kgr.  of  akiminum  in  the  alloy  represents 
a  work  of  44  horse-power  for  an  hnir. 


920  Dynamical  Electricity.  [920a- 

920(?.  Electrical  transmission  of  power. — When  a  magneto  or  dynamo 
machine  is  couple  1  up  with  a  second  one,  on  working  the  first  the  second 
is  put  in  rotation,  and  in  a  direction  opposed  to  that  of  the  first.  Two  such 
machines  coupled  in  this  way  are  called  Xho^  generator  and  the  motor.  This 
motor  may  be  geared  up  with  any  machine,  such  as  a  saw  wheel,  a  lathe,  or 
a  pump,  which  is  thereby  made  to  do  its  special  work.  On  this  depends 
the  possibility  of  transmitting  by  electricity  to  great  distances  power  from  a 
common  centre,  and  of  thereby  utilising  natural  sources  of  power,  such  as 
waterfalls,  windmills,  and  the  like. 

The  efficiency  of  any  magneto  machine,  as  we  have  seen,  is  the  ratio  of 
the  energy  7v'  developed  in  the  machine  to  the  mechanical  power  w,  expended 
in  producing  it.  Apart  from  friction,  more  than  90  per  cent,  of  the  power 
can  be  thus  converted  ;  if  such  a  machine  works  on  short  circuit  the  whole 
of  this  energy  would  appear  as  heat ;  when  external  work  is  done,  such  as  in 
producing  the  electric  light,  the  energy  is  shared  between  the  various  parts  of 
the  circuit,  and  the  amount  of  this  energy  in  any  part  can  be  easily  obtained 
if  we  know  the  fall  of  potential  between  the  part  in  question  and  the  current 
wiiich  is  passing. 

When  a  motor  is  connected  with  a  generator  at  work,  the  former  is  set 
in  motion,  and  in  a  direction  opposed  to  that  of  the  generator  ;  it  thereby 
developes  an  electromotive  force  expressed  in  volts  of  v,  opposed  to  that  of 

VA 
the  (generator  V.     The  total  work  W  of  the  venerator  in  unit  time  is 

746 

horse-power.     Part  of  this  work  appeals  in  the  heating  of  the  conducting 

vA. 
wires,  and  the  rest  in  the  form  of  the  energy  of  the  motor  w,  which  is 

746 

h.p.,  where  t>  is  the  difference  of  potentials   at   the  two  terminals  of  the 

machine.      The    ratio  ^-'  =  ^,  that  is,  the  work  of  the    motor,  is  to  that  of 

W     V 
tlie  generator  in  the  ratio  of  their  electromotive  forces,  in  other  words,  to 
the  differences  of  potentials  at  the  respective  terminals.      In  practice  the  best 
conditio  1  of  working  is  to  arrange  so  that  the  generator  has  twice  the  electro- 
motive force  of  the  motor,  the  current  being,  of  course,  the  same  in  each. 

In  some  experiments  as  much  as  4.}  horse-power  has  been  electrically 
transmitted  through  eight  miles  of  an  ordinary  galvanised  iron  telegraph  line 
4  mm.  in  diameter,  and  with  an  efficiency  of  o\er  30  per  cent,  of  the 
mechanical  power  employed. 

The  magneto-electrical  machine  has  been  applied  to  propelling  car- 
riages along  a  railway.  A  narrow-gauge  railway  was  laid  down,  and  upon 
this  a  train  of  three  or  four  carriages  was  laid,  and  on  the  first  of  these 
a  medium-sized  dynamo  machine,  so  fixed  and  connected  with  the  axle  of 
one  pair  of  wheels  as  to  give  motion  to  the  same.  The  two  rails,  being  laid 
ujjon  wooden  sleepeis,  were  sufficiently  insulated  to  serve  for  electrical  con- 
du(  tors.  Between  the  two  rails  a  bar  of  iron  was  fixed  on  wooden  supports, 
through  which  the  current  was  conveyed  to  the  train  by  brushes  fixed  to  the 
di  i\  ing  carriage,  while  the  return  circuit  was  completed  through  the  rails. 
At  the  station  the  centre  bar  and  rails  were  electrically  connected  with  ' 
liie  poles  of  a  dynamo  machine  like  that  on  the  carriage,  and  which  was 
worked  from  a  fixed  steam-engine  on  the  ground.     The  magneto  machine 


-921] 


Inductorium.     RuJinikorff' s  Coil. 


921 

exerted  5  horse-power,  and  it  travelled  with  a  velocity  of  15  to  20  miles 
an  hour. 

Another  application  is  to  what  is  called  tclpJicragc.  by  which  is  meant 
a  means  of  propelling-  light  carriages  or  buckets  along  a  single  metal  rope 
or  rod,  supported  on  posts  at  some  height  above  the  ground.  A  working- 
line  has  been  already  constructed  and  used  with  success,  and  this  method  of 
electrical  haulage  will  probabl)-  be  of  great  service  in  con\eying  minerals  in 
mountainous  countries,  from  the  facility  with  which  it  can  be  constructed  on 
uneven  ground,  and  particularly  in  those  cases  in  which  water  supply  is 
available. 

921.  Inductorium.  RubrnkorfTs  coil. — These  are  arrangements  for 
producing-  induced  currents,  in  which  a  current  is  induced  by  the  action  of 
an  electric  current,  whose  circuit  is  alternately  opened  and  closed  in  rapid 
succession.  These  instruments,  known  as  mductoriutns,  or  induction  coils, 
present  considerable  variety  in  their  construction,  but  all  consist  essentially 
of  a  hollow  cylinder  in  which  is  a  bar  of  soft  iron,  or  bundle  of  iron  wires, 
with  two  helices  coiled  round  it,  one  connected  with  the  poles  of  a  battery, 
the  current  of  which  is  alternatelj'  opened  and  closed  by  a  self-acting  arrange- 
ment, and  the  other  serving  for  the  development  of  the  induced  current.  By 
means  of  these  apparatus,  and  with  a  current  of  three  or  four  Grove's  cells, 
physical,  chemical,  and  physiological  effects  are  produced  equal  and  superior 
to  those  obtainable  with  electrical  machines  and  even  the  most  powerful 
Leyden  batteries. 

Of  all  the  forms  those  constructed  by  Ruhmkorff  are  the  most  powerful. 
Fig.  902  is  a  representation  of  one,  the  coil  of  which  is  about  14  inches  in 


P'ig.  902. 

length.  The  pritnary  or  inducing  wire  is  of  copper,  and  is  about  2  mm.  in 
diameter,  and  40  or  50  yards  in  length.  It  is  coiled  directly  on  a  cylinder  of 
cardboard  which  forms  the  nucleus  of  the  apparatus,  and  is  enclosed  in  an 
insulating  cylinder  of  glass,  or  of  caoutchouc.  On  these  is  coiled  the  sccondaiy 
or  induced  wire,  which  is  also  of  copper,  and  is  about  \  mm.  in  diameter. 
.\  great  point  in  these  apparatus  is  the  insulation.  The  wires  are  not  merely 
insulated  by  being  in  the  first  case  covered  with  silk,  but  each  individual 
coil  is  separated  from  the  rest  by  a  layer  of  melted  shellac.  The  length  of 
the  secondary  wire  varies  greatly  ;  in  the  largest  size  hitherto  made,  that  of 
the  late  Mr.  Spottiswoode,  it  is  as  much  as  280  miles,  while  the  primary  was 


922 


Dynamical  Electricity. 


[921- 


II 64  yards.  With  these  great  lengths  the  wire  is  thinner,  about  \  mm. 
The  thinner  and  longer  the  wire  the  higher  the  potential  of  the  induced 
electricity. 

The  following  is  the  working  of  the  apparatus  :— The  current  arriving  by 
the  wire  P  at  a  binding  screw,  «,  passes  thence  in  the  commutator  C,  to  be 
afterwards  described  (fig.  905),  thence  by  the  binding  screw  b  it  enters  the 
primary  wire,  where  it  acts  inductively  on  the  secondary  wire  ;  having  tra- 
versed the  primary  wire,  it  emerges  by  the  wire  s  (fig.  903).  Following  the 
direction  of  the  arrows,  it  will  be  seen  that  the  current  ascends  in  the 
binding  screw  z,  reaches  an  oscillating  piece  of  iron,  <?,  called  the  hnmtiier, 
descends  by  the  anvil  h,  and  passes  into  a  copper  plate,  K,  which  takes  it 
to  the  commutator  C.  It  goes  from  there  to  the  binding  screw  c,  and  finally 
to  the  negative  pole  of  the  battery  by  the  wire  N. 

The  current  in  the  primary  wire  only  acts  inductively  on  the  secondary 
wire  (901),  when  it  opens  or  closes,  and  hence  must  be  constantly  in- 
terrupted. This  is  effected  by  means  of  the  oscillating  hammer  o  (fig.  903). 
In  the  centre  of  the  bobbin  is  a  bundle  of  soft  iron  wires,  forming  together  a 
cylinder  a  little  longer  than  the  bobbin,  and  thus  projecting  at  the  end  as 
seen  at  A.  When  the  current  passes  in  the  primary  wire  this  hammer,  o, 
is  attracted  ;  but  immediately,  there  being  no  contact  between  o  and  h,  the 
current  is  broken,  the  magnetisation  ceases,  and  the  hammer  falls  ;  the 
current  again  passing,  the  same  series  of  phenomena  recommences,  so  that 
the  hammer  oscillates  with  great  rapidity. 

922.  Condenser. — In  proportion  as  the  current  passes  thus  intermittently 
in  the  primary  wire  of  the  bobbin,  an  induced  current,  alternately  direct 

and  inverse,  is  produced  at  each 
interruption  in  the  secondary  wire. 
But  as  this  is  perfectly  insulated, 
the  induced  current  requires  such  a 
strength  as  to  produce  very  power- 
ful effects.  Fizeau  increased  this 
strength  still  more  by  interposing 
a  condenser  in  the  primary  circuit. 
This  condenser  (fig.  904)  con- 
sists of  sheets  of  tinfoil  placed  over 
each  other  and  insulated  by  larger 
slieets  of  stout  paper,  7/,  soaked  in 
paraffinc  or  resin.  The  sheets  of 
tinfoil  project  at  the  end  of  the 
paper,  one  set  at  j  s'  s'\  and  the  other  at  the  other  end,  at  e  e'  e",  so  that 
when  joined  by  a  binding-  screw  the  odd  numbers  form  one  coating  of  a 
condenser,  and  the  even  numbers  the  other  coating.  In  large  condensers, 
tlic  surface  of  each  condenser  is  as  much  as  75  square  yards.  The  whole 
Ixing  placed  in  a  box  at  the  base  of  the  apparatus,  one  of  the  coatings, 
the  positive,  is  connected  with  the  binding  screw  z,  which  receives  the 
current  on  emerging  from  the  bobbin  ;  and  the  other,  the  negative,  is  con- 
nected with  the  binding  screw  w,  which  communicates  by  the  plate  K  with 
the  commutator  C,  and  with  the  battery. 

To  understand  the  effect  of  the  condenser,  it  must  Ijc  observed  that  at 


Fig.  903. 


Fig.  904. 


-923]  Condenser  of  Rulimkorff's  Coil.     '  923 

each  break  of  the  inducing  current  an  extra  current  is  produced  in  the  same 

direction,  which,  continuing  in  a  certain  manner,  prolongs  its  duration.     It 

is  this  extra  current  which  produces  the  spark  that  passes  at  each  break 

between  the  hammer  and  the  anvil  ;  when  the  current  is  strong  this  spark 

rapidly  alters  the  surface   of  the  hammer  and  an\il,  though   they  are  of 

platinum.       By     interposing 

the  condenser  in  the  inducing  /~ 

circuit,  the  extra  current,  in-  ^  ^I 

stead  of  producing  so  strong 

a    spark,    passes     into    the  ,  _     _ 

condenser  —  the       positive    s^^     ~  -- 

electricity    in     the     coating  « ^0^ 

connected   with   /,    and    the 

negative    in  that   connected 

with  ;//.     But  the  opposite  electricities  combining  quickly  by  the  thick  wire  of 

the  primary  coil,  by  the  battery,  and  the  circuit  C  K  ?n,  give  rise  to  a  current 

contrary  to  that  of  the  battery,  which  instantaneously  demagnetises  the 

bundle  of  soft  iron  :  the  induced  current  is  thus  shorter  and  more  intense. 

The  binding  screws  m  and  ??  on  the  base  of  the  apparatus  are  for  receiving 

this  extra  current. 

The  commutator  or  key  serv^es  to  break  contact  or  send  the  current  in 
either  direction.  The  section  in  fig.  905  is  entirely  of  brass,  excepting  the 
core.  A,  which  is  of  ebonite  :  on  the  two  sides  are  two  brass  plates,  C  C. 
Against  these  press  two  elastic  brass  springs,  joined  to  two  binding  screws, 
a  and  c,  with  which  are  also  connected  the  electrodes  of  the  battery.  The 
current  arriving  at  a  rises  in  C,  thence  by  a 
screw,  _y,  it  reaches  the  binding  screw  b  and  the 
bobbin  :  then  returning  by  the  plate  K,  which 
is  connected  with  the  hammer,  the  current  goes 
to  C  by  the  screw  x,  descends  to  c,  and  rejoins 
the  battery  by  the  wire  N.  If,  by  means  of  the 
milled  head,  the  key  is  turned  180  degrees,  it 
is  easy  to  see  that  exactly  the  opposite  takes 
place  ;  the  current  reaches  the  hammer  by  the 
plate  K  and  emerges  at  b.     If,  lastly,  it  is  only 

turned  through  90  degrees,  the  elastic  plates        ■"  . :-!a JSjJiM'^ 

rest  on  the  ebonite  A  instead  of  on  the  plate  Fig.  905. 

C  C,  and  the  current  is  broken. 

The  two  wires  from  the  bobbin  at  0  and  o'  (fig.  902)  are  the  two  ends  of 
the  secondary  wire.  They  are  connected  with  the  thicker  wires  P  P',  so 
that  the  current  can  be  sent  in  any  desired  direction.  With  large  coils  the 
hammer  cannot  be  used,  for  the  surfaces  become  so  much  heated  as  to  melt. 
But  P'oucault  invented  a  mercury  contact-breaker  which  is  free  from  this 
inconvenience,  and  which  is  an  important  improvement.  Very  powerful 
discharges  were  obtained  by  Spottiswoode  from  his  coil  by  disconnecting 
the  contact-breaker  and  sending  into  it  the  alternate  currents  of  a  powerful 
magneto-machine. 

923.  Efifects  produced  by  Ruhinkor£°'s  coil. — The  high  potential  of 
the  electricity  of  induction  coils  has  long  been  known,  and  many  luminous 


924  '  Dynamical  Electricity.  [923- 

and  heating  effects  have  been  obtained  by  their  means.  But  it  is  only 
since  the  improvements  which  Ruhmkorff  introduced  into  his  coil,  that 
it  has  been  possible  to  utilise  all  the  potential  of  induced  currents,  and  to 
show  that  these  currents  possess  po\verful  statical  as  well  as  dynamical 
properties. 

Induced  currents  are  produced  in  the  coil  at  each  opening  and  breaking 
of  contact.  But  these  currents  are  not  equal  either  in  duration  or  in 
potential.  The  direct  current,  or  that  on  opening,  is  of  shorter  duration,  but 
higher  potential  ;  that  of  closing  of  longer  duration,  but  lower  potential. 
Hence  if  the  two  ends  P  and  P'  of  the  fine  wire  (figs.  902  and  903)  are  con- 
nected, as  there  are  two  equal  and  contrary  quantities  of  electricity  in  the 
wire  the  two  currents  neutralise  each  other.  If  a  galvanometer  is  placed  in 
the  circuit,  only  a  very  feeble  deflection  is  produced  in  the  direction  of  the 
direct  current.  This  is  not  the  case  if  the  two  ends  P  and  P'  of  the  wire  are 
separated.  As  the  resistance  of  the  air  is  then  opposed  to  the  passage  of  the 
currents,  that  which  has  highest  potential — that  is,  the  direct  one  or  that  on 
opening — passes  in  excess,  and  the  more  so  the  greater  the  distance  of  P 
and  P'  up  to  a  certain  limit  at  which  neither  passes.  There  are  then  at  P 
and  P'  nothing  but  potentials  which  are  alternately  contrary. 

A  striking  distance  of  i  mm.  (788)  corresponds  to  an  electromotive  force 
of  5,490  volts,  and  the  striking  distance  of  I  inch  which  is  furnished  by  even 
a  small  machine  represents  a  potential  of  over  70,000  volts.  How  enormous 
must  then  be  the  potential  of  Spottiswoode's  larger  machine. 

The  physiological  effects  of  Ruhmkorff's  coil  are  very  powerful ;  in  fact, 
shocks  are  so  violent  that  many  experimenters  have  been  suddenly  pros- 
trated by  them.  A  rabbit  may  be  killed  with  two  of  Bunsen's  elements,  and 
a  somewhat  larger  number  of  couples  would  kill  a  man. 

The  heating  effects  are  also  easily  observed  ;  an  air  thermometer  is 
heated  by  the  alternating  currents  ;  if  a  veiy  fine  iron  wire  is  interposed 
between  the  two  ends  P  and  P'  of  the  induced  wire,  this  iron  wire  is  imme- 
diately melted,  and  burns  with  a  bright  light.  A  curious  phenomenon  may 
here  be  observed,  namely,  that  when  each  of  the  wires  P  and  P'  terminates 
in  a  very  fine  iron  wire,  and  these  two  are  brought  near  each  other,  the  wire 
corresponding  to  the  negative  pole  alone  melts,  showing  that  its  temperature 
is  higher. 

The  chemical  effects  are  very  varied  ;  thus,  according  to  the  shape  and 
distance  of  the  platinum  electrodes  immersed  in  water,  and  to  the  degree  of 
acidulation  of  the  water,  either  luminous  effects  may  be  produced  in  water 
without  decomposition,  or  the  water  may  be  decomposed  and  the  mixed 
gases  disengaged  at  the  two  poles,  or  the  decomposition  may  take  place,  and 
the  mixed  gases  separate  either  at  a  single  pole  or  at  both  poles. 

Gases  may  also  be  decomposed  or  combined  by  the  continued  action  of 
llie  spark  from  the  coil.  If  the  current  of  a  Ruhmkorff's  coil  be  passed 
through  an  hermetically  sealed  tube  containing  air,  as  shown  in  fig.  906, 
nitrogen  and  oxygen  combine  to  form  nitrous  acid. 

The  luminotts  effects  of  Ruhmkorff's  coil  are  also  \cry  remarkable,  and 
vary  according  as  they  take  place  in  air,  in  vapour,  or  m  very  rarefied 
vapours.  In  air  the  coil  produces  a  very  bright  loud  spark,  which,  with  the 
largest  sized  coil  hitherto  made,  that  of  Mr.  Spottiswoodc,  has  a  length  of  42 


Effects  produced  by  Ruhmkorff's  Coi\. 


-923]  njjects  produced  Oy  Kunmkorff's  Loi..  925 

inches.  In  vacuo  the  effects  are  also  remarkable.  The  experiment  is  made 
by  connecting  the  two  wires  of  the  coil  P  and  P'  with  the  two  rods  of  the 
electric  ^^-g  (fig.  722)  used  for  producing  in  vacuo  the 
luminous  effects  of  the  electrical  machine.  Exhaustion 
having  been  produced  up  to  i  or  2  mm.,  a  beautiful 
luminous  trail  is  produced  from  one  knob  to  the  other, 
which  is  virtually  constant,  and  has  the  same  intensity 
as  that  obtained  with  a  powerful  electrical  machine  when 
the  plate  is  rapidly  turned.  This  experiment  is  shown 
in  figs.  911  and  912.  Fig.  910  represents  a  remarkable 
•deviation  which  light  undergoes  when  the  hand  is  pre- 
sented to  the  &gg. 

The  positive  pole  of  the  current  shows  the  greatest 
brilliancy  ;  its  light  is  of  a  fiery  red,  while  that  of  the 
negative  pole  is  of  a  feeble  violet  colour  ;  moreover,  the 
latter  extends  along  all  the  length  of  the  negative  rod, 
which  is  not  the  case  with  the  positive  pole. 

The  coil  also  produces  mechanical  effects  so  powerful  that,  with  the  largest 
apparatus,  glass  plates  two  inches  thick  have  been  perforated.  This  result, 
however,  is  not  obtained  by  a  single  charge,  but  by  several  successive  charges. 

The  experiment  is  arranged  as  shown  in  fig.  907.  The  two  poles  of  the 
induced  current  correspond  to  the  binding  screws  a  and  b  ;  by  means  of  a 


Fig.  go6. 


Fig.  907. 

copper  wire,  the  pole  a  is  connected  with  the  lower  part  of  an  apparatus  for 
piercing  glass  like  that  already  described  (fig.  728)  ;  the  other  pole  is  attached 
to  the  other  conductor  by  a  wire,  d.  The  latter  is  insulated  in  a  large 
glass  tube,  r,  filled  with  shellac,  which  is  run  in  while  in  a  state  of  fusion. 
Between  the  two  conductors  is  the  glass  to  be  perforated,  V.  When  this 
presents  too  great  a  resistance,  there  is  danger  lest  the  spark  pass  in  the  coil 
itself,  perforating  the  insulating  layers  which  separate  the  wires,  and  then 
the  coil  is  destroyed.  To  avoid  this,  two  wires,  e  and  r,  connect  the  poles  of 
the  coil  with  two  metallic  rods  whose  distance  from  each  other  can  be  regu- 
lated. If  then  the  spark  cannot  penetrate  through  the  glass,  it  strikes  across, 
and  the  coil  is  not  injured. 


926 


Dyn  a  in  ical  Ekctricit) ' 


[923 


The  coil  can  also  be  used  to  charge  Leyden  jars.      With  a  large  coil 
giving  sparks  of  6  to  8  inches,  and  using  6  Bunsen's  elements  with  a  large 


Fig.  908. 

surface   Ruhmkorff  charged  large  batteries  of  6  jars  each,  having  about  3 
square  yards  of  coated  surface. 

The  experiment  with  a  single  Leyden  jar  (fig.  908)  is  made  as  follows  : — 
The  coatings  of  the  latter  are  in  connection  with  the  poles  of  the  coil  by 
the  wires  d  and  /,  and  these  same  poles  are  also  connected,  by  means  of 
tlie  wires  e  and  c,  with  the  two  horizontal  rods  of  a  universal  discharger 


(fig.  713).  Tlie  jar  is  then  being  constantly  charged  l)y  tlic  wires  /  and  c/, 
sometimes  in  one  direction  and  sometimes  in  another,  and  as  constantly 
discharged  by  the  wires  c  and  c  ;  the  discharges  from  »i  to  //  taking  place  as 
sparks  two  or  three  inches  in  length,  very  luminous,  and  producing  a  deafen- 
ing sound  ;  they  can  scarcely  be  compared  with  the  sparks  of  the  electrical 
machine,  but  are  rather  true  lightning  flashes. 

To  charge  a  battery,  the  form  of  tlic  experiment  is  somewhat  varied,  the 
outer  coating  being  connected  with  one  pole  of  the  coil  by  the  wire  d,  and 


-924]  Stratification  of  the  Electric  Light.  927 

the  inner  coating  with  the  other  by  the  rods  in  n,  and  the  wire  c  (fig-.  909). 
The  rods  in  and  ;/  are  not,  however,  in  contact.  If  they  were — as  the  two 
currents,  the  inverse  and  direct,  pass  equally — the  battery  would  not  be 
constantly  charged  and  discharged  ;  while  from  the  distance  between  m  and 
;/  the  direct  current,  that  of  breaking,  which  has  higher  potential,  passes 
alone,  and  it  is  this  which  charges  the  battery. 

923  u.  Transformers. — Ruhmkorff's  coil,  as  we  have  seen,  is  an  arrange- 
ment by  means  of  which  we  can  transform  electricity  of  low  into  electricity 
of  high  potential.  There  is  no  creation  of  electricity  ;  the  energy  produced 
in  the  secondary  circuit  is  produced  at  the  cost  of  that  in  the  primary.  The 
apparatus  acts  in  short  as  a  transformer.,  and  it  is  reversible,  for  if  we  connect 
the  long''  thin  wire  with  a  source  of  electricity  yielding  alternating  discharges 
at  high  potential,  we  get  alternating  discharges  in  the  short  thick  wire  of  low 
potential  but  of  much  stronger  current.  The  functions  of  the  wires  are  re- 
versed in  this  case  ;  the  thin  long  wire  is  the  primary  and  the  short  thick 
wire  the  secondary. 

This  modification  of  the  principle  of  Ruhmkorff's  coil  is  of  great  practical 
importance  in  the  transmission  of  electrical  energy,  as  is  illustrated  by  the 
following  example.  Suppose  we  have  a  source  of  energy  available  of  50,000 
watts,  for  example,  and  that  this  is  to  be  transmitted  to  a  certain  distance 
in  the  form  of  electrical  energy  there  to  be  utilised.  Since  a  watt  is  the 
])roduct  of  two  factors,  a  volt  into  an  ampere,  we  may  vary  these  factors 
which  make  up  the  total  in  any  way  we  like.  Thus  the  energy  may  be  trans- 
mitted and  a  current  of  500  amperes  under  a  pressure  of  100  volts.  In  order 
to  do  this  the  resistance  of  the  conductor  through  which  the  current  travels 
must  be  small,  which  could  only  be  effected  by  having  it  of  large  section  and 
of  good  very  thick  conducting  material,  that  is  of  copper  ;  the  great  weight 
of  such  a  conduction  makes  it  both  costly  and  inconvenient. 

The  energy  might,  however,  also  be  transmitted  in  the  form  of  a  weak 
current,  say  of  10  amperes,  under  a  pressure  of  5,000  volts  ;  the  current 
required  for  this  purpose  might  be  very  much  thinner,  and  therefore  less 
costly.  But  the  manipulation  of  currents  of  such  a  potential  as  this  has  its 
own  drawbacks  ;  the  insulation  must  be  very  good,  and  moreover  the 
manipulation  of  such  currents  is  attended  with  great  danger.  These  currents 
can  then  be  converted  at  the  place  of  application  into  large  currents,  but  of 
much  lower  electromotive  force,  which  is  accomplished  by  means  of  trans- 
formers or  converters.  One  form  of  such  an  apparatus  consists  of  a  long- 
length  of  fine  iron  wire  coiled  so  as  to  form  a  ring  ;  the  separate  turns  being 
insulated  from  each  other.  Round  this  is  wrapped  in  alternate  layers  sepa- 
rated from  each  other  the  carefully  insulated  primary  and  secondary  wires  ; 
the  whole  arrangement  closely  resembling  the  ring  of  Gramme's  machine 
,'fig.  892). 

Lane  Fox  showed  that  secondary  batteries  could  l)e  used  as  transformers 
for  direct  currents  of  high  E.M.F. 

Hitherto  the  chief  applications  have  been  to  the  transmission  of  energy  for 
electrical  lighting. 

924.  Stratification  of  the  electric  light. — Quet  observed,  in  studying 
the  electric  light  which  Ruhmkorff's  coil  gives  in  a  vacuum,  that  if  some  of 
the  vapour  of  turpentine,  wood  spirit,  alcohol,  or  bisulphide  of  carbon,  &c.. 


928 


Dynamical  Electricity. 


[924- 


be  introduced  into  the  vessel  before  exhaustion,  the  aspect  of  the  light  is 
totally  modified.  It  appears  then  like  a  series  of  alternately  bright  and  dark 
zones,  forming  a  pile  of  electric  light  between  the  two  poles  (fig.  911). 

In  this  experiment  it  follows,  from  the  discontinuity  of  the  current  of 
induction,  that  the  light  is  not  continuous,  but  consists  of  a  series  of  dis- 
charges which  are  near  each  other  in  proportion  as  the  hammer  o  (fig.  903) 
oscillates  more  rapidly.  The  zones  appear  to  possess  a  rapid  gyratory  and 
undulatory  motion.  Quet  considers  this  as  an  optical  illusion  :  for  if  the 
hammer  is  slowly  moved  by  the  hand,  the  zones  appear  very  distinct  and 
fixed. 


Fig.  910. 


Fig.  91 


Fig.  912 


The  light  of  the  positive  pole  is  most  frct|uently  red,  and  that  of  the 
negative  pole  violet.  The  tint  varies,  however,  with  the  vapour  or  gas  in  the 
globe. 

925.  Oelssler's  tube«.—The  brillianry  and  beauty  of  the  stratification 
of  the  electric  light  are  most  remarkable  when  the  discharge  of  the  Ruhm- 
korff  coil  takes  place  in  glass  tubes  containing  a  highly  rarefied  vapour  or 
gas.  These  phenomena,  which  were  originally  investigated  by  (lassiott,  arc 
produced  by  means  of  sealed  glass  tubes  first  constructed  by  Gcissler,  of 
l?onn,  and  generally  known  as  Gcissler's  tubes.  The  tubes  are  filled  witii 
different  gases  or  vapours,  and  are  then  exhausted,  so  that  the  pressure  does 
not  exceed  half  a  millimetre.  At  the  ends  of  the  tubes  two  platinum  wires 
are  soldered  into  the  glass. 

When  the  two  platinum  wires  are  conncctetl  with  the  ends  of  a  Ruhm- 


-925] 


Getsslcrs   Tubes. 


929 


kortTcoil  maynificent  lustrous  striae,  separated  by  dark  bands,  are  produced 
all  through  the  tube.  These  striae  vary  in  shape,  colour,  and  lustre  with  the 
degree  of  the  vacuum,  the  nature  of  the  gas  or  vapour  and  the  dimensions 
of  the  tube.  The  phenomenon  has  occasionally  a  still  more  brilliant  aspect 
from  the  fluorescence  which  the  electric  discharge  excites  in  the  glass. 

^ij?-  913  shows  the  striae  in  carbonic  acid  under  a  quarter  of  a  millimetre 
pressure  ;  the  colour  is  greenish,  and  the  striae  have  not  the  same  form  as 
hydrogen.     In  nitrogen  the  light  is  orange-yellow. 

Pliicker  found  that  the  light  in  a  Geissler's  tube  did  not  depend  on  the 
substance  of  the  electrodes,  but  simply  on  the  nature  of  the  gas  or  vapour 


^~-^^~. 

..^  j  #^^-— --"^g^^^^^T-"— --^^tti^^-s^^^ay-  V 

^Hl'iptfMnMViVillWIil^^ 

i^ii;::ss::*!ir:li:a^ 

\N 

1    '         ^  l 

t^  ,— -Tjirr^^r^^          ■■■ BiiSl 

^^^^^^^^H 

in  the  tube.  He  found  that  the  lights  furnished  by  hydrogen,  nitrogen, 
carbonic  oxide,  &c.,  give  different  spectra  when  they  are  decomposed  by 
a  prism.  The  discharge  of  the  coil  which  passes  through  a  highly  rarefied 
gas  would  not  pass  through  a  perfect  vacuum,  from  which  it  follows  that  the 
presence  of  a  ponderable  substance  is  absolutely  necessary  for  the  passage 
of  electricity. 

By  the  aid  of  a  powerful  magnet  Pliicker  tried  the  action  of  magnetism 
on  the  electric  discharge  in  a  Geissler's  tube,  as  Davy  had  done  with  the 
ordinary  voltaic  arc,  and  obtained  many  curious 
results,  one  of  which  may  be  mentioned.  He  found 
that  where  the  discharge  is  perpendicular  to  the  line 
of  the  poles,  it  is  separated  into  two  distinct  parts, 
which  can  be  referred  to  the  different  action  exerted 
by  the  electromagnet  on  the  two  extra  currents  pro- 
duced in  the  discharge. 

The  light  of  Geissler's  tubes  has  been  applied 
to  medical  purposes.  A  long  capillary  tube  is 
soldered  to  two  bulbs  provided  with  platinum  wires  ; 
this  tube  is  bent  in  the  middle,  so  that  the  two 
branches  touch,  and  their  extremities  are  twisted 
as  shown  at  a  (fig.  914).  This  tube  contains  a  highly 
rarefied  gas,  like  those  previously  described,  and  *'S-  914. 

when  the  discharge  passes  a  light  is  produced  at  a,  bright  enough  to  illu- 
minate any  cavity  of  the  body  into  which  the  tube  is  introduced. 

30 


930  Dynamical  Electricity.  [926- 

926.  3>e  la  Rue  and  IMCuller's  experiments. — -These  physicists  have 
made  a  very  extensive  and  elaborate  series  of  experiments  on  the  stratifica- 
tion of  the  electric  light  by  means  of  the  currents  produced  by  their  battery 
(812).  They  employed  for  some  of  these  experiments  as  many  as  14,400 
cells,  which  is  by  far  the  most  powerful  battery  ever  put  together.  It  is 
impossible  to  attempt  here  even  a  condensed  account  of  these  experiments  ; 
but  the  following,  which  are  some  of  the  results  obtained,  may  be  mentioned. 

The  discharge  in  a  vacuum  tube  is  essentially  of  the  same  nature  as  that 
which  takes  place  in  gases  under  the  ordinary  atmospheric  pressure.  A 
vacuum  tube  was  interposed  in  the  circuit  of  a  battery  of  2,400  cells,  to- 
gether with  a  very  long  resistance.  It  was  found  that  the  potentials  at  the 
two  ends  of  the  tube  are  virtually  the  same  ;  now  according  to  Ohm's  law 
there  should  be  a  fall  of  potential  along  the  entire  circuit  ;  it  is  accordingly 
concluded  that  the  discharge  is  not  a  current  in  the  ordinary  sense  of  the 
term,  but  is  disruptive,  the  electricity  being  carried  by  the  molecules  of  the 
gas.     At  no  degree  of  exhaustion  is  air  a  conductor. 

All  the  strata  start  from  the  positive  pole.  For  a  definite  pressure  an 
aureole  is  formed  at  the  positive  pole  ;  with  a  diminished  pressure  this  de- 
taches itself,  is  succeeded  by  others,  and  so  on. 

One  of  the  most  curious  results  is  the  definite  and  stationary  character  of 
the  strice  for  given  conditions  ;  they  are  remarkably  permanent,  and  seem 
almost  as  if  they  could  be  manipulated  ;  a  single  stratum  may  be  seen  fall- 
ing down  a  tube  like  a  feather  in  a  vacuum,  or  like  a  drop  of  water.  They 
are  not  produced  in  the  same  way  as  drops  falling,  but  all  and  each  of  the 
little  strata  are  so  many  Leyden  jars. 

The  length  of  the  arc  found  between  two  terminals  varies  with  the  square 
of  the  number  of  cells  ;  thus  while  1,000  cells  give  a  spark  of  0-0051  inch 
under  ordinary  atmospheric  pressure,  11,000  cells  give  a  spark  of  0-62  inch. 

With  an  increase  of  exhaustion  the  potential  necessary  to  cause  a  current 
to  pass  diminishes  to  a  certain  pressure  which  represents  an  exhaustion  of 
least  resistance  ;  from  this  it  again  increases,  and  the  strata  thicken  and 
diminish  in  number  until  a  point  is  reached  at  which  no  discharge  takes 
place,  however  high  be  the  potential. 

A  change  in  the  current  often  produces  an  entire  change  in  the  colour  of 
the  stratification,  thus  in  hydrogen  the  change  is  from  blue  to  pink.  If  the 
discharge  is  irregular  and  the  strata  indistinct,  an  alteration  in  the  strength 
of  the  current  makes  the  strata  distinct  and  steady.  Even  when  the  strata 
are  apparently  quite  steady  and  permanent,  a  pulsation  may  be  detected  in 
the  current  by  means  of  the  telephone. 

In  the  same  tube,  and  with  the  same  gas,  a  very  great  variety  of  phe- 
nomena can  be  produced  by  varying  the  pressure  and  the  current.  The 
peculiar  luminosity  and  form  of  stratification  in  their  various  forms  can  be 
reproduced  in  the  same  tube  or  in  others  having  similar  dimensions. 

The  colour  of  the  discharge  in  one  and  the  same  gas  greatly  depends  on 
the  degree  of  rarefaction.  The  least  resistance  to  the  discharge  in  hydrogen 
and  when  its  brilliancy  is  greatest,  is  at  a  pressure  of  0-642  mm.  or  845  M 
(M  is  a  very  convenient  symbol  for  the  millionth  of  an  atmosphere).  When 
the  rarefaction  has  attained  0-002  mm.  or  3  M,  the  discharge  only  just  passes 
even  with  a  potential  of  11,330  volts  ;   while  with  an  exhaustion  of  0-000055 


-927]  Crookes's  Experiments.  931 

mm.,  the  nearest  approach  to  a  perfect  vacuum  ever  attained,  not  only  does 
this  fail  to  produce  a  discharge,  but  the  i-inch  spark  of  an  induction  coil 
does  not  pass. 

Air  offers  a  greater  resistance  than  hydrogen  ;  a  spark  which  passes  in 
hydrogen  across  a  distance  of  5-6  mm.  will  only  strike  across  a  distance  of 
3  mm.  in  air. 

In  air  at  a  pressure  of  62  mm.,  which  corresponds  to  an  atmospheric  heig'^ht 
of  12*4  miles,  the  electric  discharge  has  the  carmine  tint  so  often  seen  in  the 
display  of  the  aurora  borealis  (991)  ;  at  a  pressure  of  1-5  mm.,  corresponding 
to  a  height  of  30'96  miles,  it  is  salmon-coloured  ;  and  at  a  pressure  of  0'8  mm., 
representing  a  height  of  33'96  miles,  it  is  of  a  pale  white.  Under  a  pressure 
of  0-379  mm.  the  discharge  has  the  greatest  brilliancy.  This  represents  a 
height  of  37'67  miles,  and  would  be  visible  at  a  distance  of  585  miles  ;  it  is  pro- 
bably the  upper  limit  of  the  height,  though  on  the  other  hand  it  is  possible  that 
the  discharge  may  sometimes  take  place  at  a  height  of  a  few  thousand  feet. 

927.  Crookes's  experiments. — Dr.  Crookes  has  made  a  remarkable 
series  of  experiments  on  the  phenomena  produced  when  the  electrical  dis- 


HI 

1 

■FJ^  ^Jr  L"  i^  k^B 

Fig.  913. 

charge  is  produced  in  tubes  very  highly  exhausted,  that  is,  beyond  the  point 
at  which  the  best  effects  of  the  stratification  are  produced. 

When  the  electrical  discharge  is  passed  through  a  Geissler's  tube  in 
which  the  exhaustion  is  as  low  as  2  mm.,  the  negative  pole  is  surrounded 
by  a  narrow  layer,  and  then  by  a  relatively  dark  bluish  space,  the  rest  of 
the  tube  being  filled  by  layers  of  reddish-yellow  light,  separated  by  dark 
spaces  ;  as  the  rarefaction  proceeds,  the  bluish  light  extends,  and  under  cer- 
tain circumstances  fills  the  entire  tube.  Wherever  the  light  strikes  against 
the  glass  it   excites  the  brightest  fluorescence.     But  the  most  remarkable 

302 


9Z^ 


Dynamical  Electricity. 


[927- 


feature  is  that  when  the  vacuum  is  almost  complete  the  nature  of  the  phe- 
nomenon changes.  The  light  now  proceeds  from  the  electrode  in  straight 
lines,  and  does  not  follow  any  bends  in  the  tubes.  This  rectilinear  propaga- 
tion is  well  illustrated  by  the  following  experiment  of  Crookes.  In  fig.  91 5,  A, 
the  negative  pole  of  the  induction  coil,  is  connected  with  the  electrode  a, 
which  is  made  of  aluminum,  and  forms  a  slightly  concave  mirror.  If  the 
exhaustion  is  not  more  than  2  mm.  pressure,  and  the  positive  pole  is  con- 
nected successively  with  the  electrodes  ^,  <:,  d^  the  discharge  takes  place  in 
curved  lines  as  shown  in  the  figure.  But  when  the  rarefaction  is  exceed- 
ingly great,  about  a  millionth  of  an  atmosphere,  the  appearance  is  that  pre- 
sented in  fig.  915,  B.  With  whatever  electrode  the  positive  pole  is  connected, 
the  rays  proceeding  in  straight  lines  cross  in  the  focus,  and,  striking  against 
the  opposite  side,  excite  there  the  most  brilliant  fluorescence. 

If  a  screen  of  mica  of  any  shape  be  interposed  in  the  path  of  the  rays  it 
stops  the  light  on  its  path,  and  a  shadow  is  formed  at  the  other  end  of  its  own 
shape,  surrounded  by  a  bright  fluorescence. 

The  discharge  can  also  produce  mechanical  effects.  A  Geisslei-'s  tube  is 
constructed  with  a  pair  of  glass  rails  in  it,  on  which  rolls  the  axis  of  a  light 
wheel,  on  the  spokes  of  which  are  mica  vanes.  If  now  the  discharge  be 
directed  against  the  top  of  the  vanes,  the  wheel 
moves  along  towards  the  positive  pole. 

The  experiment  represented  in  fig.  916  shows  the 

very  great  heat  which  the  glow  light  can  produce. 

a  is  the  negative  electrode  in  the  form  of  a  concave 

mirror,  b  a  strip  of  platinum  foil.    With  a  sufficiently 

powerful  induction  coil  the  platinum  can  be  made 

white-hot  or  even  melted. 

^^^^_^^^^H  Some  of  the  most  beautiful  of  these  experiments 

fe^T^J^^^^B    are  those  made  by  directing  the  discharge  on  various 

^B       ^^^^^1    precious  stones.     In  these  circumstances  diamond 

^T       ^^^^^H    emits  a  splendid  green  fluorescence,  ruby  a  brilliant 

■  ^I^^^^^H    i-cd,  emerald  a  carmine,  and  so  forth. 

The  electrical  discharge  does  not  pass  through 
a  vacuum,  as  is  shown  by  the  following  experiment. 
A  small  tube  containing  caustic  potash  is  fused  to 
a  Geisslei-'s  tube  connected  with  a  Sprengel  pump. 
By  continual  exhaustion  while  the  caustic  potash  is 
being  heated,  as  complete  a  vacuum  as  possible  is 
'  '*^'  '^"''  made  of  the  tube  sealed.     The  last  minute  trace  of 

aqueous  vapour  is  absorljcd  l^y  the  caustic  potash  as  it  cools.  In  this  com- 
plete vacuum  the  discharge,  however  strong,  no  longer  passes  ;  the  vacuum 
acts  as  a  complete  non-conductor. 

If,  however,  the  caustic  potash  is  gently  heated,  a  trace  of  aqueous  vapour 
is  given  off,  and  a  green  fluorescent  light  flashes  along  the  tube  ;  as  the  heating 
is  continued  and  the  vapour  becomes  denser  we  get  the  stratification,  until 
ultimately  the  electricity  passes  along  the  tube  in  the  form  of  a  narrow 
purple  line.  If  the  tube  is  allowed  again  to  cool,  the  phenomena  reproduce 
themselves  in  the  reverse  order. 

The  phenomena  here  described  are  rcgardctl  by  Crookes  as  due  to  an 


-928]  Rotation  of  Induced  Currents  by  Magnets.  933 

ttltra-gascous  state,  which  he  calls  radiant  matter.  In  gas  under  the  ordinary 
pressure  the  average  free  path  of  a  molecule  of  air  is  0-000095  ni™-  5  as  the 
gas  is  more  rarefied  the  length  of  the  path  increases,  so  that  with  the  high 
degrees  of  exhaustion  which  Crookes  employs  in  his  later  experiments — as 
much  as  the  one  twenty-millionth  of  an  atmosphere— the  length  of  the  mean 
path  is  so  much  increased  that  its  dimensions  are  comparable  with  those  of 
the  vessel,  and  along  with  this  increase  the  number  of  intramolecular  shocks 
diminishes  in  a  corresponding  ratio.  It  is  to  this  condition,  in  which  the 
molecules  move  forward  with  their  own  motion,  and,  striking  against  the  sides, 
give  rise  to  the  fluorescence,  that  Crookes  accounts  for  the  effects  produced. 

The  theoretical  views  to  which  Crookes  has  been  led  by  his  experiments 
have  met  with  a  considerable  degree  of  criticism,  and  it  must  be  added  that 
none  of  the  explanations  of  these  singularly  beautiful  experiments  have  met 
with  general  adoption. 

928.  Rotation  of  induced  currents  by  mag-nets. — De  la  Rive  devised 
an  experiment  which  shows  in  a  most  ingenious  manner  that  magnets  act  on 
the  light  in  Geissler's  tubes  in  accordance  with  the  laws  with  which  they 
act  on  any  other  movable  conductor. 

This  apparatus  consists  of  a  glass  globe  or  electrical  egg  (fig"- 91 7),  pro- 
vided at  one  end 
with  two  stopcocks, 
one  of  which  can  be 
screwed  on  the  air- 
pump,  and  the  other, 
which  is  a  stopcock 
like  that  of  Gay 
Lussac  (383),  serves 
to  introduce  a  few 
drops  of  the  liquid 
into  the  globe.  At 
the  other  end  a 
tubulure  is  ce- 
mented, through 
which  passes  a  soft 
iron  rod  about  | 
of  an  inch  in  dia- 
meter, the  top  of 
which  is  about  the 
centre  of  the  globe. 
Except  at  the  two 
ends,  this  rod  is  en- 
tirely covered  with 
a  very  thick  insulat- 
ing layer  of  shellac, 
then  with  a  glass 
tube  also  coated  with 
shellac,  and  finally 
with  another  glass 
tube  uniformly  coated  jvith  a  layer  of  wax.     The  insulating  layer  must  be 


^^ 


934  Dyjianiical  Electricity.  [928- 

at  least  |  of  an  inch  thick.  Inside  the  globe,  the  insulating  layer  is  sur- 
rounded at  ;r  with  a  copper  ring,  connected  with  a  binding  screw,  f,  by  means 
of  a  copper  wire. 

The  vessel  having  been  exhausted  as  completely  as  possible,  a  few  drops 
of  ether  or  of  turpentine  are  introduced  by  means  of  a  stopcock  a;  it  is 
again  exhausted,  so  that  the  vapour  remaining  is  highly  rarefied. 

A  thick  disc  of  soft  iron,  c,  provided  with  a  binding  screw,  is  then  placed 
on  one  of  the  branches  of  a  powerful  electromagnet,  and  the  end  in  of  the 
rod  mtt  is  placed  on  this  disc,  while  at  the  same  time  one  of  the  ends  of  the 
secondary  wire  of  Ruhmkorfif' s  coil  is  connected  with  the  binding  screw,  r, 
and  the  other  with  the  knob,  o.  If  then  the  coil  is  worked  without  setting  in 
action  the  electromagnet,  the  electricity  of  the  wire  s  passes  to  the  top,  ;z,  of 
the  soft  iron  rod,  and  that  of  the  second  wire  to  the  ring  x%  and  a  more  or 
less  irregular  luminous  sheaf  appears  on  the  inside  of  the  globe  round  the 
rod,  as  in  the  experiment  of  the  electric  &'g'g. 

But  if  a  voltaic  current  passes  into  the  electromagnet,  the  phenomenon 
is  different  ;  instead  of  starting  from  different  points  of  the  upper  surface 
;z,  and  the  ring  x,  the  light  is  condensed  and  emits  a  single  arc,  from 
n  to  X.  Further — and  this  is  the  most  remarkable  part  of  the  experiment 
— this  arc  turns  slowly  round  the  magnetised  c\iinder  ;;/;?,  sometimes  in 
one  direction,  and  sometimes  in  another,  according  to  the  direction  of  the 
induced  current,  or  the  direction  of  the  magnetisation.  As  soon  as  the  magne- 
tisation ceases,  the  luminous  phenomenon  reverts  to  its  original  appearance. 
This  experiment  is  remarkable  as  having  been  devised  a  priori  by  De  la 
Rive  to  explain,  by  the  influence  of  terrestrial  magnetism,  a  kind  of  rotatory 
motion,  from  east  to  west,  observed  in  the  aurora  borealis.  The  rotation  of 
the  luminous  arc  in  the  above  experiment  can  evidently  be  referred  to  the 
rotation  of  currents  by  magnets  (868). 

Geissler  has  constructed  a  veiy  useful  form  of  the  above  experiment,  in 
which  the  globe  is  exhausted  once  for  all.  Apart  from  the  purpose  for  which 
it  was  originally  devised,  it  is  a  very  convenient  arrangement  for  demon- 
strating the  action  of  magnets  on  movable  currents. 

929.  Heat  developed  by  tbe  Indactlon  of  powerful  magrnets  on  bodies 
In  motion. — We  have  already  seen  in  Arago's  experiments  (914)  that  a  rota- 
ting copper  disc  acts  at  a  distance  on  a  magnetic  needle,  communicating  to  it 
a  rotatory  motion.  We  shall  presently  see  that  a  cube  of  copper,  rotating 
with  great  velocity,  is  suddenly  stopped  by  the  influence  of  the  poles  of  two 
strong  magnets  (938).  It  is  clear  that,  in  order  to  prevent  the  rotation  of  the 
needle  or  of  the  copper,  a  certain  mechanical  force  must  be  consumed  in 
overcoming  the  resistance  which  arises  from  the  inductive  action  of  the  mag- 
net. Reasoning  upon  the  theory  of  the  transformation  of  mechanical  work 
into  heat  (497,  it  has  been  attempted  to  ascertain  what  quantity  of  heat 
is  developed  by  the  action  of  induced  currents  under  the  influence  of  power- 
ful magnets.  Joule,  with  a  view  of  determining  the  mechanical  equivalent 
of  heat,  coiled  a  quantity  of  copper  wire  round  a  cylinder  of  soft  iron,  and 
having  enclosed  the  whole  in  a  glass  tube  full  of  water,  he  imparted  to  the_- 
systcm  a  rapid  rotation  between  the  branches  of  an  electromagnet.  A 
thermometer  placed  in  the  liquid  served  to  measure  the  quantity  of  heat 
produced  by  the  induced  currents  in  the  soft  iron  and  the  wire  round  it. 


-929]     Heat  Developed  by  Magnets  on  Bodies  in  Motion.        935 

It  was  thus  found  that  the  heat  developed  was  proportional  to  the  square  of 
the  magnetism  evoked,  and  was  equivalent  to  the  work  used  in  the  rotation. 
Foucault  made  a  remarkable  experiment  by  means  of  the  apparatus 
represented  in  fig.  918.  It  consists  of  a  powerful  electromagnet  fixed 
horizontally  on  a  table.  Two  pieces  of  soft  iron,  A  and  B,  are  in  contact 
with  the  poles  of  the  magnet,  and,  becoming  magnetised  by  induction, 
they  concentrate  their  magnetic  inductive  action  on  the  two  faces  of  a 
copper  disc,  D,  3  inches  in  diameter   and    a    quarter   of   an   inch    thick  ; 


Fig.  918. 

this  disc  partly  projects  between  the  pieces  A  and  B,  and  can  be  moved  by 
means  of  a  handle  and  a  series  of  toothed  wheels  with  a  velocity  of  1 50  to 
200  turns  in  a  second. 

So  long  as  the  current  does  not  pass  through  the  wire  of  the  electro- 
magnet, very  little  resistance  is  experienced  in  turning  the  handle,  and 
when  once  it  has  begun  to  rotate  rapidly,  and  is  left  to  itself,  the  rotation 
continues  in  virtue  of  the  acquired  velocity.  But  when  the  current  passes,  the 
disc  and  other  pieces  stop  almost  instantaneously  ;  and  if  the  handle  is 
turned  considerable  resistance  is  felt.  If,  in  spite  of  this,  the  rotation  be 
continued,  the  force  used  is  transformed  into  heat,  and  the  disc  becomes 
heated  to  a  remarkable  extent.  In  an  experiment  made  by  Foucault  the 
temperature  of  the  disc  rose  from  10°  to  61°,  the  current  being  fonned  by 
three  of  Bunsen's  elements  ;  with  six  the  resistance  was  such  that  the  rotation 
could  not  long  be  continued.  The  currents  thus  produced  in  solid  conductors, 
and  which  are  converted  into  heat,  are  often  spoken  of  as  Foucault  or  eddy 
currents. 

Such  currents  are  of  constant  occurrence  in  magneto-electrical  machines, 
and  weaken  their  force,  first,  by  owing  their  existence  to  some  part  of  the 
work  expended  ;  secondly,  they  weaken  the  magnetism  of  the  armatures  by 
their  direction  ;  and,  lastly,  they  are  converted  into  heat,  which  increases 
the  internal  resistance  of  the  machine. 


936 


Dynamical  Electricity. 


[930- 


930.  The  Telephone. — To  the  number  of  instruments  depending  on  in- 
duction may  be  added  this  discovery,. which  is  equally  remarkable  for  the 
surprising  character  of  the  results  which  it  produces,  and  for  the  sim- 
plicity of  the  means  by  which  they  are  produced.  Fig.  919  represents  a 
perspective,  and  fig.  920  a  section  of  Graham  Bell's  telephone. 

It  consists  essentially  of  a  steel  magnet,  of  about  4  inches  in  length  by 
half  an  inch  in  diameter,  enclosed  in  a  wooden  case.  Round  one  end  of  this 
magnet  is  fitted  a  thin  flat  bobbin,  BB,  of  fine 
insulated  copper  wire.  For  a  magnet  of  this 
size  a  length  of  250  metres  of  No.  38  wire, 
offering  a  resistance  of  350  ohms,  is  well 
suited. 

The  ends  of  this  coil  pass  through  longi- 
tudinal holes,  LL,  in  the  case,  and  are  con- 
nected with  the  binding  screws  CC.  In  front 
of  the  magnet  and  at  a  distance  which  can 
be  regulated  by  a  screw,  but  which  is  some- 
thing less  than  a  millimetre,  is  the  essential 
feature  of  the  instrument,  a  diaphragm,  D,  of 
soft  iron,  not  much  thicker  than  a  sheet  of 
stout  letter-paper.  This  diaphragm  is  screwed 
down  by  the  mouthpiece  E,  which  is  similar 
to,  though  somewhat  larger  than,  that  of  a 
stethoscope. 

The  instruments  are  connected  b)'  wires, 
for  one  of  which  the  earth  maybe  substituted, 
as  in  ordinary  telegraphic  communication 
(886).  Each  instrument  can  be  used  either 
as  sender  or  receiver,  though  in  actual  prac- 
tice it  is  more  convenient  for  each  operator 
to  have  two  telephones,  one  of  which  is 
held  to  the  ear,  while  the  other  is  used  for 
speaking  into  ;  the  latter  being  larger  and 
more  powerful  than  the  receiver. 
The  action  of  the  instrument  depends  on  the  fact  that  whenever  the 
relative  positions  of  a  magnet  and  of  a  closed  coil  of  wire  are  altered  there 
is  produced  within  the  coil  a  current  or  currents  of  electricity.  This  may 
be  illustrated  by  reference  to  fig.  865.  When  the  magnet  is  suddenly 
brought  into  the  coil,  a  current  is  produced  in  the  coil  in  a  particular  direc- 
tion. There  is  no  current  so  long  as  the  coil  and  the  magnet  are  stationaiy. 
When,  however,  the  magnet  is  suddenly  withdrawn,  a  current  is  produced 
in  the  opposite  direction.  Similar  effects  are  produced  if,  while  the  magnet 
is  in  the  coil,  its  magnetism  is  by  any  means  increased  or  diminished. 

Now  in  the  telephone  the  magnet  and  the  coil,  when  once  properly 
adjusted,  remain  fi.xed.  But  the  magnet  M  magnetises  by  induction  the 
soft  iron  membrane  D  in  front  of  it,  that  is,  converts  it  into  a  magnet. 
When,  by  the  mouthpiece  being  spoken  into,  this  iron  membrane  vibrates 
backwards  and  forwards,  tlicsc  vibrations  give  rise  to  an  alteration  in  the 
magnetism  of  the  permanent  magnet,  the  effect  of  which  is  that  currents 


930] 


The  Telephone. 


937 


Fig.  920. 


are  produced  in  alternate  directions  in  the  coil  surrounding  the  pole. 
Moreover,  the  alteration  in  the  relative  positions  of  the  magnetised  dia- 
phragm, thus  magnetised  by  induction,  and  of  the  coil,  give  rise  to  currents 
in  the  same  direction  as  the  above.  These  alternating  currents,  being 
transmitted  through  the  circuit  to  the  distant  coil,  alternately  attract,  and 
cease  to  attract,  __ 
the  corresponding 
diaphrag-m.  They  C 
thereby  put  this  in  ^s 
vibration,  and  when 
the  mouthpiece  of 
this  telephone  is 
held  to  the  ear, 
these  vibrations  are 
perceived  as  sound 
corresponding  to 
that  which  is  trans- 
mitted. Hence, 
whatever  sound  produces  the  vibration  of  the  diaphragm  of  the  sending 
instrument  is  repeated  by  that  of  the  receiver. 

The  reproduction  of  the  sound  in  the  receiving  instrument  is  perfect  as 
far  as  articulation  is  concerned,  but  it  is  considerably  enfeebled,  as  might  be 
expected.  The  sound  has  something  of  a  metallic  character,  appearing  as 
if  heard  through  a  long  length  of  tubing,  while  it  faithfully  reproduces  the 
characteristics  of  the  person  speaking.  It  does  not  result  from  a  series  of 
sharp  and  distinct  makes  and  breaks,  but  in  each  of  the  momentary  currents 
there  is  a  continuous  rise  and  fall,  corresponding  in  every  gradation  and 
inflection  to  the  motion  of  the  air  agitated  by  the  speaker. 

Various  attempts  have  been  made  to  improve  the  loudness  of  the  sounds 
produced  in  the  telephone,  by  varying  the  form  of  the  various  parts,  and 
using  more  powerful  magnets  of  horseshoe  and  circular  forms  ;  but  experi- 
ment shows  that  increased  loudness  is  always  produced  at  the  expense  of 
distinctness. 

The  amplitude  of  the  vibration  of  the  disc  is  extremely  small.  According 
to  Bosscha  a  unit  current  produced  a  displacement  of  0-034  of  a  mm.,  and  as 
currents  of  y^^Vjo  ^^  ^^^'^  ^^^  perceptible,  it  follows  that  the  amount  of  displace- 
ment must  be  about  the  —-^  of  the  wave-length  of  yellow  light  (637). 

The  current  in  a  telephone  is  estimated  by  De  la  Rue  as  not  exceeding 
that  which  would  be  produced  by  one  Daniell's  cell  in  a  circuit  of  copper 
wire  4  mm.  in  diameter  of  a  length  sufficient  to  go  290  times  round  the  earth. 
This  current  would  have  to  pass  19  years  through  a  voltameter,  to  produce 
I  cc.  of  detonating  gas.  This  is  about  1,000  million  times  less  than  the 
currents  in  ordinary  use.  Such  currents  are,  however,  sufficient  to  cause 
the  contraction  of  a  frog's  leg  (797).  According  to  Pellat  the  energy  con- 
tained in  one  test  unit  (water  gramme  degree)  would  maintain  a  continuous 
sound  for  10,000  years. 

Siemens  estimates  that  not  more  than  y^Joo  of  the  mass  of  sound  which 
the  sender  receives  is  produced.  That  it  is  possible  to  perceive  this,  is  due 
to  the  great  sensitiveness  and  range  of  the  ear,  which  can  endure  the  sound 


938  Dynamical  Electricity.  [930- 

of  a  cannon  at  a  distance  of  5  yards,  and  still  perceives  it  at  a  distance 
10,000  times  as  great.  This  represents  a  ratio  of  intensities  of  one  to  one 
hundred  millions. 

From  some  experiments  on  the  transmission  of  the  sound  of  a  high- 
pitched  tuning-fork  (251)  Rontgen  concludes  that  no  less  than  24,000  currents 
are  transmitted  in  one  second. 

This  extreme  delicacy  of  the  telephone  is  its  drawback  to  speaking 
through  ordinary  telegraph  circuits.  The  currents  in  adjacent  wires,  the 
vibration  of  the  posts  and  of  the  insulators,  or  the  passage  of  a  cart  over 
the  streets,  acts  by  induction  on  the  telephone  circuit,  and  overpowers  its 
indications.  When  a  telephone  circuit  was  placed  at  a  distance  of  20  metres 
from  a  well-insulated  line,  through  which  signals  were  sent  by  means  of  a 
battery  of  a  few  elements,  sounds  were  distinctly  heard  in  the  telephone. 
Speaking  under  such  circumstances  is  like  speaking  in  a  storm.  The 
powerful  currents  used  for  systems  of  electric  lighting  produce  such  a  roar 
in  an  adjacent  telephone  circuit  that  it  is  impossible  to  speak  through  the 
telephone.  The  only  effective  way  of  diminishing  the  inductive  action  of 
adjacent  systems  is  to  have  two  wires  in  close  proximity  to  each  other. 
They  are  thus  at  the  same  distance  from  the  inducing  circuit,  and  as  one  of 
the  wires  is  used  for  going  and  the  other  for  returning,  the  similar  influences 
must  be  in  opposite  directions,  and  therefore  neutralise  each  other. 

If  a  telephone  is  inserted  in  the  circuit  of  a  Morse's  instrument,  the 
sound  of  the  working  is  heard,  and  the  messages  can  be  read ;  this  is  the 
case  also  of  the  telephone  in  the  branch  circuit  of  a  Morse.  If  one  telephone 
is  joined  up  with  the  primary,  and  another  with  the  secondary  wire  of  an 
induction  coil,  communication  is  almost  as  good  as  if  the  two  apparatus  were 
directly  united. 

Telephones  have  been  constructed  in  which  the  thin  iron  plate  is  re- 
placed by  a  thicker  one,  or  by  an  unmagnetic  one  ;  or  if  the  telephone  is 
held  close  to  the  ear,  the  plate  can  be  dispensed  with  altogether.  In  the 
latter  two  cases  the  sounds  are  only  perceived  when  the  spiral  surrounding 
the  magnet  can  vibrate  with  it. 

A  telephone  may  be  constructed  with  a  rod  of  soft  iron  instead  of  a 
magnet  ;  when  the  rod  is  held  in  the  line  of  dip,  and  the  mouthpiece  is  sung 
into,  the  sounds  are  reproduced. 

From  its  extreme  sensitiveness,  being  perhaps  the  most  delicate  galvano- 
scope  we  possess,  the  telephone  has  become  of  great  service  in  scientific 
research.  It  may  be  used  instead  of  a  galvanometer  in  a  Wheatstone's 
bridge.  If  inserted  in  either  of  the  circuits  of  an  induction  coil,  the  number 
of  breaks  can  be  determined  from  the  height  of  the  tone  which  is  produced. 
When  inserted  in  the  current  of  a  Holtz's  machine,  the  disc  of  which  is 
rotating  with  a  uniform  velocity,  the  height  of  the  note  varies  with  the  re- 
sistance of  the  circuit,  and  with  the  capacity  of  the  condensers.  It  can  be 
shown  also  that  the  circumstances  most  favourable  for  the  production  of  a 
most  distinct  stratification  in  a  Geissler's  tube  correspond  to  a  definite  pitch 
in  the  telephone. 

The  telephone  has  been  used  to  test  hardness  of  hearing.  If  the  mag- 
netism of  a  telephone  be  e.\cited  by  galvanic  currents  which  are  made  inter- 
mittent by  a  vibrating  tuning-fork,  and  if  a  telephone  is  inserted  in  a  branch 


-931] 


The  Microphone. 


939 

circuit  (961),  then  by  varying  the  strength  of  the  principal  current,  by  the 
insertion  of  resistances,  the  strength  of  the  sounds  in  the  telephone  may  be 
varied  at  will. 

When  a  telephone  is  held  to  the  ear  during  a  thunderstorm,  every  lightning 
flash  in  the  sky  is  simultaneously  heard  to  be  accompanied  by  a  sharp  crack. 

Dolbear  has  constructed  a  telephone  in  which  the  electrostatic  action  of 
currents  is  used.  It  consists  of  two  circular  flat  discs  of  metal  rigidly  fixed 
to  each  other  in  an  insulated  case  of  ebonite.  One  of  the  discs  is  in  metallic 
connection  with  the  line  wire,  in  which  is  a  battery  and  an  induction  coil ; 
in  this  way,  while  one  disc  is  electrified  positively,  the  other  is  negatively 
electrified  by  induction,  and  if  the  current  be  varied  by  speaking  through  a 
transmitter  in  the  circuit  their  var>'ing  effects  are  faithfully  reproduced,  and 
reappear  as  sound  vibrations  on  the  receiver. 

931.  The  Microphone. — When  the  wires  of  an  electrical  circuit,  in  which 
is  interposed  a  telephone,  are  broken,  and  rest  loosely  on  each  other,  sounds 
produced  near  the  point  of  contact 
are  reproduced  and  magnified  in 
the  telephone.  The  micropho?te^ 
invented  by  Prof  Hughes,  depends 
on  this  fact  ;  its  arrangement  may 
be  greatly  varied ;  one  of  the  simplest 
and  most  convenient  forms  is  that 
represented  in  fig.  921.  A  piece 
of  thin  wood  is  fitted  vertically  on 
a  base  of  the  same  material  ;  two 
small  rods  of  gas  carbon,  C  C,  about 
\  of  an  inch  thick,  are  fixed  hori- 
zontally in  the  upright  ;  by  means  of 
binding  screws,  they  are  in  metallic 
connection  with  the  wires  of  a  cir- 
cuit in  which  is  a  small  battery  and 
a  telephone  ;  and  in  each  of  them 
is  a  cavity.  A  third  piece,  D,  of  the  same  material,  and  about  one  inch  long, 
is  pointed  at  each  end,  one  of  which  rests  in  the  lower  cavity,  while  the  other 
pivots  loosely  in  the  upper  one.  When  a  watch  is  placed  on  the  base  B,  its 
ticking  is  heard  in  the  telephone  with  surprising  loudness  ;  the  walking  of 
a  fly  on  the  base  suggests  the  stamping  of  a  horse  ;  the  scratching  of  a 
quill,  the  rustling  of  silk,  the  beating  of  the  pulse,  are  perceived  in  the  tele- 
phone at  a  distance  of  a  hundred  miles  from  the  source  of  sound  ;  while  a 
drop  of  water  falling  on  the  base  has  a  loud  crashing  sound.  To  obtain  the 
best  results  with  a  particular  instrument,  the  position  of  the  carbon  must  be 
carefully  adjusted  by  trial  ;  and  indeed  the  form  of  the  instrument  itself 
must  be  variously  modified  for  the  special  object  in  view  :  in  some  cases 
great  sensitiveness  is  required  :  in  others  great  range.  In  order  to  eliminate 
as  far  as  possible  the  effect  of  accidental  vibrations  due  to  the  supports,  the 
base  should  rest  on  pieces  of  vulcanised  tubing,  or  on  wadding. 

It  is  known  that  the  compression  of  a  semiconductor,  such  as  carbon, 
diminishes  its  resistance,  while  a  diminution  in  the  compression  in- 
creases  the  resistance.     The  action  of  the  microphone  is  to  be  ascribed 


'^"tv5Tiyir/r- 


f^^^^ir- 


I  ig.  921 


940 


Dynamical  Electricity, 


[931- 


it==t 


c±. 


to  this  ;  in  consequence  of  the  minute  aherations  in  the  pressure  and  in  the 
degree  of  contact  at  the  break,  the  electrical  resistance  in  the  circuit  varies 
in  accordance  with  the  sound-waves,  and  consequently  the  strength  of  the 
currents  varies  too.  The  result  of  this  is,  that  what  we  may  call  undulating 
currents  of  electricity  are  produced,  whose  amplitude,  height,  and  form  are 
in  exact  correspondence  with  the  sound-waves.  The  effect  of  the  micro- 
phone is  to  draw  supplies  of  energy  from  the  battery,  which  then  appear  in 
the  telephone. 

932.  Hugrhes's  induction  balance. — The  principle  of  this  apparatus  may 
be  thus  stated  : — Suppose  we  have  two  exactly  equal  primary  induction  coils, 
A  and  A',  and  near  them  two  secondary  coils,  B  and  B',  also  exactly  equal, 
and  connected  up  with  a  galvanometer,  so  that  the  coils  act  upon  it  in 
opposite  directions.  If  now  the  current  of  a  battery  be  sent  through  the 
primary  coils,  joined  in  series,  the  inductive  effects  on  each  of  the  secondary 
coils  will  be  the  same,  and,  as  their  action  on  the  galvanometer  is  opposed, 
no  deflection  of  the  needle  will  be  produced.     If,  however,  a  piece  of  iron 

be  introduced  into  the 
cZiM]  c-i^  coreof  one  of  the  secon- 

dary coils,  the  equality 
in  the  induction  effects 
will  be  destroyed,  and 
the  needle  of  the  gal- 
A-anometer  at  once  de- 
flected. 

This  principle  was 
first  applied  by  Bab- 
bage,  Herschell,  and  in 
a  special  apparatus  by 
Dove  ;  but  the  micro- 
phone and  the  tele- 
])hone  have  led  the 
inventor  of  the  former 
to  the  invention  of  an 
apparatus  which  has 
opened. out  new  possi- 
bilities, and  has  placed 
in  the  hands  of  the 
physicist  an  elegant 
and  powerful  engine  of 
research,  which  in  cer- 
tain departments  of  in- 
vestigation promises  to 
be  of  great  service. 
"^■'^''-  The  form  of  instru- 

ment as  devised  by  Professor  Hughes  is  represented  in  fig.  922,  where  the 
essential  parts  are  drawn  to  scale,  though  the  relative  distances  of  the  parts 
are  not  so  ;  a  and  a'  arc  the  two  primary  coils,  each  of  which  consists  of  100  " 
metres  of  No.  32  silk-covcrcd  copper  wire  (o'oog  in  diameter)  wound  on  a  flat 
boxwood  spool  10  inches  in  depth  ;  b  and  <J'are  two  secondaiy  coils,  all  four  coils 


T 


-932]  Hughes's  Induction  Balance.  941 

being,  in  intention  at  least,  exactly  alike.  The  two  primary  coils  are  joined 
in  series  with  a  battery  of  three  or  four  small  Daniell's  cells,  in  which  circuit 
a  microphone,  ;«,  is  also  inserted  ;  the  ticking  of  a  small  clock  on  the  table 
acts  as  make  and  break. 

The  secondary  coils  are  joined  up  with  a  telephone  in  such  a  manner 
that  their  action  upon  it  is  opposed. 

Now,  whatever  care  be  taken  in  winding  the  wire  on  the  coils,  it  is  not 
possible  to  get  at  the  outset  an  exact  balance.  Hence,  while  one  of  the 
secondary  coils,  b,  is  at  a  fixed  distance  from  <•?,  the  corresponding  one,  b\  is 
not  so  ;  its  distance  from  a'  can  be  slightly  modified  by  means  of  a  micro- 
metric  screw,  and  thus,  connection  with  the  battery  circuit  having  been  made, 
a  balance  is  obtained  by  slightly  varying  the  adjustment,  and  the  accomplish- 
ment of  this  is  known  by  there  being  silence  in  the  telephone.  But  if  now 
any  metal  whatever  be  introduced  in  one  of  the  secondary  coils,  a  sound 
is  at  once  heard. 

This  arrangement  is  so  far  a  simple  differential  one,  and  furnishes  as  yet 
no  means  of  measuring  the  forces  brought  into  play,  and  for  this  purpose 
Hughes  uses  what  is  called  a  sonometer  or  audiometer.  This  consists  of 
three  similar  coils,  f,  ^,  and  ^,  placed  vertically  on  a  horizontal  graduated  rule 
along  which  d  can  be  moved.  By  means  of  a  switching  key  or  switch, 
the  primary  coils  c  and  e  can  be  put  in  communication  with  the  battery  and 
microphone  circuit  quite  independently  of  the  balance,  and  it  is  so  ar- 
ranged that  the  ends  of  the  coils  c  and  e  facing  each  other  are  of  the  same 
polarity  ;  the  third  coil,  d,  the  secondary  one,  is  connected  with  the  telephone 
circuit. 

If  these  primary  coils  c  and  e  were  quite  equal,  then,  when  connected  up 
with  the  battery  circuit,  no  sound  would  be  heard  in  the  telephone,  when  the 
secondary  d  is  exactly  midway  between  them.  But  as  the  coil  is  moved 
from  this  position  either  towards  c  or  e  a  sound  is  heard,  due  to  the  prepon- 
derance of  one  or  the  other.  In  practice  the  coils  are  so  arranged  that  a 
balance  is  obtained  when  the  secondary  circuit  is  near  one  of  the  coils,  c 
for  instance  ;  this  represents  a  zero  of  sound,  and  as  the  coil  d  is  moved 
nearer  to  ^  a  sound  of  gradually  increasing  intensity  is  heard  ;  distances 
measured  off  along  this  scale  represent  values  of  sound  on  an  arbitrary  scale. 

Suppose  now  that  a  balance  has  been  obtained  in  the  induction  balance, 
and  that  the  coil  d  in  the  sonometer  is  at  zero  ;  no  sound  is  then  heard 
in  the  telephone  when  the  current  is  switched  either  in  one  or  the  other 
circuit.  But  if  the  balance  is  disturbed  by  placing  a  piece  of  metal  in  the 
core  of  b,  a  definite  continuous  sound  is  heard.  The  current  is  then  switched 
into  the  sonometer,  and  the  secondary  coil  e  is  moved  until  the  air  perceives 
the  same  sound  in  both  circuits.  The  distance  then  along  which  the  coil  d 
has  been  moved  is  thus  an  arbitrary  measure  of  the  effect  produced. 

Although  by  the  switch  the  transition  from  one  circuit  to  the  other 
can  be  effected  with  great  rapidity,  and  the  ear  can  appreciate  minute 
differences,  this  has  not  the  value  of  a  null  method.  Hughes  has  still 
further  improved  the  balance  by  the  following  device,  in  which  the  sono- 
meter is  dispensed  with  : — A  graduated  strip  of  zinc  about  200  mm.  in  length 
by  25  mm.  wide,  and  tapering  from  a  thickness  of  4  mm.  at  one  end  to  a  fine 
edge  at  the  other,  is  made  use  of     The  metal  to  be  tested  is  placed  in  a 


Dynamical  Electricity. 


942  vynamicai  t.Lectrtcity.  [932- 

plane  between  a  and  b  on  the  left  of  the  plate,  and  the  strip  is  moved  along 
the  top  of  b'  until  a  balance  is  obtained. 

The  instrument  is  of  surprising  delicacy  ;  a  milligramme  of  copper  or  a 
fine  iron  wire  introduced  into  one  of  the  coils  which  has  been  balanced  can 
be  loudly  heard,  and  appreciated  by  direct  measurement.  If  two  shillings 
fresh  from  the  Mint  be  balanced,  rubbing  one  of  them  or  breathing  on  it  at 
once  disturbs  the  balance.  A  false  coin  balanced  against  a  genuine  one 
is  at  once  detected.  The  instrument  furnishes  a  means  of  testing  the  deli- 
cacy of  hearing  ;  such  a  piece  of  wire  as  the  above,  or  a  fine  spiral  of  copper, 
furnishes  a  kind  of  test  object  for  this  purpose. 

933.  Tasimeter. — This  instrument,  invented  by  Edison,  consists  essen- 
tially of  an  arrangement  by  which  a  disc  of  carbon  forming  part  of  a  voltaic 
circuit  is  exposed  to  varying  pressure.  It  depends  on  the  fact  that  the 
resistance  of  carbon  varies  very  greatly  with  the  pressure  to  which  it  is 
exposed.  It  consists  of  an  iron  base,  on  which  are  two  rigid  supports  (fig. 
923),  one  of  which,  a^  is  connected  with  the  galvanometer,  g^  by  means  of 
a  wire.  An  ebonite  disc,  rtf,  is  screwed  into  a,  and  in  a  circular  cavity  in 
this  ebonite  is  a  small  carbon  disc,  not  shown   in  the  figure,  in  the  outer 


Fig.  923. 

surface  of  which  is  a  strip  of  platinum  in  metallic  connection  with  one  pole 
of  an  element,  /.  The  disc  of  carbon  is  closed  in  the  cavity  by  a  metal 
plug,  f,  in  which  is  a  cavity.  There  is  a  similar  plug,  ^,  with  a  correspond- 
ing cavity  at  the  end  of  a  screw,  b,  which  works  in  the  upright  support  ;  in 
the  two  cavities  is  placed  the  strip  of  substance,  y^  with  which  the  experiment 
is  made. 

A  gentle  pressure  being  applied  by  the  screw,  the  needle  is  deflected 
through  a  few  degrees,  and  its  position,  when  it  comes  to  rest,  is  noted. 
The  slightest  subsequent  contraction  or  expansion  is  indicated  by  a  deflec- 
tion of  the  needle  of  the  galvanometer. 

The  sensitiveness  of  the  instrument  is  ver)'  great  :  a  thin  strip  of  ebonite 
is  expanded  by  the  heat  of  the  hand  held  near  it,  so  as  to  aflfect  a  not  very 
delicate  galvanometer.  A  strip  of  gelatine,  inserted  instead  of  the  ebonite, 
is  expanded  by  the  moisture  of  a  damp  strip  of  paper  held  two  or  three 
inches  away. 

The  apparatus  seems  well  adapted  for  the  qualitative  observation   of 


-934]  Edison's  Loiid-spcaking  Telepho7te.  943 

minute  changes  in  length  ;  it  has  been  used,  for  instance,  to  show  the  very 
small  elongation  of  an  iron  rod  when  it  is  magnetised  (880).  Great  care  is 
required  in  the  preparation  of  the  carbon  disc  ;  the  best  kind  seems  to  be 
made  from  lampblack  prepared  at  a  low  temperature,  and  then  powerfully 
compressed  into  a  button. 

934.  Edison's  loud-speaking:  telephone. — Although  depending  on  a 
different  principle,  we  may  give  a  description  here  of  this  instrument. 

An  adjustable  metal  spring  passes  on  the  surface  of  a  small  cylinder, 
made  of  chalk,  moistened  with  solutions  of  caustic  potash  and  acetate  of 
mercury  ;  both  the  spring  and  the  cylinder  form  part  of  a  circuit  in  which 
is  a  battery  and  a  Reis's  transmitter  (884).  The  spring  is  connected  in  a 
suitable  manner  with  a  mica  disc,  which  is  the  vibrating  part  of  a  mouth- 
piece like  that  of  an  ordinary  telephone.  The  cylinder  can  be  turned  at  a 
uniform  rate,  either  by  hand  or  by  an  automatic  clockwork  arrangement. 

Now  while  the  spring  is  pressing  on  the  cylinder,  if  the  latter  be  rotated 
in  a  direction  away  from  the  mouthpiece,  in  consequence  of  the  friction 
between  the  spring  and  the  surface  of  the  cylinder,  a  certain  pull  will  be 
exerted  on  the  disc,  which  will  tend  to  drag  it  outwards.  If  the  direction  of 
rotation  were  the  opposite,  the  disc  would  be  pushed  inwards.  Now  the 
amount  of  pull  or  push  will  depend  on  the  friction  between  the  point  and 
the  surface.  If  a  momentary  current  be  passed,  there  will  be  a  momentary 
decomposition  at  the  surface  of  the  cylinder,  its  friction  will  be  altered  in 
consequence  of  this  momentary  decomposition,  the  effect  of  which  is  that 
the  disc  moves  inwards,  and  a  series  of  such  intermissions  of  the  current 
produces  a  corresponding  series  of  pulsations  of  the  disc,  which  if  sufficiently 
rapid  produce  a  sound.  The  friction  of  the  surfaces  in  contact  is  in  fact 
modified  by  means  of  electrical  decomposition,  a  lubricator  is  liberated  in 
correspondence  with  the  sound-waves,  and  thus  the  sound  which  they  repre- 
sent is  reproduced.  The  reproduction  is  so  loud  as  to  be  heard  throughout 
a  room,  the  sounding'  instrument  being  at  a  distance.  Although  ordinaiy 
speech  and  music  can  thus  be  transmitted,  yet  the  sounds  have  a  harsh 
metallic  character  which  is  not  pleasing,  but  at  the  same  time  the  individual 
character  of  the  voice  is  preserved. 


944 


Dynamical  Electricity. 


[935- 


CHAPTER   VII. 

OPTICAL   EFFECTS   OF   POWERFUL   MAGNETS.      DL\MAGNET1SM. 

935.  Optical  effects  of  powerful  magrnets. — Faraday  observed,  in  1845, 
that  a  powerful  electromagnet  exercises  an  action  on  many  substances,  such 
that  if  a  polarised  ray  traverses  them  in  the  direction  of  the  line  of  the  mag- 
netic poles,  the  plane  of  polarisation  is  deviated  either  to  the  right  or  to  the 
left  according  to  the  direction  of  the  magnetisation. 

Fig.  924  represents  Faraday's  apparatus,  as  constructed  by  Ruhmkorff. 
It  consists  of  two  very  powerful  electromagnets,  AI  and  N,  fi.xed  on  two  iron 


Fig.  9-4- 

supports,  O  O',  which  can  be  moved  on  a  support,  K.  The  current  from  a 
Ijattery  of  10  or  12  Bunsen's  elements  passes  by  the  wire  A  to  the  commu- 
tator, H,  the  coil  M,  and  then  to  the  coil  N,  by  the  wire^,  descends  in  the 
wire  /,  passes  again  to  the  commutator,  and  emerges  at  B.  The  two 
cylinders  of  soft  iron,  which  are  in  the  axis  of  the  coils,  are  perforated  by 
cylindrical  holes,  to  allow  the  light  to  pass.  At  b  and  a  there  arc  two  Nicol's 
prisms,  b  serving  as  polariser  and  a  as  analyser.  By  means  of  a  limb  this 
latter  is  turned  round  the  centre  of  a  graduated  circle,  P. 

The  two  prisms  being  then  placed  so  that  their  principal  sections  are 
perpendicular  to  each  other,  the  prism  a  completely  extinguishes  the  light 
transmitted  through  the  prism  b.  If  at  f,  on  the  axis  of  the  two  coils,  a  plate" 
be  placed  with  parallel  faces,  either  of  ordinary  or  flint  glass,  light  supposed 


-936]  PhotopJionc.  945 

to  be  monocliromatic  is  still  extinguished  so  long  as  the  current  does  not 

pass  ;  but  when  the  connections  are  made,  the  light  reappears,  and  in  order 

to  extinguish  it  the  analyser  must  be  turned  through  an  angle  which  can  be 

read  off  on  the  limb,  and  which  measures  the  rotation.     By  reversing  the 

direction  of  the  current  twice  the   rotation  is  observed.     If  the  source  of 

light  is  not  monochromatic,  and  if  the  analyser  be  turned  from  left  or  right, 

according  Jo   the  direction  of  the  current,  the   light   passes  through  the 

different  tints  of  the  spectrum,  as  is  the  case  with  plates  of  quartz   cut 

perpendicularly  to  the  axis  (674).     Becquerel  showed  that  a  large  number  of 

substances  can  also  rotate  the  plane  of  polarisation  under  the  influence  of 

powerful  magnets.     For  a  given  substance  the  direction  of  the  rotation  is 

independent     of    the 

direction  in  which  the       ~ 

rays    of    light   pass  ; 

and  also  of  whether 

the     propagation     of 

the    light    is    in    the 

direction  of  the  lines 

of    force,    or   in    the  '^'  ^'^^" 

opposite  direction.     Hence  if  the  ray  is  reflected  on  itself  (fig.    925),  and 

traverses  the  substance  a  second  time  in  the  opposite  direction,  the  rotation 

is  doubled.     By  thus  increasing  the  path  of  the  ray  by  successive  reflections, 

the  rotation  may  be  increased  in  the  same  proportion. 

TJie  rotation  of  the  plane  of  polarisation  between  ttvo  points  is  propor- 
tional to  the  difference  of  magnetic  potential  \v\\\ch  exists  bet-ween  these  poiftts. 
This  is  known  as  Verdefs  law. 

If  V  and  V  are  the  magnetic  potentials  at  two  points  on  the  path  of  the 
ray,  then  the  angle  d  by  which  the  plane  of  polarisation  has  been  turned  is 
6  =  0)  (V- V)  ;  0)  being  the  rotation  which  for  the  body  in  question  would  be 
due  to  unit  difference  of  potential.  This  quantity  is  called  VerdeCs  constant. 
For  different  rays  it  is  nearly  as  the  inverse  square  of  the  wave  length.  For 
the  ray  D  and  at  0°  it  is  o'-o4o  for  bisulphide  of  carbon  and  o'-oi3  for  water. 
It  diminishes  with  rise  of  temperature. 

By  means  of  Faraday's  apparatus  it  has  been  found  that  thin  layers  of 
iron,  cobalt,  and  nickel,  so  fine  as  to  be  transparent,  exert  a  powerful  rota- 
tion of  the  plane  of  polarisation  for  transmitted  light.  The  rotation  for  the 
central  rays  of  the  spectrum  in  iron  is  32,000  times  that  of  glass  of  the  same 
thickness.  In  all  the  above  substances  the  rotation  is  in  the  direction  of 
the  magnetising  current. 

936.  Pbotopbone. — Mr.  Graham  Bell,  the  inventor  of  the  telephone, 
has  invented  an  apparatus  by  which  articulate  speech  can  be  transmitted  to 
a  considerable  distance  by  the  simple  agency  of  a  ray  of  light. 

The  essential  features  of  the  apparatus  are  represented  in  fig.  926,  in 
which  m  is  the  transmitter.  This  consists  of  a  wooden  box  closed  by  a  thin 
plate  of  microscope  glass  silvered  in  front,  which  acts  as  mirror  ;  in  the 
back  of  the  box  is  an  aperture  provided  with  a  flexible  tube  and  mouthpiece. 
A  powerful  beam  of  solar  or  of  the  electrical  light  falls  agamst  a  large 
mirror,  //,  and  is  reflected  by  it  on  a  lens,  (^,  by  which  the  rays  are  concentrated 

3F 


946  Dynamical  Electi'icity.  [936- 

on  the  mirror,  w,  of  the  transmitter.  An  alum  cell,  a^  is  sometimes  interposed, 
to  cut  ofif  the  influence  of  the  heating  rays. 

From  the  mirror  m  the  reflected  rays  pass  through  a  lens,/,  by  which  they 
are  rendered  parallel,  and  fall  on  a  parabolic  mirror,/,  at  the  distant  station. 
Here  they  are  concentrated  on  what  may  be  called  a  selcnitun  r/ieostate,  s, 
which  is  interposed  in  a  circuit  consisting  of  a  few  Leclanche  cells  and  a 
telephone,  /. 

The  action  depends  on  the  alterations  in  the  resistance  of  selenium 
produced  by  the  action  of  light.  The  construction  of  the  rheostate  is  as 
follows  : — A  number  of  discs  of  thin  sheet  brass  are  taken,  separated  from 
each  other  by  thin  discs  of  mica  of  somewhat  smaller  diameter,  and,  the 
whole  having  been  tightly  screwed  together,  the  interstitial  spaces  are  filled 


Fig.  926. 

with  melted  selenium.  All  the  odd  numbers  of  brass  discs  arc  in  metallic 
connection  with  each  other  and  with  one  pole  of  the  circuit,  and  all  the  even 
ones  are  also  in  metallic  connection  with  each  other  and  with  the  other 
pole.  In  this  way  two  conditions  are  realised — namely,  that  the  surface  of 
selenium  exposed  to  the  action  of  light  is  as  large,  and  its  resistance  as 
small,  as  possible. 

This  being  premised,  when  light  falls  on  the  plane  mirror  at  rest,  its  rays 
are  reflected  parallel  against  the  parabolic  mirror  by  which  they  are  con- 
centrated on  the  cell,  the  cylindrical  shape  being  well  adapted  for  this.  But 
if,  by  being  spoken  against,  the  transmitting  mirror  vi  is  put  in  vibration, 
it  bulges  in  and  out — that  is,  becomes  convex  and  concave— and  the  rays  no 
longer  fall  parallel  on  the  parabolic  mirror  ;  tlicy  diverge  or  converge — in 
other  words,  the  whole  of  the  light  is  no  longer  concentrated  on  the  selenium 
cell ;  its  intensity  changes  at  every  instant,  and  these  variations  in  the  action 
of  the  light  produce  corresponding  variations  in  the  resistance  of  the  sele- 
nium, which  again  produce  corresponding  variations  in  the  strength  of  the 
current,  and  these  are  revealed  by  the  articulate  sounds  of  the  telephone. 

Mr.  Bell  has  found  that  a  great  number  of  substances  are  thrown  into 
vibration  by  the  intermittent  action  of  light,  as  we  have  seen  (446(/).  Lord 
Raylcigh's  calculations  show  that  there  is  no  reason  for  discarding  the  ex- 


-937 J  Kerrs  Electro-optical  Experiments.  947 

planation  that  the  sounds  in  question  arc  due  to  the  bendiny  of  the  plates  in 
consequence  of  unequal  heating'. 

937.  Kerr's  electro-optical  experiments. —  Dr.  Kerr  has  discovered  a 
remarkable  relationship  between  electricity  and  light.  He  finds  that  when 
certain  dielectrics  are  subjected  to  a  state  of  electrical  strain,  they  develop 
doubly  refringent  properties  (639).  The  general  arrangement  of  the  experi- 
ments is  as  follows  :  a  cell,  P  (fig.  927),  is  suitably  constructed  of  stout  glass 
plates,  in  which  is  placed  the  liquid  under  examination  ;  its  dimensions  are 
4  inches  in  length  by  i  inch  in  width,  and  about  J,  of  an  inch  in  thickness. 


i-F- -^■- l«-""-i -~-—W- 


c 

1 

Fig.  927. 

Two  copper  plates  placed  horizontally,  and  kept  at  a  distance  of  about  ^r,  of 
an  inch,  can  be  connected  with  the  poles  of  a  Holtz  machine  (fig.  687),  or 
what  is  more  convenient,  with  the  opposite  coatings  of  a  Leyden  jar,  which 
in  turn  is  worked  by  such  a  machine.  B  is  the  mirror  of  a  heliostat, 
by  which  a  beam  of  light  may  be  sent  in  any  direction.  M  and  N  are 
two  Nicol's  prisms  (660)  ;  C  is  a  compensator,  while  D  is  a  condensing 
lens. 

Of  the  two  Nicol's  prisms,  M  serves  as  polariser,  and  N  as  analyser 
(656) ;  at  the  outset  they  are  arranged  so  that  their  principal  sections  are  at 
right  angles  to  each  other,  and  make  an  angle  of  45°  with  the  vertical. 
Thus  the  light  polarised  by  the  prism  M  is  extinguished  by  the  analyser  N, 
so  that  the  field  between  them  is  quite  dark,  and  remains  so  even  when 
the  cell  is  filled  with  liquid  ;  the  cell  is  so  arranged  that  the  observer 
looks  through  the  slit  of  dielectric  which  is  between  the  conductors  in  the 
cell. 

If  now  the  plates  are  placed  in  opposite  electrical  conditions,  the  field  at 
once  becomes  clear.  Of  all  dielectrics  hitherto  examined,  carbon  bisulphide 
IS  that  which  best  exhibits  the  phenomenon.  A  fraction  of  a  turn  of  a  Holtz 
machine  is  at  once  sufficient  to  produce  light  in  the  field,  which  disappears 
immediately  the  plates  are  discharged.  As  the  machine  is  worked  and  the 
potential  rises,  the  light  between  the  conductors  gradually  increases  in  bright- 
ness until  a  pure  and  brilliant  white  is  obtained  ;  with  increase  of  potential 
a  fine  progression  of  chromatic  effects  is  obtained  ;  the  luminous  band 
between  the  conductors  changes  first  from  white  to  a  straw  colour,  which 
deepens  gradually  to  a  rich  yellow  ;  it  then  passes  through  orange  to  a  deep 
brown,  next  to  a  pure  and  dense  red,  through  purple  and  violet  to  a  rich 
and  full  blue,  and  then  to  green.  All  the  colours  are  beautifully  dense  and 
pure,  and  as  fine  as  anything  seen  in  experiments  with  crystals  in  the  polari- 
scope.  The  phenomenon  generally  ceases  at  the  green  of  the  second  order 
with  a  discharge  of  electric  spark?.  The  action  of  bisulphide  of  carbon 
under  electrical  strain  is  similar  to  that  of  glass  stretched  in  a  direction 

3  p  2 


948  Dynmiiical  Electricity.  [937- 

parallel  to  the  lines  of  force  ;  it  is  an  action  of  the  same  kind  as  that  of 
a  uniaxial  birefringent  ctystal  (640) ;  in  this  respect  carbon  bisulphide  oc- 
cupies a  place  among  dielectrics  similar  to  that  of  Iceland  spar  among 
crystals. 

In  order  to  measure  the  effect  produced,  a  compensator,  C,  is  placed 
behind  the  cell ;  the  plates  are  connected  with  a  Thomson's  electrometer 
in  such  a  manner  that  the  potential  can  be  directly  measured,  and  then 
compared  simultaneously  with  the  difference  of  the  path  of  the  extraordinarj' 
and  ordinary  ray  in  the  dielectric.  Kerr  arrived  thus  at  the  law  :  '  the 
strength  of  the  electro-optical  action  of  a  given  dielectric,  that  is,  the 
difference  in  the  path  of  the  ordinary  and  extraordinary  rays,  for  unit 
thickness  of  the  dielectric,  varies  directly  as  the  square  of  the  resultant 
electrical  force.'  Kerr  also  found  that  when  a  pencil  of  plane  polarised 
light  is  reflected  from  the  polished  surface  of  either  pole  of  an  electromagnet 
of  iron,  it  undergoes  a  rotation  in  a  direction  contrary  to  that  of  the  mag- 
netising current.  This  result  is  also  obtained  when  it  is  reflected  from  the 
sides  of  the  electromagnet,  if  the  magnet  is  excited. 

938.  Diamag-netism. — Coulomb  observed,  in  1802,  that  magnets  act  upon 
all  bodies  in  a  more  or  less  marked  degree  ;  this  action  was  at  first  attributed 
to  the  presence  of  ferruginous  particles.  Brugmann  also  found  that  certain 
bodies — for  instance,  bars  of  bismuth — when  suspended  between  the  poles  of 
a  powerful  magnet,  do  not  set  axially  between  the  poles,  that  is,  in  the  line 
joining  the  poles,  but  egtiatorially^  or  at  right  angles  to  that  line.  In  other 
words,  while  a  magnetic  substance  such  as  iron  sets  along  the  lines  of  force 
of  the  magnetic  field,  a  bar  of  bismuth  sets  at  right  angles  to  the  field. 
This  phenomenon  was  explained  by  the  assumption  that  the  bodies  were 
transversely  magnetic.  Faraday  made  the  important  discovery  in  1845  that 
all  solids  and  liquids  which  he  examined  are  cither  attracted  or  repelled  by 
a  powerful  electromagnet.  The  bodies  which  are  attracted  are  called  mag- 
netic or  parainagnetic,  or  also  ferromagnetic,  substances,  and  those  which 
are  repelled  or  take  a  magnetisation  opposite  that  of  the  lines  of  force  are 
diamagnctic  bodies.  Among  the  metals,  iron,  nickel,  cobalt,  manganese, 
platinum,  cerium,  osmium,  and  palladium  are  magnetic  ;  while  bismuth, 
antimony,  zinc,  tin,  mercury,  lead,  silver,  copper,  gold,  and  arsenic  are 
diamagnetic,  bismuth  being  the  most  so  and  arsenic  the  least.  Diamagnetic 
effects  were  first  observed  by  Faraday  in  a  particular  kind  of  glass  called 
heavy  glass  ;  they  can  only  be  produced  by  means  of  veiy  powerful  mag- 
nets, and  it  is  by  means  of  Faraday's  apparatus  that  they  have  been  dis- 
covered and  studied.  In  experimenting  on  the  diamagnetic  effects — solids, 
liquids,  and  gases— armatures  of  soft  iron,  S  and  Q  (tigs.  928-930),  of  dif- 
ferent shapes,  are  screwed  on  the  magnets. 

i.  Diamagnetisin  of  solids.  If  a  small  cube  of  copper,  suspended  by  a 
fine  silk  thread  between  the  poles  of  the  magnet  (fig.  929),  be  in  rapid  rota- 
tion between  the  poles  of  an  electromagnet,  it  stops  the  moment  the  current 
passes  through  the  coils.  If  the  movable  piece  have  the  form  of  a  small 
rectangular  bar  it  sets  cquatorially,  or  at  right  angles  to  the  axis  of  the  bob- 
bins, if  it  is  a  diamagnctic  substance,  such  as  bismuth,  antimony,  or  copper-,' 
but  axially,  or  in  the  direction  of  the  axis,  if  it  is  a  magnetic  substance,  such 
as  iron,  nickel,  or  cobalt.     Besides  the  substances  enumerated  above,  the 


-938] 


Diainai^-nctisiii. 


949 


following-  are  diamaynetic  :  rock  crystal,  alum,  glass,  phosphorus,  iodine, 
sulphur,  sugar,  bread  ;  and  the  following-  are  magnetic  :  many  kinds  of 
paper  and  sealing-wax,  fluorspar,  graphite,  charcoal,  O^cc. 

ii.  DiiDiuignctism  of  liquids.     To  experiment  with  liquids,  very  thin  glass 
tubes  tilled  with  the  substance  are  suspended  between  the  poles  instead  of 


Fig.  928. 


Fig.  929 


Fig.  930. 


the  cube  in  in  the  figure  929.  If  the  liquids  are  magnetic,  such  as  solutions 
of  iron  or  cobalt,  the  tubes  set  axially  ;  if  diamagnetic,  like  water,  blood, 
milk,  alcohol,  ether,  oil  of  turpentine,  and  most  saline  solutions,  the  tubes  set 
equatorially.  Very  remarkable  changes  take  place  in  the  direction  of  mag- 
netic and  diamagnetic  substances  when  they  are  suspended  in  liquids.  A 
magnetic  substance  is  indifferent  in  an  equally  strong  magnetic  liquid  ;  it 
sets  equatorially  in  a  stronger  magnetic  substance,  and  axially  in  a  sub- 
stance which  is  less  strongly  magnetic  ;  it  sets  axially  in  all  diamagnetic 
liquids. 

A  diamagnetic  substance  surrounded  by  a  magnetic  or  diamagnetic  sub- 
stance sets  equatorially.  According  to  its  composition  glass  is  sometimes 
magnetic  and  sometimes  diamagnetic,  and  as  glass  tubes  are  used  for  con- 
taining the  liquids  in  these  investigations  its  deportment  must  first  be  deter- 
mined, and  then  taken  into  account  in  the  experiment. 

The  action  of  powerful  magnets  on  liquids  may  also  be  observed  in  the 
following  experiment  devised  by  Pliicker.  A  solution  of  a  magnetic  liquid 
is  placed  on  a  watch-glass  between  the  two  poles,  S  and  Q,  of  a  powerful 
electromagnet.  When  the  current  passes,  the  solution  forms  the  enlarge- 
ment represented  in  fig.  930  ;  this  continues  as  long  as  the  current  passes, 
and  is  produced  to  different  extents  with  all  magnetic  liquids.  The  changes 
in  the  aspects  of  the  liquids  are,  however,  so  small  as  to  require  careful 
scrutiny  to  detect  their  existence.  A  method  of  magnifying  these  changes 
so  as  to  render  them  visible  to  larger  audiences  was  devised  by  Prof. 
Barrett.  A  source  of  light  is  placed  above  the  watch-glass  containing  a  drop 
of  the  solution  to  be  tried.  Below  the  watch-glass,  and  between  the  legs  of 
the  magnet,  is  placed  a  mirror  at  an  angle  of  45°.  By  this  means  the  beam 
of  light  passing  through  the  watch-glass  is  reflected  at  right  angdes  on  to  a 
screen,  where  an  image  of  the  drop  is  focussed  by  the  lens.  If  now  a  drop  of 
diamagnetic  liquid,  such  as  water,  or,  better,  sulphuric  acid,  be  placed  on  the 
watch-glass,  as  soon  as  the  current  passes,  the  flattened  drop  retreats  from 


950  Dynamical  Electricity.  [938- 

the  two  poles,  and  gathers  itself  up  into  a  little  heap,  as  at  A  (fig.  930).  So 
doing,  it  forms  a  double  convex  lens,  by  which  the  light  is  brought  to  a  short 
focus  below  the  drop,  an  effect  instantly  seen  on  the  screen.  When  the  current 
is  interrupted  the  drop  falls,  and  the  light  returns  to  its  former  appearance. 
A  magnetic  liquid,  such  as  a  solution  of  perchloride  of  iron,  has  exactly  the 
opposite  effect.  The  drop  attracted  to  the  two  poles  becomes  flattened,  and 
instead  of  a  plano-convex  shape,  at  which  it  rests,  it  becomes  nearly^concavo- 
convex,  as  at  B.  The  light  is  dispersed,  and  the  effect  manifest  on  the  screen. 
Instead  of  a  mirror  and  lens,  a  sheet  of  white  paper  may  be  placed  in  an  in- 
clined position  under  the  watch-glass,  and  the  effects  are  somewhat  varied, 
but  equally  well-pronounced. 

iii.  Diai)iag7ietisin  of  gases.  Bancalari  observed  that  the  flame  of  a  candle 
placed  between  the  two  poles  in  Faraday's  apparatus  was  strongly  repelled 
(fig.  9?8).  All  flames  present  the  same  phenomenon  to  different  extents, 
resinous  flames  or  smoke  being  most  powerfully  affected. 

The  magnetic  deportment  of  gases  maybe  e.xhibited  for  lecture  purposes 
by  inflating  soap  bubbles  with  them  between  the  poles  of  the  electromagnet, 
and  projecting  on  them  either  the  lime  or  the  electric  light. 

Faraday  experimented  on  the  magnetic  or  diamagnetic  nature  of  gases. 
He  allowed  gas  mixed  with  a  small  quantity  of  a  visible  gas  or  vapour,  so 
as  to  render  it  perceptible,  to  ascend  between  the  two  poles  of  a  magnet, 
and  observed  their  deflections  from  the  vertical  line  in  the  axial  or  equatorial 
direction  ;  in  this  way  he  found  that  oxygen  was  least,  nitrogen  more,  and 
hydrogen  most  diamagnetic.  With  iodine  vapour,  produced  by  placing  a 
little  iodme  on  a  hot  plate  between  the  two  poles,  the  repulsion  is  strongly 
marked.  Becquerel  found  that  oxygen  is  the  most  strongly  magnetic  of  all 
gases,  and  that  a  cubic  yard  of  this  gas  condensed  would  act  on  a  magnetic 
needle  like  5-5  grains  of  iron.  This  magnetism  of  gases  may  be  shown  by 
suspending  a  glass  globe  to  the  pan  of  a  balance,  above  the  pole  of  a 
powerful  magnet  ;  this  globe  being  exhausted  it  is  exactly  counterpoised, 
and  having  been  filled  with  a  given  gas  the  weight  is  ascertained  which  is 
required  to  detach  them.  With  oxygen  the  attraction  is  appreciable,  and 
is  five  times  as  much  as  air  under  the  same  pressure.  Faraday  found  that 
oxygen,  although  magnetic  under  ordinary  circumstances,  became  diamag- 
netic when  the  temperature  was  much  raised,  and  that  the  magnetism  or 
diamagnctism  of  a  substance  depends  on  the  medium  in  which  it  is  placed. 
A  suljstance,  for  instance,  which  is  magnetic  in  \'acuo  may  be  diamag'netic 
in  air. 

In  the  crystallised  bodies  which  do  not  belong  to  the  regular  system,  the 
directions  in  which  the  magnetism  or  diamagnetism  of  a  body  is  most  easily 
excited  are  generally  related  to  the  crystallographic  axis  of  the  substance. 
The  optic  axis  of  the  uniaxial  crystals  sets  either  axially  or  equatorially  when 
a  crystal  is  suspended  between  the  poles  of  an  electromagnet.  Faraday  has 
assumed  from  this  the  existence  of  a  inag>ietfl-crystalli?ic  force,  but  it  appears 
probable  from  Knoblauch's  researches  that  the  action  arises  from  an  unequal 
density  in  different  directions,  inasmuch  as  unequal  pressure  in  different 
directions  produces  the  same  result. 

According  to  Pliicker,  for  a  given  unit  of  magnetising  force,  the  specific 
magnetisms  developed  in  equal  weights  of  the  undermentioned  substances 


-938]  Diaiiiagnctisiii.  95 1 

are  represented  by  the  following  numbers,  those  bodies  with  the  minus  signs 
prefixed  being  diamagnetic  : — 


Iron 

.     1 ,000,000 

Nickel  oxide 

.       287 

Cobalt      . 

.     1,009,000 

Water   . 

•     -25 

Nickel      . 

465,800 

Bismuth 

.     -23-6 

Iron  oxide 

759 

Phosphorus  . 

.     -13-1 

iv.  Detonation  produced  by  the  rupture  of  a  current  under  the  influence 
of  a  pozuerful  electromagnet.  The  following  experiment  by  Ruhmkorfif  is  a 
remarkable  effect  of  Faraday's  apparatus.  When  the  two  ends  of  a  stout  wire 
in  which  the  current  of  the  electromagnet  passes  are  placed  between  the  two 
poles  S  and  Q  of  fig.  928 — that  is  to  say,  when  the  current  is  closed  between 
S  and  Q — this  closing  takes  place  without  a  spark  and  without  noise,  or 
merely  a  feeble  noise  and  a  spark.  But  when  the  two  ends  are  separated, 
and  the  current  is  hence  broken,  a  violent  noise  is  heard,  almost  as  strong  as 
the  report  of  a  pistol.  This  appears  to  be  the  extra  current,  the  intensity  of 
which  is  greatly  increased  by  the  influence  of  two  poles. 

The  repulsion  produced  in  a  diamagnetic  body  under  the  influence  ot  a 
powerful  magnet  is  due  to  the  fact  that  the  magnet  develops  in  the  end 
nearest  to  it  like  polarity,  and  in  the  end  furthest  away  unlike  polarity  ;  a 
phenomenon  the  exact  opposite  of  that  of  iron. 

The  following  experiment,  which  is  due  to  Weber,  is  considered  to  prove 
that  diamagnetism  is  a  polar  force.  A  coil  was  placed  near  the  end  of  an 
electromagnet,  its  axis  being  in  the  prolongation  of  the  axis  of  the  magnet, 
and  its  ends  being  connected  with  a  sensitive  galvanometer.  When  a  bar 
of  bismuth  was  suddenly  introduced  and  removed  from  the  coil,  induction 
currents  were  produced  in  the  circuit,  the  direction  of  which,  as  shown  by 
the  galvanometer,  was  the  exact  opposite  of  that  which  iron  would  ha\e 
produced  under  the  same  circumstances. 


95- 


Dynaviical  Electricity. 


[939- 


CHAPTER   VIII. 

THERMO-ELECTRIC    CURRENT. 


Fig.  931. 


939.  Thermo-electricity. — In  1821,  Professor  Seebeck,  of  Berlin,  found 
that  by  heating  one  of  the  junctions  of  a  metallic  circuit,  consisting  of  two 
metals  soldered  together,  an  electric  current  was  produced.  This  pheno- 
menon may  be  shown  by  means  of  the  apparatus  represented  in  fig.  931, 

which  consists  of  a  plate 
of  copper,  inn,  the  ends 
of  which  are  bent  and 
soldered  to  a  plate  of  bis- 
muth, op.  Inside  the  cir- 
cuit is  a  magnetic  needle, 
a,  moving  on  a  pivot. 
When  the  apparatus  is 
placed  in  the  magnetic 
meridian,  and  one  of  the 
solderings  gently  heated, 
as  shown  in  the  figure, 
the  needle  is  deflected  in 
a  manner  which  indicates 
the  passage  of  a  current 
from  n  to  in,  that  is,  from  the  heated  to  the  cool  junction  in  the  copper.  If, 
instead  of  heating  the  junction  n,  it  is  cooled  by  ice,  or  by  placing  upon  it 
cotton-wool  moistened  with  ether,  the  other  junction  remaining  at  the  ordi- 
nary temperature,  a  current  is  produced,  but  in  the  opposite  direction,  that 
is  to  say,  from  in  to  n  ;  in  both  cases  the  current  is  in  general  stronger  in 
proportion  as  the  difference  in  temperature  of  the  solderings  is  greater. 

Seebeck  gave  the  name  thermo-electric  to  this  current,  and  to  the  couple 
\\  liich  produces  it,  to  distinguish  it  from  the  hydro-electric  or  ordinary  voltaic 
current  and  couple. 

940.  Thermo-electric  series. — If  small  bars  of  two  dififerent  metals  are 
soldered  together  at  one  end  while  the  free  ends  are  connected  with  the 
wires  of  a  galvanometer,  and  if  now  the  point  of  junction  of  the  two  metals 
lie  heated,  a  current  is  produced,  the  direction  of  which  is  indicated  by  the 
deflection  of  the  needle  of  the  galvanometer.  Moreover,  the  strength  of  the 
current,  calculated  from  the  deflection  of  the  gahanometer,  is  proportional 
to  the  electromotive  force  of  the  therino-elcinent.  By  experimenting  in  this 
way  with  different  metals,  they  may  be  formed  in  a  list  such  that  each  metal 
gives  rise  to  positive  electricity  when  associated  with  one  of  the  following,  - 
and  negative  electricity  with  one  of  those  that  precede  : — that  is,  that,  in 
heating  the  soldering,  the  positive  current  goes  from  the  positive  to  the  ncga- 


940] 


ThcDiw-electric  Series. 


953 


5 

Gas  coke    . 

-o-i 

9 

Zinc    . 

0-2 

5-5 

Cadmium  . 

0-3 

5 

Strontium  . 

2-0 

3 

Arsenic 

3-8 

1-03 

Iron   . 

5-2 

I 

Red  Phosphorus 

9-6 

I 

Antimony  . 

9-8 

i-o 

Tellurium  . 

179-9 

07 

Selenium   . 

—  290-0 

tive  metal  across  the  soldering,  just  as  if  the  soldering  represented  the  liquid 
in  a  hydro-electrical  element  ;  hence  out  of  the  element — in  the  connecting 
wire  and  the  galvanometer,  for  instance — the  current  goes  from  the  negative 
to  the  positive  metal. 

Thus  a  couple,  bismuth-antimony,  heated  at  the  junction  would  corre- 
spond to  a  couple,  zinc-copper,  immersed  in  sulphuric  acid.  The  following 
is  a  list  drawn  up  from  Matthiessen's  researches,  which  also  gives  compara- 
tive numeVical  values  for  the  electromotive  force  : — 

Bismuth 

Cobalt  . 

Potassium    . 

Nickel. 

Sodium 

Lead     . 

Tin       .         .         . 

Copper 

Silver    . 

Platinum 

Such  a  list  represents  what  is  called  a  thermo-electric  series,  and  the 
meaning  of  the  numbers  in  this  series  is  that,  taking  the  electromotive  force 
of  the  copper-silver  couple  as  unity,  the  electromotive  force  of  any  pair  of 
metals  is  expressed  by  the  difference  of  the  numbers  where  the  signs  are  the 
same  and  by  the  sum  where  the  signs  are  different.  Thus  the  electromotive 
force  of  a  bismuth-nickel  couple  would  be  25  — 5  =  20;  of  a  cobalt-iron 
9-(  — 5-2)  =  14-2,  and  of  an  iron-antimony  —  5-2-9-8  = —4-6,  Where  the 
positive  sign  is  affixed,  the  current  is  from  the  other  metal  to  silver  across 
the  soldering  ;  and  where  the  negative,  from  silver  to  that  metal. 

It  will  be  observed  how  great  is  the  electromotive  force  of  the  highly 
crystalline  metals.  Alloys  are  not  always  intermediate  to  the  metals  of  which 
they  are  composed,  and,  therefore,  the  position  of  the  metals  is  greatly 
affected  by  slight  admixtures.  The  thermo-electric  behaviour  of  substances 
is  greatly  affected  by  hardness,  direction  of  crystallisation,  and  so  forth,  and 
to  this  is  no  doubt  due  many  of  the  discrepancies  in  the  lists  given  by  different 
observers. 

Of  all  the  bodies  mentioned  in  the  above  series,  bismuth  and  selenium 
produce  the  greatest  electromotive  force  ;  but  from  the  expense  of  this 
latter  element,  and  on  account  of  its  low  conducting  power  and  the  difficulty 
of  making  good  joints,  antimony  is  generally  substituted.  The  antimony  is 
the  negative  metal  but  the  positive  pole,  and  the  bismuth  the  positive  metal 
but  the  negative  pole,  and  the  current  goes  from  bismuth  to  antimony  across 
the  junction. 

If  copper  wires  connected  with  the  ends  of  a  galvanometer  are  soldered 
together  to  the  ends  of  an  antimony  rod,  and  if  one  of  the  junctions  is  heated 
to  50°,  the  other  being  maintained  at  0°,  a  certain  deflection  is  observed  in 
the  galvanometer.  If,  similarly,  a  compoundbar,  consisting  of  antimony  and 
tin  soldered  together,  be  connected  with  the  ends  of  the  galvanometer,  and  if 
the  junction  copper-tin  as  well  as  the  junction  tin-antimony  be  heated  to  50°, 
while  the  junction  antimony-copper  is  kept  at  0°,  the  deflection  is  the  same 


954  Dynamical  Electricity.  [940- 

as  in  the  previous  case.  Hence  the  electromotive  force  produced  by  heating 
the  two  junctions,  copper-tin  and  tin-antimony,  is  equal  to  the  electromotive 
force  produced  by  heating  the  copper-antimony  ;  and,  generally,  if  a  metal,  b, 
is  associated  with  a  metal,  a,  which  is  above  it  in  the  list,  and  in  like  manner 
if  b  is  associated  with  c,  which  is  below  it  in  the  list,  then  the  electromotive 
force  produced  by  heating  the  combination  ac  is  equal  to  the  sum  of  the 
electromotive  forces  produced  by  heating  ab  and  be  separately. 

If  the  two  junctions  of  a  given  couple  be  heated  to  the  temperatures  t 
and  6,  and  then  to  6  and  f,  respectively,  the  electromotive  force  produced  by 
heating  the  junctions  to  the  temperatures,  /  and  /',  is  equal  to  the  sum  of  the 
electromotive  forces  produced  in  the  other  two  cases  ;  that  is,  that  for  small 
intervals  the  electromotive  force  is  directly  proportional  to  the  temperature. 

With  greater  ranges  this,  no  longer  holds  ;  as  the  temperature  increases 
the  differences  of  potential  gradually  diminish,  and  at  a  certain  temperature 
of  the  hot  junction  no  current  is  produced  ;  this  temperature  is  called  the 
neutral  temperature.  In  the  case  of  a  silver-iron  couple  this  is  when  one 
junction  is  at  o°,  the  other  is  at  223°  ;  in  the  case  of  copper-iron,  it  is  when 
the  hot  junction  is  at  276°. 

When  the  couple  is  heated  beyond  the  neutral  temperature,  the  pheno- 
menon of  inversion  now  takes  place — that  is,  the  direction  of  the  current 
changes.  Thus,  with  iron-copper,  whereas  below  276°  copper  is  positive  to 
iron,  above  that  temperature  iron  is  positive  to  copper. 

There  is  another  general  case  in  which  no  current  is  produced  by  heating 
the  two  junctions,  and  that  is  whenever  the  arithmetical  mean  of  the  tempe- 
ratures of  the  junction  is  equal  to  this  neutral  temperature.  Thus,  for  silver 
and  iron  this  temperature  is  228-5°,  ^^id  "o  current  is  produced  when  the 
temperature,  /,  of  the  one  is  186,  145,  and  1 18,  the  corresponding  one  of  the 
other  being  260,  302,  and  328.  If  the  mean  temperature  in  one  case  is  above 
and  in  another  below,  the  current  has  different  directions  in  the  two  cases  ; 
hence  the  electromotive  force  cannot  always  be  increased  by  raising  the 
temperature  of  one  or  lowering  the  temperature  of  another. 

As  compared  with  ordinary  hydro-electric  currents,  the  electromotive 
force  of  thermo  currents  is  very  small  ;  thus  the  electromotive  force  of  a 
bismuth-copper  element  with  a  difference  of  100°  C.  in  the  temperatures  of 
their  junctions  is,  according  to  Neumann, ,,!,,  that  of  a  Daniell's  element  :  the 
electromotive  force  of  an  iron-argentan  couple  with  10°  to  IS"^  difterence  of 
temperature  at  their  junctions  is  ,.j,^^-  that  of  a  Daniell's,  according  to  Kohl- 
rausch  that  of  a  copper-argentan  couple  by  ,^,'„-,  of  a  Daniell  for  100°  C. 
The  E.M.F.  of  a  bismuth-antimony  couple  is  0000057  volt  for  a  degree 
Centigrade. 

941.  Causes  of  ttaermo-electrlc  currents.— Thermo-electric  currents 
are  probably  to  be  attributed  to  an  electromoU\  e  force  produced  by  the  con- 
tact of  heterogeneous  substances,  a  force  which  \  aries  with  the  temperature. 
When  all  the  parts  of  a  circuit  are  homogeneous,  no  current  is  produced  on 
heating,  because  the  heat  is  equally  propagated  in  all  directions.  This  is 
the  case  if  the  wires  of  the  galvanometer  are  connected  by  a  second  copper 
wire.  But  if  the  uniformity  of  this  is  destroyed  by  coiling  it  in  a  spiral,  or 
]by  knotting  it,  the  needle  indicates  by  its  deflection  a  current  going  from  \\\(: 
heated  part  to  that  in  which  the  homogeneity  has  been  destroyeil.     If  the 


-942J 


Thernw-electric  Battery. 


955 

ends  of  the  galvanometer  wires  be  coiled  in  a  spiral,  and  one  end  heated  and 
touched  with  the  other,  the  current  goes  from  the  heated  to  the  cooled  end. 

When  two  plates  of  the  same  metal,  but  at  different  temperatures,  are 
placed  in  a  fused  salt  such  as  borax,  which  conducts  electricity  but  exerts 
no  chemical  action,  a  current  passes  from  the  hotter  metal  through  the  fused 
salt  to  the  colder  one.     Hot  and  cold  water 
in    contact   produce   a   current  which    goes 
from  the  warm  water  to  the  cold. 

Svanberg  has  found  that  the  thermo- 
electromotive  force  is  influenced  by  the 
crystallisation  ;  for  instance,  if  the  cleavage 
of  bismuth  is  parallel  to  the  face  of  contact, 
it  is  greater  than  if  both  are  at  right  angles, 
and  that  the  reverse  is  the  case  with  anti- 
mony. Thermo-electric  elements  may  be 
constructed  of  either  two  pieces  of  bismuth 
or  two  pieces  of  antimony,  if  in  the  one  the 
principal  cleavage  is  parallel  to  the  place  of 
contact,  and  in  the  other  is  at  right  angles. 
Hence  the  position  of  metals  in  thermo- 
electric series  is. influenced  by  their  crystalline  structure. 

Many  crystallised  minerals  have  great  electromotive  force  when  heated 
with  metals  or  with  each  other.  Thus  the  combination  copper  pyrites — 
copper  when  heated  in  a  spirit  lamp  has  an  electromotive  force  of  o-i2,  and 
copper  pyrites — iron  pyrites  of  o-i8  of  a  volt. 

942.  Ttaermo-electric  battery. — From  what  has  been  said  it  will  be 
understood    that   a  thermo-electric  couple  consists  of  two  metals  soldered 


Fig.  932. 


Fig.  93  S. 

together,  the  two  ends  of  which  can  be  joined  by  a  conductor.  Fig.  932 
represents  a  bismuth-copper  couple  ;  fig.  933  represents  a  series  of  couples 
used  by  Pouillet.  The  former  consists  of  a  bar  of  bismuth  bent  twice  at 
right  angles,  at  the  ends  of  which  are  soldered  two  copper  strips,  f,  d^  which 
terminate  in  two  binding  screws  fixed  on  some  insulating  material. 

When  several  of  these  couples  are  joined  so  that  the  second  copper  of 
the  first  is  soldered  to  the  bismuth  of  the  second,  then  the  second  copper  of 


956 


•  D)  ma  VI  ical  Elect ricit) ' 


[942- 


this  to  the  bismuth  of  the  third,  and  so  on,  this  arrangement  constitutes  a 
thermo-electric  battery,  which  is  worked  by  keeping  the  odd  solderings,  for 
instance,  in  ice,  and  the  even  ones  in  water,  which  is  heated  to  ioo°. 

943.  Nobili's  thermo-electric  pile. — NobiH  devised  a  form  of  thermo- 
electric batteiy,  or  pile^  as  it  is  usually  termed,  in  which  there  are  a  large 
number  of  elements  in  a  very  small  space.  For  this  purpose  he  joined  the 
couples  of  bismuth  and  antimony  in  such  a  manner  that,  after  having  formed 
a  series  of  five  couples,  as  represented  in  fig.  935,  the  bismuth  from  b  was 
soldered  to  the  antimony  of  a  second  series  arranged  similarly  ;  the  last 
bismuth  of  this  to  the  antimony  of  a  third,  and  so  on  for  four  vertical  series, 
containing  together  20  couples,  commencing  by  antimony,  finishing  by 
bismuth. 

Thus  arranged,  the  couples  are  insulated  from  one  another  by  means 
of  small  paper  bands  covered  with  varnish,  and  are  then  enclosed  in  a 
copper  frame,  P  (fig.  934),  so  that  only  the  solderings  appear  at  the  two 
ends  of  the  pile.      Two  small  copper  binding  screws,  ni  and  «,  insulated 

in  an  ivory  ring,  communicate  in  the 
interior,  one  with  the  first  antimony, 
representing  the  positive  pole,  and 
the  other  with  the  last  bismuth,  repre- 
senting the  negative  pole.  These 
binding  screws  communicate  with  the 
extremities  of  a  galvanometer  wire 
when  the  thermo-electric  current  is  to 
be  observed. 

944.  Becquerel's  thermo-electric 
battery. — Becquerel  found  that  arti- 
ficial sulphuret  of  copper  heated  from  200^  to  300°  is  powerfully  positive, 
and  that  a  couple  of  this  substance  and  copper  hasan  electromotive  force 
nearly  ten  times  as  great  as  that  of  the  bismuth  and  copper  couple  in  fig.  932. 


Fig-  934- 


Fig-  935- 


Native  sulphuret,  on  the  contrary,  is  powerfully  negative.  As  the  artificial 
sulphuret  only  melts  at  aljout  1,035°,  it  may  be  "^^^d  at  very  high  tempera- 
tures. The  metal  joined  with  it  is  Cierman  silver  (qo  of  copper  and  10  of 
nickel).     Fig.  936   represents  the  arrangement  of  a  battery  of  50  couples 


-945] 


CliiuioicVs   ThcrDW-clcctric  Battery. 


957 


arranged  in  two  series  of  25.  Fig".  937  gives  on  a  larger  scale  the  view  of  a 
single  couple,  and  fig.  93S  that  of  6  couples  in  two  series  of  3.  The  sulphuret 
is  cut  in  the  form  of  rectangular  prisms,  10  centimetres  in  length,  by  18  mm. 
in  breadth,  and  1 2  mm.  thick.  In  front  is  a  plate  of  Cierman  silver,  w,  intended 
to  protect  the  sulphuret  from  roasting  when  it  is  placed  in  a  gas  flame. 
Below  there  is  a  plate  of  (German  silver  MM,  which  is  bent  several  times  so 


F'g-  937- 


Fig.  938. 


as  to  be  joined  to  the  sulphuret  of  the  next,  and  so  on.  The  couples,  thus 
arranged  in  two  series  of  25,  are  fixed  to  a  wooden  frame  supported  by  two 
brass  colums,  A,  B,  on  which  it  can  be  more  or  less  raised.  Below  the  couples 
is  a  brass  trough,  through  which  water  is  constantly  flowing,  arriving  by 
the  tube  b  and  emerging  by  the  stopcock  r.  The  plates  of  German  silver 
are  thus  kept  at  a  constant  temperature.  On  each  side  of  the  trough  are  two 
long  burners  on  the  Argand  principle,  fed  by  gas  from  a  caoutchouc  tube,  a. 
The  frame  being  sufficiently  lowered,  the  ends  are  kept  at  a  temperature  of 
200°  or  300°.  For  utilising  the  current,  two  binding  screws  are  placed  on 
the  left  of  the  frame,  one  communicating  with  the  first  sulphuret,  that  is,  the 
positive  pole,  and  the  other  with  the  last  German  silver,  or  the  negative  pole. 
At  the  other  end  of  the  frame  are  two  binding  screws,  which  facilitate  the 
arrangement  of  the  couples  in  different  ways. 

945.  Clamond's  thermo-electric  battery. — Of  the  attempts  which  have 
been  made  to  apply  thermo-electric  currents  to  directly  practical  purposes 
perhaps  the  most  successful  has  been  Clamond's,  which  has  been  used 
for  telegraphic  purposes  and  also  for  electroplating.  Its  characteristic 
features  are  the  construction  and  arrangement  of  the  elements,  and  the 
manner  in  which  the  heating  is  effected. 

The  negative  element  consists  of  an  alloy  of  two  parts  of  antimony  and 
one  of  zinc,  forming  a  flat  spindle-shaped  bar  from  2  to  3  inches  in  length,  by 
I  inch  in  thickness  (fig.  940).  The  positive  metal  is  a  thin  strip  or  lug  of  tin- 
plate,  stamped  as  represented  at  a  a'  in  fig.  939  ;  this  s  then  bent  in  as  shown 
at  r,  and  being  held  in  a  mould,  the  alloy,  which  melts  at  260°  C,  is  poured 
in.  The  individual  elements  have  then  the  appearance  represented  in  fig. 
940,  and  to  connect  them  together  the  tin  lugs  are  bent  into  shape,  and  joined 
in  a  circle  of  elements  (fig.  941),  being  kept  in  their  position  by  a  paste  of 
asbestos  and  soluble  glass  ;  flat  rings  of  this  composition  are  also  made, 
and  are  placed  between  each  series  of  rings  piled  over  each  other  ;  the  con- 
nection between  the  individual  elements  and  between  the  sets  of  rings  is 


958 


Dynamical  Electricity. 


[945- 


lo. 


made  by  soldering  together  the  projecting  ends  of  the  tin  lugs.     Thin  plates 

of  mica  are  placed  between  the  alloy  and  the  tin  plate,  excepting  at  the 

place  of  soldering.     Looked  at  from  the  inside 

the  faces  of  the  battery  present  the  appearance 

of  a  perfect  cylinder. 

The  heating  is  effected  by  means  of  coal 
gas,  admitted  through  an  earthenware  tube, 
A  B,  fig.  942,  perforated  by  numerous  small 
holes  ;  this  is  surrounded  by  a  somewhat  larger 
iron  tube,  C  D,  reaching  nearly  to  the  top  of  the 
cylinder,  which  is  closed  by  a  lid,  E  F.  Air 
enters  at  the  bottom  of  this  tube,  and  the  heated  gases,  passing  up  the  tube, 
curl  over  the  top,  descend  on  the  outside,  and  escape  by  a  chimney,  G  H.  This. 


Fig.  939. 


Fig.  940. 


Fig.  941.  Fig.  942. 

arrangement  economises  gas  and  prevents  danger  from  overheating,  as  the 
gas-jets  do  not  impinge  directly  on  the  element.  The  supply  of  gas  is 
regulated  by  an  automatic  arrangement,  so  that  the  temperature  is  not 
higher  than  about  200°. 

Although  sometimes  convenient,  thermo-electric  batteries  are  not  an 
economical  source  of  electricity.  Thus  a  Clamond's  battery  of  120  elements 
has  an  E.M.F.  of  8  volts,  and  a  resistance  of  3-2  ohms;  its  maximum 
available  work  can  be  shown  to  be  5  watts  per  second  ;  and  the  consump- 
tion of  gas  per  hour  is  180  litres.  The  heat  of  combustion  of  a  litre  of  gas 
gives  5,200  gramme  calories  ;  the  heat  expended  per  second  is,  therefore, 
260  calorics,  which  would  correspond  to  1,084  watts.  The  yield  is,  there- 
fore, about  ..,',„  of  the  heat  supplied. 

946.  Mellonl's  thermomultlplier. — We  have  already  noticed  the  use 
which  IMelloni  made  of  N<)l)ili's  pile,  in  conjuiution  with  the  galvano- 
meter, for  measuring  the  n\ost  feeble  alterations  of  temperature.  Th6 
.irrangcmcnt  he  used  for  his  experiment  is  represented  in  fig.  943. 

On  a  wooden  base,  provided  with  levelling  screws,  a  graduatcil  copper 


946] 


Melloni 's   Thermoimiltiplier. 


959 

rule,  about  a  metre  long,  is  fixed  edgeways.  On  this  rule  the  various  parts 
composing  the  apparatus  are  placed,  and  their  distance  can  be  fixed  by 
means  of  binding  screws.  <?  is  a  support  for  a  Locatelli's  lamp,  or  other  source 
of  heat  ;  F  and  E  are  screens  ;  C  is  a  support  for  the  bodies  under  experi- 
A 


Fig.  943- 

ment,  and  ni  is  a  thermo-electrical  battery.  Near  the  apparatus  is  a  gal- 
vanometer, D  ;  this  has  only  a  comparatively  few  turns  of  a  tolerably  thick 
(I  mm.)  copper  wire  ;  for  the  electromotive  force  of  the  thermo-currents  is 
small,  and  as  the  internal  resistance  is  small  too,  for  it  only  consists  of  metal, 
it  is  clear  that  no  great  resistance  can  be  introduced  into  the  circuit  if  the 
current  is  not  to  be  completely  stopped.  Such  galvanometers  are  called 
thermomultiplie7-s.  The  delicacy  of  this  apparatus  is  so  great  that  the  heat 
of  the  hand  is  enough,  at  a  distance  of  a  yard  from  the  pile,  to  deflect  the 
needle  of  the  galvanometer. 

In  using  it  for  measuring  temperature,  the  relation  of  the  deflection  of  the 
needle,  and  therefore  of  the  strength  of  the  current,  to  the  difference  of  the 
temperatures  of  the  two  ends  must  be  determined.  That  known,  the  tem- 
peratures of  the  ends  not  exposed  to  the  source  of  heat  being  known,  the 
obser\'ed  deflection  gives  the  temperature  of  the  other,  and  therewith  the 
intensity  of  the  source  of  heat. 

The  most  sensitive  arrangement  of  this  class  is  the  radiojuicrotiicter 
invented  by  Mr.  Boys.  It  consists  of  a  light  thermojunction  suspended  by 
a  thin  quartz  thread  between  the  poles  of  a  strong  horse-shoe  magnet ;  it 
resembles  in  fact  D'Arsonval's  galvanometer  (fig.  761).  With  the  slightest 
difference  in  the  temperature  of  the  two  ends  of  the  bars  of  the  thermo  pair 
a  current  is  produced  in  its  circuit,  and  this  being  in  a  magnetic  field  is 
deflected  like  any  current  under  the  influence  of  a  field.  And  as  the  force 
tending  to  deflect  it  is  the  product  of  the  current  with  the  strength  of  the 
field,  it  follows  that  with  a  strong  field  only  an  extremely  feeble  current  is 
necessary  to  produce  a  considerable  deflection.  By  its  means  Mr.  Boys  can 
detect  differences  of  less  than  one  millionth  of  a  degree  Centigrade.  It 
will  clearly  respond  to  a  quantity  of  heat  not  greater  than  that  which  would  be 
received  on  a  halfpenny  by  the  flame  of  a  candle  at  a  distance  of  1,530  feet. 


960 


Dynamical  Electricity. 


[947- 


947.  Properties  and  uses  of  tbermo-electric  currents. — Thermo-elec- 
tric currents  are  of  extremely  low  potential,  but  of  great  constancy  :  for  their 
opposite  junctions,  by  means  of  melting  ice  and  boiling  water,  can  easily  be 
kept  at  0°  and  100^  C.  On  this  account.  Ohm  used  them  in  the  experimental 
establishment  of  his  law.  They  can  produce  all  the  actions  of  the  ordinary 
battery  in  kind,  though  in  less  degree.  By  means  of  a  thermo-electrical  pile 
consisting  of  769  elements  of  iron  and  German  silver,  the  ends  of  which 
differed  in  temperature  by  about  10°  to  15°,  Kohlrausch  proved  the  presence 
of  free  positive  and  negative  electricity  at  the  two  ends  of  the  open  pile 
respectively.  He  found  that  the  potential  of  the  free  electricity  was  nearly 
proportional  to  the  number  of  elements,  and  also  that  the  electromotive  force 
of  a  single  element  under  the  above  circumstances  was  about  ^-.^-^  that  of  a 
single  Daniell's  element.  On  account  of  their  low  potential,  thermo-electric 
piles  produce  only  feeble  chemical  actions.  Botto,  however,  with  120  platinum 
and  iron  wires,  decomposed  water. 

948.  Thermo-electric  diag-ram. — Thermo-electric  relations  may  be  very 
conveniently  illustrated  by  means  of  what  is  called  the  thermo-electric  dia- 
gram. In  fig.  944  the  abscissae  represent  the  temperatures  of  the  junctions 
on  the  centigrade  scale.  If,  now,  the  thermo-electric  deportment  of  any 
metal  with  another,  taken  as  standard,  be  determined  for  any  given  tempe- 


laUuc,  the  corrcsixjnding  differences  of  potential  arc  reprcscntcil  by  an 
ordinate  according  to  a  definite  scale.  In  the  diagram  the  ordinates  repre- 
sent microvolts  (964),  and  lead  is  taken  as  standard.  A  line  which  connects 
the  ordinates  thus  determined  is  called  a  thermo-ctectric  tine  ;  the  lines  arc 
here  represented  as  straight,  though  some,  such  as  iron  and  nickel,  present 
distinct  sinuosities,  and  may  thus  cross  the  straight  line  belonging  to 
another  metal  more  than  once,  indicating  therefore  more  than  one  neutral 
temperature. 


-949] 


Becquerel's  Electric  Pyrometer. 


961 


It  will  be  seen  that,  if  we  know  the  dififerences  of  potential  of  any  two 
metals  in  respect  of  lead,  the  thermo-electrical  lines  give  us  the  differences 
of  potential  of  these  two  metals  directly.  If,  for  example,  for  the  metals 
copper  and  iron  the  junctions  are  heated  to  0°  and  100°  respectively,  the 
mean  temperature  is  50°,  and  the  difference  of  the  two  ordinates_yjj/'  gives 
the  thermo-electric  force  of  the  combination  for  this  mean  temperature,  the 
metal  at  the  top,  copper,  being  electropositive  ;  the  area  xo—  iS^i  represents 
the  total  tRermo-electric  force  in  the  circuit.  If  the  temperatures  of  the  two 
junctions  were  300°  and  500°,  the  mean  temperature  will  now  be  400°,  and 
the  difference,  _y  J/',  would  represent  the  thermo-electric  force,  which  in  this 
case  would  be  from  iron  to  copper  ;  that  is,  iron  is  now  electropositive  to 
copper. 

The  point  n  where  two  lines  cross  one  another,  and  where,  therefore,  there 
is  no  electromotive  force,  represents  the  neutral  temperature,  or  temperature 
of  inversion  (940) ;  for  copper-iron  this  is  at  276°,  for  iron-cadmium  it  is  at  140°. 

949.  Becquerel's  electric  pyrometer. — This  apparatus  is  an  improved 
form  of  one  originally  devised  by  Pouillet.     It  consists  (fig.  945)  of  two  wires, 


I*"ig.  945. 

one  of  platinum  and  the  other  of  palladium,  both  two  metres  in  length  and 
a  square  millimetre  in  section.    They  are  not  soldered  at  the  ends,  but  firmly 

3Q 


962  Dynavncal  Electricity.  [949- 

tied  for  a  distance  of  a  centimetre  with  fine  platinum  wire.  The  palladium 
wire  is  enclosed  in  a  thin  porcelain  tube  ;  the  platinum  wire  is  on  the  outside, 
and  the  whole  is  enclosed  in  a  larger  porcelain  tube,  P.  At  the  end  of  this 
is  the  junction,  which  is  adjusted  in  the  place  the  temperature  of  which  is  to 
be  investigated.  At  the  other  end  project  the  platinum  and  palladium  wires 
in  and  «,  which  are  soldered  to  two  copper  wires  that  lead  the  current  to  a 
inagneto7neter,  G.  These  wires  at  the  junction  are  placed  in  a  glass  tube 
immersed  in  ice,  so  that,  being  both  at  the  same  temperature,  they  give  rise 
to  no  current. 

The  magnetometer,  which  was  devised  by  Weber,  is  in  effect  a  large 
galvanometer.  It  consists  of  a  magnetised  bar,  ab,  placed  in  the  centre  of 
a  copper  frame,  which  deadens  the  oscillations  (904)  and  rests  on  a  stirrup, 
H,  which  in  turn  is  suspended  to  a  long  and  very  fine  platinum  wire.  On 
the  stirrup  is  fixed  a  mirror,  M,  which  moves  with  the  magnet,  and  gives 
by  reflection  the  image  of  divisions  traced  on  a  horizontal  scale,  E,  at  a 
distance.  These  divisions  are  observed  by  a  telescope.  With  this  view, 
before  the  current  passes  the  image  of  the  zero  of  the  scale  is  made  to  coin- 
cide with  the  micrometer  wire  of  the  telescope  :  then  the  slightest  deflection 
of  the  mirror  gives  the  image  of  another  division,  and  therefore  the  angular 
deflection  of  the  bar  (522).  This  angle  is  always  small,  and  should  not 
exceed  3  or  4  degrees  :  this  is  effected  by  placing,  if  necessary,  a  rheostat  or 
any  resistance  coil  in  the  circuit.  The  angular  deflection  being  known,  the 
intensity  of  the  current  and  the  temperature  of  the  junction  are  deduced 
from  pyrometric  tables.  These  are  constructed  by  interpolation  when  the 
strengths  are  known  which  correspond  to  two  temperatures  near  those  to  be 
observed.  The  indications  of  the  pyrometer  extend  to  the  fusing  point  of 
palladium. 

950.  Peltier's  experiment. — When  on  a  bar  of  bismuth,  BB',  cut  half- 
way through  at  its  centre  (fig.  946),  is  soldered  a  bar  of  antimony  with  a 
similar  cut,  and  when  the  ends  A  and  B  are  connected  with  a  gahanometer, 
the  needle  of  the  galvanometer  is  deflected  in  one  direction  when  the  junction 
is  heated,  and  in  the  other  when  it  is  cooled. 

Peltier  found  by  means  of  this  apparatus,  which  is  known  as  Peltier's 
cross,  that  when  the  end  A'  was  connected  with  one  pole,  and  B'  \\ith  the 
other  pole  of  a  voltaic  element,  so  that  a  current  passed  from  A'  through  the 
junction  to  B',  the  needle  was  deflected  in  such  a  direction  as  to  show  that 
the  junction  was  heated  when  the  positive  current  passed  from  A'  to  B', 
while  it  was  cooled  when  the  current  passed  in  the  opposite  direction. 
This  is  culled  the  Peltier  effect.  In  order  to  show  the  cooling  eftect,  this 
experiment  may  be  made  by  hermetically  fixing  in  two  tubulures  in  an  air 
thermometer  a  compound  bar  consisting  of  bismuth 
and  antimony  soldered  together,  in  such  a  manner 
that  the  ends  project  on  each  side.  The  projecting 
parts  are  provided  with  binding  screws,  so  as  to  allow 
a  current  to  be  passed  through.  When  the  positive 
current  passes  from  the  antimony  to  the  bisniutii,  tlie 
air  in  the  bulb  is  heated,  it  expands,  and  the  liquid  iji 
the  stem  sinks  ;  Ijut  if  it  passes  in  the  opposite  direc- 
tion the  air  is  cooled,  it  contracts,  and  the  liquid  rises  in  the  stem.     The 


-950] 


Peltier  s  Experiment. 


963 


current  must  not  be  too  strong  ;  that  of  a  single  Bunscn's  cell  is  usually 
sufilicient  ;  it  is  best  regulated  by  a  rheostat  (949). 

By  making  a  small  hole  at  the  junction  of  a  bismuth  and  antimony  bar,  in 
which  was  placed  a  drop  of  water  and  a  small  thermometer,  the  whole  being- 
cooled  to  zero,  Lenz  found  that  when  a  current  was  passed  from  bismuth 
to  antimony  the  water  was  frozen  and  the  thermometer  sank  to  -3'5°C. 

The  Peltier  experiment  may  also  be  illustrated  by  interposing  an  iron 
wire  between  two  copper  wires,  and  surrounding  the  first  with  water  at  0°, 
and  the  second  with  ice  at  0°.  On  passing  a  feeble  current,  it  is  found  that 
as  much  ice  melts  at  one  junction  as  is  produced  at  the  other. 

The  Peltier  effect  is  independent  of  the  heating  effect  produced  when  a 
current  traverses  any  conductor,  and  which  may  be  called  the  frictional 
heating  or  Joule  effect.  The  heat  due  to  this  cause  is  proportional  to  the 
square  of  the  current,  C,  to  the  resistance,  R,  and  to  the  time,  /,  and  is 
independent  of  the  direction  of  the  current  (830) ;  while  the  Peltier  effect  is 
proportional  to  the  strength  of  the  current  and  to  the  time,  and  is  reversible 
with  its  direction.  This  suggests  a  method  of  determining  the  effect  in  ques- 
tion. If  this  be  called  /;>,  the  heat  due  to  it  will  be  /;>€/,  and  that  due  to 
the  frictional  heating  will  be  C'-R/.  Hence  if  the  current  be  passed  so  that 
in  one  case  the  Peltier  effect  coincides  with  the  Joule  effect,  while  in  the 
other  it  is  opposed  to  that  effect,  we  shall  have  for  the  total  heat  H  and  H' 
in  the  two  cases  ;  H  =  C'^R^+  ^>C/,  and  H'  =  C-R/- ^feC/,  from  which 

^~      2Ct    • 

That  the  Peltier  effect  is  independent  of  the  Joule  heating  has  been  in- 
vestigated by  Edlund,  by  a  method  the  principle  of  which  is  represented  in 
fig.  947.  M  and  N  are  two  bulbs, 
and  are  connected  by  a  narrow  glass 
tube,  in  which  is  a  drop  of  liquid 
serving  as  index.  The  rods  of  metal 
A  and  B  are  fixed  airtight  in  the  bulbs, 
and  are  soldered  at  7n  and  ?t,  while 
the  free  ends  can  be  connected 
with  a  battery.  If  the  pieces  in 
and  n  inside  the  glass  vessels 
offer  the  same  resistance,  and  these 
vessels  are  of  the  same  size,  when  the 
current  passes  the  Joule  effect  is  the 
same  in  each  case,  and  consequently 
the  index  is  equally  pressed  in  opposite  directions,  and  therefore  does  not  move- 
But  the  Peltier  effect  is  opposite  in  the  two  vessels,  and  produces  a  displace- 
ment of  the  index,  from  which  the  change  of  temperature  can  be  deduced. 

The  Peltier  effect,  as  will  be  seen,  is  greater  as  the  term  C'-R,  or  the 
strength  of  the  current,  is  less,  and  hence  it  can  only  be  shown  with  feeble 
currents. 

These  experiments  form  an  interesting  illustration  of  the  principle,  that 
whenever  the  effects  of  heat  are  reversed  heat  is  produced  ;  and  whenever 
the  effects  ordinarily  produced  by  heat  are  otherwise  produced,  cold  is  the 

3Q  2 


Fig.  947. 


964 


Dynamical  Electricity 


[950- 


result  ;  for  cooling  takes  place  when  the  current  is  in  the  same  direction 
as  the  thermo-current  which  would  be  produced  by  heating  the  junctions, 
and  heating  when  the  current  is  in  the  opposite  direction. 

950(7.  Thomson  effect. — If  we  take  two  bars  of  the  same  metal  A  B  and 
A'  B',  which  are  connected  at  the  ends  A  A' ,  by  a  wire,  while  a  current  can  be 

passed  through  the  other, 
then  the  temperature  of  each 
part  of  the  bar  due  to  the 
Joule  effect  would  be  the 
same  when  the  stationary 
condition  is  attained.  If  the 
two  ends  B  B'  are  kept  at  a 
constant  temperature  of  100° 
by  being  immersed  in  boiling 
water,  while  the  others  A  A, 
are  placed  in  melting  ice, 
and  are  thus  at  0°,  and  if 
now  a  thermopile  be  placed 
with  its  two  opposite  faces  in  contact  with  symmetrical  positions  of  the  two 
bars,  it  will  be  found  that  when  a  current  passes  through  the  system  at  A  A', 
the  galvanometer  of  the  thermopile  is  deflected,  showing  that  there  is  a  dif- 
ference of  temperature  at  the  two  ends  of  the  pile,  that  is,  that  the  corre- 
sponding parts  of  the  bars  are  not  at  the  same  temperature.  In  the  case  of 
copper,  silver,  zinc,  and  antimony  the  point  would  be  hotter  on  that  bar 
along  which  the  positive  current  passes  from  cold  to  hot  ;  in  the  case  of 
tin,  aluminum,  platinum,  bizmuth,  and  iron  it  is  when  the  negative  current 
passes. 

This  phenomenon,  which  is  known  as  the  Thomson  effect  from  its  dis- 
coverer. Sir  W.  Thomson,  is  most  marked  in  antimony  among  positive 
metals,  and  in  iron  ;  it  is  a  sort  of  electrical  convection  of  heat ;  in  copper 
the  positive  current  carries  electricity  along  with  it  more  readily  than  iron  ; 
it  has,  in  short,  a  greater  specific  lieat  of  electficity. 


'^iiiiiii!iiiiiiiriiiiiiiiiiiiiiiii!niiiiiiii]iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiniiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiMiiiiiii^ 
Fig.  948. 


-962]       Determination,  of  the  Resistance  of  a  Conductor. 


965 


CHAPTER    IX. 

DETERMINATION   OF   ELECTRICAL  CONSTANTS. 


Fig.  949. 


951.  Rbeostat. — A  Rheostat  is  an  instrument  by  which  the  resistance 
of  any  given  circuit  can  be  increased  or  diminished  without  opening  the 
circuit.     The   original   form   invented 

by  Wheatstone  consists  of  two  parallel 
cylinders,  one,  A,  of  brass,  the  other, 
B,  of  wood  (fig.  949).  In  the  latter 
there  is  a  spiral  groove,  which  termi- 
nates at  «  in  a  brass  ring,  to  which  is 
fi.xed  the  end  of  a  fine  brass  wire.  This 
wire,  which  is  about  40  yards  long,  is 
partially  coiled  on  the  groove ;  it  passes 
to  the  cylinder  A,  and,  after  a  great 
number  of  turns  on  this  cylinder,  is 
fixed  at  the  extremity  e.  Two  binding 
screws,  n  and  o,  connected  with  the 
battery,  communicate  by  two  steel 
plates  ;  one  with  the  cylinder  A,  the 
other  with  the  ring  a. 

When  a  current  enters  at  <?,  it 
simply  traverses  that  portion  of  the  wire  rolled  on  the  cylinder  B,  where  the 
windings  are  insulated  by  the  grooves  ;  passing  thence  to  the  cyHnder  A, 
which  is  of  metal,  and  in  contact  with  the  wire,  the  current  passes  directly 
to  in,  and  thence  to  n.  Hence,  if  the  length  of  the  current  is  to  be  in- 
creased, the  handle  d  must  be  turned  from  right  to  left.  If,  on  the  contraiy, 
it  is  to  be  diminished,  the  handle  is  to  be  fixed  on  the  axis  c,  and  turning 
then  from  left  to  right,  the  wire  is  coiled  on  the  cylinder  A.  The  length  of 
the  circuit  is  indicated  in  feet  and  inches,  by  two  needles,  at  the  end  of 
the  apparatus  not  seen  in  the  figure,  which  are  moved  by  the  cylinders  A 
and  B. 

952.  Determination  of  tbe  resistance  of  a  conductor.  Reduced 
lengrtb —  If  in  the  circuit  of  a  constant  element  a  tangent  galvanometer  be 
interposed,  a  certain  deflection  of  the  needle  will  be  produced.  If,  then,  dif- 
ferent lengths  of  copper  wire  of  the  same  diameter  be  successively  interposed, 
corresponding  deflections  will  in  each  case  be  produced.  Let  us  suppose 
that  in  a  particular  case  the  tangent  of  the  angle  of  deflection  (823)  observed 
with  the  element  and  tangent  galvanometer  alone  was  rSS,  and  that  when 
5,  40,  70,  and  100  yards  of  copper  wire  were  successively  placed  in  the 
circuit,  the  tangents    of  the  corresponding   deflections    were   0-849,  0*172, 


966 


D)  'iia  HI  ical  Electricity. 


[952- 


0-105,  ^"d  0-074.  Now,  in  this  experiment,  the  total  resistance  consists  of  two 
components — the  resistance  ofifered  by  the  element  and  the  tangent  gal- 
vanometer, and  the  resistance  offered  by  the  wire  in  each  case.  The  former 
resistance  may  be  supposed  to  be  equal  to  the  resistance  of  x yards  of  copper 
wire  of  the  same  diameter  as  that  used,  and  then  we  have  the  following 
relations  : — 

Lefigt/i  of  wire.  TangeiJt  of  angle  of  deflection. 

X  yards '.         .         '.     1-88 

A-  +  5  „ 0-849 

;i-+4o- 0-172 

.t-+7o        „         .  ■ 0-105 

A-+  100      „ 0-074    ■ 

If  the  intensities  of  the  currents  are  inversely  as  the  resistances — that  is, 
as  the  lengths  of  the  circuits — the  proportion  must  prevail, 

X  :  .r+  5  =0-849  :  i'88  ; 
from  which  .t-=  4-1 1.  Combining,  in  like  manner,  the  other  observations,  we 
get  a  series  of  numbers,  the  mean  of  which  is  4-08.  That  is,  the  resistance 
offered  by  the  element  and  galvanometer  is  equal  to  the  resistance  of  4-08 
yards  of  such  copper  wire,  and  this  is  said  to  be  the  reduced  length  of  the 
element  and  galvanometer  in  terms  of  the  copper  wire. 

It  is  of  great  scientific  and  practical  importance  tohave  a  ttm't  or  standard 
of  comparison  of  resistance,  and  numerous  such  have  been  proposed.  Jacobi 
proposed  the  resistance  of  a  metre  of  a  special  copper  wire  a  millimetre  in 
diameter.  Copper  is,  however,  ill  adapted  for  this  purpose,  as  it  is  difficult 
to  obtain  pure.  Matthiessen  proposed  an  alloy  of  gold  and  silver,  contain- 
ing two  parts  of  gold  and  one  of  silver  ;  its  conducting  power  is  very  little 
affected  by  impurities  in  the  metals,  by  annealing,  or  by  moderate  changes 
of  temperature. 

Siemens'  unit  is  a  metre  of  pure  mercury,  having  a  section  of  a  square 
millimetre.  Its  actual  material  reproduction  for  ordinary  use  is  a  German 
silver  wire  3-8  metres  in  length  and  0-9  mm.  in  diameter.     It  is  0-9534  of 

an   ohm   (963).      A 
„„Tm       _  mile  of  No.  16  pure 

copper  wire  repre- 
sents a  resistance 
of  13-67  ohms. 

953.  Resistance 
colls.— The  actual 
material  ])roduction 
of  a  standard  resist- 
ance is  ordinarily  a 
given  length  of  wire 
of  a  certain  defi- 
nite material,  and  is 
known  as  a  7-csist- 
ancc  coil.  An  alloy^ 
of  silver  with  about  \  of  platinum  is'best,  as  it  is  very  permanent,  and  its  re- 
sistance varies  little  with  increase  of  temperature.     Such  resistance  coils  are 


-954]  Resistance  Coils.  967 

usually  employed  in  what  are  called  resistance  boxes  (fig.  950).  Fig.  951 
represents  the  way  in  which  resistance  coils  are  affixed  inside  the  box.  On 
the  top  of  the  box,  which  is  of  slate  or  ebonite,  are  a  number  of  solid  pris- 
matic pieces  of  brass  fixed  a  little 
distance  apart ;  at  their  ends  are 
conical  perforations  in  which  fit  brass 
plugs.  Inside  the  box  are  fitted  to 
'these  brass  pieces  the  various  lengths 
of  wires  which  represent  very  accu- 
rately the  resistances  ;  they  are 
covered  with  insulated  wire,  and  are 
wound  double,  so  as  to  neutralise  any 
extraneous  inductive   action.      If  the 

1  r  •  •  1  ''''g-   951- 

termmals  of  a    circuit  are  connected 

with  T  T',  fig.  951,  and  all  the  plugs  are  inserted,  the  resistance  box  offers  no 
appreciable  resistance,  for  the  current  passes  by  the  plugs  and  the  massive 
metal ;  but  by  taking  out  any  of  the  plugs  the  current  has  to  pass  through  the 
wire  coil  between  the  two  brass  pieces,  and  thus  its  resistance  is  introduced. 
In  figure  950  this  represents  the  use  of  a  resistance  of  74  ohms. 

The  coils  are  in  multiples  and  submultiples  of  ohms,  and  are  so  arranged 
that  their  combination  may  be  as  greatly  varied  with  as  few  resistances  as 
possible.  Thus  a  set  of  eleven  coils  of  o-i,  0-2, 0-2,  0-5,  2,  2,  5, 10,  10,  20,  and 
50  enables  us  to  introduce  any  resistance  from  0"i  to  100  into  the  circuit. 

Resistance  boxes  have  almost  entirely  superseded  the  rheostat  and 
similar  instruments.  They  are  more  accurate,  and  not  nearly  so  likely  to 
suffer  from  use. 

954.  Absolute  measure  of  electrical  resistance. — When  the  resistance 
of  any  conductor  has  been  measured  and  expressed  by  reference  to  any  of 
the  standards  of  resistance  mentioned  in  the  preceding  paragraph,  the  num- 
ber denoting  the  result  of  the  measurement  still  does  not  tell  us  what  the 
resistance  of  the  conductor  in  question  really  is  ;  it  only  tells  us  what  mul- 
tiple it  is  of  the  resistance  of  the  particular  conductor  with  which  the  com- 
parison has  been  made.  It  gives  us  merely  a  relative  and  not  an  absolute 
measure.  Just  in  the  same  way,  if  we  are  told  that  the  pressure  of  the  steam 
in  a  boiler  is  equal  to  (say)  8  atmospheres  (157),  this  statement  does  not  in 
itself  enable  us  to  form  any  estimate  of  what  the  actual  pressure  of  the  steam 
is  ;  it  only  tells  us  that,  whatever  the  pressure  of  an  atmosphere  may  be, 
that  of  the  steam  is  8  times  as  great.  In  order  that  we  may  be  able  to  cal- 
culate what  effects  the  pressure  of  the  steam  is  capable  of  producing,  we 
require  to  have  it  stated  in  absolute  measure— that  is,  not  how  much  greater 
or  less  it  is  than  some  other  pressure — but  what  actual  force  is  exerted  by  it 
on  each  unit  of  surface.  So,  for  very  many  purposes,  we  require  absolute 
measures  of  electrical  resistance,  instead  of  mere  comparisons  of  the  resist- 
ance of  one  conductor  with  that  of  another. 

To  see  how  it  is  possible  to  get  an  absolute  measure  of  resistance,  we 
must  go  back  to  the  fundamental  meaning  expressed  by  the  term.  If,  by 
any  means  whatever,  a  definite  electromotive  force  or  difference  of  potential  is 
maintained  between  any  two  given  cross-sections  of  a  conductor,  a  constant 
electric  current  flows  from  one  cross-section  to  the  other,  and,  for  the  same 


968  Dynamical  Electricity.  [954- 

conductor,  the  ratio  of  the  electromotive  force  to  the  strength  of  the  resulting 
current  is  consta7it.  That  is,  if  Ej,  E,,,  E..,  ...  be  various  values  succes- 
sively given  to  the  electromotive  force,  and  Cj,  C.„  C3,  .  .  .  be  the  corre- 
sponding strengths  of  the  current,  then 

E,^E,^E3^   ...    =  R  (a  constant). 

Uj        U2        1-3 

This  constant  ratio  of  electromotive  force  to  strength  of  current  is  charac-. 
teristic  of  the  individual  conductor  employed,  and  is  called  its  electrical 
resistance.  And,  when  the  resistance  of  a  conductor  is  stated  as  the  value 
of  the  ratio  in  question,  the  statement  gives  us  the  absolute  measure  of  the 
resistance  :  that  is,  it  gives  us  definite  information  about  the  electrical  pro- 
perties of  that  particular  conductor  without  implying  a  comparison  of  it  with 
any  other  conductor. 

Hence  it  appears  that  the  absolute  resistance  of  a  given  conductor  is 
determined  if  we  can  ascertain  the  ratio  of  any  electromotive  force  to  the 
strength  of  the  current  which  it  is  capable  of  producing  in  the  conductor  in 
question.  It  is  not,  hoAvever,  needful  to  make  an  independent  measurement 
of  this  ratio  in  the  case  of  every  conductor  whose  resistance  we  require  to 
know  ;  it  is  sufficient  to  determine  it  once  for  all  for  some  one  conductor,  and 
then,  taking  this  conductor  as  a  standard,  to  compare  the  resistance  of  other 
conductors  with  that  of  this  one,  by  means  of  Wheatstone's  Bridge  (948), 
or  any  other  convenient  method. 

The  methods  available  for  determining  the  ratio  between  electromotive 
force  and  resistance,  required  for  an  absolute  measurement  of  resistance, 
depend  on  the  electromagnetic  phenomena  presented  by  electric  conductors 
and  currents  ;  it  will  be  sufficient  here  to  indicate  the  general  principles 
upon  which  such  methods  can  be  founded.  From  what  has  been  said  it  will 
be  seen  that  any  method  for  this  purpose  involves  a  measurement  of  electro- 
motive force  and  a  measurement  of  the  strength  of  a  current.  It  will  be 
convenient  to  treat  these  two  parts  of  the  process  separately. 

A.  Absolute  measurement  of  electromotive  force. — When  any  electric 
conductor  is  moved  in  a  magnetic  field  (707),  that  is  to  say,  in  any  region 
where  there  is  magnetic  force,  an  electromotive  force  is  in  general  developed 
in  the  conductor  during  its  motion.  The  magnitude  of  this  electromotive 
force  depends  upon  the  strength  of  the  magnetic  field,  on  the  length  and 
form  of  the  conductor,  and  on  the  velocity  and  direction  of  its  motion.  The 
simplest  case  is  presented  by  a  straight  conductor,  with  its  length  perpen- 
dicular to  the  direction  of  the  force  in  a  uniform  magnetic  field,  and  moving 
at  right  angles  to  its  length  and  to  the  direction  of  the  force.  If  T  be  the 
strength  of  the  field,  /  the  length  of  the  conductor,  and  v  the  velocity,  the 
electromotive  force  E  is 

E=/T77', 

where  /'  is  a  constant,  dcjicnding  on  the  unit  ado])lcd  for  the  measurement 
of  electromotive  force.  If  we  define  the  unit  of  electromotive  force  as  that 
which  is  developed  in  a  conductor  of  unit  length  mor'ing  {in  the  way  specified 
above)  with  unit  velocity  in  a  magnetic  yield  of  unit  intensity  the  constant  I: 
becomes  =  i,  and  the  value  of  E  is 

E  =  T/7'. 


-954]  Absolute  Measure  of  Electrical  Resistance.  969 

If  the  length  and  the  direction  of  motion  of  the  conductor  are  not  at  right 
angles  to  the  direction  of  magnetic  force,  we  must  project  both  on  a  plane 
perpendicular  to  the  direction  of  the  force  ;  thus,  if  the  conductor  is  inclined 
at  an  angle  a,  and  moves  in  a  direction  making  an  angle  |3,  both  being 
measured  from  the  direction  of  magnetic  force,  the  electromotive  force 
becomes 

E  =  T/  sin  a.  V  sin  /3. 

If  the  conductor  is  bent  in  any  way,  so  that  a  has  different  values  for  different 
parts,  and  if  the  direction  or  velocity  of  its  motion  varies  from  one  part  to 
another,  we  may  conceive  of  it  as  divided  into  a  great  number  of  equal  parts, 
each  so  small  that  no  sensible  variation  of  o,  /3,  or  v  can  occur  within  it,  we 
may  calculate  the  electromotive  force  due  to  each  of  these  small  parts  taken 
separately  by  the  last  formula,  and  then,  adding  all  the  results  together,  we 
obtain  the  electromotive  force  developed  in  the  whole  conductor.  A  little 
consideration  will  show  that  the  following  statement  is  equivalent  to  that  just 
given  :  namely,  the  electromotive  force  generated  in  a  conductor  moving 
in  any  manner  in  a  magnetic  tield  is  proportional  at  each  instant  to  the 
rate  of  variation  of  the  area  swept  over  by  its  projection  on  a  plane  perpen- 
dicular to  the  direction  of  the  magtietic  force  ;  and  the  average  electromotive 
force  acting  in  the  conductor  during  any  interval  of  time  is  proportional 
directly  to  the  total  area  swept  over  by  its  projection  during  the  interval, 
and  inversely  to  the  length  of  the  interval. 

In  order  to  apply  practically  the  principles  that  have  been  pointed  out, 
it  is  most  convenient  to  take  advantage  of  the  magnetic  field  due  to  the 
magnetism  of  the  earth.  Throughout  any  moderate  space  at  a  distance 
from  magnets  or  masses  of  iron,  the  magnetic  force  due  to  the  earth  is 
uniform  in  intensity  and  direction.  Suppose,  then,  a  circular  conducting 
ring,  placed  so  that  its  plane  is  perpendicular  to  the  direction  of  the  earth's 
magnetic  force — that  is,  to  the  direction  of  the  dipping  needle — to  be  turned 
through  half  a  revolution  about  one  of  its  diameters  ;  we  may  regard  its  pro- 
jection on  a  plane  perpendicular  to  the  direction  of  the  earth's  force  to  be 
made  up  of  the  projections  of  the  two  semicircles  into  which  it  is  divided  by 
the  axis  of  rotation.  During  the  half-turn  made  by  the  ring,  the  projection 
of  each  semicircle  sweeps  through  an  area  equal  to  that  of  the  whole  ring  ; 
but  one  projection  passes  over  this  area  in  one  direction,  and  the  other  in 
the  opposite  direction.  Consequently,  equal  electromotive  forces  are  gene- 
rated in  the  two  halves  of  the  ring,  in  opposite  directions  as  regarded  from 
outside,  but  both  in  the  same  direction  if  considered  as  tending  to  produce  a 
current  round  the  ring  :  the  total  electromotive  force  is  therefore  the  sum  of 
the  forces  in  the  two  halves,  and  if  r  be  the  radius  of  the  ring,  and  therefore 
7rr^  its  area,  and  n  the  number  of  revolutions  per  second,  so  that  the  time 

occupied  by  each  half-revolution  is      ,  the  average  electromotive  force  act- 
ing in  the  ring  as  it  rotates  uniformly  about  a  diameter  is 
2T  .  7rr-'-f-       -T7rr^», 

271 

where  T  stands  for  the  whole  intensity  of  the  earth's  magnetic  force.     If 
instead  of  a  single  ring,  we  have  a  circular  coil  of  wire  of  u  convolutions, 


970  Dynamical  Electricity.  [954- 

and  if  the  axis  of  rotation  makes  any  angle  a  with  the  line  of  clip,  the  elec- 
tromotive force  due  to  the  rotation  of  the  coil  is 
E  =  4T7Tr-HU  sin  a. 
Consecjucntly,  the  rotation  of  a  coil  of  wire  under  the  circumstances  named 
furnishes  the  means  of  obtaining  an  electromotive  force,  the  absolute  value 
of  which  is  given  by  the  intensity  of  the  magnetic  field,  the  dimensions  and 
speed  of  the  coil,  and  the  position  of  its  axes  of  rotation.  If  we  can  deter- 
mine the  strength  of  current  which  this  electromotive  force  is  capable  of 
producing  in  a  given  conductor,  the  absolute  resistance  of  the  conductor  is 
at  once  known. 

B.  Absolute  measureiiieiit  of  the  strength  of  currents. — The  method  ot 
measuring  the  strength  of  electric  currents  is  founded  on  the  fact  that  a 
force  is  exerted  between  a  conductor  carrying  a  current  and  any  magnetic 
pole  in  its  neighbourhood.  In  general,  both  the  distance  and  the  direction, 
as  seen  from  a  given  magnetic  pole,  vary  from  point  to  point  of  the  con- 
ductor, so  that  it  is  generally  impossible  to  give  any  simple  statement  of 
the  law  according"  to  which  a  given  current  acts  upon  a  magnetic  pole  in  a 
given  position.  But,  if  we  consider  only  a  very  small  length  of  a  current, 
neither  the  distance  of  its  various  points  from  a  given  magnetic  pole,  nor 
their  directions,  can  vary  to  a  sensible  extent  ;  and  when  these  two  condi- 
tions are  constant,  the  law  of  the  force  between  the  current  and  the  pole 
may  be  stated  as  follows  :  As  to  direction  the  force  is  perpendicular  to  a 
plane  containing  the  current  and  the  pole,  and  acts  upon  a  north  pole,  to- 
wards the  left  hand  of  an  observer  looking  at  the  pole  from  the  line  of  the 
current,  and  so  placed  that  the  nominal  direction  of  the  current  is  from  his 
feet  to  his  head,  or,  upon  a  south  pole,  towards  the  right  hand  of  an  ob- 
server similarly  placed  ;  as  to  magnitude,  the  force  is  proportional  directly 
to  the  length  (/)  and  to  the  strength  (C)  erf  the  current,  to  the  strength  of  the 
magnetic  pole  (;;/),  and  to  the  sine  of  the  angle  {6)  made  by  the  direction  of 
the  current  with  a  straight  line  drawn  from  it  to  the  pole,  and  inversely  to 
the  square  of  the  distance  {r')  from  the  current  to  the  pole.  Hence,  if  the 
force  be  denoted  by/,  we  have 

f=/&J^  sine, 

r''- 

where  /'  is  a  constant,  depending  on  the  units  in  which  the  numerical  values 
of  the  various  c]uantities  are  expressed.  If  we  define  the  unit  strength  of 
cuirent  as  the  strength  of  a  current  of  loJiich  unit  length  placed  at  unit  dis- 
taiice  from  a  magnetic  pole  of  unit  strength.,  and  nuiking  evcryiohere  a  right 
angle  with  a  line  drawti  from  it  to  the  pole,  everts  unit  force  on  the  pole.,  k 
becomes  unity,  and  wo  have 

,-    C;///    .     n        r^         fr'- 
I  =     ,.    sin  6,  or  C=     -;    .     ^. 
;-  -  ;///  sin  6 

The  most  convenient  way  of  founding  upon  these  principles  a  practical 

measurement  of  the  strength  of  a  current  is  to  cause  the  current  to  go  one 

or  more  times  round  a  vertical  circle  of  kno\vn  radius  placed  in  the  plane  _ 

of  the  magnetic  meridian,  with  a  very  short  magnet  suspended  at  the  centre. 

This  is  the  arrangement  of  the   tangent  galvanometer  already  described 

(823).     If  H  is  the  intensity  of  the  horizontal  component  of  the  earth's  mag- 


-954]         Absolute  Measure  of  Electrical  Resistance.  971 

netic  force,  the  force  which  must  be  exerted  upon  each  pole  of  a  magnet 
whose  poles  are  of  the  strength  +  in  and  — ;;;,  in  a  direction  perpendicular 
to  the  magnetic  meridian,  in  order  to  deflect  the  magnet  through  an  angle 
7,  is 

/=  Wm  tan  y. 

Putting  this  value  of/into  the  expression  given  above  for  the  strength  of 
a  current,  we  have 

,,  _  Hw  tan  7  r'- 
inl  sin  6 
But  in  the  case  supposed,  that  of  a  tangent-galvanometer  with  the  current 
going  u'  times  round  the  circle,  we  have  l  =  u'2na,  if  a  is  the  radius  of  the 
circle  ;  moreover,  the  distance  r' of  each  part  of  the  current  from  the  magnet 
is  constant  and  equal  to  the  radius,  or  r'  =  a,  and  the  angle  6  is  also  constant, 
being  everywhere  a  right  angle,  so  that  sin  6=1;  consequently  we  get  for 
the  strength  of  the  current  in  absolute  measure, 

C  =  -      ,    --  tan  y  = ^  tan  y. 

fnu  2Tta  2nu 

We  have  thus  shown  how  both  electromotive  force  and  strength  of  cur- 
rent can  be  measured  in  absolute  units,  and  if  these  two  measurements  be 
combined,  the  ratio  of  the  numerical  value  of  the  electromotive  force,  acting 
in  a  conductor,  to  that  of  the  strength  of  the  resulting  current,  is  the  measure 
of  the  resistance  of  the  conductor  in  question.  Using  the  notation  employed 
above,  this  leads  to  the  following  expression  for  the  absolute  measure  of  re- 
sistance. 

J,  _  E  _4  Tirr^tm  sin  a  .  2-nu' 
~  C  H  r'  tan  7 

Various  practical  methods  of  measurement  founded  upon  this  principle  have 
been  devised,  and  when  any  of  them  is  employed  the  value  of  the  resistance 
under  investigation  is  obtained  by  putting  in  this  formula  the  values  of  elec- 
tromotive force  and  strength  of  current  that  result  from  the  particular 
arrangement  adopted. 

It  may  be  observed  with  regard  to  the  above  expression,  that  the  factors 
TT,  u,  u',  sin  a  and  tan  3,  are  all  of  them  simple  numbers,  that  T  and  H  are 
quantities  of  the  same  kind,  so  that  their  ratio  is  also  a  pure  number.  The 
only  factors  which  involve  reference  to  physical  units  are  therefore  r'-,  r'  and 
;/,  and  the  two  former  being  both  distances,  the  ratio  r^-^r'  is  the  first  power 
of  a  distance,  while  «,  the  number  of  revolutions  per  unit  of  time,  is  the  re- 
ciprocal of  the  time  occupied  by  a  single  revolution.  Hence  the  expression 
for  the  absolute  resistance  of  a  conductor  is  in  all  cases  reducible  to 

a  distance  1  r    * 

. X  a  numerical  factor  ; 

a  time 

that  is  to  say,  electrical  resistance  may  be  expressed  in  terms  of  the  units  of 
length  (or  distance)  and  time  in  the  same  manner  as  a  velocity,  and  the 
natural  unit  of  resistance,  like  the  natural  unit  of  velocity,  would  be  repre- 
sented byaunit  of  length  per  unit  of  time.  Adopting' the  C.G.S.  system,  the  ab- 
solute unit  of  resistance  becomes  one  centimetre  per  second ;  such  a  resistance, 
however,  is  so  small  that  resistances  commonly  occurring  in  practice  would 
have   to   be   represented   by  inconveniently  great   multiples  of  it.      As   a 


9/2  Dynmnkal  Electricity.  [954- 

practical  standard  of  resistance,  it  is,  therefore,  more  usual  to  employ  the 
ohjn  (963),  which  is  a  resistance  of  one  thousand  million  centimetres  per 
second,  or, 

lo"  centimetres 
I  second 

955.  ■Wheatstone's  brldgre. — The  various  methods  of  determining  the 
electrical  conductivity  of  a  body  consist  essentially  in  ascertaining  the  ratio 
between  the  resistance  of  a  certain  length  of  the  conductor  in  question, 
having  a  given  section,  to  that  of  a  known  length  of  a  known  section  of  some 
substance  taken  as  standard.  The  most  convenient  method  of  ascertaining 
experimentally  the  ratio  between  the  resistance  of  two  conductors  is  by  a 
method  known  as  that  of  W heat  stone' s  bridge, xhe  general  principle  of  which 
may  be  thus  stated  :  — 

The  conductors,  which  may  be  denoted  by  AB  and  BC,  are  connected  end 
to  end,  as  shown  in  fig.  952,  and  one  end  of  each  is  also  connected  with  a 
battery,  say  the  end  A  of  AB  with  the  positive  pole,  and  the  end  C  of  BC 
with  the  negative  pole  ;  the  ends  that  are  ni  connection  with  the  battery  are 
likewise  connected  together  by  another  conductor,  AB'C.  A  current  will 
thus  pass  from  A  to  C  by  each  of  the  two  paths  ABC  and  AB'C,  and  there 


Fig.  952. 

will  be  a  gradual  fall  of  potential  in  passing  from  A  to  C  along  either  path, 
so  that  for  every  point  in  the  conductors  AB  and  BC  there  is  a  point  in  the 
wire  AB'C  which  has  the  same  potential.  If  one  end  of  a  galvanometer 
wire  BGB'  be  connected  with  the  point  of  junction  B,  the  point  of  AB'C 
which  has  the  same  potential  as  the  point  B  can  be  found  by  applying  the 
other  end  of  the  galvanometer  wire  to  AB'C,  and  shifting  the  point  of  con- 
tact towards  A  or  C  until  the  galvanometer  shows  no  deflection.  Let  B'  be 
the  point  so  found  ;  the  fact  that  when  it  is  connected  with  B  by  the  bridge 
BGB'  no  current  passes  from  one  to  the  other  proves  that  the  potential 
at  B'  is  the  same  as  the  potential  at  B.  From  this  it  follows  that  if  r  and  r' 
are  the  resistances  of  AB  and  BC  respectively,  and  s  and  s'  the  resistances 
of  AB'and  B'C, 

r  :  r'  =  s  :  s'. 

If  the  conductor  AB'C  is  a  wire  of  uniform  material  and  diameter,  the 
ratio  of  the  resistances  j-  and  s'  will  be  the  ratio  of  the  lengths  of  the  corre- 
sponding portions  of  wire,  and  can  therefore  be  at  once  really  ascertained. 

To  prove  this,  let  MN,  NO,  MN'  and  N'O'  (fig.  953)  be  taken  in  the 
same  straight  line,  proportional  respectively  to  the  several  resistances 
r,  r',  s,  s' ;  and  let  MP  Ijc  drawn  at  right  angles  to  O'MO  of  a  length 
])rop()rtional  to  the  difference  of  potential  between  the  points  A  and  C.  Then 
if  the  straight  lines  PO  and  PO'  be  drawn,  the  potential  at  N  (the  point  of 
junction  of  the  conductors  whose  resistances  r  and  r'  are  to  be  compared — 


-955] 


WJieatstone's  Brids:e. 


973 


i.e.  the  point  corresponding  to  B  in  the  previous  figure)  will  be  given  by  the 
length  of  the  line  NO,  drawn  from  N  at  right  angles  to  NO  ;  and  the  point 


P 
S'  S  -r  I  yp' 


Fig-  953. 

N'  (corresponding  to  B'  in  the  previous  figure),  Avhere  the  potential  is  the 
same  as  at  N,  will  be  found  by  drawing  QQ'  parallel  to  OO',  and  letting  fall 
from  Q'  the  perpendicular  Q'N'  upon  O'M.  The  geometry  of  the  figure 
gives  obviously, 

-^=^:2and-^=-^-S 
r-^r'     MP  s  +  s'      MP' 

and  therefore  since  NQ  =  NjQ, 


A  convenient  form  of  Wheatstone's  bridge,  and  one  well  adapted  for 
purposes  of  instruction,  is  that  represented  in  fig.  954.  It  consists  of  a  long 
mahogany  board,  on  which  is  fixed  a  thick  copper  band,  which  practically 
offers  no  resistance.     To  the  ends  of  this  band  is  fixed  a  straight  platinum 


fig-  954- 

wire,  near  which  is  a  scale  divided  into  100  parts.  At  c  and  ^are  breaks 
in  the  copper  band,  provided  with  binding  screws,  in  which  are  introduced 
the  resistances  to  be  compared,  O  and  x.  The  wires,  from  an  element 
which  gives  only  a  weak  current,  so  as  not  to  introduce  heating  effects,  are 
connected  with  the  binding  screws  b  and  b'.  Another  wire  connects  the 
binding  screw  g  and  one  end  of  a  sensitive  galvanometer,  the  other  end 
of  which  is  connected  with  a  sliding  spring  contact-key  g\  which  is  so 
constructed  that  when  the  knob  is  depressed  a  knife-edge  makes  contact 
with  any  part  of  the  wire.  The  resistances  to  be  compared  having  been 
introduced  at  c  and  d.,  the  position  on  the  platinum  wire  is  found  by  trial, 
at  which,  when  the  key  is  depressed,  the  needle  of  the  galvanometer  is  not 
deflected.  When  this  is  found,  for  instance,  at  34,  the  resistance  of  O  :  the 
resistance  of  x  =  34  :  66. 


974  Dynamical  Electricity.  [955- 

The  principle  of  Wheatstone's  bridge  is  of  constant  use  in  the  measure- 
ments required  in  telegraphy,  and  many  other  applications  of  electricity. 
In  practice  the  variations  of  the  resistance  are  effected  by  means  of  resist- 
ance coils  (953)  suitably  arranged. 

The  resistance  of  a  galvanometer  may  be  determined  by  making  it  one 
of  the  four  conductors  of  a  Wheatstone's  bridge  arrangement,  replacing  it 
in  the  bridge  by  an  ordinary  contact-key.  The  resistances  of  the  other  con- 
ductors are  then  varied  until,  on  making  contact,  the  deflection  of  the  galva- 
nometer is  constant. 

956.  Equivalent  conductors. — The  resistance  of  a  conductor  depends, 
as  we  have  seen  (825),  on  its  length,  section,  and  conductivity.  Two  con- 
ductors, C  and  C,  whose  length,  conductivity,  and  section  are  respectively 
X,X',  /c,(c',  co,co',  would  offer  the  same  resistance,  and  might  be  substituted  for 
each  other  in  any  voltaic  circuit,  without  altering  its  strength,  provided  that 

=  —^—  ;  and  such  conductors  are  said  to  be  equivalent  to  each  other.     An 

KM         K  Ui 

example  will  best  illustrate  the  application  of  this  principle. 

It  is  required  to  know  what  length  of  a  cylindrical  copper  wire  4  mm. 
in  diameter  would  be  equivalent  to  12  metres  of  copper  wire  i  mm.  in 
diameter. 

Let  X  =  12  the  length  of  the  copper  wire  i  mm.  in  diameter,  and  X'  the 
length  of  the  other  wire  ;  then  since  in  this  case  the  material  is  the  same,  the 

conductivity  is  also  the  same,  and  the  equation  becomes—  =--.    Now  the 

sections  of  the  wires  are  directly  as  the  squares  of  the  diameters,  and  hence 

we  have     "  =  — ,  or  X'  =  12  x  16  =  192.     That  is,  192  metres  of  copper  wire  4 
I-     4- 

mm.  in  thickness  would  only  offer  the  same  resistance  as  12  metres  of  copper 

wire  I  mm.  in  thickness. 

How  thick  must  an  iron  wire  be  \\hich  for  the  same  length  shall  offer  the 
same  resistance  as  a  copper  wire  2*5  mm.  in  diameter? 

Here,  the  length  being  the  same,  the  expression  becomes  /cw  =  k'o)',  or  since 
the  sections  are  as  the  squares  of  the  diameter,  Kif-  =  K'd''.  The  conductivity 
of  copper  is  unity,  and  that  of  iron  0-138.  Hence  we  have  2  5^  =  ^'-  x  0-138 
or  ^'-  =  6-25^0-138  =  45-3  mm,  or  d' =  6-7  mm.  That  is,  any  length  of  a 
copper  wire  2-5  mm.  in  diameter  might  be  replaced  by  iron  wire  of  the  same 
length,  provided  its  diameter  were  6-7  mm. 

957.  Determination  of  tbe  Internal  resistance  of  an  element. — The 
following  is  the  method  of  determining  tlie  internal  resistance  of  an  clement. 
A  circuit  is  formed  consisting  of  one  element,  a  rheostat,  and  a  gahanomcter, 
and  the  strength  C  is  noted  on  the  galvanometer.  A  second  element  is  then 
joined  with  the  first,  so  as  to  form  one  of  double  the  size,  and  therefore  halt 
the  resistance,  and  then  by  adding  a  length,  /,  of  the  rheostat  wire,  the 
strength  is  brought  to  what  it  originally  was.  Then  if  E  is  the  electromotive 
force,  and  R  the  resistance  of  the  element,  r  the  resistance  of  the  galvano- 
meter and  the  other  parts  of  the  circuit  ;  the  current  strength  C  in  the  one 

F  E 

case  is  C  =  ^ — ,  and  in  the  other  =  —- —  — ,, 
R  +  r  AR  +  ;'+/ 

cases  is  the  same,  R  =  2/. 


-958]  Electrical  Conductivity.  975 

Another  method  is  that  due  to  Mance.  The  element  whose  internal 
resistance  is  to  be  determined  is  placed  in  one  of  the  arms  of  a  Wheatstone 
bridge,  as  at  fig.  954,  a  resistance  box  being  placed  in  the  other.  The  gal- 
\anometer  is  connected  with  the  ends  of  the  wire,  and  a  simple  contact-key  is 
interposed  in  the  ordinary  position  of  the  galvanometer,  and  by  trial  its  posi- 
tion is  found  for  the  sliding  contact  such  that  when  the  key  is  depressed  no 
alteration  is  produced  in  the  deflection  of  the  galvanometer.  When  this 
is  found,  the  ordinary  conditions  of  the  bridge  hold,  that  is,  that  the  cross 
products  of  the  resistances  are  equal. 

958.  Electrical  conductivity. — We  may  regard  conductors  in  two 
aspects,  and  consider  them  as  endowed  with  a  greater  or  less  facility  for 
allowing  electricity  to  traverse  them,  a  property  which  is  termed  cotidiictivity., 
or  we  may  consider  conductors  interposed  in  a  circuit  as  offering  an  obstacle 
to  the  passage  of  electricity — that  is,  a  resistance  which  it  must  overcome. 
A  good  conductor  offers  a  feeble  resistance,  and  a  bad  conductor  a  great 
resistance.     Conductivity  and  resistance  are  the  inverse  of  each  other. 

The  conductivity  of  metals  has  been  investigated  by  many  physicists  by 
methods  analogous  in  general  to  that  described  in  the  preceding  paragraph, 
and  very  different  results  have  been  obtained.  This  arises  mainly  from  the 
various  degrees  of  purity  of  the  specimens  investigated,  but  their  molecular 
condition  has  also  great  influence.  Matthiessen  found  the  difference  in  con- 
ductivity between  hard-drawn  and  annealed  silver  wire  to  amount  to  8-5, 
for  copper  2-2,  and  for  gold  1-9  per  cent.  The  following  are  results  of  a 
series  of  careful  experiments  by  Matthiessen  oft  the  electrical  conductivity 
of  metals  at  0°  C.  compared  with  silver  as  a  standard  :  — 


Silver     . 

loo-o 

Platinum 

.    i8-o 

Copper . 

•  99-9 

Iron 

.   i6-8 

Gold      . 

.  8o-o 

Tin          .         .         . 

•    13-1 

Sodium 

•  37-4 

Lead       . 

•     8-3 

Aluminum     . 

•  34-0 

German  silver 

•     77 

Zinc 

.  29-0 

Antimony 

.     4-6 

Cadmium 

■  237 

Mercury 

.     1-6 

Brass     . 

.    22-0 

Bismuth 

.       1-2 

Potassium 

.    20-8 

Graphite 

.       0-07 

Silver  and  copper  have  the  smallest  resistance  for  a  given  volume^  while 
aluminum  has  the  smallest  for  a  given  weight.     ■ 

The  conductivity  of  metals  is  diminished  by  an  increase  in  temperature. 
The  law  of  this  diminution  is  expressed  hy  the  formula 

Kt  =  K„{.^- at  +  bt'-)  ; 
where  k,  and  k,j  are  the  conductivities  at  /  and  0°  respectively,  and  a  and  b 
are  constants,  which  are  probably  the  same  for  all  pure  metals.     f"or  ten 
metals  investigated  by  Matthiessen  he  found  that  the  conductivity  is  ex- 
pressed by  the  formula 

k'  —  k"  ( I  -  0-0037647/  +  0-00000834/-). 

It  seems  that  this  value  is  about  0-00368  for  each  degree  C.  This  co- 
efficient agrees  in  a  surprising  manner  with  the  coefficient  of  expansion  of 
gases,  which  is  ^■^. 

Liquids    are   far  worse   conductors   than   metals.      The  conductivity  of 


976  Dynamical  Electricity.  [958- 

a  solution   of  one    part   of    chloride  of   sodium    in    100  parts   of  water  is 
__J_.._^  that  of  copper.     In  general,  acids  have  the  highest  and  solutions  of 
alkalies  and  neutral  salts  the  lowest  conductivity.     The  conducting  power 
of  a  solution  increases  with  the  number  of  molecules,  but  not  in  direct  pro- 
portion.    For  each  solution,  there  is  a  certain  strength,  which  is  short  of 
saturation,  which   represents    the   maximum   of  conductivity   (845).       For 
copper  sulphate  this  is   18  per  cent.,  and  for  sodium  chloride  26-4  per  cent. 
If  two  badly  conducting  liquids  be  mixed  the  conductivity  of  the  mixture  is 
greater  than  that  of  either  of  the  constituents. 

The  following  is  a  list  of  the  conductivity  of  a  few  liquids  as  compared 
with  that  of  pure  silver  : — 

Pure  silver     .......        100,000,000,000 

Nitrate  of  copper,  saturated  solution    ....         8990 

Sulphate  of  copper         ditto 5420 

Chloride  of  sodium         ditto 31520 

Sulphate  of  zinc  ditto 5770 

Sulphuric  acid,  I -ID  sp.  gr. 99070 

„     „  1-24sp.gr 132750 

„     „  1-40sp.gr 90750 

Nitric  acid,  commercial .^8680 

Distilled  water 7 

The  last  number  was  that  found  by  Kohlrausch  for  distilled  water,  which 
had  been  specially  purified.  Accordingly,  a  disc  of  water  a  millimetre  in 
thickness  offers  the  same  resistance  as  a  column  of  silver  of  the  same  dia- 
meter, but  of  a  length  equal  to  that  of  the  moon's  orbit.  The  least  trace  of 
impurity  in  water  markedly  raises  its  conductivity  :  thus  standing  in  the  air 
for  5  hours  doubles  it  ;  the  addition  of  a  millionth  part  of  sulphuric  acid— 
that  is,  a  drop  in  about  17  gallons — increases  the  conductivity  tenfold.  Ac- 
cordingly we  may  say  in  effect  that  perfectly  pure  water  is  not  a  conductor, 
and  therefore  is  not  appreciably  decomposed. 

Liquids  and  fused  conductors  increase  in  conductivity  by  an  increase  of 
temperature  (845).     This  increase  is  expressed  by  the  formula 

/f,  =  K,  (!  +  «■/), 

and  the  values  of  a  are  considerable.     Thus  for  a  saturated  solution  of  sul- 
phate of  copper  it  is  0-0286. 

The  influence  oi  light  \\\iov\.  electrical  conductivity  in  the  case  of  selenium 
has  been  already  alluded  to  (930),  and  is  directly  proved  by  the  following 
cx])erimcnt.  A  thin  strip  of  this  metalloid,  about  38  mm.  in  length  by  13 
in  breadth,  was  provided  at  the  ends  with  conducting  wires  and  placed  in  a 
box  with  a  draw-lid.  The  selenium,  having  been  carefully  balanced  in  a 
Wheatstone's  bridge,  was  exposed  to  diffused  light  by  withdrawing  the  lid, 
when  the  resistance  at  once  fell  in  the  ratio  of  1 1  to  9.  On  exposure  to  the 
various  spectral  colours,  after  having  been  in  the  dark  it  was  found  to  be  most 
affected  by  the  red ;  but  the  maximum  action  was  just  outside  the  red,  where 
the  resistance  fell  in  the  ratio  of  3  to  2.  Momentary  cxposiu-e  to  the  light'of 
a  gas  lamp  or  even  to  that  of  a  candle  caused  a  diminution  of  resistance.' 
Exposure  to  full  sunlight  diminished  the  resistance  to  one  half. 


-959]  Determination  of  Electromotive  Force.  977 

The  effect  produced  on  exposure  to  light  is  immediate,  while  recurrence 
to  the  normal  state  takes  place  more  slowly.  A  vessel  of  hot  water  placed 
near  the  strip  produced  no  effect,  and  hence  the  phenomenon  cannot  be 
due  to  heat,  but  there  appear  to  be  certain  rays  which  have  the  power  of 
producing  a  molecular  change  in  the  selenium  by  which  its  conductivity  is 
increased. 

If  the  two  electrodes  of  a  Ruhmkorff's  coil  are  connected  with  a  Geissler's 
tube,  suitably  e.\hausted,  so  that  a  discharge  just  does  not  pass  when  the 
apparatus  is  in  the  dark,  it  is  at  once  formed  when  the  path  is  exposed  to 
the  ultra  violet  rays  of  light. 

When  a  large  and  small  induction  coil  are  inserted  in  the  same  circuit 
so  that  they  spark  simultaneously,  it  is  found  that  by  interposing  a  screen 
between  the  two  the  smaller  spark  is  shorter  than  when  it  is  exposed  to  the 
light  of  the  other.  The  action  diminishes  as  the  distance  between  the  two 
sets  of  sparks  increases.  By  varying  the  nature  of  the  screen  and  other 
experiments,  it  has  clearly  been  established  that  this  alteration  is  not  due 
to  any  electrical  effect,  but  is  to  be  ascribed  solely  to  the  ultra  violet  rays. 

959.  Setermination  of  electromotive  force. — IVheatstone's  metbod. 
In  the  circuit  of  the  element  whose  electromotive  force  is  to  be  determined 
a  tangent  galvanometer  and  a  rheostat  are  inserted,  the  latter  being  so 
arranged  that  the  strength,  C,  of  the  current  is  a  definite  amount  ;  for 
example,  the  galvanometer  indicates  45°.  By  increasing  the  amount  of  the 
rheostat  wire  by  the  length,  /,  a  diminished  strength,  c  (for  instance,  40°),  is 
obtained. 

A  second  standard  element  is  then  substituted  for  that  under  trial,  and 
by  arranging  the  rheostat,  the  strength  of  the  current  is  first  made  equal  to 
C,  and  then,  by  addition  of  /,  length  of  the  rheostat,  is  made  =  c. 

Then  if  E  and  E,  are  the  two  electromotive  forces,  R  and  Ri  their  resist- 
ances when  they  have  the  intensity  I,  and  /  and  l^  the  lengths  added,  we 
have 

Trial  Element.  Standard  Element. 

c=iL  c=E, 

R  Ri 

.=    E  -        E. 


RW  Rj+// 

from  which  we  have 

E  =  E,^. 

Hence  the  electromotive  forces  of  the  elements  compared  are  directly  as  the 
lengths  of  the  wire  interposed. 

Another  method  is  that  of  Wiedemann.  The  two  elements  are  con- 
nected in  the  same  circuit  with  a  tangent  galvanometer,  or  other  apparatus 
for  measuring  strength,  first,  in  such  a  manner  that  their  currents  go  in 
the  same  direction,  and  secondly,  that  they  are  opposed.  Then  if  the  elec- 
tromotive forces  are  E  and  E',  their  resistances  are  R  and  R',  the  other 
resistances  in  the  circuits  r,  while  C,  is  the  intensity  when  the  elements  are 
in  the  same  direction,  and  C,  the  intensity  when  they  go  in  opposite  direc- 
tions, then 

3R 


978 


whence 


Dynamical  Electricity. 


[959- 


Cs 


E;E'_andC„- 
R  +  R'  +  r 

E-E' 
R  +  R'  + 

^,    E(C,-Cd) 

The  difference  of  potentials  or  E.M.F.  between  any  two  points  of  a 
circuit  conveying  a  current,  such  as  that  of  a  magneto  machine,  may  be 
determined  by  charging  a  condenser  from  the  terminals  at  the  points  in 
question,  and  discharging  it  through  a  galvanometer  with  a  high  resistance, 
and  then  repeating  the  operation  with  a  standard  cell,  such  as  that  of  Latimer 
Clarke,  the  E.M.F.  of  which  is  1-433  volts  (964).  If  ^is  the  deflection  of  the 
galvanometer  when  the  standard  cell  is  used,  and  D  the  deflection  after  the 

discharge  of  the  current,  and  if  a  shunt  be  used  so  that  only      of  the  current 

nV> 

passes  througli  the  galvanometer,  then  E.M.F.   =  _— -  x    i'433. 

959(^«.  Measurement  of  capacity. — In  order  to  compare  the  capacities 
of  two  condensers,  the  two  armatures  are  severally  connected  with  the  two 
poles  of  a  battery,  and  are  then  discharged  through  a  ballistic  galvanometer  ; 
the  amount  of  charge,  and  therefore  the  capacities,  are  proportioned  to  the 
angles  of  throw  of  the  needle. 

If  we  have  a  condenser  of  known  capacity  this  method  may  be  used  to 
measure  the  E.M.F.  of  a  battery,  or  rather  to  compare  the  E.M.F.  of  two 
couples.  Two  capacities,  C  and  C,  may  also  be  compared,  by  an  arrange- 
ment (fig.  955)  resembling  that  of  Wheatstone's  bridge,  by  connecting  the 


Fi^.  955. 

inner  coaluigs  at  c  and  d  respectively  (fig.  954),  their  outer  coatings  being  put 
to  earth.  The  two  resistances  «  and  <j' are  adjusted,  so  that  by  raising  or 
lowering  the  key  K,  which  puts  the  battery  E  in  connection  with  A,  no 
current  is  shown  in  the  galvanometer. 

The  condition  of  equilibrium  is  that  tlie  two  points  of  the  bridge  B  and 
B'  arc  at  the  same  potential,  that  is  to  say,  that  at  a  given  lime  the  charges 
(,)  and  ()^  arc  jiroportional  to  the  capacities  C  and  C,  ;  as  these  charges  are 
proportional  to  the  currents  which  produce  them,  and  as  these  latter  again 
are  inversely  as  the  resistances,  we  have  the  proportion 
(Z:Z,  =  a'  :  a. 

</>o.  Siemens'  electrical    resistance    thermometer. — Supposing  in  a 
\\  htalstonc  ;>  bridge  arrangement,  after  the  ratio  r  :  r^     s  :  s^  has  been  esta- 


-961]  Divided  or  Branch   Currents.  979 

blished,  the  temperature  of  one  of  the  coils,  r,  for  instance,  be  increased,  the 
above  ratio  will  no  longer  prevail,  for  the  resistance  of  r  will  have  been 
altered  by  the  temperature  (958),  and  the  ratio  oi  s  and  s^  must  be  altered  so 
as  to  produce  equivalence.  On  this  idea  Siemens  has  based  a  mode  of  ob- 
serving the  temperature  of  places  which  arc  difficult  of  direct  access.  He 
places  a  coiipf  known  resistance  in  the  particular  locality  whose  temperature 
is  to  be  observed  :  it  is  connected  by  means  of  long  good  conducting  wires 
with  the  place  of  observation,  where  it  forms  part  of  a  Wheatstone's  bridge 
arrangement.  The  resistance  of  the  coil  is  known  in  terms  of  the  rheostat, 
and  by  preliminary  trials  it  has  been  ascertained  how  much  additional  wire 
must  be  introduced  to  balance  a  given  increase  in  the  temperature  of  the  re- 
sistance coil.  This  being  known,  and  the  apparatus  adjusted  at  the  ordinary 
temperature,  when  the  temperature  of  the  resistance  coils  varies,  this  variation 
in  either  direction  is  at  once  known  by  observing  the  quantity  which  must 
be  brought  in  or  out  of  the  rheostat  to  produce  equivalence. 

This  apparatus  has  been  of  essential  service  in  watching  the  tempera- 
ture of  large  coils  of  telegraph  wire,  which,  stowed  away  in  the  hold  of  vessels, 
are  very  liable  to  become  heated.  It  might  also  be  used  for  the  continuous 
and  convenient  observation  of  underground  and  submarine  temperatures. 
If  a  coil  of  platinum  wire  were  substituted  for  the  copper,  the  apparatus  could 
be  used  for  watching  the  temperature  of  the  interior  of  a  furnace.  It  has 
been  found  that  the  magnetism  of  ships  (715)  excited  so  perturbing  an 
influence  on  the  needle  of  the  galvanometer  as  to  make  its  indications 
untrustworthy.  Hence  for  use  in  such  cases  Siemens  replaces  the  galvano- 
meter, as  an  indicator,  by  a  voltameter  specially  constructed  for  the  purpose. 
The  same  principle  has  Ipeen  applied  by  Professor  Langley  to  the  inven- 
tion of  an  instrument  called  the  Bolometer,  or  actinic  balance,  for  measuring 
radiant  heat.  In  the  two  arms  of  a  Wheatstone's  bridge  are  introduced 
resistances  which  have  very  small  mass,  each  consisting  of  a  band  of  iron 
half  a  millimetre  in  breadth,  and  0-004  mr"-  i"  thickness,  folded  on  itself  14 
times  so  as  to  form  a  rectangle  07  cm.  in  length  by  12  cm.  in  breadth. 
The  sensitiveness  is  far  greater  than  that  of  the  most  sensitive  thermopile, 
and  makes  it  possible  to  measure  a  difference  of  temperature  of  the  ,„J„j  of 
a  degree  between  the  two  resistances.  It  has  been  used  by  the  inventor  to 
measure  the  distribution  of  heat  in  the  solar  spectrum.  By  its  means  he 
has  been  able  to  map  the  dark  heat  of  the  spectrum,  and  to  extend  it  far 
beyond  the  limits  which  were  previously  known. 

961.  Blvided  or  brancb  currents. —  In  fig".  956  the  current  from  Bunsen's 
element  traverses  the  wire  rqpiun.  Let  us  take  the  case  in  which  any  two 
points  of  this  circuit,  //  and  q,  are  joined  by  a  second  wire,  nxq.  The  current 
will  then  divide  at  the  point  q  into  two  others,  one  of  which  goes  in  the 
direction  qpnni,  while  another  takes  the  direction  qxntn.  The  two  points  q 
and  //  from  which  the  second  conductor  starts,  and  at  which  it  ends,  are  called 
the  points  of  derivation,  the  wire  qpm  and  the  wire  qxn  are  derived  wires. 
The  currents  which  traverse  these  wires  are  called  the  derived  or  partial 
currents  ;  the  current  which  traverses  the  circuit  rqpnin  before  it  branches 
is  the  primitive  current ;  and  the  name  principal  current  is  given  to  the 
whole  of  the  current  which  traverses    the   circuit  when    the   derived  wire 

3  R2 


980  Dynamical  Electricity.  [961- 

has  been  added.  The  principal  current  is  stronger  than  the  primitive  one, 
because  the  interposition  of  the  wire  qxn  lessens  the  total  resistance  of  the 
circuit. 

If  the  two  derived  wires  are  of  the  same  length  and  the  same  section, 

their  action 

would     be     the 

same  as  if  they 

werejuxtaposed, 

and  they  might 

be   replaced   by 

;i  single  wire  of 

the  same  length 

but      of     twice 

^'S-  956.  the  section,  and 

therefore  with   half  the  resistance.     Hence  the  current  would  divide  into 

two  equal  parts  along  the  two  conductors. 

When  the  two  wires  are  of  the  same  length  but  of  different  sections,  the 
current  would  divide  unequally,  and  the  quantity  which  traversed  each  wire 
would  be  proportional  to  its  section,  just  as  when  a  river  divides  into  two 
branches,  the  quantity  of  water  which  passes  in  each  branch  is  proportional 
to  its  dimensions.  Hence  the  resistance  of  the  two  conductors  joined  would 
be  the  same  as  that  of  a  single  wire  of  the  same  length,  the  section  of  which 
would  be  the  sum  of  the  two  sections. 

If  the  two  conductors  qpn  and  qx7i  are  different,  both  in  kind,  length, 
and  section,  they  could  always  be  replaced  by  two  wires  of  the  same  kind 
and  length,  with  such  sections  that  their  resistances  would  be  equal  to  the 
two  conductors  ;  in  short,  they  might  be  replaced  by  equivalent  conductors. 
These  two  wires  would  produce  in  the  circuit  the  same  effect  as  a  single 
wire,  which  had  this  common  length,  and  whose  section  would  be  the  sum 
of  the  sections  thus  calculated.  The  current  divides  at  the  junction  into  two 
parts  proportional  to  these  sections,  or  inversely  as  the  resistances  of  the  two 
wires.  Suppose,  for  instance,  qpn  is  an  iron  wire  5  metres  in  length  and 
3  mm.  square  in  section,  and  qxn  a  copper  wire. 

The  first  might  be  replaced  by  a  copper  wire  a  metre  in  length,  whose 
section  would  be  f  x  i  (taking  the  conductivity  of  copper  at  7  times  that  of 
iron)  or  if^^  square  mm.  The  second  wire  might  be  replaced  by  a  copper 
wire  a  metre  in  length  with  a  section  of  |  square  mm.  These  two  wires 
would  present  the  same  resistance  as  a  copper  wire  a  metre  in  length,  and 
with  a  section  of  ~  +  \  =  3Y5  square  millimetres. 

The  principal  current  would  divide  along  the  wires  into  two  portions, 
which  would  be  as  ,\  :  \. 

The  most  important  laws  of  divided  circuits  are  as  follows  :  — 
i.    The  sum  of  the  strcnt^tJis  in  the  divided  parts  of  a  ciycidt  is  equal  to 
the  strength  of  the  principal  current. 

ii.  The  strengths  of  the  currents  in  the  divided  parts  of  a  circuit  are 
inversely  as  their  resistances ;  or,  what  is  the  same,  the  division  of  a  current 
into  partial  currents  which  lie  between  two  points  is  directly  as  the  respective 
conductivities  of  these  branches. 

And  as  problems  on  divided  or  shunt  circuits  frequently  occur  in  tele- 


962] 


Electrical  Mcasiiritisr  Instninicnts. 


981 


graphy,  the  following  foimuhu,  which  include  these  laws,  are  given  for  a 
simple  case. 

If  C  be  the  strength  of  the  current  in  the  undivided  part  of  the  circuit 
rqp/nn,  and  if  c  is  the  strength  in  one  branch  (say)  in  the  above  figure  gpn 
and  c'  in  qxn  ;  if  R,  r,  and  r^  are  the  corresponding  resistances,  the  electro- 
motive force  being  E,  then 

P  _  •  E  (r  +  rj  Er  ,  Er, 


Rr  +  Rr,  +  rr,  Rr  +  Rrj  +  rr. 

The  resistance  R,  of  the  whole  circuit  is 


C': 


Rr  +  R^j  +  rr^ 


and  therefore  the  total  resistance  of  the  branch  currents  gpn  and  qxn  is 


961a.  XTse  of  shunts. — The  principle  of  divided  or  branch  circuits  has 
an  important  application  in  shutits,  by  which  any  given  proportion  of  even  a 
powerful  current  may  be  transmitted  through  a  delicate 
galvanometer,  and  thus  their  range  is  greatly  extended. 

They  consist  of  a  set  of  resistances  usually  J,  g\,  and 
gig,  of  that  of  the  galvanometer,  arranged  as  represented 
in  fig.  957.  G  and  G'  are  in  connection  with  the  ter- 
minals of  the  galvanometer,  and  P,  P'  with  those  of  the 
battery.  The  gaps,  O,  A,  B,  C  can  be  closed  by  plugs, 
and  thus  the  corresponding  resistances  introduced.  When 
they  are  all  open,  the  entire  current  would  pass  through  the 
galvanometer.  By  plugging  O  the  current  is  short-circuited, 
and  none  of  it  passes  through  the  galvanometer. 

If  g  is  the  resistance  of  the  galvanometer,  s  that  of 
the  shunt,  C  the  total  current,  and  c  that  which  passes 
through  the  galvanometer  and  produces  the  deflection, 
we  may  deduce  from  the  laws  of  branch  circuits 


o^nrv^j^^j 


gc  =  s{C-c)  or  C^ 


.J^s 


Fig.  957- 


The  expressions^ — =in  is  called  the  inidtiplying poiuer  of  the  shunt  ; 

it  is  the  value  by  which  the  observed  current  must  be  multiplied  to  obtain 
the  principal  currents.  In  the  above  cases  the  multiplying  powers  are  10, 
100,  and  1000  respectively, 

962.  Electrical  IVXeasurlng:  Instruments. — The  numerous  and  impor- 
tant technical  applications  of  electricity  have  given  rise  to  the  invention  of 
numerous  instruments  for  the  simple  and  direct  measurement  of  powerful 
electrical  currents.  The  amperomcter^  or  briefly  avwieter,  for  instance,  gives 
at  once  the  strength  of  a  current  in  amperes. 

As  a  type  of  this  instrument  we  may  take  a  recent  form  of  that  invented 
by  Professors  Ayrton  and  Perry  ;  it  depends  on  the  principle  that  when  a 
portion  of  an  iron  core  is  partly  within  and  partly  without  a  magnetising 


Dynamical  Electricity. 


[962- 


coil,  it  is  drawn  inwards  when  a  current  is  passed  through  the  coil.  The 
essential  feature  of  the  apparatus  is  a  coil  of  insulated  wire,  in  the  axis  of 
which  is  a  spiral  attached  at  one  end  to  an  index  moving  over  a  graduated 
scale.  At  the  other  end  of  the  spiral  is  a  brass  cap  to  which  is  attached  a 
thin  cylinder  of  fine  sheet  iron,  which  is  in  fact  the  core  ;  it  encircles  the 
spiral  and  projects  outside  the  coil.  The  spiral  itself  is  formed  of  a 
ribbon  of  thin  phosphorus  bronze  coiled  so  as  to  form  a  very  narrow  cylinder. 
This  construction  gives  it  the  property  that,  unlike  ordinary  spirals,  when  its 
length  increases  the  free  end  rotates  through  a  considerable  distance. 
Accordingly,  when  the  current  passes  through  the  coil,  the  iron  tube  is 
drawn  within  the  spiral  to  an  extent  varying  with  the  strength  of  the  current  ; 
this  thereby  elongates  the  spiral  to  which  it  is  attached,  and  the  index 
attached  to  the  latter  moves  over  the  scale,  finally  taking  up  a  position 
which  depends  on  the  strength  of  the  current.  Such  instruments  are 
graduated  empirically  and  within  any  desired  range  by  observing  the  de- 
flection caused  by  passing  through  them  currents  of  known  strength. 

The  voltmeter^  which  is  not  to  be  confounded  with  the  voltameter  (846), 
measures  the  difference  of  potential  between  any  two  points  of  a  circuit. 
It  consists  essentially  of  a  coil  such  as  the  above,  but 
with  a  great  length  of  long  fine  wire.  This  can  be  in- 
serted as  a  shunt  without  appreciably  altering  the  resist- 
ance of  the  circuit.  Like  the  ammeter,  this  is  empirically 
graduated. 

Cardcw's  voltmeter  depends  on  the  heating  effect  pro- 
duced when  a  current  tra\crses  a  wire  and  consists  essen- 
tially of  a  long  fine  platinum  wire,  stretched  by  a  spring  or 
a  weight  to  which  is  attached  a  multiplying  motion  and 
an  index.  This  wire,  being  introduced  between  the  points 
of  the  circuit  to  be  measured,  becomes  heated  to  an  extent 
proportional  to  the  square  of  the  difference  of  potentials, 
and  the  motion  of  the  index  is  a  measure  of  this  heating. 
The  principle  of  the  clcctrodyiuDnomctcr  is  that  of 
measuring  the  repulsion  between  parallel  currents  moving 
in  opposite  directions,  one  of  them  being  fixed  and  the 
other  movable.  Fig.  958  represents  the  essential  features 
of  a  form  devised  by  Siemens  for  measuring  the  strength 
of  the  powerful  currents  used  in  electric  lighting ;  w  is 
a  coil  of  stout  copper  wire,  and  li''  a  single  wire  ;  nn 
are  mercury  cups,  and  kk  binding  screw,  by  which  con- 
nection is  made  with  the  main  circuit  LL. 

The  wire  it.''  is  surrounde/;!  by  a  stout  spiral  spring, 
which  is  connected  at  one  end  with  this  wire,  and  at  the  other  with  a  screw, 
.J- ;  this  is  provided  with  an  index,  z^  which  mo\es  o\er  a  graduated  scale,  S. 
An  index,  z'z\  is  also  fixed  to  the  wire  iv'.  At  the  outset  both  indexes  point 
to  zero ;  when  the  current  passes  it  will  be  seen  from  the  direction  of  the 
arrows  that  it  traverses  the  fixed  and  movable  coils  in  opposite  directions, 
and  the  point  z'  is  displaced  along  the  scale.  l>y  turning  the  screw  s  it 
is  brought  back  to  zero,  in  doing  which  the  index  z  is  moved  through  an' 
angle  which  is  a  measure  of  the  torsion  of  the  spiral  spring  f,  and  this 


Fig.  958. 


-963]  Absolute  Electrical  Units.  983 

angle  is  proportional  to  the  square  of  the  strength  of  the  current  by  which 
the  movable  coil  is  deflected. 

The  electrodynamometer  has  by  no  means  the  sensitiveness  which  can 
be  readily  obtained  with  galvanometers  ;  but  it  has  the  advantage  that  its 
indications  are  independent  of  tlie  strength  of  the  external  field,  and  when 
the  two  coils  are  traversed  by  the  same  current  they  are  also  independent  of 
the  direction  of  the  current ;  and  can  accordingly  be  used  with  advantage  in 
measuring  alternatnig  currents. 

963.  Absolute  electrical  units. — The  great  importance  of  having  a 
uniform  system  of  measurements  of  physical  magnitudes  which  should  be 
universally  adopted  is  at  once  obvious,  and  this  has  been  more  especially 
felt  in  the  applications  of  electricity.  The  first  step  in  this  direction  was 
taken  by  the  British  Association,  which  adopted  the  system  of  absolute  units 
known  as  the  C.("i.S.  system,  of  which  mention  has  already  been  made 
(6i(?,  709),  and  which  this  account  is  intended  to  supplement. 

The  essence  of  an  absolute  system  of  physical  measurements  is  that  the 
various  units  may  be  directly  expressed  in  mechanical  units  {b\a).  A  system 
of  absolute  electrical  units  may  be  based  on  either  the  electrostatic,  the 
electromagnetic,  or  again  on  the  electrodynamic  actions.  There  is  no 
theoretical  reason  why  one  should  be  preferred  to  another  of  these,  but  in 
practice  only  the  two  former  are  used.  Of  these  the  electrostatic  system  is 
perhaps  the  simpler,  but  that  based  on  electromagnetism  is  most  convenient, 
and  best  lends  itself  to  the  practical  determination  of  the  most  important 
standards,  such  as  those  of  electromotive  force  and  resistance. 

E/ectrostati'c  Units. 

We  shall  distinguish  the  dimensions  of  these  units  by  small  letters  placed 
in  brackets. 

Quiuitity  of  Electricity,  q.  Coulomb's  law  given  for  the  repulsive  force 

between   two  equal  quantities  q,  of  electricity  at  the  distance  /,  /=  1.    (734), 

from  which  q  =  l  ^f.  Hence  we  have  for  the  dimensions  of  unit  quantity  of 
electricity  [^]  =  I f\  =  UM^T-'. 

Potefitial.  V.  The  potential  of  a  quantity  of  electricity  at  the  distance  / 

is  the  quotient  of  the  quantity  by  the  distance.     Hence  [7/]  =  ^  =  L-M^T^'. 

Capacity,  c.  The  capacity  of  a  conductor  is  the  quotient  of  the  quantity 
of  electricity  with  which  it  is  charged,  by  the  potential  which  this  quantity 

produces  in  it  ;  [t"]=  -  from  which  \c\  =  L.  Hence  the  capacity  of  a  con- 
ductor is  expressed  by  a  length.  Unit  capacity  is  thus  that  of  a  body  which 
is  raised  by  unit  quantity  to  unit  potential.  An  insulated  conducting  sphere 
which  has  a  diameter  of  one  centimetre  has  unit  capacity. 

Current,  i.  The  strength  of  a  current  is  the  quantity  of  electricity  which 

passes  in  a  given  time  ;  [/]  =  2  =  L? M ^*T-.     Accordingly  unit  current  is  that 

which  conveys  unit  quantity  of  electricity  in  a  second. 

Resistance,  r.   From  Ohm's  law  (S25),  the  resistance  of  a  conductor  is 


984  Dynamical  Electricity.  [963- 

the  quotient  of  difference  of  potentials  at  the  two  ends  of  a  wire  by  the 
strength  of  a  current.  Hence  [r]  =  ^  =  L-'T,  which  shows  that  the  dimen- 
sions of  resistance  are  the  inverse  of  a  velocity. 

Electromag)ietic  Units. 

Quantity  of  magnetism.     From  Coulomb's  law/  =  — -  from  which  [M]  = 

LIM^T-',  that  is,  the  same  as  that  of  quantity  of  electricity  on  the  electro- 
static system.  Unit  magnetic  pole  is  that  which  repels  an  equal  pole  at  a 
distance  of  a  centimetre  with  a  force  of  a  dyne. 

Magnetic  Field.  H.  Unit  magnetic  field  is  that  field  in  which  unit 
quantity  magnetism  is  acted  on  by  unit  force.     Hence  F  =  HM,  from  which 

[h}=l-'m;t-'. 

Current.  I.  The  unit  of  electrical  current  in  the  electromagnetic  system 
is  that  which,  traversing  unit  length  of  an  arc  of  a  circle  of  unit  radius,  exerts 
unit  force  on  unit  pole,  or  unit  magnetism  at  its  centre.     Its  dimensions  are 

Quantity  of  electricity.  Q.  The  quantity  of  electricity  conveyed  by  a  con- 
ductor is  the  product  of  the  current  by  the  time  that  it  lasts.  Hence  unit 
quantity  is  that  which  passes  in  a  second  in  a  conductor  in  which  unit  current 
is  flowing,  [Q]  =  IT  =  UMi. 

Resistance.  R.     The  resistance  of  a  conductor  may  be  defined  by  Joule's 

law,  W  =  r^RT.  Hence  [R]  =  ^,  that  is,  the  resistance  of  a  conductor  is 
expressed  by  a  velocity. 

Electromotive  force.  Dilference  of  potentials  [E].  From  Ohm's  law, 
E  =  IR  =  UMiT--. 

964.  Practical  units. — The  values  of  the  absolute  units  in  the  C.G.S. 
system  are  not  convenient  for  measuring  the  magnitudes  which  ordinarily 
occur.  Thus  the  absolute  unit  of  resistance  is  that  represented  by  the 
twenty-thousandth  part  of  a  millimetre  of  pure  copper  wire 
a  millimetre  in  diameter.  It  has  therefore  iDeen  necessary  to 
choose  units  better  suited  for  practical  uses,  and  at  the  Inter- 
national Congress  of  Electricians  at  I'aris  in  1881  an  Inter- 
national Commission  was  formed  for  the  purpose  of  deciding 
on  such  units  and  determining  their  value.  In  1884  the 
Commission  agreed  to  recommend  the  following,  which  are 
in  the  main  those  introduced  by  the  British  Association. 

The  practical  unit  of  resistance  is  equal  to  10^  absolute 
electromagnetic  C.G.S.  units  of  resistance,  and  is  called  the 
Ohm.     It  has  been  decided  to  represent  it  by  a  column  of 
'B-  959-  pure  mercury  with  a  cross  section  of  a  square  millimetre  ; 

its  exact  length  has  been  determined  experimentally  by  the  Commission, 
and  has  been  taken  at  ro6  metre.  This  is  known  as  the  legal  ox  Congress 
ohm.  Copies  of  this  standard  may  be  made  either  in  mercury  (fig.  959),  or 
in  wire  (fig.  958),  and  each  copy  has  the  value  marked  upon  it,  which  is^ 
correct  for  a  certain  temperature.  A  wire  of  pure  copper,  a  millimetre  in 
diameter  and  46-25  metres  in  length,  has  a  resistance  of  one  ohm.  Siemens' 
unit  (952)  has  a  resistance  of  0-94339  ohm.     The  copper  conducting  wire 


-964]  Practical  Units.  985 

of   an  ordinary  submarine  cable  has  a  resistance  of  about    1 1    ohms  per 
mile. 

In  order  to  express  multiples  and  submultiples  the  prefixes  mega  or 
micro  are  used,  which  are  respectively  a  million  times  as  great  or  as  small. 
Thus  a  megohm  is  10''  ohms,  that  is,  10'^'  absolute  units  of  resistance.  In 
like  manner  a  micro/im  is  lo'"  ohm,  that  is,  10^  =  1000  such  units. 

The  Volt  is  the  practical  unit  of  electromotive  force  or  of  difference  of 
potentials,  and  is  equal  to  lo"*  absolute  units.  From  the  difficulty  of  getting 
an  element  which  is  perfectly  constant,  more  especially  when  it  is  closed,  the 
standard  of  E.M.F.  is  best  derived  from  measurements  of  resistance  and  of 
strength  of  current,  which  are  both  convenient  and  very  accurate.  Com- 
pared with  the  electrostatic  unit  of  potential  the  volt  is  very  small,  being 
only  -I-  of  such  a  unit.  The  electromotive  force  of  a  Daniell's  cell  is  about 
a  twelfth  greater  than  a  volt.  According  to  the  latest  determinations  of  Lord 
Rayleigh  a  Latimer  Clarke's  element  has  the  E.M.F.  i'433  volt. 

The  Ampere  is  the  unit  of  current,  and  is  the  current  produced  by  the 
electromotive  force  of  a  volt  in  a  circuit  having  a  resistance  of  an  ohm.  It 
is  therefore  equal  to  lO"'  C.G.S.  units.  A  millampci'e  is  the  thousandth  of 
an  ampere. 

The  resistance  of  a  Daniell's  element  with  an  external  cylinder  of  zinc, 
8  inches  high  and  ^ik  '"  diameter,  surrounding  the  porous  pot,  is  about  1*3 
ohm,  and  taking  its  E.M.F.  at  ro8  volt  its  current  when  on  short  circuit  is  about 
0-8  ampere.  In  like  manner  a  medium-sized  Bunsen  has  a  resistance  ot 
about  o-i  ohm,  and  as  its  E.M.F.  is  rS  volt,  the  current  on  short  circuit  is 
18  amperes.  A  Brush  machine  the  current  of  which  ignited  16  lamps  had  an 
E.M.F.  of  839  volts  ;  its  internal  resistance  was  10-55,  and  the  external,  in- 
cluding the  lamps,  was  73  ohms.  Accordingly  the  current  was  10-04  amperes. 
A  Holtz  machine  has  in  electromagnetic  measure  the  E.M.F.  of  90,000  volts  ; 
its  internal  resistance,  when  it  makes  two  turns  in  a  second,  is  calculated  at 
27  X  lo**  ohms,  and  accordingly  its  current  is  -^—-^^^  of  an  ampere,  or  j^j,-  of  a 
millampere.  Such  a  current  is  too  weak  for  telegraph  work  ;  the  currents 
which  are  used  with  the  ordinary  Morse  receivers  have  a  strength  of  14  to 
16  millamperes. 

The  Coulomb  is  the  unit  of  quantity  of  electricity,  and  is  that  quantity 
which  traverses  the  section  of  a  conductor  in  a  second,  when  a  current  of  an 
ampere  is  passing   through    it.     A  coulomb  of  elec-  rt 

tricity    in    traversing    an    electrolyte    decomposes    a  | 

weight  of  the  body  expressed  by  0-00001038  times  its 
electrochemical  equivalent. 

The  Farad  is  the  unit  of  capacity,  and  is  such  that 
in  a  condenser  of  that  capacity  the  quantity  of  a 
coulomb  produces  a  difference  of  potential  of  a  volt. 
It  is  IO-'  C.G.S.  units.  The  farad  is  far  too  large  a 
unit  for  practical  use,  thus  the  capacity  of  the  globe  li  -  ,  .j  J .j,,!;,!,, 
is  only  0-000636  of  a  farad,  that  of  the  sun  does  not 
amount  to  a  farad.  Accordingly  the  technical  unit  of 
capacity  is  the  millionth  part  of  this,  and  is  called  the 
microfarad.     This  is  lO"'"' units.     A  Leyden  jar  with  a  'S- 9    • 

total  coated  surface  of  a  square  metre,  and  the  glass  of  which  is  1   mm. 
thick,  has  a  capacity  of  ^  of  a  microfarad.     The  capacity  of  an  ordinary 


986  Dynamical  Electricity.  [964- 

siibmarine  cable  may  be  taken  at  about  5  of  a  microfarad  per  knot  or 
nautical  mile  of  1S52  metres.  A  sphere  nine  kilometres  in  diameter  has  a 
capacity  of  a  microfarad. 

The  practical  standards  consist  of  circular  or  square  sheets  of  tinfoil  with 
projecting  tongues,  a  and  a'  (fig.  960),  fastened  on  thin  sheets  of  mica.  Be- 
tween each  such  coated  sheet  is  placed  an  uncoated  one  of  mica,  the  two 
sets  of  tongues  being  severally  connected  with  each  other,  and  thus  the 
coatings  represent  the  coated  surfaces  of  a  condenser.  The  whole  is  en- 
closed in  a  box  ;  a  condenser  having  a  capacity  of  a  microfarad  will  repre- 
sent a  coated  surface  of  over  6  square  yards. 

Watt. — The  energy,  W,  of  an  electrical  current  in  unit  time  may  be 

TT- 

variously  expressed  ;  thus  W  =  C-R  =  -  =  CE.    This  latter  expression  is  the 

R 

most  convenient  for  practical  purposes  ;  if  the  factors  which  express  the  watt 

are  given  in  practical  units,  it  represents  the  work  done  by  unit   current 

(ampere)  when  impelled  by  an  E.M.F.  of  a  volt.     It  is  thus  a  volta7npere., 

and  on  the  proposal  of  the  late  Sir  W.  Siemens  has  been  called  a  Watt. 

If  the    factors   are   given  in  absolute  units,  \'^  A  is  equal  to  lo''  ergs.     It 

may  also  be  defined  as  the  work  done  by  the  quantity  of  electricity  of  a 

coulomb  falling  through  a  difference  of  potentials  equal  to  a  volt,  and  in  this 

form  the  definition  io  closely  analogous  to  that  of  a  kilogramme  metre. 

The  watt  is  =4^  of  an  English  horse-power,  or  one  horse-power  =  746  watts. 
The  French  cheval  vapeiir  oi  ']^  kilogramme-metres  or  543U  foot-pounds  per 
second  is  equal  to  736  watts. 

965.  Relation  of  the  electrostatic  to  the  electromaernetic  unit. — It 
we  compare  the  dimensions  of  the  units  of  quantity  and  of  the  other  electrical 
magnitudes  in  the  electrostatic  with  those  of  the  corresponding  dimensions 
as   expressed  in  the  electromagnetic   system,  we  find  that  the  ratios  are 

independent  of  the  unit  of  mass,  and  that  _,  that  is,   the  expression  of  a 

velocity,  always  enters  into  the  ratio  between  them.  Now  the  ratio  of  the 
two  sets  of  units  may  be  determined  experimentally.  Suppose,  for  in- 
stance, that  a  condenser  is  charged  with  electricity.  Knowing  its  dimen- 
sions, the  quantity,  q,  of  the  charge  may  be  determined  in  electrostatic 
measure,  by  measuring,  for  instance,  the  repulsion  which  a  given  proportion 
of  the  total  charge  produces  in  a  torsion  balance  of  known  dimensions.  The 
same  condenser,  being  charged  to  the  same  extent,  may  be  discharged 
through  a  galvanometer,  and  by  measuring  the  deflection  produced,  and 
knowing  the  constants  of  the  instrument,  the  quantity  may  be  obtained  in 
electromagnetic  units,  and  thus  the  ratio  of  the  quantity  expressed  in  the  two 
sets  of  units  maybe  deduced.  Or,  again,  the  E.M.F.  of  a  Daniell's  cell  may 
be  measured  first  by  the  aid  of  an  absolute  electrometer,  which  will  give  in 
electrostatic  units  of  potential  about  0-0036.  On  the  other  hand  the  potential 
determined  in  electromagnetic  measure  has  the  value  ^•o8SxIO^  Hence 
it  would  thus  be  found  that  in  round  numbers  the  electromagnetic  unit 
of  quantity  is  e([ual  to  3-io"'  electrostatic  units  of  quantity.  This  is  easily 
intelligible,  since  the  latter  is  the  quantity  of  electricity  which  attracts  or. 
repels  another  equal  quantity  at  a  distance  of  I  cm.  with  a  force  of  a  dyne, 
while  the  latter  is  the  quantity  which  traverses  the  wire  in  a  second  when 


-965]       Relation  of  Electrostatic  to  Electromagnetic  Unit.         987 

the  current  has  unit  intensity.  Similarly,  by  makins:^  determinations  of  the 
ratio  m  all  cases  in  which  the  same  magnitude  may  be  determined  in  elec- 
trostatic as  well  as  in  electromagnetic  measure,  it  is  found  that  the  agree- 
ment in  the  numbers  found  is  very  close,  and  as  the  mean  of  the  best 
results  is  2-9857  x  10"'.  As  the  ratio  between  the  units  is  always  of  the 
dimensions  of  a  velocity,  and  holds  under  the  condition  that  the  centimetre 
is  the  unit  of  length,  and  the  second  is  the  unit  of  time,  this  velocity  is 
298,570  kflometres,  or  185,530  miles  in  a  second.  Now  this  number  agrees 
very  closely  with  that  for  the  velocity  of  light— 185,420  miles  (507). 

Faraday,  discarding  the  idea  of  action  at  a  distance,  considered  that 
electrical  forces  are  transmitted  through  an  elastic  medium,  and  that  this 
was  the  luminiferous  ether  (637).  Maxwell,  starting  from  these  ideas,  was 
led  to  the  development  of  his  electromagfutic  theory  of  light;  this  theory 
requires  that  an  electromagnetic  wave  motion  must  be  transmitted  with  a 
velocity  represented  by  the  ratio  of  the  electrostatic  to  the  electromagnetic 
unit  of  quantity  of  electricity ;  this,  as  we  have  seen,  is  equal  to  the  velocity 
of  light.  Now,  if  luminous  and  electromagnetic  waves  are  transmitted  in 
one  and  the  same  medium  and  with  the  same  velocity,  it  is  natural  to  suppose 
that  they  are  identical  in  kind.  The  theory  also  requires  the  relation  be- 
tween the  refractive  index  of  a  body  and  the  dielectric  constant  which  we 
have  already  found  to  exist  (748). 

These  theoretical  previsions  of  what  is  known  as  the  Faraday-Maxwell 
theory  have  quite  recently  received  a  striking  confirmation  in  a  most  remark- 
able and  beautiful  series  of  experiments  by  Professor  Hertz,  of  which  we  can 
only  give  a  bare  outline  of  some  of  the  principal  results. 

In  order  to  demonstrate  that  light  is  essentially  an  electromagnetic 
phenomenon,  it  would  be  necessary  to  produce,  with  a  vibratory  motion  of 
a  purely  electromagnetic  origin,  the  same  class  of  phenomena  as  can  be 
produced  with  ordinary  light,  such,  more  especially,  as  interference  and  re- 
fraction. The  difficulty  is  the  great  length  of  the  waves  with  which  we  have 
to  deal  ;  for  from  the  laws  of  wave  motion  (253),  if  the  frequency  of  the 
electrical  oscillations  were  as  great  as  ten  thousand  in  a  second,  that  would 
represent  a  wave-length  of  300  kilometres,  and  for  a  wave-length  of  3  metres 
the  duration  should  not  be  greater  than  the  hundred-millionth  of  a  second. 
Now  in  the  discharge  of  a  Leyden  jar,  or  the  still  more  rapid  one  which  takes 
place  between  the  ends  of  the  secondary  wire  of  a  Ruhmkorff  s  coil,  the  dura- 
tion of  the  oscillation  is  comprised  within  the  ten-thousandth  and  the 
hundredth-thousandth  of  a  second. 

By  an  ingenious  but  simple  contrivance,  Hertz  has  succeeded  in  produc- 
ing electrical  oscillations,  or  true  rays  of  electrical  force,  the  duration  of  which 
is  not  greater  than  one  five-hundred-billionth  of  a  second.  The  means  by 
which  this  is  effected  is  called  the  discharger.,  and  it  has  this  remarkable 
property :  if  a  metal  wire  be  bent  in  a  circle  so  that  the  ends  are  at  a 
fraction  of  a  millimetre  apart,  and  this  be  held  in  the  vicinity  of  the  dis- 
charger, a  position  is  found  by  trial  in  which  a  continual  flow  of  microscopic 
sparks  passes  between  the  ends ;  and  this  takes  place  even  when  the  wire  is 
at  a  distance  of  some  metres.  There  is  one  dimension  for  which  the  sparks 
are  a  maximum  for  a  particular  form  of  discharger,  and  it  is  clear  that  this 
is  the  case  when  the  period  of  oscillation  of  the  wire  synchronises  with  those 


988  Dynamical  Electricity.  [965- 

of  the  discharger.  It  acts,  in  fact,  for  the  electromagnetic  waves  hke  a 
resoftator  (255)  for  sound  waves,  and  this  is  the  name  by  which  it  is  called. 
Its  diameter  was  usually  35  cm. 

By  vaiying  the  position  and  distance  of  the  resonator  in  reference  to  the 
discharger.  Hertz  was  able  to  explore  and  plot  out  the  exact  form  of  the 
wave  motion  in  the  space  about  the  discharger,  and  in  such  a  way  as  almost 
to  make  the  undulations  visible.  He  was  able  thus  to  perform  with  these 
rays  of  electrical  force  the  ordinary  elementary  experiment  made  with  light 
and  with  radiant  heat.  He  could  show  that  they  proceed  in  straight  lines, 
and  that  they  are  reflected  by  plane  metallic  surfaces ;  he  demonstrated  the 
phenomenon  of  interference,  and  from  the  distance  of  the  nodes  and  loops 
along  with  the  frequency  of  the  oscillations  he  made  a  determination  of 
the  velocity  of  electricity,  which  gave  yz  x  10°  cm.  per  second.  The  rays 
could  be  concentrated  to  a  focus  by  means  of  a  parabolic  mirror.  Using  a 
large  prism  of  pitch  5  feet  in  height,  with  a  refracting  angle  of  30°,  and  with 
a  face  of  over  a  square  yard,  he  could  demonstrate  the  refraction  of  the 
electrical  rays,  and  his  measurements  of  the  refractive  index  agree  suffi- 
ciently well  with  those  obtained  by  purely  optical  means.  By  means  of  a 
grating  of  parallel  copper  wires  he  found  that  the  rays  are  stopped  when 
the  wires  are  at  right  angles  to  the  direction  of  the  oscillations,  and  are 
transmitted  when  the  wires  are  parallel  to  the  electrical  rays.  The  grating 
acts  in  regard  to  the  rays  like  a  tourmaline  with  respect  to  plane  polarised 
light  (666).  One  of  the  most  curious  observations  in  these  experiments  is 
the  fact  that  while  a  conductor  such  as  a  sheet  of  zinc,  or  of  tinfoil,  will  cut 
off  the  rays,  insulators  do  not  stop  them ;  they  can  pass,  for  instance, 
through  a  wooden  door. 

These  remarkable  experiments  leave  no  doubt  that  light,  radiant  heat, 
and  electromagnetic  actions  are  transmitted  in  the  same  way  ;  and  it  may 
be  expected  that  they  will  lead  to  important  conclusions  both  for  the  theory 
of  light  and  of  electricity. 


-967J  Currents  of  Muscle  at  Rest.  989 


CHAPTER  X. 

ANIMAL   ELECTRICITY. 

966.  Muscular  currents. — The  existence  of  electrical  currents  in  living 
muscle  was  first  indicated  by  Galvani,  but  his  researches  fell  into  oblivion 
after  the  discovery  of  the  voltaic  pile,  which  was  supposed  to  explain  all  the 
phenomena.  Since  then,  Nobili,  Matteucci,  and  others,  especially,  in  late 
years,  Du  Bois  Reymond,  have  shown  that  electric  currents  do  exist  in  living 
muscles  and  ner\es,  and  have  investigated  their  laws. 

For  investigating  these  currents  it  is  necessary  to  have  a  delicate  gal- 
vanometer, and  also  electrodes  which  will  not  become  polarised  or  give  a 
current  of  iheir  own,  and  which  will  not  in  any  way  alter  the  muscle  when 
placed  in  contact  with  it  ;  the  electrodes  which  satisfy  these  conditions  best 
are  those  of  Du  Bois  Reymond,  as  modified  by  Bonders.  Each  consists  of 
a  glass  tube,  one  end  of  which  is  narrowed  and  stopped  by  a  plug  of  paste 
made  by  moistening  china-clay  with  a  half  per  cent,  solution  of  common  salt  ; 
the  tube  is  then  partially  filled  with  a  saturated  solution  of  sulphate  of  zinc  ; 
and  into  this  dips  the  end  of  a  piece  of  thoroughly  amalgamated  zinc  wire, 
the  other  end  of  which  is  connected  by  a  copper  wire  with  the  galvanometer  ; 
the  moistened  china-clay  is  a  conducting  medium  which  is  perfectly  neutral 
to  the  muscle,  and  amalgamated  zinc  in  solution  of  sulphate  of  zinc  does  not 
become  polarised. 

967.  Currents  of  muscle  at  rest. — In  describing  these  experiments  the 
surface  of  the  muscle  is  called  the  natural  longitudinal  section  ;  the  tendon 
the  natural  transverse  section  ;  and  the  services  obtained  by  cutting  the 
muscle  longitudinally  or  transversely  are  respectively  the  artificial  lotigitu- 
dinal  and  artificial  transverse  sections. 

If  a  living  irritable  muscle  be  removed  from  a  recently  killed  frog,  and 
the  clay  of  one  electrode  be  placed  in  contact  with  its  surface,  and  of  the 
other  with  its  tendon,  the  galvanometer  will  indicate  a  current  from  the 
former  to  the  latter ;  showing,  therefore,  that  the  surface  of  the  muscle  is 
positive  with  respect  to  the  tendon.  By  varying  the  position  of  the  elec- 
trodes, and  making  various  artificial  sections,  it  is  found — 

1.  That  any  longitudinal  section  is  positive  to  any  transverse  section. 

2.  That  any  point  of  a  longitudinal  section  nearer  the  middle  of  the 
muscle  is  positive  to  any  other  point  of  the  same  section  farther  from  the 
centre. 

3.  In  any  artificial  transverse  section  any  point  nearer  the  periphery  is 
positive  to  one  nearer  the  centre. 


990 


Dynamical  Electricity. 


[967- 


Fig.  961 


4.  The  current  obtained  between  two  points  in  a  longitudinal  or  in  a 
transverse  section  is  always  much  more  feeble  than  that  obtained  between 
two  different  sections. 

5.  No  current  is  obtained  if  two  points  of  the  same  section  equidistant 
from  its  centre  be  taken. 

6.  To  obtain  these  currents  it  is  not  necessary  to  employ  a  whole  muscle, 
or  a  considerable  part  of  one,  but  the  smallest  fragment  that  can  be  experi- 
mented with  is  sufficient. 

7.  If  a  muscle  be  cut  straight  across,  the  most  powerful  current  is  that 
from  the  centre  of  the  natural  longitudinal  section  to  the  centre  of  the  arti- 
ficial transverse  ;  but  if  the  muscle  be 

'^  ^_  _  ''  cut  across  obliquely,  as  in  fig.  961,  the 

cz — i;^^'  most  positive  point  is  moved  from  c 

"  ~  _--;=_     _^_3)         towards  b,  and  the  most  negative  from 

~~  ~-^—     ^       <■/ towards  a  {'■  currents  of  inclination'). 

To  explain  the  existence  and  rela- 
tions of  these  muscular  currents,  it  may  be  supposed  that  each  muscle  is 
made  up  of  regularly  disposed  electromotor  elements,  which  may  be  re- 
garded as  cylinders  whose  axes  are  parallel  to  that  of  the  muscle,  and 
whose  sides  are  charged  with  positive  and  their  ends  with  negative  electri- 
city ;  and,  further,  that  all  are  suspended  and  enveloped  in  a  conducting 
medium.  In  such  a  case  (fig.  961)  it  is  clear  that  throughout  most  of  the 
muscle  the  positive  electricities  of  the  opposed  surfaces  would  neutralise  one 
another,  as  would  also  the  negative  charges  of  the  ends  of  the  cylinders  ;  so 
that,  so  long  as  the  muscle  was  intact,  only  the  charges  at  its  sides  and  ends 
would  be  left  to  manifest  themselves  by  the  production  of  electromotive 
phenomena  ;  the  whole  muscle  being  enveloped  in  a  conducting  stratum,  a 
current  would  constantly  be  passing  from  the  longitudinal  to  the  transverse 
section,  and,  a  part  of  this  being  led  off  by  the  wire  circuit,  would  manifest 
itself  in  the  galvanometer. 

This  theory  also  explains  the  currents  between  two  different  points  on  the 
same  section  ;  the  positive  charge  at  b,  for  instance  (fig.  962),  would  have  more 
resistance  to  overcome  in  getting  to  the  transverse  section  than  that  at  </» 


tlicrcforc  it  has  a  higher  tension  ;  and  \i  b  and  d  are  connected  by  tlie  elec- 
trodes,/' will  be  found  positive  to  r/,  and  a  current  will  pass  from  the  former 
to  the  latter.  What  are  called  currents  of  inclination  are  also  explicable  on 
the  above  hypothesis,  for  the  oljlicjuc  section  can  be  represented  as  a  number 


-970]  Electrical  Currents  in  Nerve.  991 

of  elements  arranged  as  in  fig.  963,  so  that  both  the  longitudinal  surfaces  and 
the  ends  of  the  cylinders  are  laid  bare,  and  it  can  thus  be  regarded  as  a 
sort  of  oblique  pile  whose  positive  pole  is  towards  b  and  its  negative  at  a, 
and  whose  current  adds  itself  algebraically  to  the  ordinary  current  and  dis- 
places its  poles  as  above  mentioned. 

A  perfectly  fresh  muscle,  very  carefully  removed,  with  the  least  possible 
contact  wittT  foreign  matters,  sometimes  gives  almost  no  current  between  its 
different  natural  sections,  and  the  current  always  becomes  more  marked  after 
the  muscle  has  been  exposed  a  short  time  ;  nevertheless,  the  phenomena 
are  vital,  for  the  currents  disappear  completely  with  the  life  of  the  muscle, 
sometimes  becoming  first  irregular  or  even  reversed  in  direction. 

968.  Rbeoscoplc  frog.  Contraction  without  metals. — The  existence 
of  the  muscular  currents  can  be  manifested  without  a  galvanometer,  by  using 

l> 


Fig.  963. 

another  muscle  as  a  galvanoscope.  Thus,  if  the  nerve  of  one  living  muscle 
of  a  frog  be  dropped  suddenly  on  another  living  muscle,  so  as  to  come  in 
contact  with  its  longitudinal  and  transverse  sections,  a  contraction  of  the 
first  muscle  will  occur,  due  to  the  stimulation  of  its  nerve  by  the  passage 
through  it  of  the  electric  current  derived  from  the  surface  of  the  second. 

969.  Currents  In  active  muscle. — When  a  muscle  is  made  to  contract 
there  occurs  a  sudden  diminution  of  its  natural  electric  current,  as  indicated 
by  the  galvanometer.  This  is  so  instantaneous  that,  in  the  case  of  a  single 
muscular  contraction,  it  does  not  overcome  the  inertia  of  the  needle  of  the 
galvanometer  ;  but  if  the  contractions  be  made  to  succeed  one  another  very 
rapidly— that  is,  if  the  muscle  be  tetaitised  (827) — then  the  needle  swings 
steadily  back  towards  zero  from  the  position  in  which  the  current  of  the 
resting  muscle  had  kept  it,  often  gaining  such  momentum  in  the  swing  as  to 
pass  beyond  the  zero  point,  but  soon  reverting  to  some  point  between  zero 
and  its  original  position. 

The  negative  variation  in  the  case  of  a  simple  muscular  contraction  can, 
however,  be  made  manifest  by  using  another  muscle  as  a  rheoscope  ;  if  the 
nerve  of  this  second  muscle  be  laid  over  the  first  muscle  in  such  a  position 
that  the  muscular  current  passes  through  it,  and  the  first  muscle  be  then  made 
to  contract,  the  sudden  alteration  in  the  strength  of  its  current  stimulates 
the  nerve  laid  on  it  (827),  and  so  causes  a  contraction  of  the  muscle  to  which 
the  latter  belongs. 

The  same  phenomenon  can  be  demonstrated  in  the  muscles  of  warm- 
blooded animals  ;  but  with  less  case,  on  account  of  the  difficulty  of  keeping 
them  alive  after  they  are  laid  bare  or  removed  from  the  body.  Experiments 
made  by  placing  electrodes  outside  the  skin,  or  passing  them  through  it,  are 
inexact  and  unsatisfactory. 

970.  Electric  currents  in  nerve. — The  same  electromotor  indications. 


992  Dynamical  Electricity.  [971- 

can  be  obtained  from  nerves  as  from  muscles — at  least,  as  far  as  their  smaller 
size  will  permit  ;  the  currents  are  more  feeble  than  the  muscular  ones,  but 
can  be  demonstrated  by  the  galvanometer  in  a  similar  way.  Negative  vari- 
ation has  been  proved  to  occur  in  active  nerve  as  in  active  muscle.  The 
effect  of  a  constant  current  passed  through  one  part  of  a  nerve  on  the  amount 
of  the  normal  nerve-current,  measured  at  another  part,  has  already  been 
described  (Chap.  III.,  Electrotonus). 

971.  Electrical  fisb. — Electrical  fish  are  those  fish  which  have  the  re- 
markable property  of  giving,  when  touched,  shocks  like  those  of  the  Leyden 
jar.  Of  these  fish  there  are  several  species,  the  best  known  of  which  are  the 
torpedo,  the  gymnotus,  and  the  silurus.  The  torpedo,  which  is  very  common 
in  the  Mediterranean,  has  been  carefully  studied  by  Becquerel  and  Breschet 
in  France,  and  by  Matteucci  in  Italy.  The  gj^mnotus  was  investigated  by 
Humboldt  and  Bonpland  in  South  America,  and  in  England  by  Faraday, 
who  had  the  opportunity  of  examining  live  specimens. 

The  shock  which  they  give  serves  both  as  a  means  of  offence  and  of 
defence.  It  is  purely  voluntary,  and  becomes  gradually  weaker  as  it  is 
repeated  and  as  these  animals  lose  their  vitality,  for  the  electrical  action 
soon  exhausts  them  materially.  According  to  Faraday,  the  shock  which  the 
gymnotus  gives  is  equal  to  that  of  a  battery  of  1 5  jars  exposing  a  coating  of 
25  square  feet,  which  explains  how  it  is  that  horses  frequently  give  way  under 
the  repeated  attacks  of  the  gymnotus. 

Numerous  experiments  show  that  these  shocks  are  due  to  ordinary 
electricity.  For  if,  touching  with  one  hand  the  back  of  the  animal,  the 
belly  is  touched  with  the  other,  or  with  a  metal  rod,  a  violent  shock  is  felt 
in  the  wrists  and  arms  ;  while  no  shock  is  felt  if  the  animal  is  touched  with 
an  insulating  body.  Further,  when  the  back  is  connected  with  one  end  of  a 
galvanometer  wire  and  the  belly  with  the  other,  at  each  discharge  the  needle 
is  deflected,  but  immediately  returns  to  zero,  which  shows  that  there  is  an 
instantaneous  current ;  and,  moreover,  the  direction  of  the  needle  shows  that 
the  current  goes  from  the  back  to  the  belly  of  the  fish.  Lastly,  if  the  cur- 
rent of  a  torpedo  be  passed  through  a  helix  in  the  centre  of  which  is  a  small 
steel  bar,  the  latter  is  magnetised  by  the  passage  of  a  discharge. 

By  means  of  the  galvanometer,  Matteucci  established  the  following 
facts  : — 

I.  When  a  torpedo  is  lively,  it  can  give  a  shock  in  any  part  of  its  body, 
but  as  its  vitality  diminishes,  the  parts  at  which  it  can  give  a  shock  are 
nearer  the  organ  which  is  the  seat  of  the  development  of  electricity.  2.  .A.ny 
point  of  the  back  is  always  positive  as  compared  with  the  correspond- 
ing point  of  the  belly.  3.  Of  any  two  points  at  different  distances  from 
the  electrical  organ,  the  nearest  always  plays  the  part  of  a  positive  pole, 
and  the  farthest  that  of  a  negative  pole.  With  the  belly  the  reverse  is  the 
case. 

The  organ  where  the  electricity  is  produced  in  the  tori)cdo  is  double,  and 
formed  of  two  jjarts  symmetrically  situated  on  two  sides  of  the  head  and 
attached  to  the  skull-bone  by  the  internal  face.  Each  part  consists  of  nearly 
|iaralicl  lamella-  of  connective  tissue  inclosing  small  chambers,  in  which  lie- 
ilie  so-(  ailed  electrical  plates^  each  of  which  has  a  final  ner\e-ramification 
distributed  on  one  of  its  faces.     This  face,  on  which  the  nerve  ends,  is 


-972]  Application  of  Electricity  to  Medicine.  993 

turned  the  same  way  in  all  the  plates,  and  when  the  discharj^^e  takes  place 
is  always  negative  to  the  other. 

Matteucci  investigated  the  influence  of  tlie  brain  on  the  discharge.  For 
this  purpose  he  laid  bare  the  brain  of  a  living  torpedo,  and  found  that  the 
first  three  lobes  could  be  irritated  without  the  discharge  being  produced,  and 
that  when  they  were  removed  the  animal  still  possessed  the  faculty  of  giving 
a  shock.  The  fourth  lobe,  on  the  contrary,  could  not  be  irritated  without 
an  immediate  production  of  the  discharge  ;  but  if  it  was  removed,  all  dis- 
engagement of  electricity  disappeared,  even  if  the  other  lobes  remained 
untouched.  Hence  it  would  appear  that  the  primary  source  of  the  electricity 
elaborated  is  the  fourth  lobe,  whence  it  is  transmitted  by  means  of  the  nerves 
to  the  two  organs  described  above,  which  act  as  multipliers.  In  the  silurus 
the  head  appears  also  to  be  the  seat  of  the  electricity ;  but  in  the  gymnotus 
it  is  found  in  the  tail. 

972.  Application  of  electricity  to  medicine.— The  first  applications  of 
electricity  to  medicine  date  from  the  discovery  of  the  Leyden  jar.  Nollet 
and  Boze  appear  to  have  been  the  first  who  thought  of  the  application,  and 
soon  the  spark  and  electrical  friction  became  a  universal  panacea,  but  it 
must  be  admitted  that  the  results  of  subsequent  trials  did  not  come  up  to  the 
hopes  of  the  early  experimentalists. 

After  the  discovery  of  dynamic  electricity  Galvani  proposed  its  applica- 
tion to  medicine;  since  which  time  many  physicists  and  physiologists  have 
been  engaged  upon  this  subject,  and  yet  there  is  still  much  uncertainty  as 
to  the  real  effects  of  electricity,  the  cases  in  which  it  is  to  be  applied,  and 
the  best  mode  of  applying  it.  Practical  men  prefer  the  use  of  currents  to 
that  of  statical  electricity,  and,  except  in  a  few  cases,  discontinuous  to 
continuous  currents.  There  is,  finally,  a  choice  between  the  currents  of  the 
battery  and  induction  currents  ;  further,  the  effects  of  the  latter  differ, 
according  as  induction  currents  of  the  first  or  second  order  are  used.  In 
fact,  since  induction  currents,  although  very  intense,  have  a  verj'  feeble 
chemical  action,  it  follows  that  when  they  traverse  the  organs  they  do  not 
produce  the  chemical  effects  of  the  current  of  the  battery,  and  hence  do  not 
tend  to  produce  the  same  disorganisation.  Further,  in  electrifying  the 
muscles  of  the  face,  induction  currents  are  to  be  preferred,  for  these  currents 
only  act  feebly  on  the  retina,  while  the  currents  of  the  battery  act  energeti- 
cally on  this  organ,  and  may  affect  it  dangerously.  There  is  a  difference  in 
the  action  of  induced  currents  of  different  orders  ;  for  while  the  primary 
induced  current  causes  lively  muscular  actions,  but  has  little  action  on  the 
cutaneous  sensibility,  the  secondary  induced  current,  on  the  contrary,  in- 
creases the  cutaneous  sensibility  to  such  a  point  that  its  use  ought  to  be 
proscribed  to  persons  whose  skin  is  very  irritable. 

Hence  electrical  currents  should  not  be  applied  in  therapeutics  without 
a  thorough  knowledge  of  their  various  properties.  They  ought  to  be  used 
with  great  prudence,  for  their  continued  action  may  produce  serious  acci- 
dents. Matteucci  says  :  '  In  commencing,  a  feeble  current  must  always  be 
used.  This  precaution  now  seems  to  me  the  more  important  as  I  did  not 
think  it  so  before  seeing  a  paralytic  person  seized  with  almost  tetanic  con- 
vulsions under  the  action  of  a  current  formed  of  a  single  element.  Take 
care  not  to  continue  the  application  too  long,  especially  if  the  current  is 

3S 


994  Dynamical  Electricity.  [972- 

encrgetic.  Rather  apply  a  frequently  interrupted  current  than  a  continuous 
one,  especially  if  it  be  strong  ;  but  after  twenty  or  thirty  shocks,  at  most,  let 
the  patient  take  a  few  moments'  rest.' 

Of  late  years,  however,  feeble  continuous  currents  have  come  more  into 
use.  They  are  frequently  of  great  service  when  applied  skilfully,  so  as  to 
throw  the  nerves  of  the  diseased  part  into  a  state  of  cathelectrotonus  or 
anelectrotonus  (827),  according  to  the  object  which  is  wished  for  in  any 
g-iven  case. 


-974]  JSIeteorograph.  995 


ELEMENTARY    OUTLINES 


METEOROLOGY  AND  CLIMATOLOGY 


METEOROLOGY. 


973.  MeteoroIog:y. — The  phenomena  which  are  produced  in  the  atmo- 
sphere are  called  meteors  ;  and  mefeoj-ology  is  that  part  of  physics  which  is 
concerned  with  the  study  of  these  phenomena. 

A  distinction  is  made  between  aerial  meteors,  such  as  winds,  hurricanes, 
and  whirlwinds  ;  aqueous  meteors,  comprising  fogs,  clouds,  rain,  dew,  snow, 
and  hail  ;  and  luminous  meteors,  as  lightning,  the  rainbow,  and  the  aurora 
borcalis. 

974.  Meteorog-rapli. — The  importance  of  being  able  to  make  continuous 
observations  of  \arious  meteorological  phenomena  has  led  to  the  construc- 
tion of  various  forms  of  automatic  arrangements  for  this  purpose,  of  which 
that  of  Osier  in  England  may  be  specially  mentioned.  One  of  the  most  com- 
prehensive and  complete  is  Secchi's  meteorograph,  of  which  we  \\\\\  gi\e  here 
a  description. 

It  consists  of  a  base  of  masonry  about  2  feet  high  (fig.  964)  ;  on  this  are 
fixed  four  columns,  about  2i  yards  high,  which  support  a  table  on  which  is 
a  clockwork  regulating  the  whole  of  the  movements.  The  phenomena  are 
registered  on  two  sheets  which  move  downwards  on  two  opposite  sides,  their 
motion  being  regulated  by  the  clockwork.  One  of  them  occupies  ten  days 
in  so  doing,  and  on  it  are  registered  the  direction  and  velocity  of  the  wind, 
the  temperature  of  the  air,  the  height  of  the  barometer,  and  the  occurrence 
of  rain  ;  on  the  second,  which  only  takes  two  days,  the  barometric  height 
and  the  occurrence  of  rain  are  repeated,  but  on  a  much  larger  scale  ;  this 
gives,  moreover,  the  moisture  of  the  air. 

Direction  of  the  7i'ind.— The  four  principal  directions  of  the  wind  are 
registered  by  means  of  four  pencils  fixed  at  the  top  of  thin  brass  rods,  a,  b,  c, 
d  (fig.  964),  which  are  provided  at  the  bottom  ends  with  soft  iron  keepers 
attracted  by  two  electromagnets,  E  E',  for  west  and  north,  and  by  two  other 
electromagnets  lower  down  for  south  and  east.  These  four  electromagnets, 
as  well  as  all  the  others  on  the  apparatus,  are  worked  by  a  single  sand 
batter)'  (886)  of  twenty-four  elements.     The  passage  of  the  current  in  one  or 

3S2 


996  Meteorology.  [974- 

the  other  of  these  electromagnets  is  regulated  by  means  of  a  vane  (fig.  965) 
consisting  of  two  plates  at  an  angle  of  thirty  degrees  with  each  other,  by 


/n.      / 

/T     "1* 

-^d^-=^^j> 


'i''™''''"l!i!!1il!illil!!!Iliil!i;u  W     ■■'■'^^ 

Fig.  964. 

which  greater  steadiness  is  obtained  than  with  a  single  plate.  In  the  rod  of 

the  vane  is  a  small  brass  plate,  0  ;  this  part  is  in  the  centre  of  four  metal 


Fig.  965 


-974]  Meteorograph.  997 

sectors  insulated  from  each  other,  and  each  provided  with  a  binding  screw, 
by  which  connection  is  estabHshed  with  the  binding  screw  K,  and  the  electro- 
magnets EE'.  The  battery  current 
reaches  the  rod  of  the  vane  by  the  wire  a, 
and  thence  the  sliding  contact  0,  which 
leads  it  to  the  electromagnet  for  the  north, 
for  instancei* 

If  the  current  passed  constantly  in  this 
electromagnet,  the  pencil  on  the  rod  d 
would  be  stationary  ;  but  from  the  electro- 
magnet E'the  current  passes  into  a  second 
electromagnet,  //,  over  the  clockwork,  and 
is  thereby  alternately  opened  and  closed, 
as  will  be  seen  in  speaking  of  the  velocity 
of  the  wind.  Hence  the  armature  of  the 
rod  d,  alternately  free  and  attracted,  os- 
cillates ;  and  its  pencil,  which  is  always 
pressed  against  the  paper  AD  by  the 
elasticity  of  the  rod,  traces  on  it  a  series 
of  parallel  dashes  as  the  paper  descends, 
and  so  long  as  the  wind  is  in  the  north. 
If  the  wind  changes  then  to  west,  for 
instance,  the  rod  a  oscillates,  and  its 
pencil  traces  a  different  series  of  marks. 

The  rate  of  displacement  of  the  paper  being  known,  we  get  the  direction  of 
the  prevalent  wind  at  a  given  moment. 

Velocity  of  the  wind. — This  is  indi- 
cated by  a  Robinson's  aftemo?neter,  and 
is  registered  in  two  ways  ;  by  two  counters 
which  mark  in  decametres  and  kilometres 
the  distance  travelled  by  the  wind  ;  and 
by  a  pencil  which  traces  on  a  table  a  curve, 
the  ordinates  of  which  are  proportional  to 
the  velocity  of  the  wind. 

Robinson,  who  originally  devised  this 
form  of  anemometer  (fig.  966),  proved 
that  its  velocity  is  proportional  to  that  of 
the  wind  ;  in  this  apparatus  the  length 
of  the  arms  is  so  calculated  that  each  re- 
volution corresponds  to  a  velocity  of  ten 
metres  (975).  The  anemometer  is  placed 
at  a  considerable  distance  from  the  meteor- 
ograph, and  is  connected  with  it  by  a 
copper  wire,  d,  which  passes  to  the  electro- 
magnet,»,  of  the  counter.  On  its  rod  there 
is,  moreover,  an  excentric,  which  at  each 
turn  touches  a  metal  contact  in  connec- 
tion with  the  wire  d.  The  battery  current  reaches  the  anemometer  by  a  wire 
a    the  current  is  closed  once  at  each  rotation,  and  pr  5ses  to  the  electro- 


Fig.  566. 


998  Meteorology.  [974- 

magnet  «,  which  moves  the  needle  of  the  dial  through  one  division.  There 
are  fifty  such  divisions,  which  represent  as  many  turns  of  the  vane,  and 
therefore  so  many  multiples  of  ten  metres.  The  lower  dial  marks  the  kilo- 
metres. 

The  curve  of  velocities  is  traced  on  the  sheet  by  a  pencil,  /,  fixed  to  a 
horizontal  rod.  This  is  joined  at  its  two  ends  to  two  guide-rods,  <;  and _y, 
which  keep  it  parallel.  The  pencil  and  the  rod  are  moved  laterally  by  a 
chain  which  passes  over  two  pulleys,  r'  and  r,  and  is  then  coiled  over  a  pulley 
placed  on  the  shaft  of  the  counter,  but  connected  with  it  merely  by  a  ratchet- 
wheel  :  and  moved  thus  by  the  counter  and  the  chain,  the  pencil  traces 
every  hour  on  the  sheet  a  line  the  length  of  which  is  proportioned  to  the 
velocity  of  the  wind.  From  hour  to  hour  an  excentric  moved  by  clockwork 
detaches,  from  the  shaft  of  the  counter,  the  pulley  on  which  is  coiled  the 
chain,  and  this  pulley  becoming  out  of  gear,  a  weight,/,  connected  with  the 
pencil  z,  restores  this  to  its  starting-point.  All  the  lines,  V,  traced  succes- 
sively by  the  pencil,  start  from  the  same  straight  line  as  ordinates,  and  their 
ends  give  the  curve  of  velocities. 

The  counters  on  the  right  and  left  are  worked  by  electromagnets,  w  ?«', 
and  are  intended  to  denote  the  velocity  of  special  winds  ;  for  instance,  those 
of  the  north  and  south,  by  connecting  their  electromagnets  with  the  north 
and  south  sectors  of  the  vane  (fig.  966). 

Teniperatiir-e  of  the  air. — This  is  indicated  by  the  expansion  and  con- 
traction of  a  copper  wire  of  16  metres  in  length  stretched  backwards  and 
forwards  on  a  fir  post  8  metres  in  length.  The  whole  being  placed  on  the 
outside — on  the  roof,  for  instance — the  expansion  and  contraction  are  trans- 
mitted by  a  system  of  levers  to  a  wire,  c,  which  passes  to  the  meteorograph, 
where  it  is  jointed  to  a  bent  lever,  /.  This  is  jointed  to  a  horizontal  rod,  s, 
which  supports  a  pencil,  and  at  the  other  end  is  jointed  to  a  guide-rod,  x. 
Thus  the  pencil,  sharing  the  oscillations  of  the  whole  system,  traces  the  curve 
of  the  temperatures. 

Pressure  of  the  ai/ziosphet'e. — This  is  registered  by  the  oscillations  of  a 
barometer,  B,  suspended  at  one  end  of  a  bent  scale-beam,  I  F,  playing  on  a 
knife-edge  (fig.  968).  The  arm  F  supports  a  counterpoise  ;  to  the  arm  I  is 
suspended  the  barometer  B,  which  is  wider  at  the  top  than  at  the  bottom. 
A  wooden  flange  or  floater,  Q,  fixed  to  the  lower  part  of  the  tube,  plunges  in 
a  bath  of  mercury,  so  that  the  buoyancy  of  the  liquid  counterbalances  part  of 
the  weight  of  the  barometer.  Owing  to  the  large  diameter  of  the  barometric 
chamber,  a  very  slight  variation  of  level  in  this  chamber  makes  the  tube 
oscillate,  and  with  it  the  scale-beam  I  F.  To  the  axis  of  this  is  a  triangle, 
gkk,  jointed  to  a  horizontal  rod,  which  in  turn  is  connected  with  a  guide-rod, 
2.  In  the  middle  of  this  rod  is  a  pencil  which,  sharing  in  the  oscillations  of 
the  triangle  gk/c,  traces  the  cur\e  H  of  pressure.  A  bent  lever  at  the  bottom 
of  the  barometer  tube  keeps  this  in  a  vertical  position. 

Rainfall. — This  is  registered  between  the  direction  of  tlic  winds  and  the 
curve  II  by  a  pencil  at  the  end  of  a  rod,  ?/,  which  is  worked  l>y  an  electro- 
magnet, c.  On  the  roof  is  a  funnel  which  collects  tiie  rain,  and  a  long  tube 
leads  the  water  to  a  small  water-balance,  with  tlic  cups  placed  near  the 
meteorograph  (fig.  967).  To  the  axis  of  the  scale-beam  one  pole  of  the  battery 
is  connected  ;  the  left  cup  being  full,  tips  up,  and  a  contact,  a,  closes  the 


Fig.  967. 


-974]  Measiiniiient  of  the  Rainfall.  999 

current,  which  passes  then  to  one  of  the  binding  screws,  C,  and  hence  to  the 
electromagnet,  e.  Then  the  right  cup,  being  in  turn  full,  tips  in  the  opposite 
direction,  and  the  contact  b  now  transmits  the  current  to  the  electromagnet. 
Thus,  at  each  oscillation  this  latter  attracts  its  armature,  and  with  it  the 
rod  a^  which  makes  a  mark  by  means  of  a  pencil  at  the  end.  If  the  rain  is 
abundant  the  oscillations  of  the  beam  are  rapid,  and  the  marks  being  very 
close  together  give  a  deep  shade  ;  if,  on  the  contrary,  the  oscillations  are 
slow,  the  marks  are  at  a  greater  distance  and  give  a  light  shade.  When 
the  rain  ceases  the  oscillations  cease  also,  and  the  _ 
pencil  makes  no  mark. 

To  complete  this  description  of  the  first  face  of 
the  meteorograph  :  S  is  the  alarum-bell  of  the  clock- 
work, 00  a  cord  supporting  a  weight  which  moves 
the  works  of  the  hour-hand.  LZ  is  a  second  cord  that 
supports  the  weight  which  works  the  alarum  ;  the 
wheel  U,  placed  below  the  clockwork,  winds  up  the 
sheet  AD  when  it  is  at  the  bottom  of  its  course. 

The  second  sheet  (fig.  968)  gives  the  barometric 
height  and  the  rainfall  like  the  first,  but  on  a  larger 
scale,  since  the  motion  of  the  sheet  is  five  times  as 
rapid.  Its  principal  function  is  that  of  registering  the 
moisture  of  the  air.  This  is  effected  by  means  of  the 
psychrometer  (fig.  969).  T  and  T'  are  two  thermo- 
meters fixed  on  two  plates.  The  muslin  which  covers 
the  second  is  kept  continually  moist  by  water  dropping  on  it.  In  each  of 
the  bulbs  are  fused  two  platinum  wires  ;  the  stems  of  the  thermometers  are 
open  at  the  top,  and  in  them  are  two  platinum  wires,  m  and  «,  suspended 
to  a  metal  frame  movable  on  four  pulleys  supported  by  a  fixed  piece,  B. 
The  frame  A,  in  contact  with  the  current  of  the  battery,  is  suspended 
to  a  steel  wire,  L,  which  passes  over  a  pulley  to  the  meteorograph 
(fig.  967).  Here  is  a  long  triangular  lever,  W,  which  supports  a  small  wheel, 
to  which  is  fixed  the  wire  L.  The  lever  W,  which  turns  about  an  axis,/,  is 
moved  by  a  rod,  a,  by  means  of  an  excentric,  which  the  clock  works  every 
quarter  of  an  hour.  At  each  oscillation  the  lever  \V  transmits  its  motion 
to  a  small  chariot,  on  which  is  an  electromagnet,  x,  and  at  the  same  time  to 
the  steel  wire  L,  which  supports  the  frame  A  (fig.  969).  The  chariot,  moved 
towards  the  left  by  the  rotation  of  the  excentric,  lets  the  frame  sink.  The 
moment  the  first  platinum  wire  reaches  the  mercurial  column  of  the  drv 
bulb  thermometer,  which  is  the  highest,  the  current  is  closed,  and  passes  into 
the  electromagnet  of  the  chariot.  An  armature  at  once  causes  a  pencil  to 
mark  a  point  on  the  sheet  which  is  the  beginning  of  a  line  representing  the 
path  of  the  dry  bulb  thermometer.  As  the  frame  continues  to  descend,  the 
second  platinum  wire  touches  the  mercury  of  the  wet  bulb,  and  closes  a 
current  in  a  relay,  M,  which  opens  the  circuit  of  the  electromagnet,  .t'.  The 
pencil  is  then  detached  ;  then,  returning  upon  itself,  the  chariot  reproduces 
the  closing  and  opening  of  the  circuit  in  the  opposite  direction,  the  pencil 
makes  another  mark,  which  is  the  end  of  the  line.  There  are  thus  formed 
two  series  of  dots  arranged  in  two  curves,  one  of  which  represents  the  path  of 
the  dry,  and  the  other  the  path  of  the  wet,  bulb.    The  horizontal  distance  of  the 


looo  Meteorology.  [974- 

two  points  of  these  curves  is  proportional  to  the  difference  / — /j  of  the  tem- 
peratures indicated  at  the  same  moment  by  the  thermometers  (fig.  969). 


(2unntiiy  of  rai'fi. — Tlic  (|uantity  of  rain  wliich  falls  in  a  given  time 
is  registered  on  a  disc  of  paper  on  a  pulley,  R.  On  the  groove  of  this  is 
coiled  a  chain,  to  which  is  suspended  a  brass  tube,  P.     This  is  fixed  at  the 


975] 


Direction  and   Velocity  of  Winds. 


lOOI 


'fTh' 


bottom  to  a  float,  which  plunges  in  a  reservoir  placed  in  the  base  of  the 
meteorograph.  On  passing  out  of  the  water-balance  (fig.  964)  the  water 
passes  into  this  reservoir,  and  as  its  section  is  one-fourth  that  of  the  funnel, 
the  height  of  water  which  falls  is  quadrupled  ;  it  is  measured  on  a  scale,  (], 
divided  into  millimetres. 

As  the  float  rises,  a  weight,  Z,  moves  the  pulley  in  the  contrary  direction, 
and  its  rotation  is  proportional  to  the  height  of 
water  which  has  fallen.  A  pencil  moves  at  the 
same  time  from  the  centre  to  one  circumference  of 
the  paper  disc  with  a  velocity  of  5  mm.  in  24 
hours  :  hence  the  quantity  of  rain  which  falls  every 
day  is  noted  on  a  different  place  on  the  paper 
disc. 

975.  Birection  and  velocity  of  winds. — 
Winds  are  currents  moving  in  the  atmosphere  with 
variable  directions  and  velocities.  There  are  eight 
principal  directions  in  which  they  blow — north., 
nort/i-easf,  east,  south-east.,  south,  soutJi-iuest,  ivest, 
and  north-west.  Mariners  further  divide  each  of 
the  distances  between  these  eight  directions  into 
four  others,  making  in  all  32  directions,  which  are 
called  points  or  rhutnbs.  A  figure  of  32  rhumbs 
on  a  circle,  in  the  form  of  a  star,  is  known  as  the 
mariner's  card. 

\'elocity  is  determined  by  means  of  the 
anemometer  (fig.  966),  a  small  vane  with  fans, 
which  the  wind  turns  ;  the  velocity  is  deduced  from 
the  number  of  turns  made  in  a  given  time.  In  our 
climate  the  mean  velocity  is  from  18  to  20  feet  in  a 
second.  With  a  velocity  of  less  than  18  inches  in 
a  second  no  movement  is  perceptible,  and  smoke 
ascends  straight  ;  with  a  velocity  between  i^  and 
2  feet  per  second  the  wind  is  perceptible  and  moves  a  pennant  ;  from  13  to 
22  feet  it  is  moderate,  it  stretches  a  flag  and  moves  the  leaves  of  trees  ; 
with  from  23  to  36  feet  velocity  it  is  fresh  and  moves  the  branches  of 
trees  ;  with  36  to  56  feet  it  is  strong  and  moves  the  larger  branches  and 
the  smaller  stems  ;  with  a  velocity  of  56  to  90  feet  it  is  a  storm,  and  entire 
trees  are  moved  ;  and  from  90  to  120  it  is  a  hurricane. 

To  measure  the  pressure  of  the  wind  a  plate  is  used,  which  by  means  of  a 
vane  is  always  kept  in  a  direction  opposite  that  of  the  wind.  Behind  the 
plate  are  one  or  more  springs  which  are  the  more  pressed  the  greater  is  the 
pressure  of  the  wind  against  the  plate.  Knowing  the  distance  through  which 
the  plate  is  pressed,  we  can  calculate  the  pressure  which  the  wind  exerts  on 
the  plate  in  question. 

With  some  degree  of  appro.ximation,  and  for  low  velocities,  the  pressure 
.iirty  *uu  tat-en  as  proportional  to  the  square  of  the  velocity.  Thus,  if  the 
pressure  on  the  square  foot  is  0-005  pound,  with  a  velocity  of  1-5  foot  in 
a  second,  it  is  0-02  pound  with  a  velocity  of  3  feet,  and  0-123  '^^'•th  a  velocity 
of  7-33  feet. 


Fig.  969. 


1002  Meteorology.  [976- 

976.  Causes  of  winds. — Winds  are  produced  by  a  disturbance  of  the 
eciuilibrium  in  some  part  of  the  atmosphere  :  a  disturbance  always  resultmg 
from  a  difference  in  temperature  between  adjacent  countries.  Thus,  if  the 
temperature  of  a  certain  extent  of  ground  becomes  higher,  the  air  in  contact 
with  it  becomes  heated,  it  expands  and  rises  towards  the  higher  regions  of 
the  atmosphere  ;  whence  it  flows,  producing  winds  which  blow  from  hot  to 
cold  countries.  But  at  the  same  time  the  equilibrium  is  destroyed  at  the 
surface  of  the  earth,  for  the  barometric  pressure  on  the  colder  adjacent  parts 
is  greater  than  on  that  which  has  been  heated,  and  hence  a  current  will  be 
produced  with  a  velocity  dependent  on  the  difference  between  these  pres- 
sures ;  thus  two  distinct  winds  will  be  produced — an  upper  one  setting  out- 
luards  from  the  heated  region,  and  a  lower  one  setting  inwards  towards  it. 

977.  Regrular,  periodical,  and  variable  winds. — According  to  the  more 
or  less  constant  directions  in  which  winds  blow,  they  may  be  classed  as 
regular,  periodical,  and  variable  winds. 

i.  Regular  winds  are  those  which  blow  all  the  year  through  in  a  virtually 
constant  direction.  These  winds,  which  are  also  known  as  the  trade  winds, 
are  uninterruptedly  observed  far  from  the  land  in  equatorial  regions,  blowing 
from  the  north-east  to  the  south-west  in  the  Northern  Hemisphere,  and  from 
the  south-east  to  the  north-west  in  the  Southern  Hemisphere.  They  prevail 
on  the  two  sides  of  the  equator  as  far  as  30°  of  latitude,  and  they  blow  in 
the  same  direction  as  the  apparent  motion  of  the  sun — that  is,  from  east  to 
west. 

The  air  above  the  equator  being  gradually  heated,  rises  as  the  sun  passes 
round  from  east  to  west,  and  its  place  is  supplied  by  the  colder  air  from  the 
north  or  south.  The  direction  of  the  wind,  however,  is  modified  by  this  fact, 
that  the  velocity  which  this  colder  air  has  derived  from  the  rotation  of  the 
earth— namely,  the  velocity  of  the  surface  of  the  earth  at  the  point  from 
which  it  started — is  less  than  the  velocity  of  the  surface  of  the  earth  at  the 
point  at  which  it  has  now  arrived  :  hence  the  currents  acquire,  in  reference 
to  the  equator,  the  constant  direction  which  constitutes  the  trade  winds. 

ii.  Periodical  winds  are  those  which  blow  regularly  in  the  same  direction 
at  the  same  seasons  and  at  the  same  hours  of  the  day  :  the  monsoon, 
simoom,  and  the  land  and  sea  breeze  are  e.xamples  of  this  class.  The  name 
tnofisoon  is  given  to  winds  which  blow  for  six  months  in  one  direction  and 
for  six  months  in  another.  They  are  principally  observed  in  the  Red  Sea 
and  in  the  Arabian  C.ulf,  in  the  Bay  of  Bengal  and  in  the  Chinese  Sea. 
These  winds  blow  towards  the  continents  in  summer,  and  in  a  contrary 
direction  in  winter.  The  simoom  is  a  hot  wind  that  blows  over  the  deserts 
of  Asia  and  Africa,  and  which  is  characterised  by  its  high  temperature  and 
l)y  the  sands  which  it  raises  in  the  atmosphere  and  carries  with  it.  During 
the  prevalence  of  this  wind  the  air  is  darkened,  the  skin  feels  dry,  the 
respiration  is  accelerated,  and  a  burning  thirst  is  experienced. 

This  wind  is  known  under  the  name  oi  sirocco  in  Italy  and  Algiers,  where 
it  blows  from  the  great  desert  of  Sahara.     In  Egypt,  where  it  prevails  from 
the  end  of  April  to  June,  it  is  called  kamsi/i.    The  natives  of  Africa,  in  order  , 
to  protect  themselves  from  the  effects  of  the  too  rapid  perspiration  occasioned 
by  this  wind,  cover  themselves  with  fatty  substances. 

A  wind  characteristic  of  Switzerland  and  known  as  the  Fo/ui  originates  as 


-979]  Weather  Charts.  1003 

follows  :  a  mass  of  air  coming  from  the  south-east  being  impelled  over  a 
mountain  ridge  becomes  rarefied  as  it  ascends  ;  the  temperature  rises  and  it 
deposits  its  moisture  on  the  other  side  as  rain  or  snow.  Being  driven  still 
forward  into  the  valleys,  the  superincumbent  pressure  being  greater  the  air 
is  condensed  and  its  temperature  rises,  and  having  parted  with  its  moisture 
it  appears  as  a  wind  which  is  at  once  hot  and  dry.  One  observation  gave 
the  temperature  at  31-4  C,  while  it  only  contained  20  per  cent,  of  moisture. 

The  tajid  and  sea  breeze  is  a  wind  which  blows  on  the  sea-coast,  during 
the  day  from  the  sea  towards  the  land,  and  during  the  night  from  the  land  to 
the  sea.  For  during  the  day  the  land  becomes  more  heated  than  the  sea,  in 
consequence  of  its  lower  specific  heat  and  greater  conductivity,  and  hence,  as 
the  superincumbent  air  becomes  more  heated  than  that  upon  the  sea,  it  as- 
cends and  is  replaced  by  a  current  of  colder  and  denser  air  flowing  from  the 
sea  towards  the  land.  During  the  night  the  land  cools  more  rapidly  than  the 
sea,  and  hence  the  same  phenomenon  is  produced,  but  in  a  contrary  direction. 
The  sea  breeze  commences  after  sunrise,  increases  up  to  three  o'clock  in  the 
afternoon,  decreases  towards  evening,  and  is  changed  into  a  land  breeze 
after  sunset.  These  winds  are  only  perceived  at  a  slight  distance  from  the 
shores.  They  are  regular  in  the  tropics,  but  less  so  in  our  climates  ;  and 
traces  of  them  are  seen  as  far  as  the  coasts  of  Greenland.  The  proximity  of 
mountains,  and  also  of  forests,  likewise  gives  rise  to  periodical  daily  breezes. 

iii.  Vat  table  luinds  are  those  which  blow  sometimes  in  one  direction  and 
sometimes  in  another,  alternately,  without  being  subject  to  any  law.  In  mean 
latitudes  the  direction  of  the  winds  is  very  variable  ;  towards  the  poles  this 
irregularity  increases,  and  under  the  arctic  zone  the  winds  frequently  blow 
from  several  points  of  the  horizon  at  once.  On  the  other  hand,  in  approach- 
ing the  torrid  zone,  they  become  more  regular.  The  south-west  wind  prevails 
in  England,  in  the  north  of  France,  and  in  Germany  ;  in  the  south  of  France 
the  direction  inclines  towards  the  north,  and  in  Spain  and  Italy  the  north 
wind  predominates. 

978.  law  of  the  rotation  of  winds. — Spite  of  the  great  irregularity 
which  characterises  the  direction  of  the  winds  in  our  latitude,  it  has  been  as- 
certained that  the  wind  has  a  preponderating  tendency  to  veer  round  accord- 
ing to  the  sun's  motion — that  is,  to  pass  from  north,  through  north-east,  east- 
south-east  to  south,  and  so  on  round  in  the  same  direction  from  west  to 
north  ;  that  it  often  makes  a  complete  circuit  in  that  direction,  or  more 
than  one  in  succession,  occupying  many  days  in  doing  so,  but  that  it  rarely 
veers,  and  very  rarely  or  never  makes  a  complete  circuit  in  the  opposite 
direction.  This  course  of  the  winds  is  most  regularly  observed  in  winter. 
According  to  Leverrier,  the  displacement  of  the  north-east  by  the  south- 
west wind  arises  from  the  occurrence  of  a  whirlwind  formed  upon  the  Gulf 
Stream.     For  a  station  in  south  latitude  a  contrary  law  of  rotation  prevails. 

This  law,  though  more  or  less  suspected  for  a  long  time,  was  first  formally 
enunciated  and  explained  by  Dove,  and  is  known  as  Dove's  laiv  of  rotation 
ofwifids. 

979.  "Weatber  charts. — A  considerable  advance  has  been  made  in 
weather  forecasts  by  the  frequent  and  systematic  publication  of  lueather 
cJtarts ;  that  is  to  say,  maps  in  which  the  barometric  pressure,  the  tempe- 
rature, the  force  of  the  wind,  &c.,  are  expressed  for  considerable  areas  in  an 


T004  Meteorology.  [979- 

exact  and  comprehensive  manner.  A  careful  study  of  such  maps  renders 
possible  a  forecast  of  the  weather  for  a  day  or  more  in  advance.  We  can 
here  do  little  more  than  explain  the  meaning  of  the  principal  terms  in  use. 

If  lines  are  drawn  through  those  places  on  the  earth's  surface  where  the 
corrected  barometric  height  at  a  given  time  is  the  same,  such  lines  are 
called  isobarometric  lines,  or  more  briefly,  isobaric  lines,  or  isobars.  Between 
any  two  points  on  the  same  isobar  there  is  no  difference  of  pressure. 
Isobars  are  usually  drawn  either  for  a  difference  of  5  mm.,  or  of  y^  of  an  inch. 

If  we  take  a  horizontal  line  between  two  isobars,  and  at  that  point  at 
which  the  pressure  is  greatest  draw  a  perpendicular  line  on  any  suitable 
scale,  which  shall  represent  the  difference  in  pressure  between  the  two  places, 
the  line  drawn  from  the  top  of  this  perpendicular  to  the  lower  isobar  will 
form  an  angle  with  the  horizontal,  and  the  steepness  of  this  angle  is  a 
measure  of  the  fall  in  pressure  between  the  two  stations,  and  is  called  the 
barometric  gradient.  Gradients  are  usually  expressed  in  England  and 
America  in  hundredths  of  an  inch  of  mercury  for  one  degree  of  sixty  nautical 
miles,  and  on  the  Continent  in  millimetres  for  the  same  distance.  The 
closer  are  the  isobars  the  steeper  is  the  gradient,  and  the  more  powerful 
the  wind  ;  and  though  no  exact  numerical  relationship  can  be  proved  to  exist 
between  the  steepness  of  the  gradient  and  the  force  of  the  wind,  it  may  be 
mentioned  that  a  gradient  of  about  6  represents  a  strong  breeze  ;  and  a 
gradient  of  10,  or  a  difference  in  pressure  of  j',  of  an  inch  for  60  miles, 
is  a  stiff  gale. 

The  direction  of  the  wind  is  from  the  place  of  higher  pressure  to  that  of 
lower,  and  in  this  respect  the  law  of  Buys  Ballot  may  be  mentioned,  which 
has  been  foursd  to  hold  in  all  cases  of  the  Northern  Hemisphere,  where 
local  configuration  does  not  come  into  play.  //  ice  stand  with  our  back  to 
the  wind  the  li?ie  of  lower  pressure  is  on  the  left  hand.  For  places  in  the 
Southern  Hemisphere  exactly  the  opposite  law  holds. 

If  within  any  area  the  pressure  is  lower,  the  wind  blows  round  that  area, 
the  place  of  lowest  pressure  being  on  the  left.  The  direction  of  the  wind  is, 
in  short,  opposite  that  of  the  hands  of  a  watch.  Such  a  circulation  is  called 
cyclonic  ;  it  is  that  which  is  characteristic  of  the  West  Indian  hurricanes, 
which  are  known  as  cyclones.  Conversely  the  wind  blows  round  an  area  of 
higher  pressure  in  the  same  direction  as  the  hands  of  a  watch  ;  and  this  cir- 
culation is  called  a?iti-cyclonic. 

Cyclonic  systems  arc  by  far  the  most  frequent,  and  arc  characterised  by 
steep  gradients  ;  the  air  in  them  tends  to  move  in  towards  the  centre,  and 
thence  to  the  upper  regions  of  the  atmosphere.  They  bring  with  them  o\-er 
the  greater  part  of  the  region  which  they  cover,  much  moisture,  an  abundance 
of  cloud,  and  heavy  rain.  An  anti-cyclonic  system  has  the  opposite  charac- 
teristics ;  the  gradients  are  slight,  the  wind  light,  and  moves  with  the  hands 
of  a  watch.  The  air  is  dry,  so  that  there  is  but  little  cloud,  and  no  rain. 
Cyclonic  systems,  from  the  dampness  of  the  air,  produce  warm  weather  in 
winter,  and  cold,  wet  weather  in  summer.  Anti-cyclonic  systems  bring  our 
hardest  frosts  in  winter  and  greatest  heat  in  summer,  as  there  is  but  little  , 
moisture  in  the  air  to  temper  the  extremes  of  climalr.  Both  systems  travel 
over  the  earth's  surface — the  cyclones  rapidly,  but  the  anti-cyclones  more 
slowly. 


-981]  Clouds.  1005 

980.  Pogs  and  Mists. — When  aqueous  vapour  rising  from  a  vessel  of 
boiling  water  diffuses  in  the  colder  air,  it  is  condensed  ;  a  sort  of  cloud  is 
formed  which  consists  of  a  number  of  small  hollow  vesicles  of  water,  which 
remain  suspended  in  the  air.  These  are  usually  spoken  of  as  vapour,  yet 
they  are  not  so— at  any  rate  not  in  the  physical  sense  of  the  word,  for  in 
reality  they  are  partially  condensed  vapour. 

When  this  condensation  of  aqueous  vapour  is  not  occasioned  by  contact 
with  cold  solid  bodies,,  but  takes  place  throughout  large  spaces  of  the  atmo- 
sphere, it  constitutes /(T^j-  or  niists^  which,  in  fact,  are  nothing  more  than  the 
appearance  seen  over  a  vessel  of  hot  water. 

A  chief  cause  of  fogs  consists  in  the  moist  soil  being  at  a  higher  tem- 
perature than  the  air.  The  vapours  which  then  ascend  condense  and  become 
visible.  In  all  cases,  however,  the  air  must  have  reached  its  point  of  satura- 
tion before  condensation  takes  place.  Fogs  may  also  be  produced  when  a 
current  of  hot  and  moist  air  passes  over  a  river  at  a  lower  temperature  than 
its  own,  for  then,  the  air  being  cooled,  as  soon  as  it  is  saturated,  the  excess 
of  vapour  present  is  condensed.  The  distinction  between  mists  and  fogs  is 
one  of  degree  rather  than  of  kind.     A  fog  is  a  very  thick  mist. 

By  observations  based  on  diffraction  phenomena  (650),  the  diameter  01 
fog  vesicles  has  been  found  to  vary  from  0-0154  to  0-0521  mm. ;  the  longer 
the  continuance  of  fine  weather,  the  smaller  are  the  vesicles  ;  before  rains 
they  increase  rapidly. 

Dines,  by  direct  microscopic  measurement,  found  that  the  diameter  of 
fog  particles  varied  with  the  same  fog  from  0-015  to  0-127  irirn.  ;  the  larger 
occur  in  dense  fogs,  in  lighter  fogs  they  sink  to  0-0033.  Kamtz  found  from 
0-014  to  0-035  mm. 

When  water  is  coated  with  a  layer  of  coal-tar,  it  is  prevented  from 
evaporating.  Frankland  ascribes  the  d7y  fog  met  with  in  London  to  the 
large  quantities  of  coal-tar  and  paraffine  vapour  which  are  sent  into  the 
atmosphere,  and  which,  condensing  on  the  vesicles  of  fog,  prevent  their 
evaporation. 

Aitkin  has  shown  that  aqueous  vapour  never  condenses  unless  some 
liquid  or  solid  is  present  on  which  it  is  deposited.  Particles  of  dust  in  the 
air  are  the  nuclei  for  clouds  and  fogs.  This  he  showed  by  passing  steam 
into  filtered  air  ;  it  remained  quite  clear,  while  a  turbidity  was  produced 
under  the  same  circumstances  in  unfiltered  air.  The  density  of  the  cloud 
was  found  to  depend  on  the  number  of  particles  of  dust  in  the  air.  A  most 
abundant  source  of  dust  is  the  combustion  of  coal.  The  sulphur  in  the  coal 
in  burning  also  forms  sulphurous  acid,  which,  though  a  g'as,  is  found  to  act 
as  a  nucleus. 

981.  Clouds. — Clouds  are  masses  of  vapour,  condensed  into  little  drops 
or  vesicles  of  extreme  minuteness,  like  fogs.  There  is  no  difference  of  kind 
between  fogs  and  clouds.  Fogs  are  clouds  resting  on  the  ground.  To  a 
person  enveloped  in  it,  a  cloud  on  a  mountain  appears  like  a  fog.  They 
always  result  from  the  condensation  of  vapour  which  rises  from  the  earth. 
According  to  their  appearance,  they  have  been  divided  by  Howard  into  four 
principal  kinds  :  the  nimbus^  the  stratus,  the  cumulus^  and  the  cirrus.  These 
four  kinds  are  represented  in  fig.  970,  and  are  designated  respectively  by  one 
two,  three,  and  four  birds  on  the  wing. 


ioo6  Meteorology.  [981- 

The  cirrus  consists  of  small  whitish  clouds,  w  hich  have  a  fibrous  or  wispy- 
appearance,  and  occupy  the  highest  regions  of  the  atmosphere.  The  name 
of  marei  tails,  by  which  they  are  generally  known,  well  describes  their 
appearance.  From  the  low  temperature  of  the  spaces  which  they  occupy^ 
it  is  more  than  probable  that  cirrus  clouds  consist  of  frozen  particles  ;  and 
hence  it  is  that  halos,  coronas,  and  other  optical  appearances,  produced  by 
refraction  and  reflection  from  ice-crystals,  appear  almost  always  in  these 
clouds  and  their  derivatives.  Their  appearance  often  precedes  a  change  of 
weather. 

The  cumulus  are  rounded  spherical  forms  which  look  like  mountains 
piled  one  on  the  other.  They  are  more  frequent  in  summer  than  in  winter, 
and  after  being  formed  in  the  morning  they  generally  disappear  towards 
evening.  If,  on  the  contrary,  they  become  more  numerous,  and  especially 
if  surmounted  by  cirrus  clouds,  rain  or  storms  may  be  expected. 


Stratus  clouds  consist  of  very  large  and  continuous  horizontal  sheets, 
which  form  chiefly  at  sunset  and  disappear  at  sunrise.  They  are  frequent 
in  autumn  and  unusual  in  spring-time,  and  arc  lower  than  the  preceding. 

The  nimbus,  or  ram  clouds,  which  are  sometimes  classed  as  one  of  the 
fundamental  varieties,  are  properly  a  combination  of  the  three  preceding 
kinds.  They  affect  no  particular  form,  and  are  solely  distinguished  by  a 
uniform  grey  tint  and  l)y  fringed  edges.  They  are  indicated  on  the  right  of 
the  figure  by  the  presence  of  one  bird. 

The  fundamental  forms  pass  into  one  another  in  ilic  most  varied  manner;  - 
Howard  has  classed  these  transitional  forms  as  cirro-cumulus,  cirro-stratus, 
and  cumulo-stratus,  and  it  is  often  very  diflicult  to  tell,  from  the  appearance 


For  mat  ion  of  Clouds.  1007 

of  a  cloud,  wliich  type  it  most  resembles.  The  cirro-cumulus  is  most  cha- 
racteristically known  as  a  'mackerel  sky;'  it  consists  of  small  roundish 
masses,  disposed  with  more  or  less  irregularity  and  connection.  It  is  fre- 
quent in  summer,  and  attendant  on  warm  and  dry  weather.  Cirro-strattis 
appears  to  result  from  the  subsidence  of  the  fibres  of  cirrus  to  a  horizontal 
position  which  at  the  same  time  approach  laterally.  The  form  and  relative 
position  wjien  seen  in  the  distance  frequently  give  the  idea  of  shoals  of  fish. 
The  tendency  of  ciunulo-stratus  is  to  spread,  settle  down  into  the  nimbus., 
and  finally  fall  as  rain. 

The  height  of  clouds  varies  greatly;  in  the  mean  it  is  from  1,300  to  1,500 
yards  in  winter,  and  from  3,300  to  4,300  yards  in  summer.  But  they  often 
exist  at  greater  heights  ;  Gay-Lussac,  in  his  balloon  ascent,  at  a  height  of 
7,630  yards,  observed  cirrus  clouds  above  him,  which  appeared  to  be  at  a 
considerable  height.  In  Ethiopia,  D'Abbadie  observed  storm-clouds  whose 
height  was  only  230  yards  above  the  ground. 

In  order  to  explain  the  suspension  of  clouds  in  the  atmosphere,  Halley 
first  proposed  the  hypothesis  of  vesicular  vapours.  He  supposed  that  clouds 
are  formed  of  an  infinity  of  extremely  minute  vesicles,  hollow,  like  soap- 
bubbles  filled  with  air,  which  are  hotter  than  the  surrounding  air  ;  so  that 
these  vesicles  float  in  the  air  like  so  many  small  balloons.  Others  assume 
that  clouds  and  fogs  consist  of  extremely  minute  droplets  of  water  which  are 
retained  in  the  atmosphere  by  the  ascensional  force  of  currents  of  hot  air, 
just  as  light  powders  are  raised  by  the  wind.  Ordinarily,  clouds  do  not 
appear  to  descend,  but  this  absence  of  downward  motion  is  only  apparent. 
In  fact,  clouds  do  usually  fall  slowly,  but  then  the  lower  part  is  continually 
dissipated  on  coming  in  contact  with  the  lower  and  more  heated  layers  ;  at 
the  same  time  the  upper  part  is  always  increasing  from  the  condensation  of 
new  vapours,  so  that  from  these  two  actions  clouds  appear  to  retain  the 
same  height. 

982.  Formation  of  clouds. — Many  causes  may  concur  in  the  formation 
of  clouds.  The  usual  cause  of  the  formation  of  a  cloud  is  the  ascent,  into 
higher  regions  of  the  atmosphere,  of  air  laden  with  aqueous  vapour ;  it 
thereby  expands,  being  under  diminished  pressure  ;  and  in  consequence 
of  this  expansion  it  is  cooled,  and  this  cooling  produces  a  condensation  of 
vapour.  Hence  it  is  that  high  mountains,  stopping  the  currents  of  air  and 
forcing  them  to  rise,  are  an  abundant  source  of  rain.  If  the  air  is  quite  dry 
its  temperature  would  be  one  degree  lower  for  every  300  metres.  The  case 
is  different  with  moist  air  ;  for  when  the  air  has  ascended  so  high  that  its 
temperature  has  fallen  to  the  dew-point,  aqueous  vapour  is  condensed,  and 
in  consequence  of  this  heat  is  liberated  ;  when  the  dew-point  is  thus  attained, 
and  the  air  is  saturated,  the  cooling  due  to  the  ascent  and  expansion  of  air 
is  counteracted  by  this  liberation  of  latent  heat,  so  that  the  diminution  of 
temperature  with  the  height  is  considerably  slower  in  the  case  of  moist  than 
of  diy  air.  About  one  half  of  the  entire  quantity  of  moisture  in  the  air  is 
contained  in  the  first  six  or  seven  thousand  feet  upon  the  ground. 

The  following  calculation  will  give  us  the  quantity  of  water  separated  in 
a  given  case  :  Suppose  air  at  a  temperature  of  20°  to  be  saturated  with 
acjueous  vapour  at  that  temperature  ;  the  pressure  of  the  vapour  will  be  17-4 
mm.,  and  the  weight  contained  in  one  cubic  metre  of  air  17-1  grammes. 


ioo8  Meteorology.  [982- 

If  the  air  has  risen  to  a  height  of  3,500  metres,  it  has  come  under  a 
pressure  which  is  only  \  of  what  it  was  ;  its  temperature  is  4°,  and  its 
volume  about  li  times  what  it  originally  was.  As  it  remains  saturated  the 
pressure  will  be  6"i  mm.,  and  the  quantity  of  vapour  will  be  6*4  grammes 
in  a  cubic  metre,  that  is  to  say,  6-4  x  1^  =  9-6  grammes  in  the  whole  mass  of 
what  was  originally  a  cubic  metre.  The  pressure  of  aqueous  vapour  has 
sunk  during  the  ascent  from  17-4  mm.  to  6-i  mm.,  and  its  weight  17-1 
grammes  to  9-6  grammes  ;  that  is,  a  weight  of  7-5  grammes  has  been  deposited 
for  that  mass  of  air  which  at  the  sea-level  occupied  a  space  of  one  cubic 
metre.  These  7-5  grammes  are  in  the  form  of  the  small  droplets  which 
constitute  fogs  or  clouds. 

If  the  mass  of  air  had  risen  to  a  height  of  8,500  metres,  where  the  pres- 
sure is  only  one-third  that  on  the  sea-level,  the  temperature  is  —28°,  and 
the  space  it  occupies  three  times  as  great  as  at  first.  The  pressure  of 
aqueous  vapour  is  0-5  mm.,  and  its  weight  o-6  gramme  in  a  cubic  metre. 
Hence  there  is  now  only  i'8  gramme  left  of  the  entire  quantity  of  aque- 
ous vapour  originally  present,  and  the  remaining  15 -3  grammes  would  be 
separated  as  water  or  ice.  A  similar  calculation  will  show  that  at  a  height 
of  4,200  metres,  where  the  temperature  is  zero  and  the  pressure  |,  the  quan- 
tity of  water  present  in  the  original  cubic  metre  is  only  0-82  gramme,  the 
rest  being  deposited. 

Thus,  a  mass  of  air  which,  at  the  sea-level,  occupies  a  space  of  a  cubic 
metre,  and  is  saturated  with  aqueous  vapour  at  20°,  and  then  contains  17-1 
grammes,  will  only  contain  9-6  grammes  at  a  height  of  3,500  metres,  8-2 
grammes  at  4,200  metres,  and  i-8  gramme  at  8,500  metres.  Hence,  while 
a  mass  of  air  rises  from  the  sea-level  to  a  height  of  4,200  feet,  8-9  grammes  of 
aqueous  vapour  are  separated  as  cloud-vesicles  ;  at  8,500  metres,  or  about 
double  the  height,  6-4  grammes  are  separated  in  the  form  of  ice. 

A  hot  moist  current  of  air  mixing  with  a  colder  current  undergoes  a 
cooling,  which  brings  about  a  condensation  of  the  vapour.  Thus  the  hot 
and  moist  winds  of  the  south  and  south-west,  mixing  with  the  colder  air  of 
our  latitudes,  give  rain.  The  winds  of  the  north  and  north-east  tend  also, 
in  mixing  with  our  atmosphere,  to  condense  the  vapours  ;  but  as  these  winds, 
owing  to  their  low  temperature,  are  veiy  dry,  the  mixture  rarely  attains 
saturation,  and  generally  gives  no  rain. 

The  formation  of  clouds  in  this  way  is  thus  explained  by  Hutton.  The 
tension  of  aqueous  vapour,  and  therewith  the  quantity  present  in  a  given 
space  when  saturated,  diminishes  according  to  a  geometric  progression, 
while  the  temperature  falls  in  arithmetical  progression,  and  therefore  the 
elasticity  of  the  vapour  present  at  any  time  is  reduced  by  a  fall  of  temperature 
more  rapidly  than  in  direct  proportion  to  the  fall.  Hence,  if  a  current  of 
warm  air,  saturated  with  aqueous  vapour,  meets  a  current  of  cold  air  also 
saturated,  the  air  acquires  the  mean  temperature  of  the  two,  but  can  only 
retain  a  portion  of  the  vapour  in  the  invisible  condition,  and  a  cloud  or  mist 
is  formed.  Thus,  suppose  a  cubic  metre  of  air  at  io°  C.  mixes  with  a  cubic 
metre  of  air  at  20°  C,  and  that  they  are  respccti\cly  saturated  with  aqueous 
vapour.  By  formula  (401)  it  is  easily  calculated  that  the  weight  of  water-' 
contained  in  the  cubic  metre  of  air  at  10°  C.  is  9*397  grammes,  and  in  that 
at  20°  C.  is  17-632  grammes,  or  27-029  grammes  in  all.     When  mixed  they 


-983]  Rain.  1009 

produce  two  cubic  metres  of  air  at  15°  C.  ;  but  as  the  weight  of  water 
required  to  saturate  this  is  only  2  x  12-8  =  25-6  grammes,  the  excess,  1-429 
gramme,  will  be  deposited  in  the  form  of  mist  or  clouds. 

983.  Rain. — When  the  individual  vapour-vesicles  become  larger  and 
heavier  by  the  condensation  of  aqueous  vapour,  and  when  finally  individual 
vesicles  unite,  they  form  regular  drops,  which  fall  as  rain. 

The  quantity  of  rain  which  falls  annually  in  any  given  place,  or  the  annual 
rainfall,  is  measured  by  means  of  a  rain-gauge^  ox pluviotneter.    Ordinarily  it 

consists  of  a  cylindrical  vessel 
M  (figs.  971  and  972),  closed  at 
the  top  by  a  funnel-shaped  lid, 
in  which  there  is  a  very  small 
hole,  through  which  the  rain 
falls.  At  the  bottom  of  the 
vessel  is  a  glass  tube.  A,  in 
which  the  water  rises  to  the 
same  height  as  inside  the  rain- 
gauge,  and  is  measured  by  a 
scale  on  the  side,  as  shown  in 
the  figures. 

Fig.  971.  Fig.  972.  The  apparatus  being  placed 

in  an  exposed  situation,  if  at 
the  end  of  a  month  the  height  of  water  in  the  tube  is  two  inches,  for  example, 
it  shows  that  the  water  has  attained  this  height  in  the  vessel,  and,  conse- 
quently, that  a  layer  of  two  inches  in  depth  expresses  the  quantity  of  rain 
which  this  extent  of  surface  has  received. 

It  has  been  noticed  that  the  quantity  of  rain  indicated  by  the  rain-gauge 
is  greater  as  this  instrument  is  nearer  the  ground.  This  has  been  ascribed 
to  the  fact  that  the  raindrops,  which  are  generally  colder  than  the  layers  of 
air  which  they  traverse,  condense  the  vapour  in  these  layers,  and  therefore 
constantly  increase  in  volume.  Hence  more  rain  falls  on  the  surface  of  the 
ground  than  at  a  certain  height.  But  it  has  been  objected  that  the  excess 
of  the  quantity  of  rain  which  falls,  over  that  at  a  certain  height,  is  six  or 
seven  times  that  which  could  arise  from  condensation,  even  during  the  whole 
course  of  the  raindrops  from  the  clouds  to  the  earth.  The  difterence  must 
therefore  be  ascribed  to  purely  local  causes,  and  it  is  now  assumed  that  the 
difference  arises  from  eddies  produced  in  the  air  about  the  rain-gauge,  which 
are  more  perceptible  as  it  is  higher  above  the  ground  ;  as  these  eddies  dis- 
perse the  drops  which  would  otherwise  fall  into  the  instrument,  they  diminish 
the  quantity  of  water  which  it  receives. 

In  any  case  it  is  clear  that  if  raindrops  traverse  moist  air,  they  will,  from 
their  temperature,  condense  aqueous  vapour  and  increase  in  volume.  If,  on 
the  contrary,  they  traverse  dry  air,  the  drops  tend  to  vaporise,  and  less  rain 
falls  than  at  a  certain  height  ;  it  might  even  happen  that  the  rain  did  not 
reach  the  earth. 

From  measurements  of  the  coron^e  (981)  Delezenne  determined  the 
diameter  of  the  globules  in  the  case  of  rain-clouds  just  about  to  fall,  and  in 
the  case  of  the  cloud  from  a  low-pressure  steam-engine  (471).  The  former 
was  found  to  vary  from  0-0565  to  0'0226  mm.,  and  the  latter  from  0'005i  to 

3T 


1 010  Meteorology.  [983- 

0-0042  mm.  With  the  former  5,500  droplets  would  be  needed  to  make  a 
drop  of  water  a  millimetre  in  diameter,  and  with  the  latter  50,000. 

According  to  the  same  author  there  would  be  about  1 5  mgr.  of  globules  in 
a  cubic  metre  of  a  cloud  which  produced  a  rainfall  of  10  mm.  of  water  in  an 
hour.  With  this  number  the  mean  distances  of  the  vesicles  with  the  above 
magnitudes  are  respectively  r845,  0706,  0-167,  and  0-148  mm. 

The  rainfall  varies  with  the  height  of  a  station  above  the  sea-level  at  the 
rate  of  3  or  4  per  cent,  for  each  100  feet  of  altitude  above  the  sea. 

Many  local  circumstances  may  affect  the  quantity  of  rain  which  falls  in 
different  countries  ;  but,  other  things  being  equal,  most  rain  falls  in  hot  cli- 
mates, for  there  the  vaporisation  is  most  abundant.  The  rainfall  decreases, 
in  fact,  from  the  equator  to  the  poles.  At  London  it  is  23-5  inches  ;  at 
Bordeaux  it  is  25-8  ;  at  Madeira  it  is  27-7  ;  at  Havannah  it  is  91-2  ;  and  at 
St.  Domingo  it  is  107-6.  The  quantity  varies  with  the  season  :  in  Paris,  in 
winter,  it  is  4-2  inches  ;  in  spring,  6-9  ;  in  summer,  6*3  ;  and  in  autumn,  4-8 
inches.  The  heaviest  annual  rainfall  at  any  place  on  the  globe  is  on  the 
Khasi  Hills  in  Bengal,  where  it  is  600  inches  ;  of  which  500  inches  fall  in 
seven  months.  On  July  i,  1851,  a  rainfall  of  25^  inches  on  one  day  was 
observed  at  Cherrapoonjee.  At  Kurrachec,  in  the  north-west  of  India,  the 
rainfall  is  only  7  inches. 

The  driest  recorded  place  in  England  is  Lincoln,  where  the  mean  rainfall 
is  20  inches  ;  and  the  wettest  is  Stye,  at  the  head  of  Borrowdale  in  Cumber- 
land, where  it  amounts  to  165  inches.  The  greatest  average  amount  of  rain- 
fall in  any  one  day,  taking'  the  means  of  all  stations,  is  i^  inch  ;  though 
individual  stations  far  exceed  this  amount,  sometimes  reaching  4  inches. 

An  inch  of  rain  on  a  square  yard  of  surface  expresses  a  fall  of  46-74 
pounds,  or  4-67  gallons.  On  an  acre  it  corresponds  to  22,622  gallons,  or 
100-9935  tons.  100  ions  per  i?ich  per  acre  is  a  ready  way  of  remembering 
this. 

984.  'Waterspouts.— On  hot  summer  days,  and  when  the  weather  is- 
otherwise  calm,  we  often  notice  sand  and  dust  carried  forward  in  a  column 
with  a  whirling  motion.  As  storms  come  on,  larger  whirlwinds  of  this  kind 
are  formed,  which  carry  with  them  leaves,  straw,  and  even  small  branches. 
When  they  are  of  larger  dimensions  they  form  real  whirlwinds.  They  are 
probably  due  to  the  contest  of  two  winds  blowing  in  the  upper  regions  of  the 
atmosphere.  When  they  pass  over  land  they  form  large  conical-shaped 
masses  of  dust  which  makes  them  visible  at  a  distance  ;  when  they  pass 
over  rivers  or  the  sea  they  present  a  curious  phenomenon.  The  water  is 
disturbed,  and  rises  in  the  form  of  a  cone,  while  the  clouds  are  depressed 
in  the  form  of  an  inverted  cone  ;  the  two  cones  then  unite  and  form  a 
continuous  column  from  the  sea  to  the  clouds  (fig.  973).  Even,  however^ 
on  the  high  seas  the  water  of  these  waterspouts  is  never  salt,  proving 
that  they  are  formed  of  condensed  vapour,  and  not  of  sea- water  raised  by 
aspiration. 

985.  Influence  of  aqueous  vapour  on  oliniate. — Tyndall  applied  the 
property  possessed  by  aqueous  vapour  of  powerfully  absorbing  and  radiating 
lieat  to  the  explanation  of  some  obscure  points  in  nieteorologj'.  He  estalj- 
lishcd  the  fact  that  in  a  tube  4  feet  long  the  atmospheric  vapour  on  a  day  of 
average  dryness  absorbs  10  per  cent,  of  obscure  heat.    With  the  earth  warmed 


-985] 


bifincncc  of  Aqueous   Vapour  on  Climate. 


ion 

by  the  sun  as  a  source,  at  the  very  least  lo  per  cent,  of  its  heat  is  intercepted 
within  lo  feet  of  the  surface.  The  absorption  and  radiation  of  aqueous 
vapour  is  more  than  16,000  times  that  possessed  by  dry  air. 

The  7-adiati7<e  power  of  acjueous  vapour  may  be  the  main  cause  of  the 
torrent-hke  rains  that  occur  in  the  tropics,  and  also  of  the  formation  of 
cumulus  clouds  in  our  own  latitudes.  The  same  property  probably  causes 
the  descent  of  very  fine  rain,  called  serein^  which  has  more  the  characteristics 
of  falling  dew,  as  it  appears  a  short  time  after  sunset,  when  the  sky  is  clear  ; 
its  production  has  therefore  been  attributed  to  the  cold  resulting  from  the 


Fig.  973. 

radiation  of  the  air.  It  is  not  the  air,  however,  but  the  aqueous  vapour  in 
the  air,  which  by  its  own  radiation  chills  itself,  so  that  it  condenses  into 
serehi. 

The  absorbent  power  of  aqueous  vapour  is  of  even  greater  importance. 
Whenever  the  air  is  dry,  terrestrial  radiation  at  night  is  so  rapid  as  to  cause 
intense  cold.  Thus,  in  the  central  parts  of  Asia,  Africa,  and  Australia,  the 
daily  range  of  the  thermometer  is  enormous  ;  in  the  interior  of  the  last- 
named  continent  a  difference  in  temperature  of  no  less  than  40°  C.  has  been 
recorded  within  24  hours.  In  India,  and  even  in  the  Sahara,  ice  has  been 
formed  at  night,  owing  to  the  copious  radiation.  But  the  heat  which  aqueous 
vapour  absorbs  most  largely  is  of  the  kind  emitted  from  sources  of  low 
temperature  ;  it  is  to  a  large  extent  transparent  to  the  heat  emitted  from  the 
sun,  whilst  it  is  almost  opaque  to  the  heat  radiated  from  the  earth.  Con- 
sequently, the  solar  rays  penetrate  our  atmosphere  with  a  loss,  as  estimated 
by  Pouillet,  of  only  25  per  cent.,  when  directed  vertically  downwards,  but 
after  warming  the  earth  they  cannot  re-traverse  the  atmosphere.     Through 

3T  2 


IOI2  Meteorology.  [985- 

thus  preventing  the  escape  of  terrestrial  heat,  the  aqueous  vapour  in  the  air 
moderates  the  extreme  chilhng  which  is  due  to  the  unchecked  radiation  from 
the  earth,  and  raises  the  temperature  of  that  region  over  which  it  is  spread. 
In  Tyndall's  words,  'aqueous  vapour  is  a  blanket  more  necessary  to  the 
vegetable  life  of  England  than  clothing  is  to  man.  Remove  for  a  single 
summer  night  the  aqueous  vapour  from  the  air  which  overspreads  this 
country,  and  every  plant  capable  of  being  destroyed  by  a  freezing  tempera- 
ture would  perish.  The  warmth  of  our  fields  and  gardens  would  pour  itself 
unrequited  into  space,  and  the  sun  would  rise  upon  an  island  held  fast  in  the 
iron  grip  of  frost.' 

986.  Tyndall's  researches. — Tyndall  found  that  by  the  action  of  the 
sun  and  the  electric  light  on  vapours  under  a  great  degree  of  attenuation, 
they  are  decomposed.  He  used  a  glass  tube  with  glass  ends,  which  could 
be  exhausted  and  then  filled  with  air  charged  with  the  vapours  of  volatile 
liquids,  by  allowing  the  air  to  bubble  through  small  Wolff  bottles  containing 
them.  By  mixing  the  air  charged  with  vapour  with  different  proportions  of 
pure  air,  and  by  varying  the  degree  of  exhaustion,  it  was  possible  to  have  a 
vapour  under  any  degree  of  attenuation.  The  tube  could  also  be  filled  with 
the  vapour  of  a  liquid  alone.  The  tube  having  been  filled  with  air  charged 
with  vapour  of  nitrite  of  amyle,  a  somewhat  convergent  beam  from  the  elec- 
tric lamp  was  passed  into  the  tube.  For  a  moment  the  tube  appeared 
optically  empty,  but  suddenly  a  shower  of  liquid  spherules  was  precipitated 
on  the  path  of  the  beam,  forming  a  luminous  white  cloud.  The  nature  of 
the  substance  thus  precipitated  was  not  specially  investigated.  This  effect 
was  not  due  to  any  chemical  action  between  the  vapour  and  the  air,  for 
when  either  dry  oxygen  or  dry  hydrogen  was  used  instead  of  air,  or  when 
the  vapour  was  admitted  alone,  the  effect  was  substantially  the  same.  Nor 
was  it  due  to  any  heating  effect,  for  the  beam  had  been  previously  sifted  by 
passing  through  a  solution  of  alum,  and  through  the  thick  glass  of  the  lens. 
The  unsifted  beam  produced  the  same  effect  ;  the  obscure  calorific  rays  did 
not  seem  to  affect  the  result.  The  sun's  light  also  effects  the  decomposition 
of  nitrite  of  amyle  vapour  ;  and  this  decomposition  was  found  to  be  mainly 
due  to  the  more  refrangible  rays.  When  the  electric  light,  before  entering 
the  experimental  tube,  was  made  to  pass  through  a  layer  of  liquid  nitrite  of 
amyle  an  eighth  of  an  inch  in  thickness,  the  luminous  effect  was  not  appre- 
ciably diminished,  but  the  chemical  action  was  almost  entirely  stopped. 
Thus  that  special  constituent  of  the  luminous  radiation  which  effects  the 
decomposition  of  the  vapour  is  absorbed  by  the  liquid.  The  decomposition 
of  liquid  nitrite  of  amyle  by  light,  if  it  take  place  at  all,  is  far  less  rapid  and 
distinct  than  that  of  the  vapour.  The  circumstance  that  the  absorption  is 
the  same  whether  the  nitre  is  in  the  liquid  or  in  the  vaporous  state,  is  con- 
sidered by  Tyndall  as  a  proof  that  the  absorption  is  not  the  act  of  the 
molecule  as  a  whole,  but  that  it  is  atomic ;  that  is,  that  it  is  to  the  atoms 
that  the  peculiar  rate  of  vibration  is  transferred  which  brings  about  the 
decomposition  of  the  body,  liy  vaiying  the  nature  of  the  vapour  the  shape 
of  a  cloud  could  be  greatly  varied,  and  in  many  cases  presented  the  most 
fantastic  and  beautiful  forms. 

It  was  also  found  that  a  vapour  which  when  alone  resists  the  action  of 
light  may,  by  being  associated  with  another  gas  or  vapour,  exhibit  a  vigor- 


-986J  TyndaWs  Researches.  1013 

ous  action.  Thus  when  the  tube  was  filled  with  atmospheric  air,  mixed  with 
nitrite  of  butyle  vapour,  the  electric  light  produced  very  little  efifect ;  but  with 
half  an  atmosphere  of  this  mixture,  and  half  an  atmosphere  of  air  which  had 
passed  through  hydrochloric  acid,  the  action  of  the  light  was  almost  instan- 
taneous. In  another  case  mixed  air  and  nitrite  of  butyle  vapour  were  passed 
into  the  tube  so  that  the  mixture  was  under  a  pressure  of  2*5  mm.  Air 
passed  through  aqueous  hydrochloric  acid  was  introduced  until  the  pressure 
was  3  inches.  The  condensed  beam  passed  through  at  first  without  change, 
but  afterwards  a  superb  blue  cloud  was  formed. 

In  cases  where  the  vapours  are  under  a  sufficient  degree  of  attenuation, 
whatever  otherwise  be  their  nature,  the  visible  action  commences  with  the 
formation  of  a  blue  cloud.  The  term  cloud,  however,  must  not  be  understood 
in  its  ordinary'  sense  ;  the  blue  cloud  is  invisible  in  ordinary  daylight,  and 
to  be  seen  must  be  surrounded  by  darkness,  it  alone  being  illuminated  by  a 
powerful  beam  of  light.  The  blue  cloud  differs  in  many  important  particulars 
from  the  finest  ordinary  clouds,  and  may  be  considered  to  occupy  an  inter- 
mediate position  between  these  clouds  and  true  cloudless  vapour. 

By  graduating  the  quantity  of  vapour,  the  precipitation  may  be  obtained 
of  any  required  degree  of  fineness  ;  forming  either  particles  distinguishable 
by  the  naked  eye,  or  particles  beyond  the  reach  of  the  highest  microscopic 
power.  The  case  is  similar  to  that  of  carbonic  acid  gas,  which,  diffused 
in  the  atmosphere,  resists  the  decomposing^  action  of  solar  light,  but  is 
decomposed  when  in  contact  with  the  chlorophyle  in  the  leaves  of  plants. 

When  the  blue  cloud  produced  in  these  experiments  was  examined  by 
any  polarising  arrangement,  the  light  emitted  laterally  from  the  beam — that 
is,  in  a  direction  at  right  angles  to  its  axis— was  found  to  be  perfectly  polar- 
ised. This  phenomenon  was  observed  in  its  greatest  perfection  the  more 
perfect  the  blue  of  the  sky.  It  is  produced  by  any  particles,  provided  they 
are  sufficiently  fine.  This  is  quite  analogous  to  the  light  of  the  blue  sky. 
When  this  is  examined  by  a  Nicol's  prism,  or  any  other  analyser,  it  is  found 
that  the  light  emitted  at  right  angles  to  the  path  of  the  sun's  rays  is  polarised. 

The  phenomena  of  the  firmamental  blue,  and  the  polarisation  of  the 
sky  light,  thus  find  definite  explanations  in  these  experiments.  We  need  only 
assume  the  existence,  in  the  higher  regions  of  the  atmosphere,  of  excessively 
fine  particles  of  water  ;  for  particles  of  any  kind  produce  this  effect.  It 
is  easy  to  conceive  the  existence  of  such  particles  in  the  higher  regions, 
even  on  a  hot  summer's  day.  For  the  vapour  must  there  be  in  a  state  of 
extreme  attenuation  ;  and  inasmuch  as  the  oxygen  and  nitrogen  of  the  atmo- 
sphere behave  like  a  vacuum  to  radiant  heat,  the  extremely  attenuated  particles 
of  aqueous  vapour  are  practically  in  contact  with  the  absolute  cold  of 
space. 

'  Suppose  the  atmosphere  surrounded  by  an  envelope  impervious  to 
light,  but  with  an  aperture  on  the  sunward  side,  through  which  a  parallel 
beam  of  solar  light  could  enter  and  traverse  the  atmosphere.  Surrounded 
on  all  sides  by  air  not  directly  illuminated,  the  track  of  such  a  beam  would 
resemble  that  of  the  parallel  beam  of  the  electric  light  through  an  incipient 
cloud.  The  sunbeam  would  be  blue,  and  it  would  discharge  light  laterally  in 
the  same  condition  as  that  discharged  by  the  incipient  cloud.  The  azure  re- 
vealed by  such  a  beam  would  be  to  all  intents  and  purposes  a  blue  cloud.' 


1014  Meteorology.  [987- 

987.  Bew.  Hoarfrost. — Deiu  is  aqueous  vapour  which  has  condensed 
on  bodies  during  the  night  in  the  form  of  minute  globules.  It  is  occasioned 
by  the  chilling  which  bodies  near  the  surface  of  the  earth  experience  in 
consequence  of  nocturnal  radiation.  Their  temperature  having  then  sunk 
several  degrees  below  that  of  the  air,  it  frequently  happens,  especially  in  hot 
seasons,  that  this  temperature  is  below  that  at  which  the  atmosphere  is 
saturated.  The  layer  of  air  which  is  immediately  in  contact  with  the  chilled 
bodies,  and  which  has  virtually  the  same  temperature,  then  deposits  a  por- 
tion of  the  vapour  which  it  contains  (396)  ;  just  as  when  a  bottle  of  cold  water 
is  brought  into  a  warm  room  it  becomes  covered  with  moisture,  owing'  to  the 
condensation  of  aqueous  vapour  upon  it. 

According  to  this  theory,  which  was  first  propounded  by  Dr.  Wells,  all 
causes  which  promote  the  cooling  of  bodies  increase  the  quantity  of  dew. 
These  causes  are  the  emissive  power  of  bodies,  the  state  of  the  sky,  and  the 
agitation  of  the  air.  Bodies  which  have  a  great  radiating  power  more  readily 
become  cool,  and  therefore  ought  to  condense  more  vapour.  In  fact  there 
is  generally  no  deposit  of  dew  on  metals,  whose  radiating  power  is  very 
small,  especially  when  they  are  polished  ;  while  the  ground,  sand,  glass  and 
plants,  which  have  a  great  radiating  power,  become  abundantly  covered 
with  dew. 

The  state  of  the  sky  also  exercises  a  great  influence  on  the  formation  of 
dew.  If  the  sky  is  cloudless,  the  planetary  spaces  send  to  the  earth  an  in- 
appreciable quantity  of  heat,  while  the  earth  radiates  very  considerably,  and 
therefore  becoming  very  much  chilled,  there  is  an  abundant  deposit  of  dew. 
But  if  there  are  clouds,  as  their  temperature  is  far  higher  than  that  of  the 
planetary  spaces,  they  radiate  in  turn  towards  the  earth,  and  as  bodies  on  the 
surface  of  the  earth  only  experience  a  feeble  chilling,  no  deposit  of  dew  takes 
place. 

Wind  also  influences  the  quantity  of  vapour  deposited.  If  it  is  feeble,  it 
increases  it,  inasmuch  as  it  renews  the  air  ;  if  it  is  strong,  it  dmiinishes  it, 
as  it  heats  the  body  by  contact,  and  thus  does  not  allow  the  air  time  to 
become  cooled.  Finally,  the  deposit  of  dew  is  more  abundant  according  as 
the  air  is  moister,  for  then  it  is  nearer  its  point  of  saturation. 

Hoarfrost  and  rime  are  dew  which  has  been  deposited  on  bodies  cooled 
below  zero,  and  has  become  frozen.  The  flocculent  form  which  the  small 
crystals  present,  of  which  rime  is  formed,  shows  that  the  vapour  solidifies 
directly  without  passing  through  the  liquid  state.  Hoarfrost,  like  dew,  is 
formed  on  bodies  which  radiate  most,  such  as  the  stalks  and  leaves  of  vege- 
tables, and  is  chiefly  deposited  on  the  parts  turned  towards  the  sky. 

We  must  distinguish  between  the  dew  formed  in  consequence  of  lowering 
of  temperature  by  radiation,  and  the  deposit  formed  by  warm  moist  air 
passing  over  a  cold  wall  ;  in  mild  weather  this  deposit  forms  a  liquid, 
and  in  severe  weather  a  snow  or  icy  coating.  Unlike  dew,  a  deposit  of 
this  kind  is  most  abundantly  found  on  good  conductors,  for  they  are  the 
coldest. 

988.  Snow.  Sleet. — Snow  is  water  solidified  in  stellate  ciystals,  vari-. 
ously  modified,  and  floating  in  the  atmosphere.  These  crystals  arise  frorrr' 
the  congelation  of  the  minute  vesicles  which  constitute  the  clouds,  when  the 
temperature  of  the  latter  is  below  zero.   They  are  more  regular  when  formed 


-989]  Hail.  1015 

in  ;i  calm  atmosphere.  Their  form  may  1)C  investigated  by  collecting  them 
on  a  black  surface,  and  viewing  them  through  a  strong  lens.  The  regularity, 
and  at  the  same  time  variety,  of  their  forms  are  truly  beautiful.  Fig.  974 
shows  some  of  these  forms  as  seen  through  a  microscope.  Very  roughly  a 
fall  of  one  foot  of  snow  may  be  taken  as  equal  to  an  inch  of  rain. 

It  snows  most  in  countries  near  the  poles,  or  which  are  high  above  the 
sea-level.  By  the  limit  of  perpetual  snow — or,  briefly  snow-line — is  meant  that 
height  above  the  sea-level  at  which  the  snow  does  not  melt,  even  in  the 
hottest  summers.  It  is  lower  nearer  the  poles  than  the  equator  :  it  does  not 
depend  solely  on  the  latitude,  but  is  influenced  by  many  local  circumstances. 


Fis.  974. 

Sleet  is  also  solidified  water,  and  consists  ot  small  icy  needles  pressed 
together  in  a  confused  manner.  Its  formation  is  ascribed  to  the  sudden 
congelation  of  the  minute  globules  of  the  clouds  in  an  agitated  atmo- 
sphere. 

When  the  ground  is  cooled  below  zero  after  severe  frost  and  a  thaw  sets 
in,  the  moist  air  passing  over  the  ground  deposits  its  moisture,  which  is 
converted  into  a  continuous  sheet  of  ice  ;  this  is  known  as  glazed  frost  (the 
French  verglas) ;  it  may  also  occur  when  raindrops  which  have  been  cooled 
below  zero  in  the  higher  regions  of  the  air,  and  are  accordingly  in  a  state  of 
snperfusion  (345),  fall  on  the  ground,  which  may  even  be  above  the  freezing 
point. 

989.  Hall. — Hail  is  a  mass  of  compact  globules  of  ice  of  different  sizes, 
which  fall  in  the  atmosphere.  In  our  climate  hail  falls  principally  during 
spring  and  summer,  and  at  the  hottest  times  of  the  day  ;  it  rarely  falls  at 
night.     The  fall  of  hail  is  always  preceded  by  a  peculiar  noise. 

Hail  is  generally  the  precursor  of  storms,  it  rarely  accompanies  them, 
and  follows  them  more  rarely  still.  Hail  falls  from  the  size  of  small  peas  to 
that  of  an  ^g'g  or  an  orange,  with  a  core  of  compressed  snow  which  is  sur- 
rounded by  concentric  layers  of  ice.  While  snowstorms  may  last  for  days, 
hailstorms  do  not  last  for  more  than  a  quarter  of  an  hour.  The  formation 
of  hailstones  has  never  been  altogether  satisfactorily  accounted  for  ;  nor 
more  especially  their  great  size. 


ioi6  Meteorology.  [990- 

990.  Ice.  Regrelation. — Ice  is  an  aggregate  of  sno\v-cr>'stals,  such  as 
are  shown  in  fig.  974.  The  transparency  of  ice  is  due  to  the  close  contact 
of  these  crystals,  which  causes  the  individual  particles  to  blend  into  an  un- 
broken mass,  and  renders  the  substance  optically.,  as  well  as  mechanically, 
continuous.  When  large  masses  of  ice  slowly  melt  away,  a  crystalline  form 
is  sometimes  seen  by  the  gradual  disintegration  into  rude  hexagonal  prisms  ; 
a  similar  structure  is  frequently  met  with,  but  in  greater  perfection,  in  the 
ice-caves  or  glaciers  of  cold  regions. 

An  experiment  of  Tyndall  shows  the  beautiful  structure  of  ice.  When  a 
piece  of  ice  is  cut  parallel  to  its  planes  of  freezing,  and  the  radiation  from 
any  source  of  light  is  permitted  to  pass  through  it,  the  disintegration  of 
the  substance  proceeds  in  a  remarkable  way.  By  observing  the  plate  of 
ice  through  a  lens,  numerous  small  crystals  will  be  seen  studding  the  interior 
of  the  block  ;  as  the  heat  continues  these  crystals  expand,  and  finally  assume 
the  shape  of  six-rayed  stars  of  exquisite  beauty. 

This  is  a  kind  of  negative  crystallisation,  the  crystals  produced  being 
composed  of  water  :  they  owe  their  formation  to  the  molecular  disturbance 
caused  by  the  absorption  of  heat  from  the  source.  Nothing  is  easier  than  to 
reproduce  this  phenomenon,  if  care  be  taken  in  cutting  the  ice.  The  planes 
of  freezing  can  be  found  by  noting  the  direction  of  the  bubbles  in  ice,  which 
are  either  sparsely  arranged  in  striae  at  right  angles  to  the  surface,  or  thickly 
collected  in  beds  parallel  to  the  surface  of  the  water.  A  warm  and  smooth 
metal  plate  should  be  used  to  level  and  reduce  the  ice  to  a  slab  not  exceeding 
half  an  inch  in  thickness. 

A  still  more  important  property  of  ice  remains  to  be  noticed.  Faraday 
discovered  that  when  two  pieces  of  melting  ice  are  pressed  together  they 
freeze  into  one  at  their  points  of  contact.  This  curious  phenomenon  is  now 
known  under  the  name  of  Regelation.  The  cause  of  it  has  been  the  subject 
of  much  controversy,  but  the  simplest  explanation  seems  to  be  that  given 
by  its  discoverer.  The  particles  on  the  exterior  of  a  block  of  ice  are  held  by 
cohesion  on  one  side  only  ;  when  the  temperature  is  at  0°  C,  these  exterior 
particles  being  partly  free  are  the  first  to  pass  into  the  liquid  state,  and  a  film 
of  water  covers  the  solid.  But  the  particles  in  the  interior  of  the  block  are 
bounded  on  all  sides  by  the  solid  ice,  the  force  of  cohesion  is  here  a  maximum, 
and  hence  the  interior  ice  has  no  tendency  to  pass  into  a  liquid,  even  when 
the  whole  mass  is  at  0°.  If  the  block  be  now  split  in  halves,  a  liquid  film 
instantly  covers  the  fractured  surfaces,  for  the  force  of  cohesion  on  the 
fractured  surfaces  has  been  lessened  by  the  act.  By  placing  the  halves 
together,  so  that  their  original  position  shall  be  regained,  the  liquid  films 
on  the  two  fractured  surfaces  again  become  liounded  by  ice  on  both  sides. 
The  film  being  excessively  thin,  the  force  of  cohesion  is  able  to  act  across 
it  ;  the  consequence  of  this  is,  the  liquid  particles  pass  back  into  the  solid 
state,  and  the  block  is  reunited  by  regelation.  Not  only  do  ice  and  ice  thus 
freeze  together,  but  regelation  also  takes  place  between  moist  ice  and  any 
non-conducting  solid  body,  as  flannel  or  sawdust  ;  a  similar  explanation  to 
tliat  just  given  has  been  applied  here,  substituting  another  solid  for  the  ice, 
(in  one  side.  It  must  be  remarked,  however,  that  many  eminent  philosophers 
dissent  from  the  explanation  here  given. 

Whatever  may  be  the  true  cause  of  regelation,  there  can  be  no  doubt  that 


-992]     Atmospheric  Electricity.     Franklin's  Experiment.      1017 

this  interesting  observation  of  Faraday's  explains  many  natural  phenomena 
For  example,  the  formation  of  a  snowball  depends  on  the  regelation  of  the 
snow-granules  composing  it ;  and  as  regelation  cannot  take  place  at  tem- 
peratures below  0°  C,  for  then  both  snow  and  ice  are  dry,  it  is  only  possible 
to  make  a  coherent  snowball  when  the  snow  is  melting. 

The  snow-bridges,  also,  which  span  wide  chasms  in  the  Alps  and  else- 
where, and  over  which  men  can  walk  in  safety,  owe  their  existence  to  the 
regelation  of  gradually  accumulating  particles  of  snow. 

Bottomley  has  made  a  very  instructive  experiment  which  illustrates  rege- 
lation. A  block  of  ice  is  suspended  on  two  supports,  and  a  fine  piano  wire 
with  heavy  weights  at  each  end  is  laid  across  it.  After  some  time  the  wire 
has  slowly  cut  its  way  through,  but  the  cut  surfaces  have  reunited,  and,  except- 
ing a  few  bubbles,  show  no  trace  of  the  operation  ;  the  wire  is  below  zero,  as 
is  proved  by  placing  it  in  cold  water,  upon  which  some  ice  forms  round  it. 

991.  Glaciers. — Tyndall  has  applied  this  regelating  property  of  ice  to 
an  explanation  of  the  formation  and  motion  of  glaciers,  of  which  the  follow- 
ing is  a  brief  description  :  In  elevated  regions,  the  sttow-line  (988)  marks  the 
boundary'  of  eternal  snow,  for  above  this  the  heat  of  summer  is  unable  to 
melt  the  winter's  snow.  By  the  heat  of  the  sun  and  the  consequent  percola- 
tion of  water  melted  from  the  surface,  the  lower  portions  of  the  snow-field 
are  raised  to  0°  C.  ;  at  the  same  time  this  part  is  closely  pressed  together  by 
the  weight  of  the  snow  above  ;  regelation  therefore  sets  in,  converting  the 
loose  snow  into  a  coherent  mass. 

By  increasing  pressure  the  intermingled  air  which  renders  snow  opaque 
becomes  ejected  and  the  snow  becomes  transparent ;  ice  then  results.  Its 
own  gravity,  and  the  pressure  from  behind,  urge  downwards  the  glacier 
which  has  thus  been  formed.  In  its  descent  from  the  mountain  the  glacier 
behaves  in  all  respects  like  a  river,  passing  through  narrow  gorges  with 
comparative  velocity,  and  then  spreading  out  and  moving  slowly  as  its  bed 
widens.  Further,  just  as  the  central  portions  of  a  river  move  faster  than 
the  sides,  so  Forbes  ascertained  that  the  centre  of  a  glacier  moves  quicker 
than  its  margin,  and  from  the  same  reason  (the  difference  in  the  friction 
encountered)  the  surface  moves  more  rapidly  than  the  bottom.  To  explain 
these  facts  Forbes  assumed  ice  to  be  a  viscous  body  capable  of  flexure,  and 
flowing  like  lava  ;  but  as  ice  has  not  the  properties  of  a  viscous  substance, 
the  now  generally  accepted  explanation  of  glacier  motion  is  that  supplied  by 
the  theory  of  regelation.  According  to  this  theory,  the  brittle  ice  of  the 
glacier  is  crushed  and  broken  in  its  passage  through  narrow  channels,  such 
as  that  of  Trelaporte  on  Mont  Blanc  ;  and  then,  as  it  emerges  from  the  gorge 
which  confined  it,  becomes  reunited  by  virtue  of  regelation  ;  in  this  instance 
forming  the  well-known  Mer  de  Glace.  By  numerous  experiments  Tyndall 
has  established  that  regelation  is  adequate  to  furnish  this  explanation,  and 
has  artificially  imitated,  on  a  small  scale,  the  moulding  of  glaciers  by  the 
crushing  and  subsequent  regelation  of  ice. 

We  see  an  example  of  this  formation  of  ice  from  pressure  from  the  glazed 
appearance  of  the  tracks  in  snow  in  roads  over  which  heavy  carts  have 
passed. 

992.  Atmospberlc  electricity.  Franklin's  experiment. — The  most 
frequent  luminous  phenomena,  and  the  most  remarkable  for  their  effects, 


ioi8 


Meteorology. 


[992- 


are  those  produced  by  the  free  electricity  in  the  atmosphere.  The  first 
physicists  who  observed  the  electric  spark  compared  it  to  the  gleam  of 
lightning,  and  its  crackling  to  the  sound  of  thunder.  But  Franklin,  by  the 
aid  of  powerful  electrical  batteries,  first  established  a  complete  parallel 
between  lightning  and  electricity  ;  and  he  indicated,  in  a  memoir  published 
in  1749,  the  experiments  necessary  to  attract  electricity  from  the  clouds  by 
means  of  pointed  rods.  The  experiment  was  tried  by 
Dalibard  in  France  ;  and  Franklin,  pending  the  erec- 
tion of  a  pointed  rod  on  a  spire  in  Philadelphia,  had  the 
happy  idea  of  flying  a  kite,  provided  with  a  metal 
point,  which  could  reach  the  higher  regions  of  the 
atmosphere.  In  June  1752,  during  stormy  weather, 
he  flew  the  kite  in  a  field  near  Philadelphia.  The 
kite  was  flown  with  ordinary  pack-thread,  at  the  end 
of  which  Franklin  attached  a  key,  and  to  the  key  a 
silk  cord,  in  order  to  insulate  the  apparatus  :  he  then 
fixed  the  silk  cord  to  a  tree,  and  having  presented 
his  hand  to  the  key,  at  first  he  obtained  no  spark. 
He  was  beginning  to  despair  of  success,  when,  rain 
having  fallen,  the  cord  became  a  good  conductor,  and 
a  spark  passed.  Franklin,  in  his  letters,  describes  his 
emotion  on  witnessing  the  success  of  the  experiment  as 
being  so  great  that  he  could  not  refrain  from  tears. 

Franklin  imagined  that  the  kite  drew  from  the 
cloud  its  electricity  ;  it  is,  in  fact,  a  simple  case  of 
induction,  and  depends  on  the  inductive  action  which 
the  thunder-cloud  exerts  upon  the  kite  and  the  cord. 

993.  Apparatus  to  investigate  the  electricity  of 
the  atmosphere. — To  observe  the  electricity  in  fine 
weather,  when  the  quantity  is  generally  small,  an  ap- 
paratus may  be  used,  as  devised  by  Saussure  for  this 
kind  of  investigation.  It  is  an  electroscope  similar  to 
that  already  described  (751),  but  the  rod  to  which  the 
gold  leaves  are  fixed  is  surmounted  by  a  conductor 
2  feet  in  length,  and  terminates  either  in  a  knob  or 
a  point  (fig.  975).  To  protect  the  apparatus  against 
rain,  it  is  covered  with  a  metal  shield  4  inches  in 
diameter.  The  glass  case  is  square  instead  of  being  round,  and  a  divided 
scale  on  its  inside  face  indicates  the  divergence  of  the  gold  leaves.  This 
electrometer  only  gives  signs  of  atmospheric  electricity  as  long  as  it  is 
raised  in  the  atmosphere  so  that  it  is  in  layers  of  air  of  higher  electrical 
potential  than  its  own. 

To  ascertain  the  electricity  of  the  atmosphere,  Saussure  also  used  a 
copper  ball,  which  he  projected  vertically  with  his  hand.  This  ball  was 
fixed  to  one  end  of  a  metal  wire,  the  other  end  of  which  was  attached  to  a 
ring,  which  could  glide  along  the  conductor  of  the  electrometer.  From  the^ 
divergence  of  the  gold  leaves,  the  electrical  condition  of  the  air  at  the 
height  which  the  ball  attained  could  be  determined.  Becquerel,  in  experi- 
ments made  on  the  St.  Bernard,  improved  Saussure's  apparatus  by  substi- 


Fig.  975. 


-993]     Apparatus  to  Investigate  Atmospheric  Electricity.      1019 

tuting  for  the  knob  an  arrow,  which  was  projected  into  the  atmosphere  by- 
means  of  a  bow.  A  gilt  silk  thread,  88  yards  long,  was  fixed  with  one  end 
to  the  arrow,  while  the  other  end  was  attached  to  the  stem  of  an  electro- 
scope. Peltier  used  a  gold-leaf  electroscope,  at  the  top  of  which  was  a 
somewhat  large  copper  globe.  Provided  with  this  instrument,  the  observer 
places  himself  in  a  prominent  position  ;  it  is  then  quite  sufficient  to  raise  the 
electroscope  even  a  foot  or  so  to  obtain  signs  of  electricity. 

To  observe  the  electricity  of  clouds,  where  the  potential  is  very  con- 
siderable, use  is  made  of  a  long  bar  terminating  in  a  point.  This  bar, 
which  is  insulated  with  care,  is  fixed  to  the  summit  of  a  building,  and  its 
lower  end  is  connected  with  an  electrometer,  or  even  with  electric  chimes 
(fig.  695),  which  announce  the  presence  of  thunder-clouds.     As,  however,  the 


Fig.  976. 

bar  can  then  give  dangerous  shocks,  a  metal  ball  must  be  placed  near  it, 
which  is  well  connected  with  the  ground,  and  which  is  nearer  the  bar  than 
the  observer  himself;  so  that  if  a  discharge  should  ensue,  it  will  strike 
the  ball  and  not  the  observer.  Richmann,  of  St.  Petersburg,  was  killed  in  an 
experiment  of  this  kind,  by  a  discharge  which  struck  him  on  the  forehead. 

Sometimes  also  captive  balloons  or  kites  have  been  used,  provided  with 
a  point,  and  connected  by  means  of  a  gilt  cord  with  an  electrometer. 

\  good  collector  of  atmospheric  electricity  consists  of  a  fishing-rod  with 
an  insulated  handle  which  projects  from  an  upper  window.  At  the  top  is 
a  bit  of  lighted  tinder  held  in  a  metallic  forceps,  the  smoke  of  which,  being 
an  excellent  conductor,  conveys  the  electricity  of  the  air  down  a  wire  attached 
to  the  rod.  A  sponge  moistened  with  alcohol,  and  set  on  fire,  is  also  an 
excellent  conductor. 

A  convenient  instrument  for  investigating  atmospheric  electricity  has 
been   introduced   by  Sir  W.   Thomson  ;   one  form  of  which,  used  in  the 


I020  Meteorology.  [993- 

Meteorological  Observatory  of  Montsouris,  is  represented  in  fig.  976.  It 
consists  of  a  large  metal  vessel  A  resting  on  three  insulating  glass  legs  fixed 
to  the  top  of  a  tall  column  of  cast  iron.  A  sheet  metal  mantle  B  protects  the 
supports  from  the  rain.  The  apparatus  is  arranged  in  the  open,  and  can  be 
filled  with  water  from  a  pipe  C.  The  Avater  issues  through  a  long  lateral 
jet  in  A,  in  a  stream  so  fine  that  the  volume  of  the  water  is  not  appreciably 
altered.  An  insulated  wire  z,  passing  through  the  column,  connects  the  vessel 
A  with  an  electrometer  placed  indoors.  This  plan  of  collecting  the  atmo- 
spheric electricity  is  adopted  in  balloons,  where  a  flame,  for  instance,  is  out  of 
the  question. 

The  manner  in  which  the  electricity  of  the  atmosphere  is  registered  is  seen 
from  fig.  977,  which  represents  the  form  in  use  at  the  above  observatory. 


In  a  light  tight  box  is  a  band  of  sensitised  photographic  paper,  stretched  on 
the  surface  of  a  cylinder  and  moved  by  clockwork. 

In  one  side  of  the  box  is  a  long  cyhndrical  glass  lens,  in  front  of  which 
at  E  are  two  quadrant  electrometers  (780).  Both  of  these  are  connected  with 
the  same  collector  of  electricity,  placed  outside,  and  their  sectors  are  charged 
by  the  same  source  of  electricity,  but  one  of  them  is  ten  times  as  sensitive 
as  the  other.  Near  one  side  of  the  box  is  a  gas  burner  with  an  opaque 
chimney  A,  in  two  opposite  sides  of  which  arc  longitudinal  slits,  through- 
which  the  light  passes  to  two  total-reflection  prisms  (545)  //',  which  are 
arranged  so  as  to  send  two  pencils  of  light  on  the  mirrors  ;//  w'  of  the 
electrometer.     This  is  shown  on  a  larger  scale  on  the  left  of  the  figure  :  the 


-994]  Ordinary  Electricity  of  the  Atmosphere.  1021 

two  pencils  fall  upon  the  lens  L,  which  concentrates  in  a  point  the  slices  of 
light  issuing  from  the  chimney  and  reflected  from  the  mirror.  These  follow 
the  motion  of  the  mirror,  and  thus  impress  on  the  sensitive  paper  the  curves 
which  measure  the  electrical  potential  of  the  air.  There  is  also  an  arrange- 
ment by  which  an  electromagnet  puts  the  electrometers  to  earth  for  a  i&w 
minutes  at  every  hour,  and  thus  discharges  them.  The  mirrors  revert  then 
to  their  original  position  and  commence  a  new  trace. 

If  we  replace  the  electrometer  with  its  mirror  attached,  by  a  magneto- 
meter, we  can  easily  see  how  the  variations  in  the  magnetic  declination  may 
be  recorded  (702). 

994.  Ordinary  electricity  of  the  atmospbere. — By  means  of  the  dif- 
ferent apparatus  which  have  been  described,  it  has  been  found  that  the 
presence  of  electricity  in  the  atmosphere  is  not  confined  to  stormy  weather, 
but  that  the  atmosphere  always  contains  free  electricity,  in  the  vast  majority 
of  cases  positive,  but  occasionally  negative.  When  the  sky  is  unclouded, 
the  electricity  is  always  positive,  and  it  increases  with  the  height  above  the 
ground.  The  amount  is  greatest  in  the  highest  and  most  isolated  places. 
No  trace  of  positive  electricity  is  found  in  houses,  streets,  and  under  trees  : 
in  towns  positive  electricity  is  most  perceptible  in  large  open  spaces,  on  quays, 
or  on  bridges.     Sir  W.  Thomson  found  in  the  Isle  of  Arran  at  a  height  of 

9  feet  above  the  ground  a  difference  of  potential  equal  to  200  to  400  Daniell's 
elements,  or  from  216  to  432  volts.  This  represents  a  rise  of  potential  of 
from  24  to  48  volts  for  each  foot  of  ascent.  This  is  subject  to  great  varia- 
tion ;  with  winds  from  the  north  and  north-east  the  potential  was  often  6  to 

10  times  as  much  as  the  higher  of  these  amounts.  The  charge  of  potential 
is  most  rapid  in  cold  dry  weather,  when  the  quantity  of  moisture  in  the  air 
is  at  its  lowest.  Thus,  at  a  temperature  of  -  8°  to  -  12°  C,  Exner  found  a 
charge  of  600  Daniells  per  metre  in  the  direction  of  the  vertical.  With  a 
vapour  pressure  of  2-3  mm.  the  charge  was  325,  with  6-8  it  was  116,  and 
with  12-5  it  was  68. 

Between  5  and  7.30  a.m.  the  positive  electricity  in  the  air  is  at  a  mini- 
mum ;  it  increases  from  7  to  9.30  .A.-M.,  according  to  the  season,  and  then 
attains  its  first  maximum.  It  then  decreases  rapidly  until  from  2.30  to 
4.30  P.M.,  and  again  increases  till  it  reaches  its  second  maximum,  from  6.30 
to  9.30  P.M.  ;  the  remainder  of  the  night  the  electricity  decreases  until  sun- 
rise. Thus  the  greatest  amount  of  electricity  is  observed  when  the  baro- 
metric pressure  is  highest.  These  increasing  and  decreasing  periods,  which 
are  observed  all  the  year,  are  more  perceptible  when  the  sky  is  clearer,  and 
the  weather  more  settled.  The  positive  electricity  of  fine  weather  is  much 
stronger  in  winter  than  in  summer.  It  may,  in  short,  be  said  that  electricity 
of  the  air  follows  the  opposite  course  to  that  of  temperature  and  moisture.  ■ 

When  the  sky  is  clouded,  the  electricity  is  sometimes  positive  and  some- 
times negative.  According  to  Palmieri  the  occurrence  of  negative  electricity 
is  a  certain  indication  that  within  a  distance  of  40  miles  it  either  rains, 
snows,  or  hails.  It  often  happens  that  the  electricity  changes  its  sign 
several  times  in  the  course  of  the  day,  owing  to  the  passage  of  an  electrified 
cloud.  During  storms,  and  when  it  rains  or  snows,  the  atmosphere  may  be 
positively  electrified  one  day,  and  negatively  the  next,  and  the  number  of  the 
two  sets  of  days  are  virtually  equal. 


I022  Meteorology.  [994- 

During  a  thunderstorm  the  changes  in  potential  and  sign  of  electricity- 
are  so  rapid  that  the  photographic  method  of  registration  fails. 

From  a  long  series  of  observations  on  the  electricity  of  the  atmosphere 
made  in  the  early  morning,  Dellman  found  that  the  electricity  increased 
with  the  density  of  the  fog,  but  in  a  far  more  rapid  ratio. 

The  electricity  of  the  ground  has  been  found  by  Peltier  to  be  always 
negative,  and  this  is  the  cardinal  fact  in  reference  to  atmospheric  electricity  ; 
it  is  so,  however,  to  different  extents,  according  to  the  hygrometric  state 
and  temperature  of  the  air.  The  density  is,  however,  exceedingly  small, 
being  calculated  at  0-00036  dynes  per  square  centimetre,  from  which  it 
follows  that  the  electrical  pressure  {lyj)  is  0-00000082  dynes  per  square 
centimetre,  or  less  than  the  millionth  of  a  milligramme  in  weight.  Even  if 
the  pressure  were  ten  times  as  great  it  would  be  insufficient  to  raise  even 
the  lightest  bodies. 

995.  Causes  of  atmospheric  electricity. — Although  many  hypotheses 
have  been  propounded  to  explain  the  origin  of  atmospheric  electricity,  it 
must  be  confessed  that  our  knowledge  is  in  an  unsatisfactory  state. 

Volta  first  showed  that  the  evaporation  of  water  produced  electricity. 
Pouillet  subsequently  showed  that  no  electricity  is  produced  by  the  evapo- 
ration of  distilled  water  ;  but  that  if  an  alkali  or  a  salt  is  dissolved,  even 
in  small  quantity,  the  vapour  is  positively  and  the  solution  is  negatively 
electrified.  The  reverse  is  the  case  if  the  water  contains  acid.  Hence  it 
has  been  assumed  that  as  the  waters  which  exist  on  the  surface  of  the  earth 
and  on  the  sea  always  contain  salt  dissolved,  the  vapours  disengaged  ought 
to  be  positively  and  the  earth  negatively  electrified.  The  development  of 
electricity  by  evaporation  may  be  observed  by  heating  strongly  a  platinum 
dish,  adding  to  it  a  small  quantity  of  liquid,  and  placing  it  on  the  upper 
plate  of  the  condensing  electroscope  (fig.  716),  taking  care  to  connect  the 
lower  plate  with  the  ground.  When  the  water  of  the  capsule  is  evaporated, 
the  connection  with  the  ground  is  broken,  and  the  upper  plate  raised.  The 
gold  leaves  then  diverge  if  the  water  contained  salts,  but  remain  quiescent 
if  the  water  was  pure. 

Reasoning  from  such  experiments,  Pouillet  ascribed  the  development 
of  electricity  by  evaporation  to  the  separation  of  particles  of  water  from 
the  substances  dissolved  ;  but  Reich  and  Ricss  showed  that  the  electricity 
disengaged  during  evaporation  could  be  attributed  to  the  friction  which 
the  particles  of  water  carried  away  in  the  current  of  vapour  exert 
against  the  sides  of  the  vessel,  just  as  in  Armstrong's  electrical  machine 
(758).  By  a  recent  scries  of  experiments,  Gaugain  has  arrived  at  the  same 
result. 

Sohnckc  recalls  an  experiment  of  Faraday  which  he  has  repeated — that 
the  friction  of  minute  vesicles  of  water  against  dry  ice  is  an  abundant  source 
of  electricity  ;  he  ascribes  atmospheric  electricity  to  this  origin,  showing  that 
in  the  upper  regions  both  particles  of  water  and  of  ice  may  coexist.  The  ice 
particles  become  positively  electrified,  while  tliose  of  water  arc  negative. 
When  these  fall  in  rain,  they  carry  with  them  their  negative  electricity.  A 
similar  theory  has  been  propounded  by  Luvini. 

996,  Electricity  of  clouds. — Clouds  are  in  general  electrified  usually 
positively  but    sometimes    negatively,  and    only  differ   in   their   higher   or 


-997J  Lightning.  1023 

lower  potential.  The  formation  of  positive  clouds  is  by  some  ascribed  to 
the  vapour  disengaged  from  the  ground  and  condensed  in  the  higher 
regions.  Negative  clouds  are  supposed  to  result  from  fogs,  which,  by  their 
contact  with  the  ground,  become  charged  with  negative  electricity,  which 
they  retain  on  rising  into  the  atmosphere  ;  or  that,  separated  from  the 
ground  by  layers  of  moist  air,  they  have  been  negatively  electrified  by 
induction  from  the  positive  clouds,  which  have  repelled  into  the  ground 
positive  electricity. 

Whatever  be  the  origin  of  atmospheric  electricity,  there  can  be  no  doubt 
that  the  invisible  aqueous  vapour  is  the  carrier  of  it,  and  it  is  easy  to 
explain  the  high  potential  of  clouds  from  the  condensation  of  this  vapour. 
For  suppose  1,000  vapour-particles,  each  possessing  the  same  charge  of 
electricity,  coalesce  to  form  a  single  droplet,  the  diameter  of  such  a  droplet 
will  be  ten  times  that  of  the  individual  particles,  that  is,  its  capacity  is  ten 
times  as  great,  since  the  capacity  is  equal  to  the  radius  (739)  ;  but  the 
quantity  of  electricity  will  be  1,000  times  as  great  as  on  the  small  one,  and 
therefore  the  potential  will  be  100  times  as  great.  Now  the  number  of 
vapour-particles  which  go  to  form  a  single  droplet  is  rather  to  be  counted 
by  billions  ;  hence,  however  small  be  the  finite  value  which  we  assign  to 
the  potential  of  the  electricity  of  the  vapour-particles,  that  of  the  drops  will 
be  infinitely  greater,  and  sufficient  to  account  for  the  high  potential  of  clouds. 
Thunder-clouds  are  sometimes  as  low  as  700  to  1,000  feet  ;  but  their  usual 
height  appears  to  be  3,000  to  6,000  feet. 

997.  liig-htnlng-.— This,  as  is  well  known,  is  the  dazzling  light  emitted  by 
the  electric  spark  when  it  shoots  from  clouds  charged  with  electricity.  In 
the  lower  regions  of  the  atmosphere  the  light  is  white,  but  in  the  higher 
regions,  where  the  air  is  more  rarefied,  it  takes  a  violet  tint  ;  as  does  the 
spark  of  the  electrical  machine  in  a  rarefied  medium  (787). 

The  flashes  of  lightning  are  often  more  than  a  mile,  and  sometimes, 
extend  to  four  or  five  miles,  in  length  ;  they  generally  pass  through  the 
atmosphere  in  a  zigzag  direction — a  phenomenon  ascribed  to  the  resistance 
offered  by  the  air  condensed  by  the  passage  of  a  strong  discharge.  The 
spark  then  diverges  from  a  right  line,  and  takes  the  direction  of  least  resist- 
ance.    In  a  vacuum,  electricity  passes  in  a  straight  line. 

De  la  Rue  and  Miiller  have  calculated  that  the  potential  required 
to  produce  a  flash  a  mile  in  length,  would  be  that  of  3,516,480  of  their 
cells  (812). 

We  cannot,  however,  regard  the  length  of  a  lightning  flash  as  the  direct 
striking  distance  between  two  conductors.  Owing  to  the  number  of  droplets 
met  on  its  path  the  discharge  is  rather  to  be  compared  with  that  of  the 
luminous  tubes  and  panes  (789).  The  experiments  of  Alascart  on  the  rela- 
tion between  the  striking  distance  ijT])  and  the  potential  required  to  pro- 
duce it  show  that  the  striking  distance  increases  far  more  rapidly  than  the 
potential.  Thus  while  the  potential  required  for  a  striking  distance  of  i  cm. 
is  represented  by  8-3  ;  for  4  cm.  it  is  15-9  ;  for  8  cm.  20-5  ;  and  for  15  cm. 
23-3.  From  this  it  is  possible  that  a  lightning  discharge  is  produced  by  a 
difference  of  potentials  between  two  clouds  which  is  not  out  of  proportion 
w-ith  those  obtained  by  our  electrical  machines. 

Several  kinds  of  lightning  flashes  may  be  distinguished — i,  the  zigzag 


I024  Meteorology.  [997- 

flashes,  which  move  with  extreme  velocity  in  the  form  of  a  Hne  of  fire  with 
sharp  outHnes,  and  which  closely  resemble  the  spark  of  an  electrical  machine. 
The  recent  investigation  of  the  shape  of  lightning  discharges  by  means  of 
extra  rapid  photographic  dry  plates  (6io)  has  shown  that  the  path  of  a  dis- 
charge is  not  so  sharply  zigzag  as  is  usually  represented,  but  has  more  the 
shape  of  the  course  of  a  river  as  shown  on  a  map,  and  with  frequent  branch- 
ings ;  2,  the  sheet  flashes,  which,  instead  of  being  linear,  like  the  preceding, 
fill  the  entire  horizon  without  having  any  distinct  shape.  This  kind,  which 
is  most  frequent,  appears  to  be  produced  in  the  cloud  itself,  and  to  illuminate 
the  mass.  According  to  Kundt,  the  number  of  sheet  discharges  are  to  the 
zigzag  discharged  as  1 1  :  6  ;  and  from  spectrum  observations  it  would  appear 
that  the  former  are  brush  discharges  between  clouds,  while  the  latter  are 
true  electrical  discharges  between  the  clouds  and  the  earth.  Another  kind, 
called  heat  lightni?ig,  is  ascribed  to  distant  lightning  flashes  which  are  below 
the  horizon,  but  illuminate  the  higher  strata  of  clouds  so  that  their  bright- 
ness is  visible  at  great  distances  ;  they  produce  no  sound,  probably  in  con- 
sequence of  the  fact  of  their  being  so  far  off  that  the  rolling  of  thunder 
cannot  reach  the  ear  of  the  observer.  There  is  further  the  very  unusual 
phenomenon  of  globe  lightning.,  or  the  flashes  which  appear  in  the  form 
of  globes  of  fire.  These,  which  are  sometimes  visible  for  as  much  as  ten 
seconds,  descend  from  the  clouds  to  the  earth  with  such  slowness  that  the 
eye  can  follow  them.  They  often  rebound  on  reaching  the  ground  ;  at 
other  times  they  burst  and  explode  with  a  noise  like  that  of  the  report  of 
many  cannon.  No  adequate  explanation  has  been  given  of  these,  though 
Plante  with  a  large  battery  of  his  cells  has  imitated  the  phenomena. 

The  duration  of  the  light  of  the  first  three  kinds  does  not  amount  to  the 
millionth  of  a  second,  as  was  determined  by  Wheatstone  by  means  of  his 
rotating  wheel,  which  was  turned  so  rapidly  that  the  spokes  were  invisible  ; 
on  illuminating  it  by  the  lightning  flash,  its  duration  was  so  short  that 
whatever  the  velocity  of  rotation  of  the  wheel,  it  appeared  quite  stationary  ; 
that  is,  its  displacement  is  not  perceptible  during  the  time  the  lightning  exists. 
The  light  produced  by  a  lightning  flash  must  be  comparable  to  the  sun 
in  brightness,  though  it  does  not  appear  to  us  brighter  than  ordinary  moon- 
light. Tkit  considering  its  excessively  brief  duration,  and  that  the  full  effect 
of  any  light  on  the  eye  is  only  produced  when  its  duration  is  at  least  the 
tenth  of  a  second,  it  follows  that  a  landscape  continuously  illuminated  by  the 
lightning  flash  would  appear  100,000  times  as  bright  as  it  actually  appears 
to  us  during  the  flash. 

Here  also  may  be  mentioned  the  phenomenon  known  as  St.  Elmds  fire., 
which  occurs  in  a  highly  electrical  state  of  the  atmosphere  when  the  clouds 
arc  low.  It  is  a  sort  of  brush  discharge  (787),  appearing  like  small  flames 
issuing  from  prominent  point-objects  such  as  masts,  tops  of  trees,  lightning- 
conductors  ;  it  has  also  been  observed  on  the  points  of  helmets  or  lances, 
alpenstocks  ;  it  is  of  course  most  easily  seen  in  the  dark,  and  is  accompanied 
by  a  slight  rustling  noise.  On  the  sea  it  is  not  uncommon  in  thunderstorms 
on  mastheads  and  yard-arms. 

99S.  Thunder. — Thunder  is  the  violent  report  which  succeeds  liglUning  in 
stormy  weather.  The  lightning  and  the  thunder  are  practically  simultaneous, 
but  an  interval  of  several   seconds  is  always  observctl  between   these  two 


-999 j  Ejfccts  of  Lightning.  1025 

phenomena,  which  arises  from  the  fact  that  sound  only  travels  at  the  rate  of 
about  1,100  feet  in  a  second  (232),  while  the  passage  of  light  is  almost  instan- 
taneous. Hence  an  observer  will  only  hear  the  noise  of  thunder  five  or  six 
seconds,  for  instance,  after  the  lightning,  according  as  the  distance  of  the 
thunder-cloud  is  live  or  six  times  1,100  feet.  The  noise  of  thunder  arises 
from  the  disturbance  which  the  electric  discharge  produces  in  the  air,  and 
which  may_^be  witnessed  in  Kinnersley's  thermometer  (fig.  729).  Near  the 
place  where  the  lightning  strikes,  the  sound  is  sharp  and  of  short  duration. 
At  a  greater  distance  a  series  of  reports  are  heard  in  rapid  succession.  At  a 
still  greater  distance  the  noise,  feeble  at  first,  changes  into  a  prolonged  rolling 
sound  of  varying  intensity.  If  the  lightning  is  at  a  greater  distance  than  14 
or  15  miles  it  is  no  longer  heard,  for  sound  is  more  imperfectly  propagated 
through  air  than  through  solid  bodies  :  hence  there  are  lightning  discharges 
without  thunder  ;  these  occur  at  times  when  the  sky  is  cloudless. 

Some  attribute  the  noise  of  the  rolling  of  thunder  to  the  reflection  of 
sound  from  the  ground  and  from  the  clouds.  Others  have  considered  the 
lightning  not  as  a  single  discharge,  but  as  a  series  of  discharges,  each  of 
which  gives  rise  to  a  particular  sound.  But  as  these  partial  discharges 
proceed  from  points  at  different  distances,  and  from  zones  of  unequal  density, 
it  follows  not  only  that  they  reach  the  ear  of  the  observer  successively,  but 
that  they  bring  sounds  of  unequal  density,  which  occasion  the  duration  and 
inequality  of  the  rolling.  The  phenomenon  has  finally  been  ascribed  to 
the  zigzags  of  lightning  themselves,  assuming  that  the  air  at  each  salient 
angle  is  at  its  greatest  compression,  which  would  produce  the  unequal  in- 
tensity of  the  sound.  The  distance  between  the  nearest  point  of  a  hghtning 
flash  IS  obtained  in  kilometres  if  we  multiply  the  time  in  seconds  between 
the  lightning  flash  and  the  beginning  of  the  thunder  by  3. 

999.  Effects  of  lightning.— The  lightning  discharge  is  the  electric 
discliarge  which  strikes  between  a  thunder-cloud  and  the  ground.  The  latter, 
by  the  induction  from  the  electricity  of  the  cloud,  becomes  charged  with 
contrary  electricity  ;  and  when  the  tendency  of  the  two  electricities  to  com- 
bine exceeds  the  resistance  of  the  air,  the  spark  passes  which  is  often  ex- 
pressed by  saying  that  '  a  thunderbolt  has  fallen.'  Lightning  in  general 
strikes  from  above,  but  ascending  lightning  is  also  sometimes  observed  ; 
probably  this  is  the  case  when  the  clouds  being  negatively  the  earth  is  posi- 
tively electrified,  for  experiments  show  that  at  the  ordinary  pressure  the 
positive  fluid  passes  through  the  atmosphere  more  easily  than  negative  elec- 
tricity. 

From  the  first  law  of  electrical  attraction  the  discharge  ought  to  fall  first 
on  the  nearest  and  best  conducting  objects,  and,  in  fact,  trees,  elevated 
buildings,  metals,  are  particularly  struck  by  the  discharge.  Hence  it  is  im- 
prudent to  stand  under  trees  during  a  thunderstorm. 

The  effects  of  lightning  are  very  varied,  and  of  the  same  kind  as  those 
of  batteries  (783),  but  of  far  greater  power.  The  lightning''  discharge  kills 
men  and  animals,  ignites  combustililes,  melts  metals,  breaks  bad  con- 
ductors in  pieces.  When  it  penetrates  the  ground  it  melts  the  silicious 
substances  on  its  path,  and  thus  produces  in  the  direction  of  the  discharge 
those  remarkable  vitrified  tubes  caWtid  fulgurites,  some  of  which  are  as  much 
as  12  yards  in  length  ;  in  most  cases  there  are  found  to  be  accumulations  of 

3U 


I026  Meteorology.  [999- 

water  below  such  fuls,''urites.  When  it  strikes  bars  of  iron,  it  magnetises 
them,  and  often  inverts  the  poles  of  compass  needles. 

After  the  passage  of  lightning  a  highly  peculiar  odour  is  frequently 
produced,  like  that  perceived  in  a  room  in  which  an  electrical  machine 
is  being  worked.  This  is  due  to  the  formation  of  ozone,  a  peculiar  allotro- 
pic  modification  of  oxygen  (793).  An  electrified  cloud  forms  with  the  earth 
below  a  condenser,  the  intervening  mass  of  air  being  the  dielectric.  This 
mass  of  air  is  therefore  in  a  state  of  strain  like  the  dielectric  in  a  Leyden 
jar,  and  it  is  to  this  state  of  strain  which  precedes  the  actual  discharge,  rather 
than  to  the  discharge  itself,  that  is  due  the  production  of  ozone. 

Heated  air  conducts  better  than  cold  air,  probably  only  owing  to  its 
lesser  density.  Hence  it  is  that  large  numbers  of  animals  are  often  killed 
by  a  single  discharge,  as  they  crowd  together  in  a  storm,  and  a  column  of 
warm  air  rises  from  the  gloom. 

1000.  Return  shock. — This  is  a  violent  and  sometimes  fatal  shock  which 
men  and  animals  experience,  even  when  at  a  great  distance  from  the  place 
where  the  lightning  discharge  passes.  It  is  caused  by  the  inductive  action 
which  the  thunder-cloud  exerts  on  bodies  placed  within  the  sphere  of  its 
activity.  These  bodies  are  then,  like  the  ground,  charged  with  the  opposite 
electricity  to  that  of  the  cloud  ;  but  when  the  latter  is  discharged  by  the 
recombination  of  its  electricity  with  that  of  the  ground,  the  induction  ceases, 
and  the  bodies  reverting  rapidly  from  the  electrical  state  to  the  neutral  state, 
the  concussion  in  question  is  produced— the  return  shock.  A  gradual  de- 
composition and  reunion  of  the  electricity  produces  no  visible  effects  ;  yet  it 
is  alleged  that  such  disturbances  of  the  electrical  equilibrium  are  perceived 
by  nervous  persons. 

The  return  shock  is  always  less  violent  than  the  direct  one  ;  there  is  no 
instance  of  its  having  produced  any  inflammation,  yet  plenty  of  cases  in 
which  it  has  killed  both  men  and  animals  ;  in  such  cases  no  broken  limbs, 
wounds,  or  burns  are  observed. 

The  return  shock  may  be  imitated  by  placing  a  gold-leaf  electroscope 
connected  by  a  wire  with  the  ground  near  an  electrical  machine  ;  when  the 
machine  is  worked,  at  each  spark  taken  from  the  prime  conductor  the  gold 
leaves  of  the  electroscope  suddenly  diverge. 

It  is  stated  that  persons  struck  by  lightning  often  lose  their  lives  only 
by  a  temporary  injury  to  the  nerves  which  control  the  act  of  respiration  ;  so 
that  under  favourable  circumstances  such  persons  might  probably  be  saved 
by  producing  artificial  respiration. 

TOOL  l,ig-litnIng--conductor.— This  was  invented  by  Franklin  in  1755. 

There  are  two  principal  parts  in  a  lightning-conductor,  the  rod  and  the 
conductor.  The  rod  (fig.  Q78)  is  a  pointed  bar  of  iron,  preferably  galvanised, 
or  of  copper,  P,  fixed  vertically  to  a  tube  or  rod  of  iron,  which,  by  moans  of 
a  collar,  a  a,  and  tube  .^r,  is  fitted  on  the  roof  of  the  edifice  to  be  protected  ; 
it  is  from  6  to  10  feet  in  height,  and  its  basal  section  is  about  2  or  3  inches 
in  diameter.  The  conductor  is  best  formed  of  a  wire  rope,  C,  such  as  are 
used  for  rigging  or  for  telegraph  wires,  attached  to  the  rod  by  a  metal  collar, 
b.  The  use  of  copper  instead  of  iron  wire  in  these  conductors  is  recom-' 
mended,  inasmuch  as  copper  is  a  better  conductor  than  iron.  The  metallic 
section  of  the   conductor  ought  to  be  about  half  a  square  inch,  and  the 


-1001]  Liglitning-Conductor.  1027 

individual  wires  0-04  to  o-o6  inch  in  diameter ;    they  ought  to  be  twisted 

in    strands,  hke    an   ordinary   cord.      The   conductor   is    usually   led   into 

a  well,  and   to   connect  it  better  with  the   soil   it   ends  in 

two  or  three   branches.     If  there   is   no  well  near,  a  hole 

is  dug  in  the    soil  to  the  depth  of  6  or  7  yards,  and  the 

foot  of   the   conductor   having   been    introduced,  the   hole 

is  filled  with   powdered    coke,    which    conducts  very  well. 

The  best  earth  contact    is  obtained  when  it  is  possible  to 

connect  the  wire  conductors   with  large  iron  gas  or  water  cl 

pipes. 

The  action  of  a  lightning-conductor  is  an  illustration  of 
the  action  of  induction  and  of  the  property  of  points  (731)  ; 
when  a  storm  cloud  positively  electrified,  for  instance,  forms 
in  the  atmosphere,  it  acts  inductively  on  the  earth,  repels 
the  positive  and  attracts  the  negative  electricity,  which  accu- 
mulates on  bodies  placed  on  the  surface  of  the  soil,  the 
more  abundantly  as  these  bodies  are  at  a  greater  height. 
The  density  is  then  greatest  on  the  highest  bodies,  which 
are  therefore  most  exposed  to  the  electric  discharge  ;  but  if 
these  bodies  are  provided  with  metal  points,  like  the  rods  of 
conductors,  the  negative  electricity,  withdrawn  from  the  soil 
by  the  influence  of  the  cloud,  flows  into  the  atmosphere,  and 
neutralises  the  positive  electricity  of  the  cloud.  Hence,  not 
only  does  a  lightning-conductor  tend  to  prevent  the  accumu- 
lation of  electricity  on  the  surface  of  the  earth,  but  it  also 
tends  to  restore  the  clouds  to  their  natural  state,  both  which 
concur  in  preventing  lightning  discharges.  This  mode  of 
action  of  lightning-conductors  is  often  overlooked  ;  it  is  stated  in  reference 
to  Pietermaritzburg  that  until  lightning-conductors  became  common  in  that 
town  it  was  constantly  visited  by  thunderstorms  at  certain  seasons.  They 
come  as  frequently  as  ever,  but  cease  to  give  flashes  on  reaching  the  town  ; 
they  do  so,  however,  when  they  have  passed  over  it.  The  disengagement 
of  electricity  is,  however,  sometimes  so  abundant  that  the  lightning-conductor 
is  inadequate  to  discharge  the  electricity  accumulated,  and  the  lightning 
strikes  ;  but  the  conductor  receives  the  discharge,  in  consequence  of  its 
greater  conductivity,  and  the  edifice  is  preserved. 

A  conductor,  to  be  efficient,  ought  to  satisfy  the  following  conditions  : — 
(i.)  the  rod  ought  to  be  so  large  as  not  to  be  melted  if  the  discharge  passes  ; 
(ii.)  it  ought  to  terminate  in  a  point,  or  in  several  points,  to  give  readier  issue  to 
the  electricity  disengaged  by  induction  from  the  ground  ;  (iii.)  the  conductor 
must  be  continuous  from  the  point  to  the  ground,  and  the  connection  between 
the  rod  and  the  ground  must  be  as  intimate  as  possible  ;  this  is  the  most 
important  of  all,  and  the  one  point  most  frequently  neglected  in  the  older 
arrangements.  A  lightning-conductor  with  load  earth  contact  is  not  only 
useless  but  dangerous.  The  continuity  of  the  conductor  may  be  tested  by 
means  of  a  voltaic  cell  and  a  portable  form  of  galvanometer,  (iv.)  If  the 
building  which  is  provided  with  a  lightning-conductor  contains  metallic 
surfaces  of  any  extent,  such  as  zinc  roofs,  metal  gutters,  or  ironwork,  these 
ought  to  be  connected  with  the  conductor,  or,  still  better,  have  each  a  sepa- 

3  u  2 


:028 


Meteofology. 


[1001- 


rate  earth  connection.  If  the  last  two  conditions  are  not  fulfilled,  there  is  a 
great  danger  of  lateral  discharges — that  is  to  say,  that  the  discharge  takes 
place  between  the  conductor  and  the  edifice,  and  then  it  increases  the 
danger. 

Colladon  concludes,  from  the  observation  of  a  series  of  lightning  dis- 
charges, that  a  tall  tree,  such  qs  a  poplar,  whose  roots  are  in  dry  ground, 
may  act  as  a  good  lightning-conductor,  if  on  the  other  side  of  the  house 
there  does  not  happen  to  be  a  well  or  pool,  towards  which  the  electricity  can 
spring  through  the  house. 

I002.  Rainbow. — The  rainbow  is  a  luminous  phenomenon  which  appears 
in  the  clouds  opposite  the  sun  when  they  are  resolved  into  rain.  It  consists 
of  seven  concentric  arcs,  presenting  successively  the  colours  of  the  solar 
spectrum.  Sometimes  only  a  single  bow  is  perceived,  but  there  are  usually 
two  :  a  lower  one,  the  colours  of  which  are  very  bright  ;  and  an  external  or 
seco?idary  one,  which  is  paler,  and  in  which  the  order  of  the  colours  is  re- 
versed. In  the  interior  rainbow  the  red  is  the  highest  colour  ;  in  the  other 
rainbow  the  violet  is.  It  is  seldom  that  three  bows  are  seen  ;  theoretically 
a  greater  number  may  exist,  but  their  colours  become  so  faint  that  they  cannot 
be  perceived. 

The  phenomenon  of  the  rainbow  is  produced  by  decomposition  of  the 
white  light  of  the  sun  when  it  passes  into  the  drops,  and  by  its  reflection 
from  their  inside  face.  In  fact,  the  same  phenomenon  is  witnessed  in  dew- 
drops  and  in  jets  of  water — in  short,  wherever  sunlight  passes  into  drops 
of  water  under  a  certain  angife. 

The  appearance  and  the  extent  of  the  rainbow  depend  on  the  position  of 
the  observer,  and  on  the  height  of  the  sun  above  the  horizon  ;  hence  only 
some  of  the  rays  refracted  by  the  raindrops,  and  reflected  in  their  concavity 
to  the  eye  of  the  spectator,  are  adapted  to  produce  the  phenomenon.  Those 
which  do  so  are  called  effective  rays. 

To  explain  this  let  n  (fig.  979)  be  a  drop  of  water,  into  which  a  solar  ray 
S  a  penetrates.     At  a  point  of  incidence,  a,  part  of  the  light  is  reflected  from 


(he  surface  of  the  liquid  ;  another,  entering  it,  is  decomposed  and  traverses 
the  drop  in  the  direction  a  b.     Arrived  at  b,  part  of  the  light  emerges  from 


n 


-1003]  Raijibozv.  1029 

the  raindrop,  the  other  part  is  reflected  from  the  concave  surface,  and  tends 
to  emerge  at^.  At  this  point  the  hght  is  again  partially  reflected  ;  the  re- 
mainder emerges  in  a  direction  ^O,  which  forms  with  the  incident  ray,  S  a, 
an  angle  called  the  angle  of  deviation.  It  is  such  rays  as  gO,  proceeding 
from  the  side  next  the  observer,  which  produce  on  the  retina  the  sensation 
of  colours,  provided  the  light  is  sufficiently  intense. 

It  csok  be  shown  mathematically  that  in  the  case  of  a  series  of  rays  which 
impinge  on  the  same  drop,  and  only  undergo  a  reflection  in  the  interior,  the 
angle  of  deviation  increases  from  the  ray  S"//,  for  which  it  is  zero,  up  to  a 
certain  limit,  beyond  which  it  decreases,  and  that  near  this  limit  rays  passing 
parallel  into  a  drop  of  rain  also  emerge  parallel.  From  this  parallelism  a 
beam  of  light  is  produced  sufficiently  intense  to  impress  the  retina  ;  these 
are  the  rays  which  emerge  parallel  and  are  efficient. 

As  the  ditfercnt  colours  which  compose  white  light  are  unequally  refran- 
gible, the  maximum  angle  of  deviation  is  not  the  same  for  all.  For  red  rays 
the  angle  of  deviation  corresponding  to  the  active  rays  is  42°  2',  and  for 
violet  rays  it  is  40°  17'.  Hence,  for  all  drops  placed  so  that  rays  proceeding 
from  the  sun  to  the  drop  make,  with  those  proceeding  from  the  drop  to  the 
eye,  an  angle  of  42°  2',  this  organ  will  receive  the  sensation  of  red  light  ; 
this  will  be  the  case  with  all  drops  situated  on  the  circumference  of  the 
base  of  a  cone,  the  summit  of  which  is  the  spectator's  eye  ;  the  axis  of 
this  cone  is  parallel  to  the  sun's  rays,  and  the  angle  formed  by  the  two 
opposed  generating  lines  is  84°  4'.  This  explains  the  formation  of  the  red 
band  in  the  rainbow  ;  the  angle  of  the  cone  in  the  case  of  the  violet  band 
is  80°  34'. 

The  cones  corresponding  to  each  band  have  a  common  axis  called  the 
visual  axis.  As  this  right  line  is  parallel  to  the  rays  of  the  sun,  it  follows 
that  when  this  axis  is  on  the  horizon,  the  visual  axis  is  itself  horizontal,  and 
the  rainbow  appears  as  a  semicircle.  If  the  sun  rises,  the  visual  axis  sinks, 
and  with  it  the  rainbow.  Lastly,  when  the  sun  is  at  a  height  of  42°  2',  the 
arc  disappears  entirely  below  the  horizon.  Hence  the  phenomenon  of  the 
rainbow  never  takes  place  except  in  the  morning  and  evening. 

What  has  been  said  refers  to  the  interior  arc.  The  secondary  bow  is 
formed  by  rays  which  have  undergone  two  reflections,  as  shown  by  the  ray 
^'idfeO,  in  the  drop  p.  The  angle  STO  formed  by  the  emergent  and 
incident  rays  is  called  the  angle  of  deviation.  The  angle  is  no  longer  suscep- 
tible of  a  maximum,  but  of  a  minimum,  which  varies  for  each  kind  of  rays, 
and  to  which  also  efficient  rays  correspond.  It  is  calculated  that  the  mini- 
mum angle  from  violet  rays  is  54°  7',  and  for  red  rays  only  50°  57';  hence  it 
is  that  the  red  bow  is  here  on  the  inside,  and  the  violet  arc  on  the  outside. 
There  is  a  loss  of  light  for  every  internal  reflection  in  the  drop  of  rain,  and 
therefore  the  colours  of  the  secondary  bow  are  always  feebler  than  those  of 
the  internal  one.  The  secondary  bow  ceases  to  be  visible  when  the  sun  is 
54°  above  the  horizon. 

The  moon  sometimes  produces  rainbows  like  the  sun,  but  they  are  veiy 
pale. 

1003.  Aurora  borealis. — The  aurora  borealis^  or  northern  light,  or  more 
Y^xo'^&xXy  polar  aurora^  is  a  remarkable  luminous  phenomenon  which  is  fre- 
quently seen  in  the  atmosphere  at  the  two  terrestrial  poles.     The  following 


1030  Meteorology.  [1003- 

is  a  description  of  an  aurora  borealis  observed  at  Bossekop,  in  Lapland,  lat. 
70°,  in  the  winter  of  1838-39  : — 

In  the  evening,  between  4  and  8  o'clock,  the  upper  part  of  the  fog  which 
usually  prevails  to  the  north  of  Bossekop  became  coloured.  This  light 
became  more  regular,  and  formed  an  indistinct  arc  of  a  pale  yellow,  with  its 
concave  side  turned  towards  the  earth,  while  its  summit  was  in  the  magnetic 
meridian. 

Blackish  rays  soon  separated  the  luminous  parts  of  the  arc.  Luminous 
rays  formed,  becoming  alternately  rapidly  and  slowly  longer  and  shorter, 
their  lustre  suddenly  increasing  and  diminishing.  The  bottom  of  these  rays 
always  showed  the  brightest  light,  and  formed  a  more  or  less  regular  arc. 
The  length  of  the  rays  was  very  variable,  but  they  always  converged  towards 
the  same  point  of  the  horizon,  which  was  in  the  prolongation  of  the  north 
end  of  the  dipping-needle  ;  sometimes  the  rays  were  prolonged  as  far  as 
their  point  of  meeting,  and  thus  appeared  like  a  fragment  of  an  immense 
cupola. 

The  arc  continued  to  rise  in  an  undulatory  motion  towards  the  zenith. 
Sometimes  one  of  its  feet  or  even  both  left  the  horizon  ;  the  folds  became 
more  distinct  and  more  numerous  ;  the  arc  was  now  nothing  more  than  a 
long  band  of  rays  convoluted  in  very  graceful  shapes,  forming  what  is  called 
the  boreal  crown.  The  lustre  of  the  rays  varied  suddenly  in  intensity,  and 
attained  that  of  stars  of  the  first  magnitude  ;  the  rays  darted  with  rapidity, 
the  curves  formed  and  re-formed  like  the  folds  of  a  serpent,  or  like  a  flag 
moved  by  the  wind  (fig.  9S0),  the  base  was  red,  the  middle  green,  while  the 


Fig.  980. 

remainder  retained  its  bright  yellow  colour.     Lastly,  the  lustre  diminished, 
the  colours  disappeared  ;  everything  became  feebler  or  suddenly  went  out. 

Plate  III.  represents  a  very  beautiful  aurora  observed  by  Lemstrom  on 
tlie  north  coast  of  Norway.  The  work  of  this  author  {IjAurorc  Bor^ale^ 
(iauthicr  Villars,  Paris)  is  a  storehouse  of  information  on  this  subject. 


-1003]  Aurora  Borealis.  103 1 

A  French  scientific  commission  to  the  North  observed  150  auror^e 
boreales  in  200  days  ;  it  appears  that  at  the  poles,  nights  without  an  aurora 
boreahs  are  quite  exceptional,  so  that  it  may  be  assumed  that  they  take  place 
every  night,  though  with  varying  intensity.  They  are  visible  at  a  consider- 
able distance  from  the  poles,  and  over  an  immense  area.  Sometimes  the  same 
aurora  borealis  has  been  seen  at  the  same  time  at  places  so  widely  apart  as 
Moscow,  Warsaw,  Rome,  and  Cadiz.  It  seems  difficult  to  assign  a  higher 
limit  for  the  occurrence  of  the  aurora  ;  this  is  probably  lower  than  has  gene- 
rally been  stated.  Lemstrom  holds  that  from  22  to  44  miles  is  a  close 
approximation  to  the  truth  ;  and  it  may  be  regarded  as  certain  that  even  in 
more  southern  latitudes  the  aurora  is  often  seen  much  lower — at  a  height  of 
two  or  three  miles,  for  instance.  In  polar  countries  certain  forms  of  aurora, 
more  especially  those  of  weak  flames,  are  seen  to  proceed  from  the  ground 
on  the  tops  of  certain  mountains.  They  are  most  frequent  at  the  equinoxes, 
and  least  so  at  the  solstices.  The  number  differs  in  different  years,  attain- 
ing a  maximum  every  11  years  at  the  same  time  as  the  sun-spots,  and 
like  these  a  minimum  which  is  about  5  or  6  years  from  the  maximum. 
The  years  1844,  1855,  i860,  and  1877  are  poor  in  the  appearance  of  the 
aurora. 

There  is,  moreover,  a  period  of  about  60  years  ;  for  the  years  1728,  1780, 
and  1842  have  been  remarkable  for  the  prevalence  of  the  aurora.  The  last 
two  periods  are  also  remarkable  for  the  occurrence  of  disturbances  in  the 
earth's  magnetism. 

Numerous  hypotheses  have  been  devised  to  account  for  the  aurorse 
boreales.  As  they  share  the  rotation  of  the  earth,  they  must  have  an  atmo- 
spheric origin.  Their  direction,  which  is  always  parallel  to  that  of  the  dipping 
needle,  and  their  action  on  the  magnetic  needle  (702),  seem,  however,  to 
prove  that  they  ought  to  be  attributed  to  electric  currents  in  the  higher 
regions  of  the  atmosphere.  In  high  latitudes  the  aurora  borealis  acts  power- 
fully on  the  wires  of  the  electric  telegraph  ;  the  alarums  are  for  a  long  time 
violently  rung,  and  telegraphic  messages  frequently  interrupted  by  the 
spontaneous  abnormal  working  of  the  apparatus.  In  the  lower  discharges 
a  crackling  sound  has  been  heard,  and  during  balloon  ascents  a  strong 
smell  of  ozone  has  been  perceived  when  the  balloon  was  among  the  luminous 
rays. 

The  spectrum  of  the  aurora  borealis  has  been  found  to  consist  of  several 
lines  in  the  green,  and  of  an  indistinct  line  in  the  blue  ;  to  which  must  be 
added  a  red  line  due  to  the  red  protuberances  ;  these  lines  are  the  same  as 
those  of  nitrogen,  greatly  rarefied  and  at  a  low  temperature  ;  one  line  be- 
tween the  green  and  the  yellow,  and  called  the  yellow  line,  is  so  charac- 
teristic of  the  aurora  that  it  is  visible  even  when  the  eye  can  discern  no  other 
trace  of  this  light. 

De  la  Rive  held  that  auroras  boreales  were  due  to  electric  discharges 
■which  take  place  in  polar  regions  between  the  positive  electricity  of  the 
atmosphere  and  the  negative  electricity  of  the  earth.  The  positively  elec- 
trified aqueous  vapours  are  supposed  to  be  carried  by  the  equatorial  current 
in  the  higher  regions  of  the  atmosphere  to  the  poles,  where  the  neutralisa- 
tion takes  place.  These  discharges  produce  luminous  appearances  of  the 
same  kind  as  are  observed  in  Geissler's  tubes  ;  and  De  la  Rive  showed  by 


I032  Meteorology.  [1003- 

means  of  an  apparatus  specially  devised  for  the  purpose  (fig.  917)  that  the 
forms  of  the  luminous  phenomena  are  in  accordance  with  this  theory. 

By  direct  experiments  Lemstrom  has  been  able  to  imitate  and  reproduce 
a  peculiar  form  of  aurora  observed  in  winter  as  a  flame-like  appearance  on 
the  tops  of  two  mountains  800  and  1,100  metres  in  height,  and  to  show 
that  it  is  of  electrical  origin.  He  erected  on  the  summit  of  a  hill  a  system 
of  Dointcd  rods  extending  over  a  surface  of  nearly  4,000  square  feet  ;  each 
rod  was  carefully  insulated  from  the  earth  by  means  of  a  Mascart's  insulator 
ffig.  67o\  but  was  connected  with  the  rest,  and  an  insulated  wire  led  down 
from  this  system  into  the  valley  where  it  Avas  connected  with  one  ter- 
minal of  a  galvanometer,  the  other  being  put  to  earth.  The  existence  of 
a  positive  current  from  the  air  to  the  earth  was  observed,  and  at  the  same 
time  yellowish-white  columns  of  light,  reaching  to  a  height  of  120  metres, 
were  observed  to  issue  from  the  points.  Observed  Avith  the  spectroscope 
it  gave  the  characteristic  lines  between  D  and  E. 

The  recent  investigations  of  Exner  relative  to  the  fall  of  atmospheric 
electrical  potential  lend  a  further  support  to  the  view  that  the  aurora  is  due 
to  electricity.  In  the  polar  regions  the  fall  of  potential  is  13  times  greater 
in  summer,  and  18  times  o-reater  in  winter  than  at  the  equator.  Hence  an 
electrical  phenomenon  which  depends  on  the  magnitude  of  this  fall  of 
potential  mu/t  be  more  intense  in  winter  and  in  high  latitudes,  than  in 
summer  and  in  the  torrid  zones. 

The  occurrence  of  irregular  currents  of  electricity  which  manifest  them- 
selves by  abnormal  disturbances  of  telegraphic  communications  is  not  in- 
frequent :  such  currents  have  received  the  name  of  earth  currents.  Sabine 
found  that  these  magnetic  disturbances  are  due  to  a  peculiar  action  of 
the  sun,  and  probably  independently  of  its  radiant  heat  and  light.  It  has 
also  been  ascertained  that  the  aurora  borealis  as  well  as  earth  currents  in- 
variably -^iccompanies  these  magnetic  disturbances.  According  to  the  late 
Balfour  Stewart,  aurora;  and  earth  currents  are  to  be  regarded  as  secondary 
currents  due  to  small  but  rapid  chansjes  in  the  earth's  magnetism  :  he  likened 
the  body  of  the  earth  to  the  magnetic  core  of  a  Ruhmkoi-fif's  machine  (905)  ; 
the  lower  strata  of  the  atmosphere  forming  the  insulator,  while  the  upper 
and  rarer,  and  therefore  electrically  conducting  strata,  may  be  considered 
as  the  secondaiy  coil. 

On  this  analoev  the  sun  may  perhaps  be  likened  to  the  primary  current 
which  performs  the  part  of  producing  changes  in  the  magnetic  state  of  the 
core.  Now  in  Ruhmkorff's  machine  the  energy  of  the  secondary  current  is 
derived  from  that  of  the  priman'  current.  Thus,  if  the  analogy  be  correct, 
the  energy  of  the  aurora  borealis  may  in  like  manner  come  from  the  sun  ; 
but  until  we  know  more  of  the  connection  between  the  sun  and  terrestrial 
magnetism,  these  ideas  are  to  be  accepted  with  some  reserve. 


S      . J  /!  *  3        ji =       _-        »       ^'1         r,  t 


-1005]  .    Climate.  1033 


CLIMATOLOGY. 

1004.  Mean  temperature. — The  inciui  daily  teviperatiire.,  or  simply  tem- 
pcra/ufc,  is  that  obtained  by  adding  together  24  hourly  observations,  and 
dividing  by  24.  A  very  close  approximation  to  the  mean  temperature  is 
obtained  by  taking  the  mean  of  the  highest  and  lowest  temperatures  of  the 
day  and  of  tne  night,  which  are  determined  by  means  of  the  maximum  and 
minimum  thermometers.  These  ought  to  be  protected  from  the  sun's  rays, 
to  be  raised  above  the  ground,  and  far  from  all  objects  which  might  influence 
them  by  their  radiation. 

The  temperature  of  a  month  is  the  mean  of  those  of  30  days,  and  the 
temperature  of  the  year  is  the  mean  of  those  of  12  months.  Finally,  the 
temperature  of  a  place  is  the  mean  of  its  annual  temperature  for  a  great 
sei'ies  of  years.  The  mean  temperature  of  London  is  8 -28°  C,  or  46 -9°  F. 
The  temperatures  in  all  cases  are  those  of  the  air,  and  not  those  of  the 
ground. 

1005.  Causes  whicli  modify  the  temperature  of  the  air. — The  principal 
causes  which  modify  the  temperature  of  the  air  are  the  latitude  of  a  place,  its 
height,  the  direction  of  the  winds,  and  proximity  of  seas. 

Influence  of  the  latitude. — The  influence  of  the  latitude  arises  from  the 
greater  or  less  obliquity  of  the  solar  rays,  for  as  the  quantity  of  heat  absorbed 
is  greater  the  more  perpendicular  are  the  rays  (414),  the  heat  absorbed  de- 
creases from  the  equator  to  the  poles,  for  the  rays  are  then  more  oblique. 
This  loss  is,  however,  in  summer,  in  the  temperate  and  arctic  zones,  partially 
compensated  by  the  length  of  the  days.  Under  the  equator,  where  the 
length  of  the  days  is  constant,  the  temperature  is  almost  invariable  ;  in  the 
latitude  of  London,  and  in  more  northerly  countries,  where  the  days  are 
very  unequal,  the  temperature  varies  greatly  ;  but  in  summer  it  sometimes 
rises  almost  as  high  as  under  the  equator.  The  lowering  of  the  temperature 
produced  by  the  latitude  is  small :  thus,  in  a  latitude  1 1 5  miles  north  of 
France,  the  temperature  is  only  1°  C.  lower. 

hiflitence  of  height. — The  height  of  a  place  has  a  much  more  consider- 
able influence  on  the  temperature  than  its  latitude.  In  the  temperate 
zone  a  diminution  of  i^  C.  corresponds  in  the  mean  to  an  ascent  of  180 
yards. 

The  cooling  on  ascending  in  the  atmosphere  has  been  observed  in 
balloon  ascents,  and  a  proof  of  it  has  been  seen  in  the  perpetual  snows 
which  cover  the  highest  mountains.  It  is  due  in  part  to  the  greater  rarefac- 
tion of  the  air,  which  necessarily  diminishes  its  absorbing  power ;  besides 
which  the  air  is  at  a  greater  distance  from  the  ground,  which  heats  it  by 
contact  ;  and  finally,  dry  air  is  very  diathermanous. 

The  law  of  the  diminution  of  temperature  corresponding  to  greater 
heights  in  the  atmosphere  has  not  been  made  out,  in  consequence  of  the 
numerous  disturbing  causes  which  modify  it,  such  as  the  prevalent  winds, 
the  hygrometric  state,  the  time  of  day,  the  season  of  the  year,  &c.  The 
difference  between  the  temperatures  of  two  places  at  unequal  heights  is  not 
proportional  to  the  difference  of  level,  but  for  moderate  heights  an  approxi- 
mation to  the  law  may  be  made.     As  the  mean  of  a  series  of  very  careful 


I034  Meteorology.  [1005- 

observations  made  during  balloon  ascents,  a  diminution  of  i°  C.  corresponded 
to  an  increase  in  height  of  232  yards. 

It  will  thus  be  seen  that  at  a  certain  height  above  the  ground,  there  must 
be  a  surface  or  layer  where  the  temperature  is  uniformly  zero.  The  height 
of  this  isothermal  surface  (1007)  will  vary  materially  with  the  time  of  the  year, 
being  lower  in  the  cold  months  ;  it  varies  also  with  the  time  of  day,  rising 
rapidly  about  mid-day.  In  summer  this  height  may  be  taken  at  from  3,400 
to  3,700  metres  above  the  sea-level. 

Directio7t  of  winds. — As  winds  share  the  temperature  of  the  countries 
which  they  have  traversed,  their  direction  exercises  great  influence  on  the 
air  in  any  place.  In  Paris,  the  hottest  winds  are  the  south  ;  then  come  the 
south-east,  the  south-west,  the  west,  the  east,  the  north-west,  north,  and, 
lastly,  the  north-east,  which  is  the  coldest.  The  character  of  the  wind 
changes  with  the  seasons  ;  the  east  wind,  which  is  cold  in  winter,  is  warm  in 
summer. 

Proximity  of  the  sea. — The  neighbourhood  of  the  sea  tends  to  raise  the 
temperature  of  the  air,  and  to  render  it  uniform.  The  average  temperature 
of  the  sea  in  equatorial  and  polar  countries  is  always  higher  than  that  of  the 
atmosphere.  With  reference  to  the  uniformity  of  the  temperature,  it  has 
been  found  that  in  temperate  regions— that  is,  from  25°  to  50°  of  latitude — 
the  difference  between  the  highest  and  lowest  temperature  of  a  day  does  not 
exceed,  on  the  sea,  2°  to  3°  ;  while  upon  the  Continent  this  amounts  to  from 
12°  to  15°..  In  islands  the  uniformity  of  temperature  is  very  perceptible,  even 
during  the  greatest  heats.  In  continents,  on  the  contrary,  the  winters  for 
the  same  latitudes  become  colder,  and  the  difference  between  the  tempera- 
ture of  summer  and  winter  becomes  greater. 

1006.  Gulf  Stream. — A  similar  influence  to  that  of  the  winds  is  exerted 
by  currents  of  warm  water.  To  one  of  these,  the  Gulf  Stream,  the  mildness 
of  the  climate  in  the  north-west  of  Europe  is  mainly  due.  This  great  body 
of  water,  taking  its  origin  in  equatorial  regions,  flows  through  the  Gulf  of 
Mexico,  whence  it  derives  its  name  ;  passing  by  the  southern  shores  of 
North  America,  it  makes  its  way  in  a  north-westerly  direction  across  the 
Atlantic,  and  finally  washes  the  coast  of  Ireland  and  the  north-west  of  Europe 
generally.  Its  temperature  in  the  Gulf  is  about  28°  C.  ;  and  it  is  usually  a 
little  more  than  5°  C.  higher  than  the  rest  of  the  ocean  on  which  it  floats, 
owing  to  its  lower  specific  gravity.  To  its  influence  is  due  the  milder  climate 
of  West  Europe  as  comj^ared  with  that  of  the  opposite  coast  of  America  ;  thus 
the  river  Hudson,  in  the  latitude  of  Rome,  is  frozen  over  three  months  in  the 
year.  It  also  causes  the  polar  regions  to  be  separated  from  the  coasts  of 
Europe  by  a  girdle  of  open  sea ;  and  thus  the  harbour  of  Hammerfest  is 
open  the  year  round.  Besides  its  influence  in  thus  moderating  cHmate,  the 
Gulf  Stream  is  an  important  help  to  navigators. 

1007.  Isothermal  lines When  on  a  map  all  the  points  whose  tempera- 
ture is  known  to  be  the  same  are  joined,  curves  are  obtained  which  Hum- 
Ijoldt  first  noticed,  and  which  he  called  isothermal  lines.  If  the  temperature  . 
of  a  place  only  varied  with  the  obliquity  of  the  sun's  rays— that  is,  with  the 
latitude— isothermal  lines  would  all  be  parallel  to  the  equator  ;  but  as  the 
temperature  is  influenced  by  many  local  causes,  especially  by  the  height,  the 
isothermal  lines  are  always  more  or  less  curved.     On  the  sea,  however,  they 


-1009J  Distribution  of  Temperature.  1035 

are  almost  parallel.     Maps  4,  5,  and  6  represent  these  lines  for  the  Year, 
for  January  and  for  July. 

A  distinction  is  made  between  isothermal  lines,  isotheral  lines,  and  isO' 
cJiime7ial  lines,  where  the  ineati  general,  the  meafi  summer,  and  the  mean 
winter  temperatures  are  respectively  constant.  An  isothermal  zotie  is  the 
space  comprised  between  two  isothermal  lines.  Kupfifer  also  distinguishes 
isogeothermic  lines  where  the  mean  temperature  of  the  soil  is  constant. 

1008.  Climate. — By  the  climate  of  a  place  is  understood  the  whole  of  the 
meteorological  conditions  to  which  a  place  is  subjected  ;  its  mean  annual 
temperature,  summer  and  winter  temperatures,  and  the  extremes  within 
which  these  are  comprised.  Some  writers  distinguish  seven  classes  of 
climates,  according  to  their  mean  annual  temperature  :  a  hot  climate  from 
30°  to  25°  C.  ;  a  inarm  climate  from  25°  to  20°  C.  ;  a  mild  climate  from  20° 
to  15°  C.  ;  a  temperate  climate  from  15*^  to  10°  C.  ;  a  cold  climate  from  10°  to 
5°  C.  ;  a  very  cold  climate  from  5°  to  zero  C.  ;  and  an  arctic  climate  Avhere 
the  temperature  is  below  zero. 

Those  climates,  again,  are  classed  as  constant  climates,  where  the  dif- 
ference between  the  mean  and  summer  and  winter  temperature  does  not 
exceed  6°  to  8° ;  variable  climates,  where  the  difference  amounts  to  from 
16°  to  20°  ;  and  extreme  climates,  where  the  difference  is  greater  than  30°. 
The  climates  of  Paris  and  London  are  variable  ;  those  of  Pekin  and  New 
York  are  extreme.  Island  climates  are  generally  little  variable,  as  the 
temperature  of  the  sea  is  constant ;  and  hence  the  distinction  between  land 
and  sea  climates.  Marine  climates  arc  characterised  by  the  fact  that  the 
difference  between  the  temperature  of  summer  and  winter  is  always  less 
than  in  the  case  of  continental  climates.  But  the  temperature  is  by  no 
means  the  only  character  which  influences  climates  ;  there  are,  in  addition, 
the  moisture  of  the  air,  the  quantity  and  frequency  of  the  rains,  the  number 
of  storms,  the  direction  and  intensity  of  the  winds,  and  the  nature  of  the 
soil. 

1009.  Distribution  of  temperature  on  the  surface  of  tbe  ^lobe. — The 
temperature  of  the  air  on  the  surface  of  the  globe  decreases  from  the  equator 
to  the  poles  ;  but  it  is  subject  to  perturbing  causes  so  numerous  and  so 
purely  local,  that  its  decrease  cannot  be  expressed  by  any  law.  It  has 
hitherto  not  been  possible  to  do  more  than  obtain  by  numerous  observations 
the  mean  temperature  of  each  place,  or  the  maximum  and  minimum  tempera- 
tures. The  following  table  gives  a  general  idea  of  the  distribution  of  heat  in 
the  Northern  Hemisphere  : — 

Mean  temperature  at  diffcrc/it  latitudes. 


Abyssinia 

.   31-0°  c. 

Cairo     . 

.      22-4= 

Calcutta. 

.     28-5 

Constantine 

.       17-2 

Jamaica. 

.      26-1 

Naples . 

.            .       167 

Senegal . 

.     24-6 

Mexico. 

.     i6-6 

Rio  de  Janeiro 

.     23-1 

Marseilles 

.     14-1 

Constantinople 

.     137 

London 

.         .       8-3 

Pekin     . 

.     127 

Stockholm 

.         .       5-6 

Paris      . 

.     IO-8 

Moscow 

•       5-6 

1036  Meteorology.  [1009- 

Brussels          .         .         .     io-2°  C.  St.  Petersburg  .  .          3-5°  C. 

Strasburg        .         .         .9-8  St.  Gothard  .  .  .       -ro 

Geneva  .         .         .         -97  Greenland     .  .  •      -77 

Boston    ....       9-3  Melville  Island  .  .  -187 

These  are  mean  yearly  temperatures.  The  highest  temperature  which 
has  been  observed  on  the  surface  of  the  globe  is  47*4°  at  Esne,  in  Egypt, 
and  the  lov^^est  is  —75°  in  the  Arctic  Expedition  of  1876;  which  gives  a 
difference  of  122°  between  the  extreme  temperatures  observed  on  the  surface 
of  the  globe. 

The  highest  temperature  observed  at  Paris  was  38-4°  on  July  8,  1793, 
and  the  lowest  —23-5°  on  December  26,  1798.  The  highest  observed  at 
Greenwich  was  35°  C.  in  1808,  and  the  lowest  -20°  C.  in  1838. 

No  arctic  voyagers  have  succeeded  in  reaching  the  poles,  in  consequence 
of  these  seas  being  completely  frozen,  and  hence  the  temperature  is  not 
known.  In  our  hemisphere  the  existence  of  a  single  glacial  pole — that  is,  a 
place  where  there  was  the  maximum  cold — has  been  long  assumed.  But 
the  bendings  which  the  isothermal  linespresent  in  the  Northern  Hemisphere 
have  shown  that  in  this  hemisphere  there  are  two  cold  poles — one  in  Asia, 
to  the  north  of  Gulf  Taymour  ;  and  the  other  in  America,  north  of  Barrow's 
Straits,  about  15°  from  the  earth's  north  pole.  The  mean  temperature  of 
the  first  of  these  poles  has  been  estimated  at  —  17°,  and  that  of  the  second 
at  —  19°.  With  respect  to  the  austral  hemispheres,  the  observations  are 
not  sufficiently  numerous  to  tell  whether  there  are  one  or  two  poles  of 
greatest  cold,  or  to  determine  their  position. 

loio.  Temperature  of  lakes,  seas,  and  sprlngrs. — In  the  tropics  the 
temperature  of  the  sea  is  generally  the  same  as  that  of  the  air  ;  in  polar 
regions  the  sea  is  always  warmer  than  the  atmosphere. 

The  temperature  of  the  sea  under  the  torrid  zone  is  always  about  26°  to 
27°  at  the  surface  :  it  diminishes  as  the  depth  increases,  and  in  temperate 
as  well  as  in  tropical  regions  the  temperature  of  the  sea  at  great  depths  is 
between  2-5°  and  3*5°.  The  temperature  of  the  lower  layers  is  caused  by 
submarine  currents  which  carry  the  cold  water  of  the  polar  seas  towards  the 
equator. 

The  variations  in  the  temperature  of  lakes  are  more  considerable  ;  their 
surface,  which  becomes  frozen  in  winter,  may  become  heated  to  20°  or  25°  in 
summer.  The  temperature  of  the  bottom,  on  the  contrary,  is  virtually  4°, 
which  is  that  of  the  maximum  density  of  water. 

Springs,  which  arise  from  rain  water  which  has  penetrated  into  the  crust 
of  the  globe  to  a  greater  or  less  depth,  necessarily  tend  to  assume  the  tempe- 
rature of  the  terrestrial  layers  which  they  traverse.  Hence,  when  they  reach 
the  surface  their  temperature  deperrds  on  the  depth  which  they  have  attained. 
If  this  depth  is.  that  of  the  layer  of  invariable  temperature,  the  springs  ha\-e 
a  temperature  of  10°  or  1 1°  in  this  country,  for  this  is  the  temperature  of  this 
layer,  or  about  the  mean  annual  temperature.  If  the  sjirings  are  not  very 
copious,  their  temperature  is  raised  in  summer  and  cooled  in  winter  by  that.- 
of  the  layers  which  they  traverse  in  passing  from  the  invariable  layer  to  the 
surface.  But  if  they  come  from  below  the  layer  o(  inxariable  temperature 
their  temperature  may  considerably  exceed  t}ie  n\ean  temperature  of  the 


-1011] 


Distribution  of  Land  and  Water.  1037 

The  following  list  gives 


place,  and  they  are  then  called  thermal  springs. 
the  temperature  of  some  of  them  :  — 

Wildbad       .......     37-5°  C. 

Vichy  .  .  .  .  .  .  .40 

Bath  .  .  .  .  .  .  .46 

Ems  .  .  .  .  .  .  .46 

Baden-Baden  ......     67-5 

Chaudes-Aigues      .  .  .  .  .  ,88 

Trincheras  .  .  .  .  .  .  -67 

Great  C^eyser,  in  Iceland,  at  a  depth  of  66  feet.    .  .   124 

From  their  high  temperature  they  have  the  property  of  dissolving  many 
mineral  substances  which  they  traverse  in  their  passage,  and  hence  form 
mineral  zvatcrs.  The  temperature  of  mineral  waters  is  not  modified  in 
g-eneral  by  the  abundance  of  rain  or  of  dryness  ;  but  it  is  by  earthquakes, 
after  which  they  have  sometimes  been  found  to  rise  and  at  others  to  sink. 

loil.  Distribution  of  land  and  water. — The  distribution  of  water  on 
the  surface  of  the  earth  exercises  great  influence  on  climate.  The  area 
covered  by  water  is  considerably  greater  than  that  of  the  dry  land  ;  and  the 
distribution  is  unequal  in  the  two  hemispheres.  The  entire  surface  of  the 
globe  occupies  about  200  millions  of  square  miles,  nearly  three-fourths  of 
which  are  covered  by  water  ;  that  is,  the  extent  of  the  water  is  nearly  three 
times  as  great  as  that  of  the  land.  The  surface  of  the  sea  in  the  Southern 
Hemisphere  is  to  that  in  the  Northern  in  about  the  ratio  of  13  to  9. 

The  depth  of  the  open  sea  is  very  variable  ;  the  lead  generally  reaches 
the  bottom  at  about  300  to  450  yards  ;  in  the  ocean  it  is  often  1,300  yards, 
and  instances  are  known  in  which  a  bottom  has  not  been  reached  at  a  depth 
of  4,500.  It  has  been  computed  that  the  total  mass  of  the  water  does  not 
-exceed  that  of  a  liquid  layer  surrounding  the  earth  with  a  depth  of  about 
1,100  yards. 


PROBLEMS    AND    EXAMPLES 
IN   PHYSICS. 


I.  EQUILIBRIUM. 

1.  A  body  being  placed  successively  in  the  two  pans  of  a  balance,  requires  i8o- 
grammes  to  hold  it  in  equilibrium  in  one  pan,  and  i8i  grammes  in  the  other;  required 
the  weight  of  the  body  to  a  milligramme. 

From  the  formula  x=  s/p  p,  we  have 

X  =    -\/i8o  X   iSi   =   1808',  499. 

2.  What  resistance  does  a  nut  offer  when  placed  in  a  pair  of  nutcrackers  at  a 
distance  of  4  of  an  inch  from  the  joint,  if  a  pressure  of  5  pounds  applied  at  a  distance 
of  4  inches  from  the  joint  is  just  sufficient  to  crack  it?  Ans.  26^  pounds. 

3.  What  force  is  required  to  raise  a  cask  weighing  6  cwt.  into  a  cart  o'S  metre 
high  along  a  ladder  275  metres  in  length  ?  Ans.  195A  pounds. 

4.  If  a  horse  can  move  30  cwt.  along  a  level  road,  what  can  it  move  along  a  road 
the  inchnation  of  which  is  i  in  80,  the  coefficient  of  friction  on  each  road  being  ^  ? 

Ans.  265  cwt. 

5.  The  piston  of  a  force-pump  has  a  diameter  of  8  centimetres,  and  the  arms  of 
the  lever  by  which  it  is  worked  are  respectively  12  and  96  centimetres  in  length  ;  what 
force  must  be  exerted  at  the  longer  arm  if  a  pressure  of  12-36  pounds  on  a  square  cen- 
timetre is  to  be  applied?  Ans.  77*69  pounds. 

II.  GRAVITATION. 

6.  A  stone  is  thrown  from  a  balloon  with  a  velocity  of  50  metres  in  a  second.  How 
soon  will  the  velocity  amount  to  99  metres  in  a  second,  and  through  what  distance 
will  the  stone  have  fallen  ? 

To  find  the  time  requisite  for  the  body  to  have  acquired  the  velocity  of  99  metres  in 
a  second,  we  have 

V  =   V  -^  gt; 
in  which  V  is  the  initial  velocity,  g  the  acceleration  of  gravity,  which,  with  sufficient 
approximation,  is  equal  to  9'8  metres  in  a  second,  and  /  the  time.     Substituting  these 
values,  we  have 

/  =  99  -is  ^49^   5  seconds. 
9-8  9-8 

For  the  space  traversed  we  have 

s  =   Vt  -^  i^/2  _  ^o  X  5  +  4-9  X  25  =372-5  metres. 

7.  A  projectile  was  thrown  vertically  upwards  to  a  height  of  5io'"'22.  Disregard- 
ing the  resistance  of  the  air,  what  was  the  initial  velocity  of  the  body  ? 

The  velocity  is  the  same  as  that  which  the  body  would  have  acquired  on  falling 
from  a  height  of  510-22  metres. 

From  the  formula  v  =   \/2gs  we  get 

V  =   ^/2  X  98  X  5io'22  =   \/ioooo  =   100  metres, 

8.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  100  metres. 
After  what  time  would  it  return  to  its  original  position. 


1 040  Problems  and  Examples  in  Physics. 

The  time  of  rising  and  falling  is  the  same,  but  the  time  of  falling  is  -   (from  the 

g 

formula  v=gt)  or  —  =io"2,  which  is  half  the  time  required  ;  therefore  ^=20'4  sec. 
9-8 

9.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  100  metres  ;  after 
X  seconds  a  second  stone  is  thrown  with  the  same  velocity.  The  second  stone  is  rising 
87  seconds  before  it  meets  the  first.     What  interval  separated  the  throws? 

The  rising  stone  will  have  the  velocity  v  =  V  —  gt,  whence  v  =  100  —  9"8  x  S'/. 
On  the  other  hand,  the  falling  stone,  at  the  moment  the  stones  meet,  will  have  the  velocity 
given  by  the  equation  v  =  gt'  in  which  t'  is  the  time  during  which  the  stone  falls 

before  it  meets  the  second  one.    This  time  is  equal  to  87  seconds  +  x  —  ^~.    Hence 

9'8 
its  velocity  is  ^  ^^^v 

,  =  ,.8(8,.,--). 

Equating  the  two  values  of  v  and  reducing,  we  obtain  x  =   ■^  seconds. 

10.  A  body  moving  with  a  uniformly  accelerated  motion  traverses  a  space  of  1000 
metres  in  10  seconds.  What  would  be  the  space  traversed  during  the  eighteenth 
second  if  the  motion  continued  in  the  same  manner  ? 

The  formula  J  =  ^  ^g^/ 2  gjyes  for  the  accelerating  force  ^  =  20  metres  per  second. 
The  space  traversed  during  the  eighteenth  second  will  be  equal  to  the  difference  of 
the  space  traversed  in  18  seconds  and  that  traversed  at  the  end  of  the  seventeenth. 

20  X  18^       20  X  17^ 
^  _  ^u  _  J./     _  ^^^  metres. 

2  2 

11.  A  cannon-ball  has  been  shot  vertically  upwards  with  a  velocity  of  250  metres  in 
a  second.  After  what  interval  of  time  would  its  velocity  have  been  reduced  to  54  metres 
under  the  retarding  influence  of  gravity,  and  what  space  would  have  been  traversed  by 
the  ball  at  the  end  of  this  time  ? 

If  t  be  the  time,  then  at  the  end  of  each  second  the  initial  velocity  would  be  dimi- 
nished by  9™ -8.     Hence  we  shall  have 

54  =   250  —  ^  X  9'8,  whence  t  =■  10  seconds  ; 

and  for  the  space  traversed 

q"8  X  20- 
=   250  X  20  —  ■'- =   3040  metres. 

12.  Required  the  time  in  which  a  body  would  fall  through  a  height  of  2000  metres, 
■neglecting  the  resistance  of  the  air. 

From  s  =   \  gt-  and  substituting  the  values,  we  ha\-e 


9-8 


t~,  whence  t  =   2o'2  seconds. 


13.  A  body  falls  in  air  from  a  height  of  4000  metres.     Required  the  time  of  its  fall 
and  its  velocity  when  it  strikes  the  ground.  

From  the  formula  j  =  ^gfi  we  have  for  the  time  /  =       /  ^  ;    and,  on  the  other 

V    g 

hand,  from  the  formula  for  velocity  v  =  gt  we  have  /  =      =~     =20*4. 

g    98 

Hence  ^  =      /— ,  from  which  y  =    Vs -f^,  and  substituting  the  values  for  5  and 
g        ^    g 
g,  V  =  280  metres. 

14.  A  stone  is  thrown  into  a  pit  150  metres  deep  and  reaches  the  bottom  in  4 
■  conds.     With  what  velocity  was  it  thrown,  and  what  velocity  had  it  acquired  on 

r'-aching  the  ground?    Ans.  The  stone  was  thrown  with  a  velocity  of  ly-g,  and  on 
reaching  the  ground  had  acquired  the  velocity  S7'i. 

15.  A  stone  is  thrown  downwards  from  a  height  of  150  metres  with  a  velocity  of  10 
metres  per  second.     How  long  will  it  require  to  fall  ? 

The  distance  through  which  the  stone  falls  is  cciual  to  the  sum  of  the  distances 


Gravitation.  104 1 

through  which  it  would  fall  in  virtue  of  its  initial  impulse  and  of  that  which  it  would 

traverse  under  the  influence  of  gravity  alone  ;  that  is,  150  =   10  ^  +  ^^  ^  . 

2 
Taking  the  positive  value  only  we  get  t  =  4-61  seconds. 

16.  How  far  will  a  heavy  body  fall  in  vacuo  during  the  time  in  which  its  velocity 
increases  from  40"25  feet  per  second  to  88"55  feet  per  second  ? 

A /IS.  Taking  the  value  of  ^  at  32-2  feet,  the  body  falls  through  96-6  feet. 

17.  Required  the  time  of  oscillation  of  a  single  pendulum  whose  length  is  o"9938, 
and  in  a  place  where  the  intensity  of  gravity  is  g'Si. 

From  the  general  formula/"  =  w      /   ,   in  which    /  expresses  the   time    of  one 

oscillation,  /the  length  of  the  pendulum,  and  ^  the  intensity  of  gravity,  we  have 

/  =  3-1416      /°^^  =   I  second. 
V      9-81 

18.  Wliat  is  the  intensity  of  gravity  in  a  place  in  which  the  length  of  the  seconds 
pendulum  is  o™'99i  ? 

In  this  case/  =  n  /  ,;  and  also  /  =  n  /^  I  and  therefore  ^'  =  I ,  from 
which  g'  =  ?—.  Substituting  in  this  latter  equation  the  values  of  g' ,  I  and  /',  we 
have  ^'  =  9™  782. 

19.  In  a  place  at  which  the  length  of  the  seconds  pendulum  is  0-99384,  it  is  required 
to  know  the  length  of  a  pendulum  which  makes  one  oscillation  in  5  seconds. 

In  the  present  case,  as  g  remains  the  same  in  the  general  formula,  and  t  varies,  the 
length  /  must  vary  also.      We  shall  have,  then, 


V   ^    •  ^s/  §> 


from  which,  reducing  and  introducing  the  values,  we  have 
/'   =   52  X  0-99384  =   24-846. 

20.  A  pendulum,  the  length  of  which  is  i"-9S,  makes  61,682  oscillations  in  a  day. 
Required  the  length  of  the  seconds  pendulum.  Atis.  0-99385  metre. 

21.  A  pendulum  clock  loses  5  seconds  in  a  day.  By  how  much  must  it  be 
shortened  to  keep  correct  time  } 

Let  s  =  the  number  of  seconds  in  one  day,  and  s'  the  number  indicated  by  the 
clock,  then  s  :  s'  =  n  :  n'  =  f- 1=  s/ 1'  ■  sj I  .'.  86400:  86395=1  :  \i^xx.-.x=-ggg8S^43. 
Hence  i  — ^^  =  0-0001157  Ans. 

22.  What  is  the  normal  acceleration  of  a  body  which  traverses  a  circle  of  4-2 
metres  diameter  with  a  rectangular  velocity  of  3  metres  ?  Ans.  4-286  metres. 

23.  An  iron  ball  falls  from  a  height  of  68  cm.  on  a  horizontal  iron  plate,  and 
rebounds  to  a  height  of  27  cm.     Required  the  coefficient  of  elasticity  of  the  iron. 

If  an  imperfectly  elastic  ball  with  the  velocity  v  strikes  against  a  plate,  it  rebounds 
with  the  velocity  v,  =   —  kv,  from  which,  disregarding  the  sign,  k  =  -'.     Now  we 

V 

have   the  velocity  f,   =    Vz  g/i,  and  v  =   oj 2  g/i,  horn  which  A  =Y"'-     Suhstitut- 
ing  the  corresponding  values,  we  get  i  —   0-63. 

24.  Two  inelastic  bodies,  weighing  respectively  100  and  200  pounds,  strike  against 
each  other  with  velocities  of  50  and  20  feet ;  what  is  their  common  velocity,  after  the 
impact?  Ans.  30,  or  3-3,  according  as  they  move  in  the  same  or  in  opposite  directions 
before  impact. 


3.x 


1042  Problems  and  Examples  in  Physics. 


III.     ON   LIQUIDS  AND   GASES. 

25.  The  force  with  which  a  hydraulic  press  is  worked  is  20  pounds  ;  the  arm  of  the 
lever  on  which  this  force  acts  is  5  times  as  long  as  that  of  the  resistance  ;  lastly,  the 
area  of  the  large  piston  is  70  times  that  of  the  smaller  one.  Required  the  pressure 
transmitted  to  the  large  piston. 

If  F  be  the  power,  and  p  the  pressure  transmitted  to  the  smaller  piston,  we  have 
from  the  principle  of  the  lever/  x  i  =  /^  x  5.  Moreover,  from  the  principle  of  the 
equality  of  pressure 

jPxi=/x7o  =  5X2ox7o  =  7000  pounds. 

26.  Tlie  force  with  which  a  hydraulic  press  is  worked  being  30  kilos,  and  the  arm 
of  the  lever  by  which  this  force  is  applied  being  10  times  as  long  as  that  of  the  resist- 
ance, and  the  diameter  of  the  small  piston  being  two  centimetres  ;  find  the  diameter  of 
the  large  piston,  in  order  that  a  pressure  of  2000  kilos,  may  be  produced. 

Ans.  5 "164  centimetres. 

27.  One  of  the  limbs  of  a  U-shaped  glass  tube  contains  mercury,  to  a  height  of 
om-jy^  ;  the  other  contains  a  different  liquid  to  a  height  of  o™'42  ;  the  two  columns- 
being  in  equilibrium,  required  the  density  of  the  second  liquid  with  reference  to  mer- 
cury and  to  water. 

If  d  is  the  density  of  the  liquid  as  compared  with  mercury,  and  d^  the  density  com- 
pared with  water,  then  i  x  0-175  =  0-42  x  d;  and  13-6  x  o'i75  =  0-42  x  d/, 
whence  d  =  o'4i6  and  d^  =   5 '66. 

28.  What  force  would  be  necessary  to  support  a  cubic  decimetre  of  platinum  in 
mercury  at  zero  ?    Density  of  mercury  i3'6  and  that  of  platinum  21 '5. 

From  the  formula  P  =  VD  the  weight  of  a  cubic  decimetre  of  platinum  is 
I  X  21-5  =  2i''-5  and  that  of  a  cubic  decimetre  of  mercury  is  i  x  13-6  =  i3'''6. 
From  the  principle  of  Archimedes,  the  immersed  platinum  loses  part  of  its  weight 
equal  to  that  of  the  mercury  which  it  displaces.  Its  weight  in  tlie  liquid  is  therefore 
21  "5  —  i3'6  =  7 '9.  and  this  represents  the  force  required. 

29.  Given  a  body  ^  which  weighs  7'S5  grammes  in  air,  5-17  gr.  in  water,  and 
5-35  gr.  in  another  liquid,  B  ;  required  from  these  data  the  density  of  the  body  A  and 
that  of  the  liquid  B. 

The  weight  of  the  body  A  loses  in  water  7-55  —  5'i7  =  2-38  grammes  ;  this  repre- 
sents the  weight  of  the  displaced  water.  In  the  liquid  B  it  loses  7-55  -  6-35  =  1-2  gr. ; 
this  is  the  weight  of  the  same  volume  of  the  body  B,  as  that  of  A  and  of  the  displaced 
water.     The  specific  gravity  of  A  is  therefore 

755  _  0-172,  and  that  of  5    "     =  0-504. 
238        ^    '  238  ^  ^ 

30.  A  cube  of  lead,  the  side  of  which  is  4  cm.,  is  to  be  supported  in  water  by 
being  suspended  to  a  sphere  of  cork.  What  must  be  the  diameter  of  the  latter,  the 
specific  gravity  of  cork  being  0-24,  and  that  of  lead  11  "35  ? 

The  volume  of  the  lead  is  64  cubic  centimetres ;  its  weiglit  in  air  is  therefore 
64  X  1 1 '35,  and  its  weight  in  water  64  x   11-35  —  64  =  662-4  gr. 

If  r  be  the  radius  of  the  sphere  in  centimetres,  its  volume  in  cubic  centimetres  will 

be  '^  '^  - ,  and  its  weight  in  grammes  is  '^-~ ><_o24      j^r^^^,  ^.^^  jj^^  weight  of  the 

3  3 

displaced  water  is  obviously  '^  -n  r^  in  grammes,  there  will  be   an  upward  buoyancy 


3 
represented  by4'^'^_4T'^x  0-24   ^  4  "^ ';'  x  0-76   ^^,^;^.,^  ^^^^^^  ^^  ^^^^^  ^^  ^,^^ 


3  3 

11-85. 


iight  of  thclead  ;  that  is,  4" ^_S  7^   =  662-5,  from  which  r  =   5''™-925  and  the 


Oil  Liquids  and  Gases.  1043 

31.  A  cylindrical  steel  magnet  15  cm.  in  length  and  i'2  mm.  in  diameter,  is  loaded 
at  one  end  with  a  cylinder  of  platinum  of  the  same  diameter  and  of  such  a  length  that 
when  the  solid  thus  formed  is  in  mercury,  the  free  end  of  the  steel  projects  10  mm. 
above  the  surface.  Required  the  length  of  this  platinum,  specific  gravity  of  steel 
being  7-8  and  of  platinum  21-5. 

The  weight  of  the  steel  in  grammes  will  be  15  w  r-  x  7'8  and  of  the  platinum 
r  r2  X  21-5. 

These  are  together  equal  to  the  weight  of  the  displaced  mercury,  which  is 
T  r^  (14  +  x)  iy6,  from  which  x  =  9-29  cm. 

32.  A  cylindrical  silver  wire  o«»-ooi5  in  diameter  weighs  3"2875  grammes  ;  it  is  to 
be  covered  w^th  a  layer  of  gold  o"'ooo2  in  thickness.  Required  the  weight  of  the  gold, 
the  specific  gravity  of  silver  being  io"47  ^"^  ^^^^  ^^  Sol*^  i9'26. 

If  r  is  the  radius  of  the  silver  wire  and  H  its  radius  when  covered  with  gold,  then 
r  =  0= '075  and  y?  =  o"=09S.  The  volume  of  the  silver  wire  will  be  ^  r^  I  and  its 
weight  n  r^  I  io'47,  from  which  /  =  i7«768. 

The  volume  of  the  layer  of  gold  is 

IT  (/?2  _  ^2)  17768, 

and  its  weight 

■K  (o'0952  —  o'075-)  X  17768  X  i9'26  =  3'656  nearly. 

33.  A  kilogramme  of  copper  is  to  be  drawn  into  wire  having  a  diameter  of  o"i6 
centimetre.     What  length  will  it  yield  ?    Specific  gravity  of  copper  8-88. 

The  wire  produced  represents  a  cylinder  /  cm.  in  length,  the  weight  of  which  is 
T  r^  /8"88,  and  this  is  equal  to  1000  grammes.     Hence  /  =  56™'oo85. 

34.  The  specific  gravity  of  cast  copper  being  879,  and  that  of  copper  wire  being 
8 '88,   what  change  of  volume  does  a  kilogramme  of  cast  copper  undergo  in  being 

drawn  into  wire?  Ans.  __ — 

86617 

35.  Determine  the  volumes  of  two  liquids,  the  densities  of  which  are  respectively 
1-3  and  07,  and  which  produce  a  mi.\ture  of  three  volumes  having  the  density  0-9. 

If  .r  and  y  be  the  volumes,  then  from  P  =  VD,  i'3:r  +  o7_>'  =  3  x  09  and 
a:  +  J  =  3,  from  which  *   =   i  and  y  =  i. 

36.  The  specific  gravity  of  zinc  being  7  and  that  of  copper  9,  what  weight  of  each 
metal  must  be  taken  to  form  50  grammes  of  an  alloy  ha\ing  the  specific  gravity  8*2,  it 
being  assumed  that  the  volume  of  the  alloy  is  exactly  the  sum  of  the  alloyed  metals  ? 

Let  X  =  the  weight  of  the  zinc,  and  y  that  of  the  copper,  then  x  +  y  =  ^o,  and 

p 
from  the  formula  P  =   VD,  which  gives  ^  =  ^.  the  volumes  of  the  two  metals  and  of 

the  alloy  are  respectively  _+-''  =  ^°  .     From  these  two  equations  we  get  x  =   17-07 

and  J  =  32  •93. 

37.  A  platinum  sphere  3  cm.  in  diameter  is  suspended  to  the  beam  of  a  very  ac- 
curate balance,  and  is  completely  immersed  in  mercury.  It  is  exactly  counterbalanced 
by  a  copper  cylinder  of  the  same  diameter  completely  immersed  in  water.  Required 
the  height  of  the  cylinder.  Specific  gravity  of  mercury  13-6,  of  copper  8-8,  and  of 
platinum  21-5.  Atis.  2-025  centimetres. 

38.  To  balance  an  ingot  of  platinum  27  grammes  of  brass  are  placed  in  the  other 
pan  of  the  balance.  What  weight  would  have  been  necessary  if  the  weighing  had  been 
effected  in  vacuo?  The  density  of  platinum  is  21-5,  that  of  brass  8-3,  and  air  under 
a  pressure  of  760  mm.  and  at  the  temperature  0°  has  —  the  density  of  water. 

The  weight  of  brass  in  air  is  not  27  grammes,  but  this  weight  minus  the  weight  of 
a  volume  of  air  equal  to  its  own. 

Since  P  =    VD  .■ .   V  =        and  the  weight  of  the  air  is    -  -    =  ?? . 

D  Z)  X  770        8-3  X  770 

By  similar  considerations,  if  x  is  the  weight  of  platinum  in  vacuo,  its  weight  in  air 

3x2 


1 044  Problems  and  Examples  in  Phy. 


will  be  X  minus  the  weight  of  air  displaced,  that  is  ^  —  ,   and  this  weight 

21-5  X  770 

is  equal  to  that  of  the  true  weight  of  the  brass  ;  and  we  have 

X  —  — —  2j  — ?Z ;  from  which  x  =   26 •996. 

21-5  X  770  8-3  X  770 

39.  A  body  loses  in  carbonic  acid  1-15  gr.  of  its  weight.  What  woiJd  be  its  loss 
of  weight  in  air  and  in  hydrogen  respectively? 

Since  a  litre  of  air  at  0°  and  760  mm.  weighs  1-293  gramme,  the  same  volume  of 
carbonic  acid  weighs  I -293  x  i'524  =  1-97  gramme.  We  shall,  therefore,  obtain  the 
volume  of  carbonic  acid  corresponding  to  I'lS  gr.  by  dividing  this  number  by  1-97, 
which  gives  o'5837  litre.  This  being  then  the  volume  of  the  body,  it  displaces  that 
volume  of  air,  and  therefore  its  loss  of  weight  inairiso"s837X  i'293  =  07547  grammes, 
and  in  hydrogen  0-5837  x   1-293  x  0-069   =  0-052076. 

40.  Calculate  the  ascensional  force  of  a  spherical  balloon  of  oiled  silk  which,  when 
empty,  weighs  62-5  kilos,  and  which  is  filled  with  impure  hydrogen,  the  density  of 

whicli  is  i  that  of  air.     The  oiled  silk  weighs  0-250  kilo,  the  square  metre. 
13 

The  surface  of  the  balloon  is  ^^-A  _  250  square  metres.  This  surface  being  that  of 
0-25 

a  sphere,  is  equal  to  4  n-  Ji"^,  whence  j,nR~  =  250  and  R  =  4-459  ;  therefore  V  =  "^-'^ 

=  371  "52  cubic  metres. 

The  weight  of  air  displaced  is  371-52  x   1-293  kilo   =  480-375  kilos  ;  the  weight  of 
the  hydrogen  is  36 -88  kilos,  and  therefore  the  ascensional  force  is 
480-375  -  (36-88  +  62-5)   =   380-995. 

41.  A  b.illoon  4  metres  in  diameter  is  made  of  the  same  material  and  filled  with 
the  same  hydrogen  as  above.  How  much  hydrogen  is  required  to  fill  it,  and  what 
weight  can  it  support  ? 

Thevohime  is  4  „■  7?3  =  33-5 1  cubic  metres,  and  the  surface  477.^-  =  50-265  square 
3 
metres.     The  weight  of  the  air  displaced  is  33-51  x  1-293  =  43'328  kilos,  and  that  of 
the  hydrogen  is  from  the  above  data  3-333  kilos,  while  the  weight  of  the  material  is  12-566 
kilos.     Hence  the  weight  which  the  balloon  can  support  is 

43-328  -  (12-566  +  3-333)   =   27-429  kil. 

42.  Under  the  receiver  of  an  air-pump  is  placed  a  balance,  to  which  are  suspended 
t>vo  cubes;  one  of  these  is  3  centimetres  in  the  side.and  weighs  26-324  gr.  ;  and  the  other 
is  5  centimetres  in  the  side,  and  weighs  26-2597  grammes.  When  a  partial  vacuum  is 
made  these  cubes  just  balance  each  other.     What  is  the  pressure?         Ans.  o'"-374. 

43.  A  soap-bubble  8  centimetres  in  diameter  was  filled  with  a  mixture  of  one 
volume  of  hydrogen  gas  and  15  volumes  air.  The  bubble  just  floated  in  the  air  ;  re- 
quired the  thickness  of  the  film. 

The  weight  of  the  volume  of  air  displaced  is  '^  rr  /^  ^  0-001293  gramme,  and  that 

of  the   mixture  of  gases    '^  ■"  r^  x  0-001293  x     ■^ — 22  .  j,j^jj   ^]^^  difference    of 

3  16 

these  will  equal  the  weight  of  the  soap-bubble. 

This  weight  is  that  of  a  spherical  shell,  which,  since  its  thickness  /  is  very 
small,  is  with  sufficient  accuracy  4  t  r-  i  s  in  grammes,  where  s  is  the  specific  gravity 
=  1-1.     Hence 

"^  TT  r^  r -001293  -    001293  X    15  oo93\    _  ^  ^  ^2  /  j.j^ 

Dividing  each  side  by  "^  n  r",  and  putting  r  =  4,  we  get 


4  X   -001293   (^i  -  ^^^°5^^)=3'3' 


Oti  Liquids  and  Gases.  1045 


•001293     X     .23^7     _     3-3  /   ; 

4 
whence/  =    ■00009116629  cm. 

44.  In  a  vessel  whose  capacity  is  3  litres,  there  are  introduced  2  litres  of  hydrogen 
under  the  pressure  of  5  atmospheres  ;  3  litres  of  nitrogen  under  the  pressure  of  half  an 
atmosphere,  and  4  litres  of  carbonic  acid  under  the  pressure  of  4  atmospheres.  What 
is  the  final  pressure  of  the  gas,  the  temperature  being  supposed  constant  during  the 
experiment  ? 

The  pressure  of  the  hydrogen,  from  Dalton's  law,  will  be  ^  ^~^,  that  of  the  nitro- 

3 
gen  will  remain  unchanged,  and  that  of  the  carbonic  acid  will  be  ^^  ^,     Hence  the 
total  pressure  will  be 

—  +--+    —    =  9J  atmospheres. 
323 

45.  A  vessel  containing  10  litres  of  water  is  first  exposed  in  contact  with  oxygen 
under  a  pressure  of  78  cm.  until  the  water  is  completely  saturated.  It  is  then  placed 
in  a  confined  space  containing  100  litres  of  carbonic  acid  under  a  pressure  of  72  cm. 
Required  the  volumes  of  the  two  gases  when  equilibrium  is  established.  The  coeffi- 
cient of  absorption  of  oxygen  is  o'042,  and  that  of  carbonic  acid  unity. 

The  volume  of  oxygen  dissolved  is  0-42.  Being  placed  in  carbonic  acid  it  will 
act  as  if  it  alone  occupied  the  space  of  the  carbonic  acid,  and  its  pressure  will  be 

78    X    — i —  =  o'326  cm. 
10042 
Similarly  the  10  litres  of  water  will  dissolve  10  litres  of  carbonic  acid  gas,  the  total 
volume  of  which  will  be  no,  of  which  100  are  in  the  gaseous  state  and  10  are  dissolved. 

Its  pressure  is  therefore  72  X  =  65 '454  cm. 

no 
Hence  the  total  pressure  when  equilibrium  is  established  is 
0-326  +  65-454  =  65-78  cm.  ; 
and  the  volume  of  the  oxygen  dissolved  reduced  to  the  pressure  65-78  is 

o"'*42  X  ^^     =  o"'-oo2o8,  and  that  of  the  carbonic  acid  10  x  -^  45't  =  q-qc. 
^        65-78  65-78 

46.  In  a  barometer  which  is  immersed  in  a  deep  bath  the  mercury  stands  743 
mm.  above  the  level  of  the  bath.  The  tube  is  lowered  until  the  barometric  space, 
which  contains  air,  is  reduced  to  one-third,  and  the  mercury  is  then  at  a  height  of  701 
mm.    Required  the  atmospheric  pressure  at  the  time  of  observation.    Ans.  =  764""' . 

47.  ^^'hat  is  the  pressure  on  the  piston  of  a  steam  boiler  of  8  decimetres  diameter 
if  the  pressure  in  the  boiler  is  3  atmospheres?  Ans.  1038585  kilos. 

48.  What  is  the  pressure  of  the  atmosphere  at  that  height  at  which  an  ascent  of  21 
metres  corresponds  to  a  diminution  of  i"™  in  the  barometric  height?  Ans.  ^yS-g'"'". 

49.  What  would  be  the  heiglU  of  the  atmosphere  if  its  density  were  everywhere 
uniform  ?  Ans.  7954-1  metres,  or  nearly  5  miles. 

50.  How  high  must  we  ascend  at  the  sea-level  to  produce  a  depression  of  i  mm. 
in  the  height  of  the  barometer? 

Ans.  Taking  mercury  as  10,500  times  as  heavy  as  air,  the  height  will  be  10-5  metres. 

51.  Mercury  is  poured  into  a  barometer  tube  so  that  it  contains  15  cc.  of  air  under 
the  ordinary  atmospheric  pressure.  The  tube  is  then  inverted  in  a  mercury  bath  and 
the  air  then  occupies  a  space  of  25  cc.  ;  the  mercury  occupying  a  height  of  302  mm. 
What  is  the  pressure  of  the  atmosphere  ? 

Let  X  be  the  amount  of  this  pressure,  the  air  in  the  upper  part  of  the  tube  will  have 

a  pressure  represented  by  -^,  and  this,  together  with  the  height  of  the  mercurial 

25 
column  302,  will  be  the  pressure  exerted  in  the  interior  of  the  tube  on  the  level  of  the 


1046 


Problems  and  Examples  in  Physics. 


mercury  in 


the  bath,  which  is  equal  to  the  atmospheric  pressure 


that  is  -?-    +  302 

25 

=  X,  from  which  x  =  755  mm. 

52.  What  effort  is  necessary  to  support  a  cylindrical  bell-jar  full  of  mercury 
immersed  in  mercury  ;  its  internal  diameter  being  6  centimetres,  its  height  ol  above 
the  surface  of  the  mercury  (fig.  1)18  centimetres,  and  the  pressure  of  the  atmosphere 
077  centimetre? 

The  bell-jar  supports  on  the  outside  a  pressure  equal  to  that  of  a  column  of  mercury 
the  section  of  whose  base  is  cd,  and  the  height  that  of  the  barometer.  This  pressure  is 
equal  to 

TT  R'^  X  077  X   I3'6. 
The  pressure  on  the  inside  is  that  of  the  atmosphere  less  the  weight  of  a  column 
of  mercury  whose  base  is  tfl?  and  height  iJiJ.  Thisisequal  ton- /?^  x  (077  — o"i8)  x  i3'6  ; 
and  the  effort  necessary  is  the  difference  of  these  two  pres- 
sures.    Making  i?  =  3  cm.,  this  is  found  to  be  69 '216  kilo- 
grammes. 

53.  A  barometer  is  placed  within  a  tube  which  is  after- 
ds  hermetically  closed.  At  the  moment  of  closing,  the 
perature  is  15°  and  the  pressure  750  mm.  The  ax- 
ial space  is  then  heated  to  30°.  What  will  be  the  height 
he  barometer  ? 
The  effect  of  the  increase  of  temperature  would  be  to 

e  the  mercury  in  the  tube  in  the  ratio  i  +    ^°      to  i   + 

5550 
,  and  the  height  h  would  therefore  be 


75 


V       5550/ 


I    + 


15 

5550 


and  since  in   the  closed  space  the  elastic  force  of  the  air  increases  in  the  ratio 
I    +•   30  a  :  I    +    15  a.  we  shall  have  finally  A  =   30174  mm. 

54.  The  heights  of  two  barometers  A  and  B  have  been  obser%'ed  at  —  10^  and 
■V   15°    respectively,  to  be  ^   =  737  and  B  =  763.     Required  their  corrected  heights 

ato=.  ^"^-  ^   =  738 'SS-     B  =  760-94. 

55.  A  voltaic  current  gives  in  an  hour  S.p  cubic  centimetres  of  detonating  gas 
under  a  pressure  of  760  and  at  the  temperature  i2°-5  ;  a  second  voltaic  current  gives 
in  the  same  time  960  cubic  centimetres  under  a  pressure  of  755  and  at  the  temperature 
t5°-5.     Compare  the  quantities  of  gas  given  by  the  two  currents.     Atts.  i  :  1-129. 

56.  The  volume  of  air  in  the  pressure  gauge  of  an 

iparatus  for  compressing  gases  is  equal  to  152  parts. 

I'.y  the  working  of  the  machine  this   is  reduced   to 

7  parts,    and   the  mercury  is  raised    through   0-48 

UK'tre.     W'liat  is  the  pressure  of  the  gas  ? 

IIere^5  =  152,  AC  =  37  parts,  and  BC  =  o^'^S. 
The  pressure  of  air  therefore  in  ^Cis,  from  Boyle's 


152 
37 


,.tm-io8    = 


tig.  2. 


■  pressure  in  the  receiver  is  therefore 

3-122  +  048  =  3'"-6o2, 
ch  is  equal  to  4-74  atmospheres. 
57.  An  airtight  bladder  holding  two  litres  of 
at  the  standard  pressure  and  temperature  is 
iiersed  in  sea-water  to  a  depth  of  100  metres, 
•re  tlie  temperature  is  4°.  Required  the  volume 
of  tlie  gas. 


i83 


o*i8568  litre. 


A  ir  Pump.  1 047 

The  specific  gravity  of  sea-water  being  i  '026,  the  depth  of  100  metres  will  repre- 
sent a  column  of  pure  water  102  6  metres  in  height.  As  the  pressure  of  an  atmo- 
sphere is  equal  to  a  pressure  of  io'33  metres  of  pure  water,  the  pressure  of  this  column 

=   ^°=:6?  =  9.94  atm. 
10-33 
Hence,  adding  the  atmospheric  pressure,  the  bladder  is  now  under  a  pressure  of  io'94 

atmosphersB,  and  its  volume  being  inversely  as  the  pressure  will  be  -  =  o'lS?  litre, 

1094 
if  the  temperaiure  be  unaltered.    But  the  temperature  is  increased  by  4°,  and  therefore 
the  volume  is  increased  in  the  ratio  277  to  273,  and  becomes 

277 

273 

58.  To  what  height  will  water  be  raised  in  the  tube  of  a  pump  by  the  first  stroke  of  the 
piston,  thelength  of  stroke  of  which  is  o'5m.,  the  height  of  the  tube  6  metres,  and  its  section 
t",;  that  of  the  piston?    At  starting  the  air  in  the  tube  is  under  a  pressure  of  10  metres. 

If  we  take  the  section  of  the  tube  as  unity,  that  of  the  body  of  the  pump  is  10  ;  and 
the  volumes  of  the  tube  and  of  the  body  of  the  pump  are  in  the  ratio  of  6  to  5.  Then 
if  X  is  the  height  to  which  the  water  is  raised  in  the  pipe,  the  volumes  of  air  in  the 
pump  before  and  after  the  working  of  the  pump  are  6  at  the  pressure  10,  and  5  +  6  —  jr 
at  the  pressure  10  —  x. 

Forming  an  equation  from  these  terms,  and  solving,  we  have  two  values,  x'  =  18"  26 
and  xf'  =  274.  The  first  of  these  must  be  rejected  as  being  physically  impossible ; 
and  the  true  height  is  ^  =   275  metres. 

59.  A  receiver  with  a  capacity  of  10  litres  contains  air  under  the  pressure  76  cm. 
It  is  closed  by  a  valve,  the  section  of  w-hich  is  32  square  centimetres,  and  is  weighted 
with  25  kilogrammes.  The  temperature  of  the  air  is  30°  ;  its  density  at  o®  and  76  cm. 
pressure  is  that  of  water.     The  coefficient  of  the  expansion  of  gases  is  o '00366. 

Required  the  weight  of  air  which  must  be  admitted  to  raise  the  valve. 

The  air  already  present  need  not  be  taken  into  account  as  it  is  under  the  pressure 
of  the  atmosphere.     Let  x  be  the  pressure  in  centimetres  of  mercury  of  that  which  is 


X  X  136 


will  represent  in  kilogrammes   its  pressure  on  a  square  centi- 


57  44  _   8 '8055  grammes. 
76*00 


admitted, 

metre  ;  and  therefore  the  internal  pressure  on  the  valve,  and  which  is  equal  to  the  ex- 
ternal pressure  of  25  kilogrammes,  is  -^LJi  ^3      ^  32  _  ^^  jj     From  which  x  =  57*44. 

For  the  weight  we  shall  have 

p  _      10  X  0001293 
I  +  o'oo366  X  30 

60.  A  bell-jar  contains  3-17  litres  of  air  ;  a  pressure  gauge  connected  with  it  mark.<; 
zero  when  in  contact  with  the  air  (fig.  3).  The  jar  is 
closed  and  the  machine  worked  ;  the  mercury  rises 
to  65  cm.  A  second  barometer  stands  at  76  cm. 
during  the  experiment.  Required  the  weight  of  air 
withdrawn  from  the  bell-jar  and  the  weight  of  that 
which  remains. 

At  0°  and  76  cm.  the  weight  of  air  in  the  bell-jar  is 

1-293  ^  3'^7  —  4-09881. 
At  0°  and  under  the  pressure  76  —  65  the  weight 
of  the  residual  air  is 

4-09881    X    II  _^^ 

'*^ =  0-5932, 

76 

and  therefore  the  weight  of  that  which  is  withdrawn  is 

4-0988  -  0-5932  =  3  5056  gr. 

61.  The  capacity  of  the  receiver  of  an  air-pumi^ 


1048  Problems  and  Examples  in  Physics. 

is  7 "53  ;  it  is  full  of  air  under  the  ordinary  atmospheric  pressure  and  at  0°.  Re- 
quired the  weight  of  air  when  the  pressure  is  reduced  to  0-21  ;  the  weight  with- 
drawn by  the  piston  ;  and  the  weight  which  would  be  left  at  15°. 

The  weight  of  7-53  litres  of  air  under  the  ordinary  conditions  is  9736  grammes. 

Under  a  pressure  of  o'2i  it  will  be  2-69  grammes,  and  at  the  temperature  15° it  will 

be ?^^?- ,  =  0-2S5  gramme. 

I  +  000366  X   i5 

62.  In  a  theoretically  perfect  air-pump,  how  great  is  the  rarefaction  after  10  strokes, 
if  the  volumes  of  the  barrel  and  the  receiver  are  respectively  2  and  3  ? 

Ans.    =  4'59"'™  ;  or  about         of  an  atmosphere. 
166 

63.  What  must  be  the  capacity  of  the  barrel  of  an  air-pump  if  the  air  in  a  re- 
ceiver of  4  litres  is  to  be  reduced  to  i  the  density  in  two  strokes  ?  Ans.  2g. 

64.  The  reservoir  of  an  air-gun,  the  capacity  of  which  is  40  cubic  inches,  contains 
air  whose  density  is  8  times  that  of  the  mean  atmospheric  pressure.  A  shot  is  fired 
when  the  atmospheric  pressure  is  741  mm.  and  the  gas  which  escapes  occupies  a  volume  of 
80  cubic  inches.  What  is  the  elastic  force  of  the  residual  air?   Ans.  6 '05 atmospheres. 

65.  Suppose  that  at  the  limit  of  the  atmosphere  the  pressure  of  the  attenuated 

air  is  the    ^^  of  a  millimetre  of  mercury  and  the  temperature  —  135°,  and  that  in  a 

1000 
place  at  the  sea-level,  in  latitude  45°,  the  pressure  of  the  atmosphere  is  760™™  and  its 
temperature  15°  C.     Determine  from  these  data  the  height  of  the  atmosphere. 

From  the  formula  18400  1 1  +  o  '002  j  T  +  /  [  |  log  ,  we  get  for  the  height  in  metres 
82237,  which  is  equal  to  51-1  miles. 

66.  If  water  is  continually  flowing  through  an  aperture  of  3  square  inches  with  a 
velocity  of  10  feet,  how  many  cubic  feet  will  flow  out  in  an  hour?  Ans.  750  cubic  feet. 

67.  With  what  velocity  does  water  issue  from  an  aperture  of  3  square  inches,  if 
37-5  cubic  feet  flow  out  every  minute  ?  Ans.  30  feet. 

68.  What  is  the  ratio  of  the  pressure  in  the  above  two  cases?  Ans.  i  :  9. 

69.  What  is  the  theoretical  velocity  of  water  from  an  aperture  which  is  9  feet 
below  the  surface  of  water  ?  Ans.  24  feet. 

70.  In  a  cylinder,  water  stands  2  feet  above  the  aperture  and  is  loaded  by  a  piston 
which  presses  with  a  force  of  6  pounds  on  the  square  inch.  Required  the  velocity  of 
the  effluent  water.  Ans.  32  feet. 

71.  How  deep  must  the  aperture  of  the  longer  leg  of  a  syphon,  which  has  a  sec- 
tion of  4  square  centimetres,  be  below  the  surface  of  the  water  in  order  that  25  litres 
may  flow  out  in  a  minute?  Ans.  5'535  cm. 

72.  Through  a  circular  aperture  having  an  area  of  0-196  square  cm.  in  the  bottom 
of  a  reservoir  of  water  which  was  kept  at  a  constant  level,  55  cm.  above  the  bottom, 
it  was  found  that  98-5  grammes  of  water  flowed  in  22  seconds.  Required  the  coeffi- 
cient of  efflux. 

Since  the  velocity  of  efflux  through  an  aperture  in  the  bottom  of  a  vessel  is  given  by 
the  formula  v  =  sj^gh,  it  will  readily  be  seen  that  the  weight  in  grammes  of  water 
which  flows  in  a  given  time,/,  will  be  given  by  the  formula  iv  =  a  a  ts/zgh,  where (Z  is 
the  area  in  square  centimetres,  a  the  coefficient  of  efflux,  /  the  time  m  seconds,  and  h 
the  height  in  centimetres.     Hence  in  this  case  o  =  0-699. 

73.  Similarly  through  a  square  a])orture,  the  area  of  which  was  almost  exactly  the 
same  as  the  above,  and  at  the  same  depth,  104 '4  grammes  flowed  out  in  21 '6  seconds. 
In  this  case  «  =  073. 


Sound.  1049 


IV.    ON  SOUND. 

74.  A  stone  is  dropped  into  a  well,  and  4  seconds  afterwards  the  report  of  its 
striking  the  water  is  heard.  Required  the  depth,  knowing  that  the  temperature  of  the 
air  in  the  pit  was  10°  74. 

From  the  formula  v  =  333  \/ 1  +  at  we  get  for  the  velocity  of  sound  at  the  tem- 
perature in  question  339 -05  metres. 

Let  /  be  the  time  which  the  stone  occupies  in  falling  ;  then  Igfl  =  x  will  represent 
the  depth  of  the  well ;  on  the  other  hand,  the  time  occupied  by  the  report  will  be  4  —  /, 
and  the  distance  will  hQ  [^  —  t)  v  =  x  (i)  ;  thus  [^  —  t)  v  =  i^/2  (ii),  from  which, 
substituting  the  values, 

(4  -  t)  339-S  =  4-9  i"" 
^  =   3793  seconds,  and  substituting  this  value  in  either  of  the  equations  (i)  or  (ii), 
we  have  the  depth   =  72-6  metres  nearly. 

75.  A  bullet  is  fired  from  a  rifie  withavelocity  of  414  metres,  and  is  heard  to  strike 
a  target  4  seconds  afterwards.  Required  the  distance  of  the  target  from  the  marks- 
man, the  temperature  being  assumed  to  be  zero. 

X     ^     X  „ 

+  =    ^-  X    =    738 '2. 

414       333 

76.  At  what  distance  is  an  observer  from  an  echo  which  repeats  a  sound  after  3 
seconds,  the  temperature  of  the  air  being  10°  ? 

In  these  3  seconds  the  sound  traverses  a  distance  of  3  x  339  =  1017  metres  ;  this 
distance  is  twice  that  between  the  observer  and  the  reflecting  surface  ;  hence  the  dis- 
tance is 

££^7   =   508-5  metres. 
2 

77.  Between  a  flash  of  lightning  and  the  moment  at  which  the  corresponding 
thunder  is  first  heard,  the  interval  is  the  same  as  that  between  two  beats  of  the  pulse. 
Knowing  that  the  pulse  makes  80  beats  in  a  minute,  and  assuming  the  temperature 
of  the  air  to  be  15°  C,  what  is  the  distance  of  the  discharge?       Ans.  454'!  metres. 

78.  A  stone  is  thrown  into  a  well  with  a  velocity  of  12  metres,  and  is  heard  to 
strike  the  water  4  seconds  afterwards.  Required  the  depth  of  the  well. 

Ai/s.  About  no  metres. 

79.  What  is  the  velocity  of  sound  in  coal  gas  at  0°,  the  density  being  o'5  ? 

A/!s.  470'9  metres. 

80.  What  must  be  the  temperature  of  air  in  order  that  sound  may  travel  in  it  with 
the  same  velocity  as  in  hydrogen  at  0°  ?  Ans.  About  3680°  C. 

81.  What  must  be  the  temperature  of  air  in  order  that  the  velocity  of  sound  may 
be  the  same  as  in  carbonic  acid  at  0°  ?  Afis.  —  ios°S  C. 

82.  Kendall,  in  a  North  Pole  E.\pedition,  found  the  velocity  of  sound  at  —40° 
was  314  m.  How  closely  does  this  agree  with  that  calculated  from  the  value  we  have 
assumed  for  0°  ?  Ans.  6  64  metres  too  much. 

83.  The  report  of  a  cannon  is  heard  15  seconds  after  the  flash  is  seen.  Required 
the  distance  of  the  cannon,  the  temperature  of  the  air  being  22°. 

From  the  formula  for  the  velocity  of  sound  we  have 

15  ^  333  \/i  +  0003665  X  22  =  5190  metres. 

84.  If  a  bell  is  struck  immediately  at  the  level  of  the  sea,  and  its  sound,  reflected 
from  the  bottom,  is  heard  3  seconds  after,  what  is  the  depth  of  the  sea  ? 

Ans.  7140  feet. 


1050  Problems  and  Examples  in  Physics. 

85.  A  person  stands  150  feet  on  one  side  of  the  line  of  fire  of  a  rifie  range  450  feet 
in  length  and  at  right  angles  to  a  point  150  feet  in  front  of  the  target.     What  is  the 

velocity  of  the  bullet  if  the  person  hears  it  strike  the  target      of  a  second  later  than 

9 
the  report  of  the  gun?    The  temperature  is  assumed  to  be  i6°-5.       Ans.  2038  feet. 

86.  An  echo  repeats  five  syllables,  each  of  which  requires  a  quarter  of  a  second  to 
pronounce,  and  half  a  second  elapses  between  the  time  the  last  syllable  is  heard  and 
the  first  syllable  is  repeated.  What  is  the  distance  of  the  echo,  the  temperature  of 
the  air  being  10°  C.  ?  Ans.  297'47  metres. 

87.  The  note  given  by  a  silver  wire  a  millimetre  in  diameter  and  a  metre  in 
length  being  the  middle  C,  what  is  the  tension  of  the  wire?     Density  of  silver  10-47. 

Ans.  2267  kilogrammes. 

88.  The  density  of  iron  being  7-8  and  that  of  copper  8 '8,  what  must  be  the 
thickness  of  wires  of  these  materials,  of  the  same  length  and  equally  stretched,  so  that 
they  may  give  the  same  note  ? 

From  the  formula  for  the  transverse  vibration  of  strings  we  have  for  the  number  of 

vibrations  «  =  /  —  .     As  in  the  present  case,  the  tensions,  the  length  of  the 

rl  Sf    7r  d 
strings,  and  the  number  of  vibrations  are  the  same,  we  have 

rl  \/    ivd         r,ls/   ir  d]  r  S/    d         r^s/   d, 

whence  ^   =  '^'    =  ^^  ;  hence  ''  =      /Sj?  =   1-062. 
r^         d         7-8  r,        \/   7-8 

89.  A  wire  stretched  by  a  weight  of  13  kilos,  sounds  a  certain  note.  What  must 
be  the  stretching  weight  to  produce  the  major  third  ? 

The  major  third  having  ^  the  number  of  vibrations  of  the  fundamental  note,  and  as, 
4 
all  other  things  being  the  same,  the  numbers  of  vibrations  are  directly  as  the  square 
roots  of  the  stretching  weight,  we  shall  have  x  —  20-312  kilos. 

90.  The  diameters  of  two  wires  of  the  same  length  and  material  are  00015  and 
0-0038 m.  ;  and  their  stretching  weights  40oand  1600 grammes  respectively.  Required 
the  ratio  of  the  numbers  of  their  vibrations.  Ans.  n  :  n,  =   1-266  :  i. 

91.  A  brass  wire  i  metre  in  length  stretched  by  a  weight  of  2  kilogrammes,  and  a 
silver  wire  of  the  same  diameter,  but  3-165  metres  in  length,  give  the  same  number  of 
vibrations.     What  is  the  stretching  weight  in  the  latter  case  ? 

Since  the  number  of  vibrations  is  equal,  we  shall  have 

1      /Z    =    1     /Z; 
rlW    ivd        rl.s/  ird, 
from  which,  replacing  the  numbers,  we  get  x  =   25  kilos. 

92.  A  brass  and  a  silver  wire  of  the  same  diameter  are  stretched  by  the  weights  of  2 
and  25  kilogrammes  respectively,  and  produce  the  same  note.  What  are  their  lengths, 
knowing  that  the  density  of  brass  is  8-39,  and  of  silver  10-47  ? 

Ans.  The  length  of  the  silver  wire  is  3-16  times  that  of  the  brass. 

93.  A  copper  wire  1-25  mm.  in  diameter  and  a  platinum  one  of  0-75  mm.  are 
stretched  by  equal  weights.  What  is  the  ratio  of  their  lengths,  if,  when  the  copper 
wire  gives  the  note  C,  the  platinum  gives  F  on  the  diatonic  scale?; 

Ans.  The  length  of  the  copper  is  to  the  length  of  the  platinum   =    1-264  :  i. 

94.  An  organ  pipe  gives  the  note  C  at  a  temperature  0°  ;  at  what  temperature 
will  it  yield  the  major  third  of  this  note?  Ans.  153°  C, 

95.  A  brass  wire  a  metre  in  length,  and  Stretched  by  a  weight  of  a  kilogramme, 
yields  the  same  note  as  a  silver  wire  of  the  same  diameter  but  2-5  metres  in  length  and 
stretched  by  a  weight  of  7-5  kilogrammes.    Required  the  specific  gravity  of  the  silver. 

Ans.  10068. 

96.  How  many  beats  are  produced  in  a  second  by  two  notes,  wliose  rates  of  vibra- 
tion are  respectively  340  and  354  ?  Ans.  14. 


Heat. 


1051 


V.    ON  HEAT. 

97.  Two  mercurial  thermometers  are  constructed  of  the  same  glass  ;  the  internal 
diameter  of  one  of  the  bulbs  is  7"" "5  and  of  its  tube  2-5  ;  the  bulb  of  the  other  is 
62  in  diameter  and  its  tube  1-5.  What  is  the  ratio  of  the  length  of  a  degree  of  the 
first  thermometer  to  a  degree  of  the  second? 

Let  A  and  B  be  the  two  thermometers,  D  and  D'  the  diameters  of  the  bulbs,  and 
d  and  cH  the  diameters  of  the  tubes.  Let  us  imagine  a  third  thermometer  C  with  the 
same  bulb  as  B  and  the  same  tube  as  A,  and  let  /,  /',  and  /"  denote  the  length  of  a 
degree  in  each  of  the  thermometers  respectively.  Since  the  stems  of  A  and  C 
have  the  equal  diameters,  the  lengths  /  and  /"  are  directly  as  the  volumes  of  the 
tubes,  or  what  is  the  same,  as  the  cubes  of  their  diameters  ;  and  as  B  and  C  have 
the  same  bulk,  the  lengths  /'  and  /"  are  inversely  proportionate  to  the  sections  of 
the  stems,  or  what  amounts  to  the  same,  to  the  squares  of  their  diameters.  We 
have  then 

f  =  m^^'^v    =  d^' 

introducing  the  values  and  sohing,  we  have 
/  =  0-638. 

98.  At  what  temperature  is  the  number  on  the 
Centigrade  and  Fahrenheit  thermometers  the  same  ? 

Alls.  —  40°. 

99.  The  same  question  for  the  Fahrenheit  and 
Reaumur  scales.  Ans.  —  25-6. 

100.  A  capillary  tube  is  divided  into  180  parts 
of  equal  capacity,  25  of  which  weigh  12  gramme. 
What  must  be  the  radius  of  a  spherical  bulb  to  be 
blown  to  it  so  that  180  divisions  correspond  to  150 
degrees  Centigrade? 

Since    25    divisions    of    the   tube    contain    i"2 

gramme,  180  divisions  contain  =8  64. 


U-    ¥ 


/  li       H 


■)(>)(2 


Fig. 


And  since  these  180  divisions  are  to  represent  150  degrees,  the  weight  of  mercury 

corresponding  to  a  single  degree  is    ■^'^.     But  as  the  expansion   corresponding    to 

8'6a 
one  degree  is  only  the  apparent  expansion  of  mercury  in  glass,  the  weight      __  -   is  ■ 

I ^o        0400 

of  the  mercury  in  the  reservoir,  which  is  ^  ^R^.    From  this  ^  =  i  "8755  centimetre. 
3 

101.  By  how  much  is  the  circumference  of  an  iron  wheel,  whose  diameter  is  6  feet, 
increased  when  its  temperature  is  raised  400  degrees?  Coefficient  of  expansion  of 
iron   =  00000122.  Ans.  By  0092  foot. 

102.  What  must  be  the  length  of  a  wire  of  this  metal  which  for  a  temperature  of 
1°  expands  by  one  foot  ?  Ans.  81967  feet. 

103.  A  pendulum  consists  of  a  platinum  rod,  on  a  flattening  at  the  end  of  which 
rests  a  spherical  zinc  bob.  The  length  of  the  platinum  is  /  at  0°.  What  must  be  the 
diameter  of  the  bob,  so  that  its  centre  is  always  at  the  same  distance  from  llie  point  of 
suspension  whatever  be  the  temperature  ?  Coefficient  of  expansion  of  platinum 
o  0000088  and  of  zinc  00000294. 

Ans.  The  diameter  of  the  bob  must  be  g  of  the  length  of  the  platinum. 

104.  Two  walls,  which  when  perpendicular  are  30  feet  apart,  have  bulged  out- 
wards to  the  extent  of  24  inches.     They  are  to  be  made  perpendicular  by  the  contrac- 


1052  Problems  and  Examples  m  Physics. 

tion  of  an  iron  bar.    By  how  much  must  its  temperature  be  raised  above  that  of  the  air, 
which  is  taken  at  o°?  Ans.  546-4. 

105.  An  iron  wire  4  sq.  mm.  in  cross  section  is  stretched  — ? —  of  its  length  by  a 

81200 
weight  of  I  kilogramme.     What  weight  must  be  applied  to  a  bar  9  sq.  mm.  in  cross 
section,  when  it  is  heated  from  0°  to  20°,  in  order  to  prevent  it  from  expanding? 

Ans.  44 '5  kilo. 

106.  At  the  temperature  zero  a  solid  is  immersed  0-975  of  its  total  volume  in 
alcohol.  At  the  temperature  25°  the  solid  is  wholly  immersed.  The  coefficient  of 
expansion  of  the  solid  being  o  000026,  required  the  coefficient  of  expansion  of  the 
alcohol.  Afis.  0-001052. 

107.  Into  a  glass  globe,  the  capacity  of  which  at  0°  is  250  cc,  are  introduced 
25  cc.  of  air  measured  at  0°  and  76  cm.     The  flask  being  closed  and  heated  to  100", 

required  the  internal  pressure.     Coefficient  of  cubical  expansion  of  glass  — ^^ — 

38700 

At  100''  the  capacity  of  the  flask  is  250  (  i  +  — ^^  )  ;  again  at  100°  the  volume  of 
V         38700/ 
the  free  air  under  the  pressure  76  is  25  (i  +   100  x  o'oo366).     But   its  real  volume  is 

2:;o  X   3 — under  a  pressure  A-.     Hence 
387  gg 

76    :   Jf  =   250  X  2        :  25  X   1-366,  from  which  x  =   10-3548  cm. 
387 

108.  The  specific  gravity  of  mercury  at  0°  being  13-6,  required  the  volume  of  3 
kilogrammes  at  85°.     Coefficient  of  expansion . 

The  volume  at  0°  will  be     -^     and  at  85°  -  2-    x(i  +       ^     )   =   0-2239  litres. 
i3'6  136       V         5550^ 

109.  A  hollow  copper  sphere  20  cm.  in  diameter  is  filled  with  air  at  0°  under  a 
pressure  of  i^  atmosphere  ;  what  is  the  total  pressure  on  the  interior  surface  when  the 
enclosed  air  is  heated  to  a  temperature  of  600°?  Ans.  6226-5  kilogrammes. 

110.  Between  the  limits  of  pressure  700  to  780mm.  the  boiling-point  of  water  varies 
o°-o375  C.  for  each  mm.  of  pressure.  Between  what  limits  of  temperature  does  the 
boiling  point  vary,  when  the  height  of  the  barometer  is  between  735  and  755  mm.  ? 

A/IS.   Between  99°-o625  and  99°-8i25. 

111.  Liquid  phosphorus  cooled  down  to  30°,  is  made  to  solidify  at  this  tempera- 
ture. Required  to  know  if  the  soHdification  will  be  complete,  and  if  not,  what  weight 
will  remain  melted  ?  The  melting  point  of  phosphorus  is  44-2  ;  its  latent  heat  of  fusion 
5-4,  and  its  specific  heat  0-2. 

Let  X  be  the  weight  of  phosphorus  which  solidifies ;  in  so  doing  it  will  give  out  a 
quantity  of  heat  =  5-4  ^  ;  this  is  expended  in  raising  the  whole  weight  of  the  phos- 
phorus from  30  to  44-2.     Hence  we  have  5-4*"  =    i   x   (44-2  —  30)  0-2,   from  which 

X   =■        ^   =   0-526,  so  tliat  0-474  of  phosphorus  will  remain  liquid. 
5 '4 

112.  A  pound  of  ice  at  0°  is  placed  in  two  pounds  of  water  at  0°  ;  required  the 
weight  of  steam  at  100°  which  will  melt  the  ice  and  raise  the  temperature  of  the  mix- 
ture to  30°.  The  latent  heat  of  the  liquefaction  of  ice  is  79-2,  and  that  of  the  vaporisa- 
tion of  water  536.  A//s.   -279  pound. 

113.  65-5  grammes  of  ice  at  —  20"-"  having  been  placed  in  x  grammes  of  oil  of 
turpentine  at  13-3°,  the  final  temperature  is  found  to  be  3-1°.  The  specific  heat  of 
turpentine  is  0-4,  and  it  is  contained  in  a  vessel  weighing  25  grammes,  whose  specific 
hiMt  is  o-i.     The  specific  heat  of  ice  is  0-5.     Required  the  value  of  jr. 

Arts.  X  =  147s  grammes. 

114.  In  what  pro[)ortion  must  water  at  a  temperature  of  30°  and  linseed  oil 
(sp.  heat  =  0-5)  at  a  temperature  of  50°  be  mixed  so  that  there  are  20  kilogrammes  of 
the  mixture  at  40°?  A»s.  Water  =  6-66  kilos,  and  linseed  oil  =   13-34. 


Heat.  1053 

115.  By  how  much  will  mercury  at  0°  be  raised  by  an  equal  volume  of  water  at 
1 00°?  An5.bZ°-<)<Z. 

116.  The  specific  heat  of  gold  being  o '03244,  what  weight  of  it  at  45°  will  raise  a 
kilogramme  of  water  from  120-3  to  i5°7? 

Let  X  be  the  weight  sought  ;  then  x  kilogrammes  of  gold  in  sinking  from  45°  to 
i5«7  will  give  out  a  quantity  of  heat  represented  by  x  (450  -  15O7)  0-0324,  and  this  is 
equal  to  the  heat  gained  by  the  water,  that  is  to  i  (15-7  —  12-3)  =  3-4,  that  is  :r  =  3-58. 

117.  fhe  specific  heat  of  sulphide  of  copper  is  0-1212,  and  that  of  sulphide  of  silver 
0-0746.  5  kilos,  of  a  mi.xture  of  these  two  bodies  at  40°,  when  immersed  in  6  kilos,  of 
water  at  7-669  degrees,  raises  its  temperature  to  lo®.  How  much  of  each  sulphuret  did 
the  mi.\ture  contain  ? 

The  weight  of  the  copper  sulphuret  =  2,  and  that  of  the  silver  sulphuret  3. 

118.  Into  a  mass  of  water  at  0°,  100  grammes  of  ice  at  —  12°  are  introduced  ;  a 
weight  of  7-2  grammes  of  water  at  0°  freezes  about  the  lump  immersed,  while  its 
temperatiu-e  rises  to  zero.  Required  the  specific  heat  of  ice.  Latent  heat  of  water 
79 ■2-  Ans.  0-4752. 

119.  Four  pounds  of  copper  filings  at  130°  are  placed  in  20  pounds  of  water  at  20° 
the  temperature  of  which  is  thereby  raised  2  degrees.  What  is  the  specific  heat,  c,  of 
copper?  Ans.  c  =  00926. 

120.  Two  pieces  of  metal  weighing  300  and  350  grammes,  heated  to  a  temperature 
X,  have  been  immersed,  the  former  in  3351 -6  grammes  of  water  at  10°  and  the  latter  in 
1935-4  grammes  at  the  same  temperature.  The  temperature  in  the  first  case  rises  to 
20'',  and  in  the  second  to  30°.  Required  the  original  temperature  and  the  specific  heat 
of  the  metal.  Ans.  x  the  temperature  =  1000°;  c  the  specific  heat  =  0-114. 

121.  In  what  proportions  must  a  kilogramme  of  water  at  50°  be  divided  in  order  that 
the  heat  which  one  portion  gives  out  in  cooling  to  ice  at  zero  may  be  sufficient  to  change 
the  other  into  steam  at  100°  ?  Ans.  x  =  0-8203. 

122.  Three  mixtures  are  formed  by  mixing  two  and  two  together,  equal  quantities 
of  ice,  salt,  and  water  at  0°.  Which  of  these  mixtures  will  have  the  highest  and  which 
the  lowest  temperature  ?  Ans.  The  mixture  of  ice  and  salt  will  produce  the  lowest 
temperature,  while  that  of  ice  and  water  will  produce  no  lowering  of  temperature. 

123.  In  25-45  kilogrammes  of  water  at  i2°-5  are  placed  6-17  kilos,  of  a  body  at  a 
temperature  of  80°  ;  the  mixture  acquires  the  temperature  i4°-i.  Required  the  specific 
heat  of  the  body. 

If  <:  is  the  specific  heat  required,  then  wc  {t  —  6)  represents  the  heat  lost  by  the  body 
in  coobng  from  80°  to  14°-!  ;  and  that  absorbed  by  the  water  in  rising  from  i2°-5  to 
i4'^-i  is  m'  (9  —  /).  These  two  values  are  equal.  Substituting  the  numbers,  we  have 
c  =  0-10014. 

124.  Equal  lengths  of  the  same  thin  wire  traversed  by  the  same  electrical  current  are 
placed  respectively  in  i  kilogramme  of  water  and  in  3  kilogrammes  of  mercury.  The 
water  is  raised  10'^  in  temperature,  by  how  much  will  the  mercury  be  raised  ? 

Ans.   100° -04. 

125.  How  many  cubic  feet  of  air  under  constant  pressure  are  heated  through  1°  C. 
by  one  thermal  unit  ?  Ans.  55*3  cubic  feet. 

126.  Given  two  pieces  of  metal,  one  x  weighing  2  kilos,  heated  to  80°,  and  the  other 
y  weighing  3  kilos,  and  at  the  temperature  50°.  To  determine  their  specific  heats 
they  are  immersed  in  a  kilogramme  of  water  at  lo'^,  which  is  thereby  raised  to  26°-3. 

The  experiment  is  repeated,  the  two  metals  being  at  the  temperature  100*  and  40° 
respectively,  and,  as  before,  they  are  placed  in  a  kilogramme  of  water  at  10°,  which 
this  time  is  raised  to  28°'4.     Required  the  specific  heats  of  the  two  metals. 

Ans.  x  =  0-115;^  =  0-0555. 

127.  For  high  temperatures  the  specific  heat  of  iron  is  0-1053  "•■  0000017  ^-  ^^^lat 
is  the  temperature  of  a  red-hot  iron  ball  weighing  a  kilogramme,  which,  plunged  in  16 


I054  Problems  and  Examples  in  Physics. 

kilogrammes  of  water,  raises  its  temperature  from  12°  to  24°  ?    What  was  the  tempe- 
rature of  the  iron? 

(o'io53  +  o'ooooiy/)  [t  —  24)   =   16  (24  —  12), 
or  '000017  t-  +   "1048892  t  —  2'5272   =    192  ; 

transposing  and  dividing  by  the  coefficient  of  f^,  we  get 
/-  +  6170  t  =   11442776, 
fi  +  6170  i  +  (3085)2  =  20960001  ; 
hence  i  +  3085  =  4578-3  nearly  ;    ,'.  /  =   1493-3. 

128.  A  kilogramme  of  the  vapour  of  alcohol  at  80°  passes  tlirough  a  copper  worm 
placed  in  10-8  kilogrammes  of  water  at  12°  the  temperature  of  wliich  is  thereby  raised 
to  36°.  The  copper  worm  and  copper  vessel  in  which  the  water  is  contained  weigh 
together  3  kilogrammes.     Required  the  latent  heat  of  alcohol  vapour.    Ans.  238-77. 

129.  Determine  the  temperature  of  combustion  of  charcoal  in  burning  to  form  car- 
bonic acid. 

We  know  from  chemistry  that  one  part  by  weight  of  carbon  in  burning  unites 
with  23  parts  by  weight  of  oxygen  to  form  3§  parts  by  weight  of  carbonic  acid. 
Again  the  number  of  thermal  units  produced  by  the  combustion  of  a  pound  of  charcoal 
is  8080  ;  the  whole  of  this  heat  is  contained  in  the  33  parts  of  carbonic  acid  produced, 
and  if  its  specific  heat  were  the  same  as  that  of  water,  its  temperature  would  be 

_^—  =  2204°  C. ;  but  since  the  specific  heat  of  carbonic  acid  is  0-2163  that  of  an  equal 
3§ 


weight  of  water,  the  temperature  will  be  -- — t    =  10189°  C. 


2204 
0-2163 

130.  A  glass  globe  measuring  60  cubic  centimetres  is  found  to  weigh  19-515 
grammes  when  filled  with  air  under  a  pressure  of  752-3™""  and  at  a  temperature  of  10°  C. 
Some  ether  is  introduced  and  vaporised  at  a  temperature  of  60°,  whereupon  the  flask 
is  sealed  while  quite  full  of  vapour,  the  pressure  being  753-4™".  Its  weight  is  now 
found  to  be  19-6786  grammes.  Required  the  density  of  the  ether  vapour  compared 
with  that  of  hydrogen.  Ans.  54-4. 

131.  Calculate  the  density  of  alcohol  vapour  as  compared  with  air  by  Gay-Lussac's 
method  from  the  following  data  : — 

Weight  of  alcohol  0-1047  grm.;  vol.  of  vajiour  at  110°  C.  =82-55  c.c.  '<  height  of 
mercury  above  the  level  in  the  bath,  98  mm.  ;  barometric  height,  752-3  mm.  ;  tempera- 
ture of  the  room,  15°  C.  Ans.  1-6. 

132.  In  a  determination  of  the  vapour  density  by  Gay-Lussac's  method,  0-1163 
gramme  of  substance  was  employed.  The  volume  observed  was  50-79  cc,  the  height 
of  the  mercury  above  the  level  of  that  in  the  bath  was  80-0™",  the  height  of  the  oil 
column  reduced  to  miUimetres  of  mercury  16-9;  the  temperature  215°  C,  and  the 
height  of  the  barometer  at  the  time  of  observation  755-5"'".  Required  the  specific 
gravity  of  the  vapour  as  compared  with  that  of  hydrogen.  Ans.  50-1. 

133.  Through  a  U-tube  containing  pumice  saturated  with  sulphuric  acid  a  cubic 
metre  of  air  at  15°  is  passed,  and  the  tube  is  found  to  weigh  3-95  gmmmes  more. 
Required  the  hygrometric  state  of  the  air. 

The  pressure  of  aqueous  vapour  at  15°  is  12-699  '<  hence  the  weight  of  a  cubic 
metre  of  aqueous  vapour  .saturated  at  15°  is    ^^93  x  12    99  x  5  _    jg.^^  grammes, 

(,4.  :p  760x8 

and  the  hygrometric  state  is  ^^^    =  0-309. 
12-79 

134.  The  quantity  of  water  given  out  by  the  lungs  and  skin  may  be  taken  at 
30  ounces  in  24  hours.  How  many  cubic  inches  of  air  already  half  saturated  at  10°  will 
be  fully  saturated  by  the  moisture  exlialed  from  the  above  two  sources  by  one  man  ? 
Tension  of  aqueous  vapour  at  10°  in  inches  =  0-361.  Pressure  of  tlie  atmosphere  =  30 
inches.  Arts.  6121  cubic  feet. 


Heat.  1 05  5 

135.  A  mass  of  air  extending  over  an  area  of  60,000  square  metres  to  a  height  of 
300  metres  has  the  dew  point  at  15°,  its  temperature  being  20°.  How  much  rain  will 
fall  if  the  temperature  sinks  to  10°  ? 

The  weight  of  vapour  condensed  from  one  cubic  metre  under  these  circumstances 
will  be  3'i435  grammes,  and  therefore  from  18,000,000  cubic  metres  it  will  be  56,583 
kilogrammes,  which  is  equal  to  a  rainfall  00943  mm.  in  depth. 

136.  When  3  cubic  metres  of  air  at  io°  and  5  cubic  metres  at  18°,  each  saturated 
with  aqueous  vapour  at  those  temperatures,  are  mi.xed  together,  is  any  water  precipi- 
tated ?    And  if  so,  how  much  ? 

The  weight  of  water  contained  in  the  two  masses  under  the  given  conditions  are 
respectively  28-i8and76'59grammes;  the  weight  required  to  saturate  the  mixture  at  the 
temperatureof  15°  is  10239  grammes,  and  therefore  2'38  grammes  will  be  precipitated. 

137.  The  temperature  of  the  air  at  sunset  being  10°,  what  must  be  the  lowest  hygro- 
metric  state,  in  order  that  dew  may  be  deposited,  it  being  assumed  that  in  conse- 
quence of  nocturnal  radiation  the  temperature  of  the  ground  is  7°  below  that  of  the  air  ? 

Ans.  The  hygrometric  state  must  be  at  least  o'62  of  total  saturation. 

138.  It  is  stated  as  a  practical  rule  that  when  the  tension  of  aqueous  vapour  present 
in  the  atmosphere,  as  indicated  by  the  dew  point,  is  equal  to  x  mm.  of  mercury,  the 
weight  of  water  present  in  a  cubic  metre  of  that  air  is  x  grammes.  What  is  the  error 
in  this  statement  for  a  pressure  of  10  mm.  and  the  temperature  15°  C.  ? 

Ans.  0-1J2  gr. 

139.  A  raindrop  falls  to  the  ground  from  a  height  of  a  mile  ;  by  how  much  would 
its  temperature  be  raised,  assuming  that  it  imparts  no  heat  to  the  air  or  to  the 
ground?  Arts.  30-8  C. 

140.  A  lead  bullet  falls  through  a  height  of  10  metres  ;  by  what  amount  will  its 
temperature  have  been  raised  when  it  reaches  the  ground,  if  all  the  heat  is  expended  in 
raising  the  temperature  of  the  bullet  ?  Ans.  07515°  C. 

141.  From  what  height  must  a  lead  bullet  fall  in  order  that  its  temperature  may 
beraised  n  degrees? — and  what  velocity  will  it  have  acquired?  It  is  assumed  that  all  the 
heat  is  expended  in  raising  the  temperature  of  the  bullet  ;  the  specific  heat  of  lead  is 
taken  at  00314,  and  Joule's  equivalent  in  metres  at  424. 

Ans.  13-31  X  n  metres  ;  v  =  288  's/n. 

142.  How  much  heat  is  disengaged  if  a  bullet  weighing  50  grammes  and  having 
a  velocity  of  50  metres  strikes  a  target  ? 

Ans.  Sufficient  to  raise  one  gramme  of  water  through  1^  C. 

143.  How  much  heat  is  produced  in  the  room  of  a  manufactory  in  which  i  2  horse- 
power of  the  motor  is  consumed  each  second  in  overcoming  the  resistance  of  friction  ? 

Ans.  A  quantity  sufficient  to  raise  102561  pounds  of  water  one  degree  Centigrade. 

144.  What  is  the  ratio  between  the  quantities  of  heat  which  are  respectively  pro- 
duced, when  a  bullet  weighing  50  grammes  and  having  a  velocity  of  500  metres, 
and  a  cannon-ball  weighing  40  kilogrammes  with  a  velocity  of  400  metres,  strike  a 
target?  Ans,   i  :  512. 

145.  The  specific  heat  of  lead  is  0031,  and  its  latent  heat  5-37.  What  is  the 
mechanical  equivalent  of  the  heat  necessary  to  raise  5  pounds  of  lead  from  a  tempera- 
ture of  270°  C:.  to  its  melting-point  335°  C,  and  then  to  melt  it  ? 

Ans.  51326  foot-pounds. 

146.  Assuming  that  the  temperature  at  which  heat  leaves  a  perfect  engine  is  16°  C, 
at  what  temperature  must  it  be  taken  in  in  order  to  obtain  a  theoretical  useful  effect  of  i  ? 

Ans.  i6os°  C. 

147.  Assuming  that  in  a  perfect  engine  heat  is  taken  in  at  a  temperature  of  144°, 
and  is  given  out  at  a  temperature  of  36^  :  what  is  the  greatest  theoretical  useful  effect? 

Ans.  o"259. 


1056  Problems  and  Examples  in  Physics. 


VI.    ON  LIGHT. 

148.  How  many  candles  are  required  to  produce  at  a  distance  of  2*5  metres,  the 
same  illuminating  effect  as  one  candle  at  a  distance  of  0*45  m.  ?  Ans.  31. 

149.  Two  sources  of  light  whose  intensities  are  as  i  :  2  are  two  metres  apart.  At 
what  position  is  a  space  between  them  equally  illuminated  ? 

Ans.  o'828  metre  from  the  less  intense  light. 

150.  A  candle  sends  its  rays  vertically  against  a  plane  surface.  When  the  candle  is 
removed  to  thrice  the  distance  and  the  surface  makes  an  angle  of  60°  with  the  original 

position,  what  is  the  ratio  of  the  illuminations  in  the  two  cases?  Atis.   i   :  - 

151.  An  observer,  whose  eye  is  6  feet  above  the  ground,  stands  at  a  distance  of  18 
feet  from  the  near  edge  of  a  still  pond,  and  sees  there  the  image  of  the  top  of  a  tree, 
the  base  of  which  is  at  a  distance  of  100  yards  from  the  glace  at  which  the  image  is 
formed.     Required  the  height  of  the  tree.  Aiis.  100  feet. 

152.  What  is  the  height  of  a  tower  which  casts  a  shadow  56  "4  m.  in  length  when  a 
vertical  rod  0*95  m.  in  height  produces  a  shadow  i'38  m.  in  length?  Ans.  38 "8. 

153.  A  minute  hole  is  made  in  the  shutter  of  a  dark  room,  and  at  a  distance  of 
2 "5  metres  a  screen  is  held.  What  is  the  size  of  the  image  of  a  tree  which  is  15 '3 
metre's  high  and  is  at  a  distance  of  40  metres?  Ans.  0-95625  metre. 

154.  What  is  the  length  of  the  shadow  of  a  tree  50  feet  high  when  the  sun  is  30° 
above  the  horizon?  What  when  it  is  45°,  and  60°?    Ans.  86-6  ;  50,  and  28-867  feet. 

155.  Under  what  \'isual  angle  does  a  line  of  30  feet  appear  at  a  distance  of  18  feet  ? 

Ans.  79°"36. 

156.  The  apparent  diameter  of  the  moon  amounts  to  31'  3".  What  is  its  real  dia- 
meter if  its  distance  from  the  earth  is  taken  at  239000  geographical  miles? 

Ans.  2166  geographical  miles. 

157.  For  an  ordinary  eye  an  object  is  visible  with  a  moderate  illumination  and  pure 
air  under  a  visual  angle  of  40  seconds.  At  what  distance,  therefore,  can  a  black  circle 
(6  inches  in  diameter)  be  seen  on  a  white  ground  ?  Ans.  2578  feet. 

158.  At  what  distance  from  a  circle  with  a  diameter  of  one  foot  is  the  visual  angle  a 
second?  ,  Ans.  206265  feet. 

159.  At  what  distance  would  a  circular  disc  i  inch  in  diameter,  of  the  same  bright- 
ness as  the  sun's  surface,  illuminate  a  given  object  to  the  same  extent  as  a  vertical  sun 
in  the  tropics,  the  light  absorbed  by  the  air  being  neglected  ? 

Ans.  Taking  the  sun's  angular  diameter  at  30',  j:  =   38  inches. 

160.  What  is  the  minimum  deviation  for  a  glass  prism  (//  =  i  -53),  whose  refracting 
angle  is  60°  ?  Ans.  39°  50'. 

161.  What  is  the  minimum  deviation  for  a  prism  of  the  same  substance  when  the 
refracting  angle  is  45°  ?  Ans.  63°  38'. 

162.  The  refracting  angle  of  a  prism  of  silicate  of  lead  has  been  found  by  measure- 
ment to  be  2r°T2,  and  the  minimum  deviation  to  be  24°-46.  Required  the  refractive 
index  of  the  substance.  Ans.  2-122. 

163.  Construct  the  path  of  a  ray  which  falls  on  an  e(|uiangular  crown-glass  prism 
at  an  angle  of  30°  ;  and  find  its  deviation.  Ans.  700-45. 

164.  What  are  the  angles  of  refraction  upon  a  ray  which  passes  from  air  into  glass 
at  an  angle  of  40°  ;  from  air  into  water  at  an  angle  of  65°  ;  and  from  air  into  diamond 
at  an  angle  of  80°?  Ans.  25O-20  ;  44^-5  ;  230-12. 

165.  The  focal  distance  of  a  concave  mirror  is  8  metres.  •  What  is  the  distance  of 
the  image  from  the  mirror  when  the  object  is  at  a  distance  of  12,  5,  and  7  metres 
respectively?  Ans.   24;   -   13-3  and  -  56. 


Light. 


1057 


166.  An  object  at  a  distance  of  10  feet  produces  a  distinct  image  at  a  distance  of  3 
feet.     What  is  the  focal  distance  of  the  mirror?  Ans.  2-3077  feet. 

167.  Required  the  focal  distance  of  a  crown-glass  meniscus,  the  radius  of  curvature 
of  the  concave  face  being  45  mm.,  and  that  of  the  convex  face  30  mm.  ;  the  inde.x  of 
refraction  being  1-5.  Ans.  f  =   180  mm. 

168.  What  is  the  principal  focal  distance  of  a  double-convex  lens  of  diamond,  the 
radius  of  curvature  of  each  of  whose  faces  is  4  mm.,  and  the  refractive  index  of  dia- 
mond 2  •487^.  Ans.  1-34  mm. 

169.  A  watch-glass  with  ground  edges,  the  curvature  of  which  was  4-5  cm.,  was 
tilled  with  water,  and  a  glass  plate  slid  over  it.  The  focus  of  the  plano-convex  lens 
thus  formed  was  found  to  be  i3'5  cm.     Required  the  refractive  index  of  the  water. 

Ans.  n   =   I '33. 

170.  What  is  the  focal  distance  of  a  double-convex  lens  when  the  distances  of  the 
image  and  object  are  respectively  5  and  36  centimetres?  Aus.  4-4  centimetres. 

171.  The  radii  of  cun'ature  of  a  double-convex  lens  of  crown  glass  are  six  and 
eight  inches.     What  is  the  focal  distance  ?  ^«^.  6'85  inches. 

172.  The  focal  distance  of  a  double-convex  lens  is  4  inches  ;  the  radius  of  cur- 
vature of  one  of  its  faces  is  3  inches.     What  is  that  of  the  second?   A?is.  6  inches. 

173.  The  radius  of  curvature  of  a  plano-convex  lens  is  12  inches.  Required  its 
focal  distance.  Ans.  24  inches. 

174.  If  the  focal  distance  of  a  double-convex  lens  is  i  centimetre,  at  what  distance 
must  a  luminous  object  be  placed  so  that  its  image  is  formed  at  2  centimetres  dis- 
tance from  the  lens  ?  A /is.  2  centimetres. 

175.  A  candle  at  a  distance  of  120  centimetres  from  a  lens  forms  an  image  on  the 
other  side  of  the  lens  at  a  distance  of  200  feet.  Required  the  nature  of  the  lens  and 
its  focal  distance.  A/es.  It  is  a  convex  lens,  and  its  focal  distance  is  75  cm. 

176.  A  plano-convex  lens  was  found  to  produce  at  a  distance  of  62  cm.  a  sharp 
image  of  an  infinitely  distant  object.  In  front  of  the  same  lens,  at  a  distance  of  84  cm., 
a  miUimetre  scale  was  placed,  and  a  sharp  image  was  formed  at  a  distance  of  250  cm. 
It  was  thus  found  that  10  millimetres  in  the  object  corresponded  to  29  in  the  image. 
From  these  observations  determine  the  focal  distance  of  the  lens.  Ans.  The  mean 
of  the  results  is  62 '4. 

177.  The  image  of  a  distant  tree  was  sharply  formed  at  a  distance  of  31  cm.  from 
the  centre  of  a  concave  mirror. 

In  another  case  the  image  of  an  object  18  mm.  in  length  at  a  distance  of  405  mm. 
from  the  mirror  was  formed  at  1350  mm.  from  the  mirror  and  had  a  length  of  61  mm. 
In  another  experiment  the  distances  of  object  and  image  and  the  size  of  the  image  were 
respectively  2200,  355,  and  3  mm. 

Deduce  from  these  several  data  the  focal  distance  of  the  mirror.     Ans.  31-2  ;  30-5. 

178.  What  must  be  the  radii  of  curvature  of  the  faces  of  a  lens  of  best  form  made 
of  glass  («  =  i'5)  if  its  focal  distance  is  to  be  6  inches?    Ans.  3-5  inches  and  21  inches. 

179.  A  diffraction  grating,  with  lines  o'o5  mm.  apart,  is  held  in  front  of  a  Bunsen's 
burner  in  which  common  salt  is  volatilised,  and  when  viewed  through  a  telescope  it  is 
found  that  the  angular  distances  of  the  first,  second,  fourth,  and  sixth  bright  bands  from 
the  central  one  are  respectively  o^  41',  1°  21',  2°  42',  and  4°  3'.  Required  the  wave- 
length of  sodium  light. 

The  formula  >.  =    '.1'"  r"^  where  K  is  the  wave-length,  <i>  the  angular  distance  of 
n 
any  bright  line  of  order  n  from  the  central  one,  gives  as  the  mean  of  the  4  observa- 
tions :  Ans.  o '00059088  mm. 


3Y 


1058  Problems  and  Examples  in  Physics. 


VII.     MAGNETISM  AND  FRICTIONAL  ELECTRICITY. 

180.  A  compass  needle  at  the  magnetic  equator  makes  15  oscillations  in  a  minute  ; 
how  many  will  it  make  in  a  place  where  the  horizontal  force  of  the  earth's  magnetism  is 

—  as  great?  Ans.  12. 

25 

181.  A  compass  needle  makes  9  oscillations  a  minute  under  the  influence  of  the 
earth's  magnetism  alone  ;  how  many  will  it  make  when  re-magnetised  so  as  to  be 
half  as  strong  again  as  before?  Ans.  11. 

182.  A  small  magnetic  needle  makes  100  oscillations  in  7  min.  42  sees,  under  the 
influence  of  the  earth's  force  only  ;  when  the  south  pole  of  a  long  bar  magnet  A  is 
placed  10  inches  north  of  it,  it  makes  100  oscillations  in  4  min.  3  sees.  ;  and  with  the 
south  pole  of  another  magnet  B  in  the  same  place,  it  makes  100  oscillations  in  4  min. 
48  sees.     What  are  the  relative  strengths  of  the  magnets  A  and  B  ? 

Ans.  A.  ==■  I '404  B. 

183.  On  a  table  where  the  earth's  magnetism  is  counteracted,  the  north  pole  of  a 
compass  needle  makes  20  oscillations  in  a  minute  under  the  attraction  of  a  south  pole 
4  inches  distant ;  how  many  will  it  make  when  the  south  pole  is  3  inches  distant  ? 

Ans.  26 '6. 

184.  If  the  oscillating  magnet  be  re-magnetised  so  as  to  be  twice  as  strong  as 
before,  how  many  oscillations  in  a  minute  will  it  make  in  the  two  positions  respectively? 

Ans.  28'28  and  50*27. 

185.  At  one  end  of  a  light  glass  thread,  carefully  balanced  so  as  to  oscillate  in  a 
vertical  plane,  is  a  pith  ball.  Over  this  and  in  contact  with  it  is  a  fixed  pith  ball  of  the 
same  dimensions.  Both  balls  being  charged  with  the  same  electricity  it  is  found  that 
to  keep  them  i'4  inch  apart,  a  weight  of  "9  mgr.  must  be  placed  at  the  free  end  of  the 
glass  thread.     What  weight  must  be  placed  there  to  keep  the  balls  i"05  inch  apart  ? 

Ans.  I  "6  mgr. 

186.  A  small  insulated  sphere  A  charged  with  the  quantity  of  +  electricity  2  is 
at  a  distance  of  25  mm.  from  a  second  similar  sphere  B  charged  with  the  quantity  5  ; 
the  latter  is  momentarily  touched  with  an  unelectrified  sphere  b,  of  the  same  size,  and 
the  distance  altered  to  20  mm.  What  is  the  ratio  of  the  repulsive  forces  in  the  two 
cases?  Atis.  32  :  25. 

187.  Two  insulated  spheres  A  and  B,  whose  diameters  are  respectively  as  7  :  10, 
have  equal  quantities  of  electricity  imparted  to  them.  In  what  ratio  are  their  electrical 
densities?  Ans.  100  :  49. 

188.  Two  such  spheres  whose  diameters  are  as  3  :  5  contain  respectively  the 
quantities  of  electricity  7  and  10,     In  what  ratio  are  their  densities  ?      Ans.  35  :  18. 

189.  Three  insulated  conducting  spheres,  A,  B,  and  C,  whose  radii  are  respectively 
I,  2,  and  3,  are  charged  with  electricity,  so  that  their  respective  potentials  are  as  3  :  2  :  i, 
and  are  then  connected  by  wires,  whose  capacity  may  be  neglected.  What  is  the  total 
quantity  and  potential  of  the  system?  Ans.  Q=io  ;  V=i'66. 

190.  Supposing  each  of  the  spheres  discharged  separately,  what  would  be  the  total 
work  they  would  produce,  as  compared  with  that  produced  by  the  discharge  of  the 
whole  system  ?  Ans.  30  :  25. 


Voltaic  Electricity.  io59 


VIII.     VOLTAIC  ELECTRICITY. 

191.  A  galvanometer  offering  no  appreciable  resistance  is  connected  by  short  thick 
wires  with  the  poles  of  a  cell,  and  deflects  20°.  By  how  much  will  it  be  deflected  if  two 
exactly  similar  cells  are  connected  with  the  first  side  by  side  ?  Aits.  47° '30. 

192.  By  how  much  if  the  three  cells  are  connected  in  series  ?  Ans.  20°. 

193.  Two  cells  each  of  i  ohm  resistance  are  connected  in  series  by  a  wire  the 
resistance  of  which  is  also  i  ohm.  If  each  of  these  when  connected  singly  by  short 
thick  wires  to  a  galvanometer  of  no  appreciable  resistance  deflects  it  25°,  how  much 
will  the  combination  deflect  it,  the  connections  being  made  by  short  thick  wires  ? 

Ans.  170-16. 
A  Siemens  unit  is  equal  to  the  resistance  of  a  column  of  pure  mercury  a  metre  in 
length  and  a  square  mm.  in  cross   section.     It  is  equal  to  o'9536ofan  ohm  or   ba 
unit;  or  a  ba  unit  equals  i'0485  Siemens  unit,  or  equals  a  column  of  mercury  i'0485 
metre  in  length  and  a  square  mm.  in  cross  section. 

194.  A  single  thermo-electric  couple  deflects  a  galvanometer  of  100  ohms  resist- 
ance 0°  30';  how  much  will  a  series  of  30  such  couples  deflect  it,  the  connections  being 
made  by  short  thick  wires?  Ans.  14° -40. 

195.  Suppose  a  sine  galvanometer  had  been  used  in  the  last  question,  and  the 
first  reading  had  been  o°"3o',  what  would  the  second  be?  Ans.  i5°'io. 

196.  The  internal  resistance  of  a  cell  is  half  an  ohm  ;  when  a  tangent  galvano- 
meter of  I  ohm  resistance  is  connected  with  it  by  short  thick  wires  it  is  deflected  15° ; 
by  how  much  will  it  be  deflected  if  for  one  of  the  thick  wires  a  thm  wire  of  i^  ohm 
resistance  is  substituted  ?  Ans.  'j^'yj. 

197.  What  will  be  the  deflection  if  each  of  the  wires  is  replaced  by  a  thin  wire  of 
i^  ohm  resistance  ?  Ans.  6°  10'. 

198.  A  cell  of  one-third  of  an  ohm  resistance  deflects  a  tangent  galvanometer  of 
unknown  resistance  45°,  the  connection  being  made  by  two  short  thick  wires.  If  a  wire 
of  3  ohms  resistance  be  substituted  for  one  of  the  short  wires  the  deflection  is  30°.  What 
is  the  resistance  of  the  galvanometer?  Ans.  375  ohms. 

199.  What  would  be  the  deflection  if  for  the  cell  in  the  last  question  three  exactly 
similar  cells  in  series  were  substituted  [a]  when  the  galvanometer  alone  is  in  circuit  ; 
{b)  when  both  the  galvanometer  and  the  thin  wire  are  in  circuit  ? 

Ans.  a  67° -48.  b  =  57° '41. 

200.  A  galvanometer  off'ering  no  sensible  resistance  is  deflected  50°  by  a  cell 
connected  with  it  by  short  thick  wires.  If  a  resistance  of  3  ohms  be  put  in  the  circuit, 
the  deflection  is  20°.     Find  the  internal  resistance  of  the  cell.  Ans.  1-32. 

201.  Suppose  the  results  in  the  last  question  were  produced  by  two  exactly  similar 
cells  in  series,  find  the  internal  resistance  of  each.  Ans.  o"659. 

202.  Suppose  they  were  produced  by  two  exactly  similar  cells  placed  side  by  side, 
find  the  internal  resistance  of  each.  Ans.  2-639. 

203.  If  the  resistance  of  130  yards  of  a  particular  copper  wire   ^    of  an  inch   in 

16 

diameter  is  an  ohm,  express  in  that  unit  the  resistance  of  8242  yards  of  cojiper  wire  ~ 

12 
of  an  inch  in  diameter.  Ans.  35-66. 

204.  One  form  of  fuse  for  firing  mines  by  voltaic  electricity  consists  of  a  platinum 
wire  f  of  an  inch  long,  of  which  a  yard  weighs  2  grains.  Required  its  resistance  in 
terms  of  a  Siemens  unit.  Specific  gravity  of  platinum  22,  and  its  conducting  power 
11-25  that  of  mercury.  Ans.  0-131. 

205.  Express  in  ohms  the  resistance  of  one  mile  of  copper  wire  ^  of  an  inch  in 
diameter  of  the  same  quality  as  that  referred  to  in  203.  Am,  0-8461. 

3  Y2 


io6o  Problems  and  Examples  in  Physics. 

206.  The  whole  resistance  of  a  copper  wire  going  round  the  earth  (24800  miles)  is 
221650  ohms.     Find  its  diameter  in  inches.  Aiis.  o'oj'^Z. 

207.  What  length  of  platinum  wire  o'Oj  of  an  inch  in  diameter  must  be  taken  to 
get  a  resistance  equal  to  i  ohm,  the  specific  resistance  of  platinum  being  taken  at  5'55 
that  of  copper  ?  ^«j.  14-25  metres. 

208.  660  yards  of  iron  wir^  o'o625  of  an  inch  in  diameter  have  the  same  electrical 
resistance  as  a  mile  of  copper  wire  0-0416  of  an  inch  in  diameter.  Find  the  specific 
resistance  of  iron,  that  of  copper  being  unity.  Ans.  6-15. 

209.  Ten  exactly  similar  cells  in  series  produce  a  deflection  of  45°  in  a  tangent 
galvanometer,  the  external  resistance  of  the  circuit  being  10  ohms.  If  arranged  so 
that  there  is  a  series  of  5  cells,  of  two  abreast,  a  deflection  of  33° '42  is  produced  ; 
find  the  internal  resistance  of  the  cell.  Ans.  J  ohm. 

210.  On  the  bobbins  of  the  new  Post  Office  pattern  of  a  single  needle  instrument 
are  coiled  225  yards  of  No.  35  copper  wire  0-0087  '"ch  in  diameter,  the  resistance  of 
which  is  about  92  ohms.  Required  the  conductmg  power  of  the  wire  in  terms  of 
mercury.  Afis.  46. 

211.  Ten  exactly  similar  cells  each  of  f  of  an  ohm  resistance  give,  when  arranged 
in  five  series  of  2  each,  a  deflection  of  z-f'-^j  ;  but  when  arranged  in  2  series  of  5  each 
a  deflection  of  33^-42.  Required  the  external  resistance  of  the  circuit  including  that 
of  the  galvanometer.  Aiis. -i^. 

1X1.  A  cell  in  a  certain  circuit  deflects  a  tangent  galvanometer  18°  26' ;  two  such 
cells  abreast  in  the  same  circuit  deflect  it  23°  57' ;  two  such  cells  in  series  in  the  same 
circuit  diminished  by  i  ohm  deflect  it  29° -2.  Find  the  internal  resistance  of  one  cell 
and  that  of  the  circuit.  A/is.  R  =  r  =  i-66. 

213.  What  is  the  best  arrangement  of  6  cells,  each  of  §  of  an  ohm  resistance, 
against  an  external  resistance  of  2  ohms  ? 

A71S.  Indifferent  whether  in  6  cells  of  i  each  or  in  3  cells  of  2  each. 

214.  What  is  the  best  arrangement  of  20  cells,  each  of  o-8  ohm  resistance,  against 
an  external  resistance  of  4  ohms  ?  Ans.  10  cells  of  2  each. 

215.  In  a  circuit  containing  a  galvanometer  and  a  voltameter,  the  current  which 
deflects  the  galvanometer  45°  produces  10-32  cubic  centimetres  of  mixed  gas  in  a 
minute.  The  electrodes  are  put  farther  apart,  and  the  deflection  is  now  20°  ;  find 
how  much  gas  is  now  produced  per  minute.  Ans.  ^I'TSl  cc 

216.  100  inches  of  copperwire  weighing  100  grains  has  a  resistance  of  0-1516  ohm. 
Required  the  resistance  of  50  inches  weighing  200  grains.  Ans.  0-01895. 

217.  A  knot  of  nearly  pure  copper  wire  weighing  one  pound  has  a  resistance  of 
1260  ohms  at  i5°-5  C. ;  what  is  the  resistance  at  the  same  temperature  of  a  knot  of  the 
same  quality  of  wire  weighing  125  pounds?  Ans.  9-6  ohms. 

218.  Find  the  length  in  yards  of  a  wire  of  the  same  diameter  and 'quality  as  the 
knot  pound  in  217,  having  a  resistance  of  2  ohms.  Ans.  3-38  yards. 

219.  Find  the  length  in  yards  of  a  wire  of  the  same  quality  and  total  resistance  as 
the  knot  pound  in  217,  but  of  three  times  the  diameter.  Ans.  18261  yards. 

220.  The  specific  gravity  of  platinum  is  2J  times  that  of  copper  ;  its  resistance  s| 
as  great.  What  length  of  platinum  wire  weighing  100  grains  has  the  same  resistance 
as  100  inches  of  copper  wire  also  weighing  100  grains?  Ans.  27. 

221.  A  cell  with  a  resistance  of  an  ohm  is  connected  by  very  short  tliick  wires  with  the 
binding  screws  of  a  tangent  galvanometer,  the  resistance  of  which  is  lialf  an  ohm,  and 
the  deflection  is  45°  ;  if  the  screws  of  tlie  galvanometer  be  also  connected  at  the  same  -" 
time  by  a  wire  of  i  ohm  resistance,  find  the  deflection.  Ans.  36°  52'. 

222.  The  resistance  of  a  galvanometer  is  half  an  ohm,  and  the  deflection  when 


Voltaic  Electricity.  1 06 1 

the  current  of  a  cell  is  passed  through  it  is  30°.     When  a  wire  of  2  ohms  resistance  is 
introduced  into  the  circuit  the  deflection  is  15°  ;  find  the  internal  resistance  of  the  cell. 

Ans.  1-23. 

223.  When  the  current  of  a  cell,  the  resistance  of  which  is  f  of  an  ohm,  is  passed 
through  a  galvanometer  connected  with  it  by  very  short  thick  wires,  the  deflection  is 
45° ;  when  the  binding  screws  are  also  connected  by  a  shunt  having  a  resistance  of  i 
the  deflection  is  33° "42.     Find  the  resistance  of  the  galvanometer.  Ans.  2. 

224.  A  cell  whose  internal  resistance  is  2  ohms  has  its  copper  pole  connected  with 
the  binding  screw  A  of  a  galvanometer  formed  of  a  thick  band  of  copper.  From 
the  other  screw  B  a  wire  of  20  ohms  resistance  passes  to  the  zinc  pole,  and  the  deflection 
read  off  is  7° -8.  Find  the  deflection  when  B  is  at  the  same  time  connected  with  the 
zinc  pole  by  a  second  wire  of  30  ohms  resistance.  Ans.  ii°-8'. 

225.  What  would  be  the  deflection  in  212  if  the  second  wire  instead  of  passing 
from  B  to  the  zinc  pole  passed  directly  from  the  zinc  pole  to  the  copper  pole  ? 

Ans.  2*437. 

226.  A  Leclanch^  cell  deflects  a  galvanometer  30°  when  200  ohms  resistance  are 
introduced  into  the  circuit,  15°  when  570  ohms  are  .introduced ;  a  standard  Daniell 
cell  deflects  it  30°  when  100  ohms  are  in  circuit,  and  15°  when  250  additional  ohms  are 
introduced.  Required  the  electromotive  force  of  the  Leclanch^  in  terms  of  that  of  the 
Daniell.  Ans.  1-48. 

227.  A  Bunsen  and  a  Daniell  cell  are  placed  in  the  same  circuit  in  the  first  case 
so  that  the  carbon  of  the  first  is  united  to  the  zinc  of  the  Daniell ;  and  in  the  second 
case  so  that  their  currents  oppose  each  other.  The  currents  are  respectively  30°'2, 
and  in  the  second  10° '6.  Required  the  electromotive  force  of  the  Bunsen  in  terms  of 
the  Daniell.  Ans.  i^Sg. 

228.  A  telegraph  line  constructed  of  copper  wire,  a  kilometre  of  which  weighs  30*5 
kilogrammes,  is  to  be  replaced  by  iron  wire  a  kilometre  of  which  weighs  135 '6  kilo- 
grammes. In  what  ratio  does  the  resistance  alter?  Ans.  The  resistance  of  the  iron 
wire  will  be  i*i8  times  that  of  the  copper  wire  for  which  it  is  substituted. 

229.  A  telegraph  line  which  has  previously  consisted  of  copper  wire  weighing  30*5 
kilogrammes  to  the  kilometre  is  to  be  replaced  by  an  iron  wire  of  the  same  diameter 
which  shall  offer  the  same  resistance.  What  must  be  the  section  of  the  latter,  and 
what  its  weight  per  kilometre? 

Ans.  The  section  of  the  copper  wire  is  3*4357  sq.  mm.,  that  of  the  iron  by  which 
it  is  replaced  is  206  sq.  mm.,  and  its  weight  per  kilometre  is  160  "4  kilogrammes. 

230.  When  the  poles  of  a  voltaic  cell  are  connected  by  a  conductor  of  resist- 
ance I,  a  current  of  strength  i'32  is  produced  ;  and  when  they  are  connected  by  a 
conductor  of  resistance  5  the  strength  of  the  current  is  0*33.  Find  from  these  data 
the  internal  resistance  and  the  electromotive  force  of  the  cell.     Ahs.  R  =  \  £  =  176. 

231.  A  silver  wire  is  joined  end  to  end  to  an  iron  wire  of  the  same  length,  but  of 
double  the  diameter,  and  six  times  the  specific  resistance  ;  the  other  ends  are  joined 
to  the  battery,  the  current  of  which  is  transmitted  for  five  minutes,  during  which  time 
a  total  quantity  of  45  units  of  heat  is  generated  in  the  two  wires.  How  is  it  shared 
between  them  ?  Ans.  Ag :  Fe=  18  :  27. 

232.  A  window  casement  of  iron  faces  the  south,  and  the  hinges  which  support  it 
are  on  the  east.  What  electrical  phenomena  are  observed  {a)  when  the  window  is 
opened,  and  {b)  when  it  is  closed  ? 

233.  Two  points  135°  apart  in  a  uniform  circular  conducting  ring  are  connected 
with  the  opposite  poles  of  a  voltaic  battery.  Compare  the  strength  of  the  current  in 
the  two  portions  of  the  ring. 

234.  A  mile  of  cable  with  a  resistance  of  3 '59  ohms  was  put  in  water,  with  the 
end  B  insulated  ;  its  core  having  been  pricked  with  a  needle  the  resistance  tested  from 
the  end  A  was  found  to  be  2 'Si  ohms.  A  being  insulated,  a  test  from  B  showed  the 
resistance  to  be  276.     Required  the  distance  from  A  to  the  injured  spot. 

Ans.  867  yards. 


INDEX. 


(THE    NUMBERS    KKFER   TO   TIIK   ARTICLES.) 


AV.K 

ABEL'S  electric  fuse,  794 
Aberration,        chromatic,       5S3  ; 
spherical,  533 

Absolute  electrical  units,  963 

Absolute  expansion  of  mercury,  322 

Absolute  measure  of  electrical  resistance, 
954  ;  temperature,  496 

Absorbent  power  of  aqueous  vapour,  985 

Absorbing  power,  424 

Absorption,  electrical,  74S  ;  of  gases  by 
solids,  193  ;  of  gases  l3y  liquids,  189  ; 
of  heat  by  liquids,  434  ;  by  vapours, 
435  ;  heat  produced  by,  4S2 

Acceleration  of  a  force,  27,  6ia,  77 

Accidental  haloes,  627  ;  images,  626  ; 
magnetic  variations,  694 

Accommodation  (of  the  eye),  620 

Accumulator,  hydraulic,  151 

Accumulators,  765 

Achromatism,  584  ;  of  the  microscope, 
592 

Achromatopsy,  632 

Acidometer,  126 

Acierage,  857 

Aclinic  lines,  698 

Acoustics,  220-287 

Acoustic  foci,  237  ;  attraction  and  repul- 
sion, 290 

Actinic  rays,  433,  573 

Action  and  reaction,  39 

Adhesion,  86 

Aerial  meteors,  975  ;  perspective,  618 

Aerolites,  480 

.^sculine,  582 

Affinity,  85 

After  action,  elastic,  91 

Agents,  6 

Agonic  line,  692 

Air,  aspirating  action  of  currents  of,  207  ; 
causes  which  modify  temperature  of, 
974,  1006;  heating  by,  491  ;  thermo- 
meter, 334;  resistance  of,  48;  trap, 
167 


ANN 

Air-balloons,  196  ;  chamber,  217 
Air-brake,  209  ;  pump,  200,  467  ;  Bian- 
chi's,  203  ;  condensing,  209;  Deleuil's, 

204  ;     gauges,    2Ci  ;     rarefaction    in, 
200  ;    receiver    of,    200  ;     Sprengel's, 

205  ;  uses  of,  2IO 
Ajutage,  146 
Alarum,  electric,  S97 
Alcarrazas,  373 

Alcoholic  value  of  wines,  378 

Alcoholometer,  128;  Gay-Lussac's,  1285 
centesimal,  128 

Alcohol  thermometer,  306 

Allotropic  states,  457 

Alloys,  340 

Alternate  currents,  914 

Amalgam,  754 

Amalgamated  zinc,  816 

Amber,  723 

Amici's  camera  lucida,  603 

Ampere,  814 

Ampere's  inemoria  tcclinica,  S20  ;  theory 
of  magnetism,  879  ; 

Amplitude  of  vibration,  55 

Analogous  pole,  732 

Analyser,  656 

Analysis,  spectral,  575  ;  of  solar  light,  430 

Anamorphoses,  534 

Anelectrics,  724,  748 

Anelectrotonus,  828 

Anemometer,  974,  975 

Aneroid  barometer,  164,  187 

Angle  of  deviation,  544,  1002  ;  critical 
540;. optic,  617;  of  polarisation,  654 
of  reflection  and  incidence,  511,  536 
of  repose,  39 ;  of  refraction,  536 
visual,  617 

Angular  currents,  laws  of,  860  ;  velocity, 

53 

Animal  heat,  485 
Anione,  842 
Annealing,  90 
Annual  variations,  693 


1064 


Index. 


ANO 

Anode,  842 

Anticyclone,  980 

Antilogous  pole,  732 

Anvil,  922 

Aperiodic  galvanometer,  821 

Aperture  of  a  lens,  558 

Aplanatic  lenses,  558 

Aqueous  humour,  61 2 

Aqueous  vapour,  its  influence  on  climate, 
985  ;  tension  of,  355-361 

Arago's  experiment,  181 

Arbor  Diana;,  853  ;  Saturni,  853 

Arc  lamps,  838 

Arc  of  vibration,  55  ;  voltaic,  833 

Archimedes'  principle,  113;  applied  to 
gases,  195 

Area,  unit  of,  22 

Armatures,  718  ;  drums,  918  ;  Siemens', 
914 

Arms  of  levers,  40 

Armstrong's  hydro-electric  machine,  758 

Artesian  wells,  ill 

Artificial  magnets,  680 

Ascension,  right,  600 

Ascent  of  liquids  in  capillary  tubes,  132  ; 
between  surfaces,  133 

Aspirating  action  of  air  currents,  207 

Astatic  currents,  873  ;  needle  and  system, 
700  ;  circuits,  873 

Astronomical  telescope,  595 

Athermancy,  434 

Atmolysis,  190 

Atmosphere,  its  composition,  157;  crush- 
ing force  of,  159  ;  amount  of,  determi- 
nation of,  163  ;  electricity  in  the,  993, 

994  ;  moisture  of,  400 
Atmospheric   electricity,  causes  of,   994, 

995  ;   pressure,  158,  163,  972 
Atomic  heat,  458  ;  weight  deduced  from 

specific  heal,  458 

Atoms,  3 

Attraction,  capillary,  134  ;  and  repulsion 
produced  by  capillarity,  134;  mole- 
cular, 83  ;  universal,  66 

Attractions,  magnetic,  laws  of,  703  ; 
electrical,  laws  of,  734 

Atwood's  machine,  77 

Audiometer,  932 

Aura,  764 

Aurora  Ijorealis,  694,  1002 

Aurum  musivum,  754 

Austral  pole,  689 

Avoirdupois,  23 

Axis  of  crystal,  640  ;  electric,  732  ; 
lenses,  55 1  ;  optic,  617  ;  of  a  magnet, 
681  ;  of  oscillation,  79 

Azimuthal  circle,  695 


BAD  conductors,  404 
Bain's  electro-chemical  telegraph,. 
895 

Balance,  71  ;  beam  of,  72  ;  compensat- 
ing, 320  ;  delicacy  of,  73  ;  hydrostatic, 
120 ;  induction,  932  ;  knife-edge  of, 
71;  pendulum,  320;  physical  and 
chemical,  74 ;  spring,  88  ;  torsion,  89, 
704,  733 

Ballistic  galvanometer,  821  ;  pendulum, 
81 

Balloons,  195-199  ;  construction  and 
management  of,  197  ;  Coxwell's,  96  j 
Mcntgolfier,  196 ;  weight  raised  by, 
199 

Bands  of  spectrum,  576 

Barker's  mill,  149 

Barometers,  164;  aneroid,  187;  Bun- 
ten's,  167;  cistern,  165;  corrections 
in,  170  ;  determination  of  heights  by, 
178;  differential,  186;  fixed,  175; 
Fortin's,  166  ;  Gay-Lussac's,  167  ; 
glycerine,  176;  precautions  with,  168; 
wheel,  174;  variations  of  height  of, 
171 

Barometric  formula,  Laplace's,  178  ; 
gradients,  979 ;  height  of,  corrected 
for  heat,  327  ;  manometer,  186  ;  va- 
riations, 172 

Baroscope,  195 

Bassoon,  272 

Battery,  Bunsen's,  Sio  ;  Callan's,  810; 
chemical  efi'ects  of,  S41  ;  Daniell's, 
808  ;  electric,  774  ;  floating,  865  ; 
gas,  850  ;  gravity,  S12  ;  Grove's,  809  ; 
Leclanche's,  844  ;  Leyden,  constant, 
807  ;  charged  by  coil,  923  ;  local, 
877  ;  luminous  effects,  833  ;  magnetic, 
717  ;  measurement  of  charge,  777  ; 
mechanical  oflects  of,  839  ;  Menotti's, 
812  ;  Marie  Davy's,  S12  ;  postal,  877  ; 
secondary,  849  ;  Smee's,  811  ;  sulphate 
of  mercury,  S12  ;  tension  of,  815  ; 
thermo-electric,  944  ;  voltaic,  804, 
S05  ;  Walker's,  811  ;  \Vollaston's,  805 

Beam  of  a  balance,  72  ;  of  a  steam- 
engine,  467 

Beats,  262 

Bcaume's  hydrometer,  127 

Becquerel's  pyrometer,  949  ;  thermo- 
electric battery,  944 ;  electrical  ther- 
mometer, 948 

Bell  of  a  trumpet,  237 

Bell's  telephone,  930  ;  photophone,  936 

Bellows,  243  ;  hydrostatic,  lOl ;  water, 
207 

Bennett's  clecUoscopc,  751 


Index. 


1065 


BER 

Berthollet's  experiment,  188 

Berlin's  commutator,  870 

Bianchi's  air-pump,  203 

Biaxial  crystals,  double  refraction  in, 
644 ;  optic  axis  of,  644 ;  rings  in, 
667 

Bifurcation,  639 

Binnacle,  697 

Binocular  vision,  621 

Biot's  apparatus,  676 

Biquartz,  677 

Black's  experiments  on  latent  heat,  461 

Bladder,  swimming,  liS 

Block  and  tackle,  45 

Blood-globules,  15 

Blue  cloud,  986 

Bodies,  properties  of,  7,  122 

Bohnenberger's  electroscope,  818 

Boiler,  466 

Boiling,  350 ;  by  cooling,  367  ;  laws  of, 
363 

Boiling-point,  influence  of  dissolved  sub- 
stances on,  365  ;  of  nature  of  vessel, 
366  ;  of  pressure  on,  367  ;  in  a  ther- 
mometer, 302 ;  measurement  of  heights 
by,  369 

Bolometer,  960 

Borda's  method,  75 

Boreal  pole,  689 

Bottomley's  experiment,  990 

Boutigny's  experiments,  3S5 

Boxes,  resistance,  753 

Boyle's  law,  1S0-182 

Boys's  threads,  89 

Brake,  friction,  473 ;  air,  209 

Bramah's  hydraulic  press,  108 

Branch  currents,  961 

Breaking  weight,  91 

Breezes,  land  and  sea,  977 

Breguet's  thermometer,  309 ;  magneto- 
electrical  machine,  912 

Bridge,  Wheatstone's,  956 

British  imperial  yard,  22  ;  and  French 
system  of  weights  and  measures,  125 

Brittle  bodies,  93 

Browning's  regulator,  836 

Brush  discharge,  787  ;  dynamo-electrical 
machine,  919 

Bulbs,  specific  gravity,  123 

Bull's  eye,  591 

Bunsen's  filter-pump,  206  ;  battery,  810; 
burner,  576  ;  ice  calorimeter,  452  ; 
photometer,  509 

Bunsen  and  KirchhofPs  researches,  578 

Bunten's  barometer,  167 

Buoyancy  of  liquids,  100 

Burning  mirrors,  420 


CHE 

CABLE  telegraph,  886 
Caesium,  578 

Cagniard-Latour's  syren,  242 ;  experi- 
ments on  formation  of  vapour,  370 

Cailletet's  and  Pictet's  researches,  382 

Calibration.  298 

Callans  battery,  81 1 

Calorcscence,  433 

Caloric,  448 

Calorific  effects  of  electrical  discharge, 
790 ;  of  current  electricity,  829,  830  ; 
of  Ruhmkorff's  coil,  923  ;  of  the  spec- 
trum, 573 

Calorimeter,  450;  Bunsen's  ice,  451; 
Black's,  451 ;  Favre  and  Silbermann's, 
463  ;  Lavoisier  and  Laplace's,  45 1 

Calorimetry,  447 

Camera  lucida,  594  ;  Amici's,  603  ;  ob- 
scura,  602;  Porta's  obscura,  514  ^ 
Wollaston's,  603 

Campani's  eyepiece,  592  ^ 

Capacity,  error  of  barometric,  165  ;  elec-  y 

trical,  739  ;  specific  inductive,  748 

■Capillarity,  131  ;  attraction  and  repulsion 
produced  by,  134  ;  correction  for,  169 

Capillary  phenomena,  131-138;  electro- 
meter, 840 ;  tubes,  132 ;  ascent  and 
depression  in,  132;  between  parallel 
or  inclined  surfaces,  133 

Capsule,  of  the  eye,  612 

Carcel  lamp,  849 

Cardan's  suspension,  166 

Carre's  mode  of  freezing,  374  ;  dielectri- 
cal  machine,  760 

Carriage  lamps,  535 

Carrier,  electrical,  735 

Cartesian  diver,  116 

Cascade,  charging  by,  776 

Cataracts  of  a  .^team  engine,  467 

Cathetometer,  88 

Catoptric  telescopes,  598 

Caustics,  533,  534 

Celsius'  scale,  303 

Centesimal  alcoholometer,  128 

Centigrade  scale,  303 

Centimetre,  125 

Centre,  optical,  555  ;  of  gravity,  68  ;  of 
parallel   forces,   37  ;  of  pressure,    102 

Centrifugal  force,  53 

Centripetal  force,  53 

Charge  of  a  Leyden  jar,  penetration  of> 
773  ;  measurement  of,  787  ;  laws  of, 
778  ;  residual,  773 

Charging  by  cascade,  776 

Chatterlon's  compound,  886 

Chemical  affinity,  85  ;  combination,  483  ; 
effects  of  the  battery,  793  ;  decomposi- 


io66 


Index. 


CHE 

tion,  841  ;  of  electrical  discharge,  793; 
of  voltaic  currents,  821  ;  of  Ruhmkorff's 
coil,  923  ;  harmonicon,  278  ;  hygro- 
meter, 394;  properties  of  the  spectrum, 

573 

Chemistry,  i 

Chevallier's  microscope,  591 

Cheval-vapeur,  473 

Children's  experiment,  830 

Chimes,  electrical,  763 

Chimney,  487 

Chladni's  experiments,  284 

Chlorophane,  635 

Chlorophyl,  580 

Chords,  major  and  minor,  247  ;  physical 
constitution  of,  264  ;  tones  dominant 
and  subdominant,  248  ;  vocal,  259 

Choroid,  612 

Chromatic  scale,  250  ;  aberration,  583 

Chromium,  magnetic  limit  of,  720 

Ciliary  processes,  612 

Circle,  azimuthal,  695 

Circular  polarisation,  669 

Cirrocumulus,  981 

(Jirrostratus,  981 

Cirrus,  981 

Cistern  barometer,  165 

Clamond's  thermo-electric  battery,  945 

Clarionet,  272 

Clarke's  magneto-electrical  machine,  911 

Cleavage,  electricity  produced  by,  731 

Clef,  252 

Clement  and  Desorme's  experiment,  207 

Climate,  1008;  constant,  1008;  influence 
of  aqueous  vapour  on,  985 

Climatology,  1004-1011 

Clocks,  81  ;  crutch  of,  81  ;  electrical,  898 

Clouds,  981  ;  electricity  of,  996;  forma- 
tion of,  982 

Coatings,  769  ;  Lcydcn  jar  with  movalile, 
771 

Cobalt,  720 

Coercive  force,  687 

Coefficients  of  linear  expansion,  313,  315, 
316;  conductivity,  404,  405;  I'oisson's, 
88 

(.'ohesion,  84 

(^oil,  primary,  879  ;  Ruhmkorff's,  914  ; 
effects  produced  by,  914  ;  resistance, 
953  ;  secondary,  879 

Cold,  apparent  reflection  of,  422  ;  pro- 
duced by  evaporation,  373  ;  ex])ansion 
of  gases,  494;  by  nocturnal  radiation, 
495  ;  sources  of,  493 

Colladon  and  Sturm's  exjicrimcnts,  234 

Collecting  plate,  779 

Collimation,  595 


CON 

Collision  of  bodies,  58 

Colloids,  140 

Coloration  produced  by  rotatory  polari- 
sation, 675 

Colour,  7  ;  of  bodies,  592  ;  of  heat,  436; 
of  thin  plates,  650 

Colour  discs,  570 

Colour  disease,  632 

Co'ours,  contrast  of,  627  ;  mixed,  570 ; 
simple,  566  ;  complementary,  570  ; 
produced  by  polarised  light,  662-668  ; 
by  compressed  glass,  668 

Combustion,  483  ;  heat  disengaged  dur- 
ing, 484 

Comma,  musical,  248 

Common  reservoir,  726 

Communicator,  886 

Commutator,  887,  S89,  912,  922  ;  Ber- 
tin's,  870 

Compass,  correction  of  errors,  696  ;  de- 
clination, 695  ;  mariner's,  697  ;  incli- 
nation, 698  ;  sine,  824 ;  tangent,  823 

Compensating  cube,  438 

Comjicnsation,  method  of  magnets,  719; 
pendulum,  320  ;  balance,  320 ;  grid- 
iron, 320;  strips,  320 

Complementary  colours,  570 

Component  forces,  32 

Composition  of  velocities,  52 

Compound-wound  microscope,  591  ;  dy- 
namo, 919^ 

Comjiressed  glass,  colours  produced  by, 
668 

Compressibility,  7,  16  ;  of  gases,  154, 
180  ;  of  liiiuids,  97 

Concave  mirrors,  419,  528 

Concert  pitch,  251 

Concordant  tones,  247 

Condensatii)!!  of  vapours,  375 

Condensed  gas,  193,  209;  wave,  225 

Condenser  of  an  engine,  467,  759,  765  ; 
electrical  limits  to  charge  of,  768  ;  of 
Ruhmkorff's  coil,  922  ;  Liebig's,  377 

Condensing  engine,  471  ;  air-pump,  209  ; 
force,  calculation  of,  767  ;  electro- 
scope, 779  ;  plate,  799  ;  hygrometers, 
395 

Conduction  of  heat,  403  ;  of  electricity, 
725  ;  lightning,  I(X)I 

Conducli\ity  of  bodies  for  heat,  404  ;  co- 
efficient of,  404,  405  ;  of  gases,  409 ; 
of  li(|uiils,  407  ;  for  electricity,  955,  958 

Con<luclors,  725  ;  equivalent,  956  ;  good 
and  bad,  404;  lightning,  looi  ;  prime, 
753  ;  resistance  of,  952 

Congelation,  343 

Conjugate  mirrors,  420 ;  focus,  525,  552 


Index. 


1067 


CON 

Connecting  rod,  467 

Conservation  of  energy,  65 

Constant  currents,  807 

Contact  theory  of  electricity,  799 

Contractile  force,  319 

Contraction,  coefficient  of,  S8 

Convection,  40S  ;  currents,  445  ;  electro- 
lytic, 832 

Convex  meniscus,  131  ;  mirrors,  526,  529 

Cooling,  method  of,  455  ;  Newton's  law 
of,  416 

Corliss  engine,  47 1 

Cornea,  612 

Cornish  engine,  467 

Corona,  981 

Corpuscular  theory,  499 

Corti's  fibres,  260 

Cosine,  law  of  the,  414,  508 

Coulomb,  964 

Coulomb's  law,  703 

Couple,  36  ;  terrestrial  magnetic,  690 ; 
voltaic,  801  ;  thermo-electric,  942 

Couronne  des  tasses,  805 

Cowper's  writing  telegraph,  890 

Coxwell's  balloon,  196 

Crab,  42 

Critical  angle,  540  ;  current,  920  ;  tem- 
perature, 370 

Crookes's  radiometer,  445  ;  vacuum,  380, 
446;  experiments,  927 

Cross-wire,  595 

Crutch  of  a  clock.  Si 

Cryohydrate,  348 

Cryophorus,  373 

Crystal,  hemihedral,  732 

Crj-stalline,  612 

Crj'stallisation,  344 

Cr)-stalloids,  140 

Crystals,  343;  expansion  of,  315;  doubly 
refracting,  639,  652,  663  ;  uniaxial, 
642  ;  positive  and  negative,  643 

Cube,  Leslie's,  423 

Cumulostratus,  980 

Cumulus,  980 

Current  electricity,  800 

Currents,  action  on  currents,  862,  863  ; 
action    of    magnets,    866  ;    action    of 
earth  on,  872,   873  ;   action    on    sole- 
noids, S74,  879  ;   constant,    807  ;   di- 
vided,   961  ;    detection   and   measure- 
ment of  voltaic,  819;  diaphragm,  839; 
direct    and    inverse,    900,   901,    908; 
effects  of  enfeeblement  of,  806  ;  energj'  j 
of,  920  ;  extra,  907,  908  ;  of  inclina-   ; 
tion,   967  ;    intensity  of,  825  ;    indue-   1 
tion  by,  900  ;    laws  of  angular,   860  ; 
laws    of   sinuous,     861  ;    local,    816 ;   | 


magnetisation  by,  871  ;  motion  and 
sounds  produced  by,  884  ;  muscular, 
966  ;  in  active  muscle,  969  ;  in  nerve, 
970 ;  rotation  of  magnets  by,  856 ; 
secondary,  806  ;  terrestrial,  8S0 ;  ther- 
mal effects  of,  830,  831 ;  transmissions 
by,  844 

Curvature  of  liquid  surfaces,  135  ;  in- 
fluence of,  on  capillary  phenomena,  136 

Curves,  magnetic,  704 

Cushions,  753 

Cyanogen  gas,  380 

Cyclones,  979 

Cylinder,  467  ;  electrical  machine,  757 

Cymbal,  282 


DAGUERREOTYPE,  608 
Daltonism,  632 

Dalton's  laws  on  gases  and  vapours,  383; 
method  of  determining  the  tension  of 
aqueous  vapour,  356 

Damper,  279,  905 

Daniell's  battery,  808  ;  hygrometer,  396; 
pyrometer,  311 

Dark  lines  of  the  spectrum,  574 ;  of 
solar  spectrum,  579 

Davy's  battery,  812 

Davy's  experiment,  421 

Day,  apparent,  21 

Dead-beat  galvanometer,  821 ;  -point,  470 

Decimetre,  24,  125 

Declination  compass,  695  ;  errors  of, 
696;  magnetic,  691  ;  of  needle,  691  ; 
variations  in,  691  ;  of  a  star,  600 

Decomposition,  chemical,  841  ;  of  white 
ligli^  564  ;  of  salts,  843 

Deilagrator,  Hare's,  805,  829 

Degrees  of  a  thermometer,  303 

De  la  Rive's  floating  battery,  867  ;  ex- 
periments, 928 

De  la  Rue  and  Midler's  experiments,  926 

Deleuil's  air-pump,  204 

Delezenne's  circle,  906 

Delicacy  of  balance,  73  ;  of  thermo- 
meter, 307 

Densimeter,  130 

Density,  24  ;  of  the  earth,  67  ;  electric, 
736;  gravimetrical,  185  ;  oi  gases,  335- 
337;  maximum  of  water,  330 ;  of- 
vapours,  Gay-Lussac's  method,  386  ; 
Dumas's,  388  ;  Deville  and  Troost's, 
388  ;  Ilofmann's,  387 

Depolarisation,  665 

Depolarising  plate,  663 

Depression  of  liquids  in  capillary  tube, 
132  ;  between  surfaces,  133 


io68 


Index. 


Derived  currents,  961 
Descartes'  laws  of  refraction,  537 
Despretz's  experiment,  404 
Developer,  609 
Deviation,  angle  of,  544 
Deville  and  Troost's  method,  388 
Dew,  987 ;  point,  395 
Diabetic  urine,  analysis  of,  678 
Dial  telegraphs,  888 
Dialyser,  140 
Dialysis,  140 
Diamagnetism,  938 
Diapason,  257 
Diaphanous  bodies,  500 
Diaphragm,  591  ;  currents,  839 
Diathermancy,  434 
Diatonic  scale,  248 
Dielectrical  machine,  Carre's,  760 
Dielectric  polarisation,  747 
Dielectrics,  748 
Differential  barometer,  186 
Differential  galvanometer,  821  ;  tl-ermo- 
meter,    Leslie's,    j08  ;    Matthiessen's, 
308  ;  tone,  263 
Diffraction,  503  ;    spectra,  648  ;  fringes, 

646 
Diffusion  of  heat,  437;  of  liquids,  140 
Digester,  Papin's,  371 
Dimensions  of  units,  6i« 
Dionoea  muscipula,  827 
Dioptric  telescopes,  598 
Diosmose,  137 
Diplopy,  631 
Dip,  magnetic,  698 
Dipping  needle,  698 
Direct  Vision  Spectroscope,  511 
Disc,  Newton's,   567  ;  Maxwell's  colour, 
570 

Discharge,  electrical,  766  ;  effects  of  the, 
783  ;  lateral,  looi  ;  silent,  793,  slow 
and  instantaneous,  766  ;  universal,  775 

Discharging  rod,  766 

Dispersion,  544  ;  abnormal,  581 

Dispersive  power,  564 

Displacement,  46 

Disruptive  cischarge,  783 

Dissipation  of  energy,  498 

Dissociation,  389,  484,  845 

Dissolving  views,  604 

Distance,  estimation  of,  618;  adaptation 
of  eye  to,  620 

Distillation,  376 

Distrilaition  of  free  electricity,  735  ;  of 
magnetism,  722 ;  of  temperature, 
1009  ;  of  land  and  water,  loi  I 

Diurnal  variations,  693 

Diver,  Cartesian,  116 


EDE 

Divided  currents,  961 

Dividing  machine,  1 1 

Divisibility,  7,  12 

Dobereiner's  lamp,  482 

Dominant  chords,  248 

Doppler's  principle,  233 

Double-action  steam-engine,  467,  468 

Double  refraction,  652 

Double-weighing,  75 

Doublet,  Wollaston,  586 

Dove's  law  of  storms,  97S 

Draught  of  fire-places,  48S 

Dredging  machines,  150 

Driving  wheels,  470 

Drum  armature,  918 

Drummond's  light,  606 

Dry  piles,  817  ;  plates,  610 

Duboscq's  microscope,   606  ;    regulator,^ 

835 
Ductility,  7,  92 

Duhamel's  graphic  method,  245 
Dulong    and    Arago's    experiments    on 
Boyle's  law,    181  ;    method   of  deter- 
mining the  tension  of  aqueous  vapour, 

357  ,    , 

Dulong  and  Petit's  determmation  of  ab- 
solute   expansion    of    mercury,    322 ; 
method  of  cooling,  455  ;  law,  458 
Dumas's    method    for    vapour    density, 

388 
Duplex  telegraphy,  893 
Duration  of  electric  spark,  795 
Dutroche's  endosnn)nieter,  139 
Dynamical  theory  of  heat,  429 
Dynamic  radiation  and  absorption,  442 
Dynamo-electrical  machine,  916-918 
Dynamo-magnetic  machine,  916 
Dynamometer,  90 
Dyne,  b\a 


EAR,  the,  7,  260 
Ear  trumpet,  239 

Earnshaw  on  velocity  of  sound,  230 

Earth,  density  of,  67  ;  its  action  on 
currents,  87 1-S73  ;  action  of  solenoids, 
878  ;  current,  894  ;  flattening  of,  by 
rotation,  82  ;  magnetic  poles  of  the, 
698  ;  magnetisation  by,  714 

Earth's  magnetism,  701 

Ebullition,  350  ;  laws  of,  363 

Eccentric,  467,  468 

Eclielon  lenses,  607 

Echoes,  237  ;  monosyllabic,  Irisyilabic,- 
mulliple,  237 

Eddy  currents,  929 

Edehnann's  hygrometer,  394 


Index. 


1069 


EDI 

Edison's  Inmp,  838  ;  phonograph,  291  ; 
tasimeter,  933  ;  telephone,  934 

Efficiency  of  a  machine,  451  ;  of  heat 
engines,  454 

Effluvium  electrical,  793 

Efflux,  velocity  of,  142  ;  quantity  of, 
145  ;  influence  of  tubes  on,  146 

Effusion  of  gases,  191 

Elastic  bodies,  58  ;  after  action,  91 

Elastic  force,  152;  of  vapours,  351 

Elasticity,  7,  17  ;  limit  of,  17,  88;  .of 
traction,  88  ;  modulus  of,  88  ;  of  tor- 
sion, 89  ;  of  flexure,  90 

Electric  alarum,  897  ;  axis,  732  ;  bat- 
teries, 774,  789  ;  candles,  838  ;  charge, 
778  ;  chimes,  763  ;  clocks,  898  ;  den- 
sity, 736  ;  discharge,  783  ;  egg,  788  ; 
fish,  971  ;  fuse,  794;  glow,  787  ;  lamp, 
838  ;  light,  831-833  ;  stratification  of 
the,  924  ;  lighting,  838  ;  pendulum, 
724 ;  pistol,  793  ;  poles,  732  ;  residue, 
773  ;  shock,  770,  785  ;  spark,  762  ; 
telegraphs,  886-899  ;  tension,  736  ; 
whirl,  764  ;  tube,  7S9 

Electrical  attractions  and  repulsions, 
734  ;  endosmose,  839 ;  field,  738  ;  po- 
tential, 738  ;  capacity,  739  ;  measure- 
ment of,  740 ;  resistance,  unit  of,  954  ; 
conductivity,  958  ;  quantity,  7-33  ;  units, 

963 

Electrical  machines,  752-761  ;  precau- 
tions in,  754 

Electricity,  6,  723 ;  application  of,  to 
medicine,  972  ;  atmospheric,  992- 
looi  ;  contact  theory,  799  ;  current, 
800 ;  communication  of,  749 ;  de- 
velopment of,  by  friction,  724 ;  by 
jDressure  and  cleavage,  731  ;  distribu- 
tion of,  735  ;  dynamical,  797-961  ; 
disengagement  of,  in  chemical  actions, 
793-799 ;  frictional,  730 ;  loss  of, 
743  ;  mechanical  effects,  792  ;  power 
of  points,  742  ;  produced  by  induction, 
744 ;  velocity  of,  796 ;  theories  of, 
728  ;  work  required  for  production  of, 
761 

Electrified  bodies,  motion  of,  729,  750 

Electro-capillary  phenomena,  840 

Electrochemical  equivalent,  844 ;  tele- 
graph, 895  ;  series,  842 

Electrodes,  803  ;  polarisation  of,  806 

Electrodynamics,  858 

Electrodynamometer,  962 

Electro;;ilding,  855 

Electrolysis,  842  ;  laws  of,  846 

Electrolyte,  842 

Electrolytic  convection,  832 


EXO 

Electromagnetic  force,  883 ;  machines, 
899  ;  units,  963 

Electromagnets,  880,  884 

Electrometallurgy,  854,  855 

Electrometer,  751;  Lane's,  777;  quad- 
rant, 756  ;  Thomson's,  780 

Electromotive  series,  801  ;  force,  802, 
814,  825,  959  ;  determination  of,  959  ; 
force  of  elements,  814 

Electromotor,  886 

Electrophorus,  752 

Electropyrometer,  949 

Electroscope,  724  ;  Bohnenberger's,  818; 
Volta's  condensing,  779  ;  gold  leaf,  751 

Electrosilvering,  8 56 

Electrostatic  units,  963 

Electrotonus,  828 

Elements,  electronegative  and  electro- 
positive, 842 

Elliptical  polarisation,  672 

Emergent  rays,  542 

Emission  theory,  499 

Emissive  power,  425 

Emulsions,  140;  gelatine,  610 

Endosmometer,  135 

Endosmose,  139;  electrical,  839;  of 
gases,  190 

Endosmotic  equivalent,  139 

Endothermic  reactions,  484 

Energy,  62  ;  conservation  of,  65  ;  dissi- 
pation of,  498  ;  transformations  of,  64  ; 
varieties  of,  63 

Engines,  gas,  476  ;  steam,  465  ;  double- 
action,  467  ;  low  and  high  pressure, 
471  ;  single  action,  469  ;  locomotive, 
470  ;  fire,  219  ;  transformation  of,  64; 
Cornish,  467  ;  horizontal,  468  ;  work 
of,  472  ;  heat,  474  ;  hot  air,  475 

Equator,  681  ;  magnetic,  698 

Equilibrium  of  forces,  35  ;  of  floating 
bodies,  115  ;  of  heavy  bodies,  69  ;  of 
liquids,  106,  107  ;  mobile  of  tempera- 
ture, 414  ;  neutral,  70  ;  stable,  70  ; 
unstable,  70 

Equivalent,  electrochemical,  846  ;  en- 
dosmotic,   139  ;  conductors,  955 

Escapement,  81  ;  wheel.  Si 

Ether,  429  ;  luminiferous,  499 

Eustachian  tube,  260 

Evaporation,  350  ;  causes  which  accele- 
rate it,  362  ;  cold  due  to,  373  ;  latent 
heat  of,  372 

Evaporation  and  ebullition,  364 

Exchanges,  theory  of,  415 

Exhaustion,  produced  by  air-pump,  203  ; 

by  Sprengel's  pump,  205 
Exosmose,  139 


I070 


Index. 


EXO 

Exothermic  reactions,  484 

Expanded  wave,  225 

Expansibility  of  gases,  147 

Expansion,  296  ;  apparent  and  real,  32 1  ; 
al)SoIute,  of  mercury,  322  ;  apparent, 
of  mercury,  323  ;  of  liquids,  326  ;  of 
solids,  313  ;  of  gases,  331-333  ;  linear 
and  cubical,  coefficients  of,  313  ; 
measurement  of  linear,  314  ;  of  crystals, 
318;   applications  of,    319;    force  of, 

329 

Expansion  of  gases,  cold  produced  by, 
494  ;  problems  on,  332 

Expansive  force  of  ice,  346 

Experiment,  Berthollet's,  188;  Frank- 
lin's, 368  ;  Florentine,  97  ;  Pascal's, 
162  ;  Torricellian,  161 

Extension,  7,  9 

Extra  current,  907,  908  ;  direct,  90S  ; 
inverse,  908 

Eye,  612  ;  accommodation  of,  620;  not 
achromatic,  628  ;  refractive  indices  of 
media  of,  613;  path  of  rays  in,  615; 
dimensions  of  various  parts  of,  614 

Eye-glass,  544,  630  ;  lens,  592  ;  piece, 
583,  590,  592  ;  Campani's,  592 


FAHRENHEIT'S  hydrometer,  123  ; 
scale,  303 

Falling  bodies,  laws  of,  76 

Falsetto  notes,  259 

Farad,  964 

Faraday's  experiments,  745  ;  wheel,  625  ; 
theory  of  induction,  747  ;  voltameter, 
846 

Favre  and  Silljermann's  calorimeter, 
463  ;  determination  of  heat  of  com- 
bustion, 483 

Fibres,  Corti's,  260 

Field  lens  and  glass,  592 

Field  magnets,  915 

Field  of  a  microscope,  591  ;  of  view, 
593  ;  magnetic,  707 

Figures,  Lichtenberg's,  772 

Filter-pump,  206 

Filters,  15 

Finder,  595 

Fire-engine,  219;  -places,  487  ;  -works, 
149  ;  -ball,  997 

Fish,  electrical,  971 

Fishes,  swimming  bladder  of,  117 

Fizcau's  experiments,  '3'^')  5'-'7 

Flag  signals,  887 

Flame,  483 

Flame,  483  ;  sensitive,  278 

Flask,  specific  gravity,  121 


Flattening  of  the  earth,  82 

Flexure,  elasticity  of,  90 

Float,  466 

Floating  bodies,  115 

Florentine  experiment,  13,  97 

Fluid,  4  ;  imponderable,  6  ;  elastic,  152  ; 
magnetic,  683 

Fluidity,  7 

Fluorescence,  582 

Flute,  280 

Fluxes,  340 

Fly-wheel,  467 

Focal  distance,  419 

Foci,  acoustic,  237  ;  magnetic,  701  ;  of 
convex  mirrors,  526  ;  in  double  convex 
lenses,  552 

Focus,  419,  525  ;  of  a  parabola,  143  ;  con- 
jugate, determination  of  the  principle, 
527  ;  of  a  spherical  concave  mirror> 
525>  552 

Focussing  the  microscope,  587,  591 

Fog-signal,  242 

Fogs,  980 

Foot,  22 

Foot-pound,  61,  473 

Force,  26  ;  acceleration  of,  77  ;  centri- 
i  fiigal)  53  ;  conservation  of,  65  ;  coer- 
'  cive,  687  ;  direction  of,  30 ;  elastic, 
of  gases,  152  ;  Unes  of  magnetic,  707  ; 
of  expansion  and  contraction,  319; 
electromotive,  802,  814  ;  representation 
of,  30  ;  parallelogram  of,  33  ;  of  liquids, 
329  ;  portative,  719 

Foices,  6;  along  the  same  line,  31; 
equilibrium  of,  38  ;  impulsive,  60 ; 
magnetic,  708  ;  molecular,  S3  ;  mo- 
ments of,  38  ;  polygon  of,  35  ;  triangle 
of,  35 

Formula;  for  expansion,  318  ;  barome- 
tric, 178  ;  for  sound,  231  ;  for  splieri- 
cal  mirrors,  530,  531  ;  for  lenses, 
559 

Fortin's  barometer,  166 

Foucault's  currents,  929  ;  determination 
of  velocity  of  light,  506  ;  experiment, 
834.  929 

Fountain  in  vacuo,  210  ;  at  Giggleswick, 
214  ;  intermittent,  212  ;  Hero's,  21 1 

Fovea  centralis,  612 

Franklin's  experiment,  368,  992  ;  plale, 
769  ;  theory  of  electricity,  728 

Fraunhofer's  lines,  574,  575 

Freezing,  apparatus  for,  374 

Freezing  mixtures,  347,  34S  ;  point  in  a^ 
thermometer,  302 

French  weights  and  measures,  123 ; 
boiler,  466 


Index. 


1071 


FRE 

Fresnel's  experimentum  crucis,  645  ; 
rhomb,  671 

Friction,  26,  44,  47  ;  heat  of,  477  ;  hy- 
ciraulic,  146 ;  internal,  of  Hquids,  48, 
147  ;  of  gases,  446 ;  development  of  elec- 
tricity by,  720 

Friction  wheels,  77 

Frigorilic  rays,  422 

Fringes,  646 

Frog,  rheoscopic,  968 

Frost,  987 

Frozen  mercury,  373,  380,  384 

Fulcrum,  44 

Fulgurites,  999 

Fulminating  pane,  769 

Furnace,  electrical,  821 

Fuse,  Abel's,  794 ;  Chatham,  S29,  830 
, Fusing  point,  338 

Fusion,   laws    of,    338  ;    vitreous,    338 
latent  heat  of,  461  ;  of  ice,  450 


GALILEAN  telescope,  597 
Galleries,  whispering,  237 

Gallium,  578 

Gallon,  125 

Galvani's  experiment,  797 

Galvanometer,  821  ;  differential,  821  ; 
Sir  W.  Thomson's,  822 

Galvanoscope,  821 

Galvano-thermometer,  830 

Gas  battery,  850  ;  engines,  476 

Gases,  absorption  of,  by  liquids,  189 ; 
by  solids,  193  ;  by  vapours,  435  ; 
appHcation  of  Archimedes'  principle 
to,  195  ;  cold  produced  by  expansion 
of,  494;  compressibility  of,  154,  iSo  ; 
condensed,  193,  209  ;  conductivity  of, 
409  ;  diamagnetism  of,  937  ;  density 
of,  335-337  ;  dynamical  theory  of, 
293;  expansion  of,  153,  331-334; 
endosmose  of,  190  ;  effusion,  191  ; 
transpiration  of,  192  ;  Gay-Lussac's 
method,  331  ;  index  of  refraction  of, 
550  ;  laws  of  mixture  of,  188  ;  and 
vapours,  mixtures  of,  383  ;  permanent, 
380 ;  problems  in,  332,  3S3  ;  lique- 
faction of,  380  ;  physical  properties  of, 
152  ;  pressure  exerted  by,  156  ;  radia- 
tion of,  441  ;  Regnault's  method,  336  ; 
specific  heat  of,  460 ;  velocity  of  sound 
in,  230,  231,  232  ;  viscosity  of,  446  ; 
weight  of,  155 

Gaseous  state,  4 

Gassiott's  battery.  Si 5 

Gauge,  air-pump,  201  ;  rain,  983 

Gay-Lussac's  alcoholometer,  128  ;  baro- 


meter, 167  ;  determination  and  expan- 
sion of  gases,  331  ;  of  vapour-density, 
385  ;  stopcock,  382 

Geissler's  tubes,  205,  578,  925 

Generating  plate,  Soi 

Geographical  meridian,  691 

Geometrical  shadows,  503 

Giffard's  injector,  207 

Gilding  metal,  855 

Gimbals,  697 

Glacial  pole,  1009 

Glaciers,  991 

Glashier's  balloon  ascents,  196  ;  factors, 
398 

Glass,  compressed,  668  ;  expansion  of, 
325  ;  magnifying,  583  ;  object,  590 ; 
opera,  597  ;  unannealed,  668 

Glasses,  periscopic,  629 ;  weather,  174 

Globe  lightning,  997 

Glow,  electrical,  787  ;  worm,  635 

Glycerine  barometer,  176 

Gold-leaf  electroscope,  751 

Goldschmid's  aneroid,  182 

Gong,  282 

Goniometers,  534 

Good  conductors,  404 

Governor,  468 

Gradient,  barometric,  978 

Gramme,  24,  125 

Gramme's  magneto-electrical  machine,9i  7 

Graphic  method,  Duhamel's,  245  ;  Fos- 
ter's, 831 

Graphite,  810 

Gratings,  647 

Cirave  harmonic,  263 

(jravesand's  ring,  295 

Gravimetrical  density,  185 

Gravitation,  6,  82  ;  terrestrial,  67  ;  ac- 
celerative  effect  of,  27 

Gravity,  battery,  812 

Gravity,  centre  of,  68  ;  Jolly's  determina- 
tion of  constant  of,  75 

Gregorian  telescope,  599 

Gridiron  pendulum,  320 

Grimaldi's  experiment,  645 

Grotthiiss'  hypothesis,  845 

Grove's  battery,  809  ;  gas,  850 

Guericke's  air-pump,  200 

Guide-blades,  150 

Guitar,  279 

Gulf  Stream,  1006 

Guthrie's  researches,  348 


HADLEY'S  reflecting  sextant,  521 
Hail,  9S9, 
Hair  hygrometer,  399 


lo/: 


Index. 


Haldat's  apparatus,  loi 

Hall's  experiment,  88 1 

Hallstrom's  experiments,  329 

Haloes,  627,  646,  981 

Hammer,  279,  921 

Hardening,  90 

Hardness,  7  ;  scale  of,  93 

Hare's  deflagrator,  805,  S29,  830 

Harmonicon,  chemical,  278 

Harmonics,  254,  273 

Harmonic  triad,  247  ;  grave,  263 

Harp,  279  ;  Marloye's,  281 

Harris's  unit  jar,  778 

Heat,  292  ;  animal,  485  ;  absorption  of, 
by  vapours,  &c.,  435,  439 ;  atomic, 
458  ;  conduction  of,  403  ;  diffusion  of, 
437 ;  developed  by  induction,  929  ; 
dynamical  theory  of,  429  ;  hypothesis 
on,  292  ;  influence  of  the  nature  of, 
435  ;  latent,  341  ;  mechanical  equi- 
valent of,  497  ;  polarisation  of,  679  ; 
produced  by  absorption  and  imbibi- 
tion, 482  ;  radiated,  403 ;  radiant, 
411,  4.46a;  reflection  of,  418;  scat- 
tered, 424;  sources  of,  477-496; 
specific,  448,  454-460 ;  transmission 
of,  403  ;  terrestrial,  481 

Heaters,  466 

Heating,  486  ;  by  steam,  490 ;  by  hot 
air,  491  ;  by  hot  water,  492 

Height  of  barometer,  165  ;  variations 
in,  171 

Heights  of  places,  determination  of,  by 
barometer,  178,  179  ;  by  Ijoiling  point, 

369 

Heliograph,  523 

Heliostat,  534 

Helix,  45,  8S2 

Helmholtz's  analysis  of  sound,  255  ;  re- 
searches, 258 

Hemihedral  crystal,  732 

Hemispheres,  Magdeburg,  160 

Henley's  electrometer,  756  ;  discharger, 
792 

Henry's  experiment,  909 

1  fcrepath's  salt,  656 

Hero's  fountain,  211 

Ilerschelian  rays,  430  ;  telescope,  601 

Ilirn's  experiments,  474 

I  loar-frost,  9S7 

llofmann's  density  of  vapours,  387 

Holmes's  magneto-electrical  machine,  913 

I  loltz's  electrical  machine,  759 

Homogeneous  light,  572  ;  medium,  502 

I  lope's  experiments,  330 

I  Ic^rizontal  line,  67  ;  plane,  67 

Horse-power,  61,  472 


Hot-air  engines,  475,  491 

Hotness,  297 

Hot-water,  heating  by,  492 

Hour,  21 

Howard's  nomenclature  of  clouds,  981 

Hughes's  microphone,  931  ;  induction 
balance,  932 

Humour,  aqueous,  612 

Huyghen's  barometer,  177 

Hyaloid  membrane,  612 

Hydraulic  press,  108  ;  engine,  151  ;  fric- 
tion, 146  ;  lift,  loS  ;  ram,  150;  tourni- 
quet, 149 

Hydraulics,  95 

Hydrodynamics,  141 

Hydro-electric  machine,  758  ;  currents, 
939 

Hydrometers,  119;  Nicholson's,  120; 
Fahrenheit's,  123  ;  with  variable 
volume,  126;  Beaume's,  127;  of  con- 
stant volume,  126  ;  specific  gravities, 
119  ;  uses  of  tables  of,  125 

Hydrostatic  bellows,  loi  ;  paradox,  103  ; 
balance,  120 

Hydrostfitics,  95 -98 

Hygrometers,  393  ;  of  absorption,  399  ; 
chemical,  394 ;  condensing,  395  ; 
Daniell's,  396  ;  wet -bulb,  398;  Mason's, 
398  ;  Regnault's,  397 

Hygrometric  stale,  392  ;  substances,  391 

Hj'grometry,  391  ;  problem  on,  401 

Hygroscope,  399 

Hypothesis,  5 

Hypsometer,  369 


ICE,  990  ;  method  of  fusion  of,  450 
Ice    calorimeter,     450  ;     Bunsen's, 
451;  expansive   force    of,    346;    ma- 
chine, 494 

Iceland  spar,  659 

Idioelectrics,  724 

Image  and  object,  magnitudes  of,  561 

Images,  accidental,  626  ;  condition  of 
distinctness  of,  587  ;  formation  of,  in 
concave  mirrors,  528  ;  in  convex  mir- 
rors, 529;  in  plane  mirrors,  513;  of 
multiple,  516;  magnitude  of,  532; 
produced  by  small  apertures,  504 ; 
virtual  and  real,  514  ;  inversion  of,  616 

Imbibition,  193  ;  heat  produceil  by,  4S2 

Impenetrability,  7 

Imperial  British  yard,  22 

Imponderable  matter,  6 

Impulsive  forces,  57 

Incandesceni  lamps,  83S 

Inch,  125 


Index. 


1073 


INC 

Incident  ray,  536 

Inclination,  708  ;  compass,  698 

Inclined  plane,  43  ;  motion  on,  50 

Index  of  refraction,  538  ;  measurement 
of,  in  solids,  548  ;  in  liquids,  549 ;  in 
gases,  550 

Indicator,  473,  886,  888,  889 

Indices,  refractive,  table  of,  550 

Indium,  57S 

Induced  currents,  900-911 

Induction,  apparatus  founded  on,  911  ; 
balance,  932  ;  by  the  earth,  905  ;  liy 
currents,  900  ;  of  a  current  on  itself, 
907  ;  electrical,  744 ;  in  telegraph 
cables,  891  ;  limit  to,  746 ;  Faraday's 
theory  of,  747  ;  heat  developed  by, 
929 ;  by  magnets,  904 ;  magnetic,  686 ; 
vertical,  715 

Inductive  capacity,  specific,  748 

Inductorium,  921 

Inelastic  bodies,  58 

Inertia,  19  ;  applications  of,  20 

Influence,  magnetic,  686  ;  electrical,  744 

Ingenhaus's  experiment,  404 

Injector,  Giffard's,  207 

Insects,  sounds  produced  by,  242 

Insolation,  635,  636 

Instruments,  optical,  585 ;  polarising, 
656 ;  mouth,  271  ;  reed,  272 ; 
stringed,  279  ;  wind,  270,  280 

Insulating  bodies,  726  ;  stool,  762 

Insulators,  725 

Intensity  of  the  current,  825  ;  of  the 
electric  light,  837  ;  illumination,  508  ; 
of  reflected  light,  519;  of  a  musical 
tone,  246  ;  of  radiant  heat,  414  ;  of 
sound,  causes  which  influence,  226  ; 
of  terrestrial  magnetism,  701  ;  of  ter- 
restrial gravity,  82 

Interference  of  light,  645;  of  sound,  261 

Intermittent  fountain,  212  ;  springs,  214  ; 
syphon,  214 

Interpolar,  825 

Intervals,  musical,  247 

Intrapolar  region,  828 

Inversion  of  images,  616 

I  ones,  842 

Iris,  612 

Iron,  passive  state  of,  851  ;  electrical 
deposition  of,  857 

Iron  ships,  magnetism  of,  715 

Irradiation,  627 

Irregular  reflection,  518 

Isobars,  979 

Isochimenal  line,  1007 

Isoclinic  lines,  698 

Isodynamic  lines,  701 


Isogeothermic  lines,  1007 

Isogonic  lines,  692 

Isothcral  lines,  1007 

Isothermal  lines,  466,  1007  ;  zone,  1007 


T  ABLOCIIKOFF  candle,  838 
I      Jacobi's  unit,  846,  952 
Jar,  Leyden,  770-780 

Jar,  luminous,  785  ;  Harris's  unit,  778 

Tet,  lateral,   143  ;  height  of,    144  ;  form 
of,  148 

Jew's  harp,  272 

Jolly's  spring  balance,  88 ;  air  thermo- 
meter, 334 

Jordan's  barometer,  176 

Joule's  experiment  on  heat   and   work, 
497  ;  equivalent,  497 

Jupiter,  505 

Jurin's  laws  of  capillarity,  132 


KALEIDOPHONE,  625 
Kaleidoscope,  516 
Kamsin,  977 
Kater's  pendulum,  82 
Kathelectrotonus,  828 
Kathode,  842 
Katione,  842 
Keepers,  718 

Kerr's  electro-optical  experiments,  937 
Key,  887,  906,  912,  922  ;  note,  249 
Kienmayer's  amalgam,  754 
Kilogramme,  24,  125 
Kilogrammetre,  472 
Kinetic  energy^  62 
Kinnersley's  thermometer,  792 
Kirk's  ice  machine,  494 
Knife-edge,  71 
Kbnig's    apparatus,     256 ;     manometric 

flames,  288 
Kravogl's  machine,  899 
Kiilp's  method  of  compensation,  719 
Kundt's  velocity  of  sound,  277 


LABYRINTH  of  the  ear,  260 
Lactometer,  129 
Ladd's  dynamo-electrical  machine,  916 
Lambert's  method,  570 
Lamps,  incandescent,   836;  Dobereiner, 

482 
Land  and  water,  ion 
Lane's  electrometer,  777 
Lantern,  magic,  604 
Laplace's  barometric  formula,  178 
Laryngoscope,  563 


I074 


Index. 


Larynx,  259 

Latent   heat,    341  ;  of  fusion,    461  ;   oi 

vapours,  372,  462 
Lateral  jet,  143 
Latitude,  magnetic,  698  ;  influence  of  on 

the  air,  1005  ;  parallel  of,  82 
Lavoisier  and  Laplace's  calorimeter,  450  ; 
method  of  determining  linear  expan- 
sion, 314 
Law,  5 

Laws  of  mixture  of  gases  and  liquids,  383 
Lead  tree,  853 

Leclanche's  elements,  813,  814 
Ledger  lines,  252 
Leidenfrost's  phenomenon,  385 
Lemniscate,  667 

Length,  unit  of,  22  ;  of  undulation,  225 
Lens,  axis  of,  551 

Lenses,  551-559;  achromatic,  582; 
aplanatic,  558  ;  centres  of  curvature, 
551;  combination  of,  560;  echelon, 
607  ;  foci  in  double  convex,  552  ;  in 
double  concave,  553  ;  formation  of 
images  in  double  convex,  556 ;  in 
double  concave,  557  ;  formulas  relat- 
ing to,  559  ;  lighthouse,  607  ;  optical 
centre,  secondary  axis  of,  555 
Lenz's  law,  901 
Leslie's   cube,    423  ;    experiment,    373  ; 

thermometer,  308 
Level,  water,  109;  spirit,  no 
Level  surface,  67 
Levelling  staff,  109 
Lever,  40 

Leyden  discharge,  inductive  action  of,  903 
Leyden    jars,     770-780 ;     charged     by 
Ruhmkorffs  coil,    923  ;    potential  of, 
782  ;  work  by,  784 
Lichlenberg's  figures,  772 
Liebig's  condenser,  377 
Lift,  hydraulic,  108 
Ligament,  suspensory,  6l2 
Light,  499  ;  diffraction  of,  646  ;  homo 
gencous,  569,   572  ;  intensity  of,  508  ; 
interference  of,  645  ;  laws  of  reflection 
of,  511  ;  medium,  502  ;  oxyhydrogen, 
606  ;    polarisation    of,     652  ;    relative 
intensities    of,    510  ;  sources  of,   634 
theory   of  polarised    light,    661  ;    un- 
dulatory  theory  of,  499,  637  ;  velocity 
of,  505-507 
Lighthouse  lenses,  607 
Lighting,  electric,  838 
Lightning,  999  ;  ascending,  997;  effects 
of,  997  ;  conductor,  lOOl  ;  globe,  999; 
heat,  997  ;  brusli,  997  ;  flashes,  997  ; 
zigzrig.  997 


]NL\G 

Limit  of  elasticity,    17;  magnetic,   720; 

to    induction,     746  ;     of    perceptible 

sounds,  244 
Line,  aclinic,  698 ;  of  collimation,  595  ; 

isoclinic,  698  ;  agonic,  692  ;  isogenic, 

692 ;     isodynamic,      701  ;     of    sight, 

595 
I^inear    expansion,    coefficients    of,    313, 

Lines  of  magnetic  force,  707  ;  of  elec- 
trical force,  738 

Lippmann's  capillary  electrometer,  840 

Liquefaction  of  gases,  380,  381  ;  of 
vapours,  375 

Liquids,  99  ;  active  and  inactive,  667  ; 
buoyancy  of,  lOO  ;  compressibility  of, 
97  ;  conductivity  of,  407  ;  calculation 
of  density  of,  107  ;  diffusion  of,  140  ; 
diamagnetism  of,  93S  ;  expansion  of, 
321  ;  equilibrium  of,  104;  manner  in 
which  they  are  heated,  408  ;  pressure 
on  sides  of  vessel,  102  ;  refraction  of, 
549  ;  rotatory  power  of,  676  ;  sphe- 
roidal form  of,  84  ;  spheroidal  state  of, 
385  ;  specific  heat  of,  456  ;  volatile 
and  fixed,  349  ;  tensions  of  vapours  of, 
359  ;  of  mixed  liquids,  360 

Lissajous's  experiments,  284-2S6 

Lithium,  578 

Litre,  24,  125 

Local  action,  806  ;  attraction,  715  ;  bat- 
tery, 889  ;  currents,  816 

Locatelli's  lamp,  428 

Locomotives,  470,  471 

Lodestone,  680 

Long  sight,  629 

Loops  and  nodes,  269 

Loss  of  electricity,  743  ;  of  weight  in  air, 
correction  for,  402 

Loudness  of  a  musical  tone,  246 

Lullin's  experiment,  792 

Luminifcrous  other,  499 

Luminous  bodies,  500  ;  effects  of  the 
electric  discharge,  773,  833  ;  of  the 
electric  current,  923  ;  of  Ruhmkorfl  's 
coil,  923  ;  heat,  434  ;  jar,  790  ;  me 
teors,  993  ;  paint,  636  ;  pane,  789  ; 
pencil,  501  ;  radiation,  432;  ray,  501  ; 
lul)e,  789  ;  square,  and  bottle,  789 


MACIIINK,    Atwood's,    77;    elec- 
trical,   752-760 ;  \'on    Ebner's, 
794 ;  electro-magnetic,  886 
Mackerel-sky,  981 
Macleod's  gauge,  206 
Magazine,  717 


Index. 


1075 


Magdeburg  hemispheres,  160 

Magic  lantern,  604 

Magnetic  attractions  and  repulsions,  702  ; 
battery,  717;  couple,  690;  curves, 
706;  declination,  691;  dip,  698; 
effects  of  the  electrical  discharge,  791  ; 
equator,  69S  ;  field,  707,  963  ;  fluids, 
683  ;  induction,  686  ;  influence,  686  ; 
limit,  720;  meridian,  691;  needle, 
691,  692  ;  oscillations  of,  705  ;  obser- 
vatories, 702  ;  poles,  698  ;  saturation, 
716 ;  storms,  694 

Magnetisation,  710  ;  by  the  action  of  the 
earth,  714;  by  currents,  882;  single 
touch,  711 

Magnetism,  6,  700  ;  determination  of, 
in  absolute  pressure,  709  ;  earth's,  701  ; 
of  iron  ships,  715  ;  Ampere's  theory 
of,  879  ;  remanent,  883  ;  theory  of, 
683  ;  terrestrial  distribution  of  free,  721 

Magneto  and  dynamo-electrical  machines, 
918-920 

Magneto-electrical  apparatus,  911  ; 
Gramme's,  917  ;  machines,  913-916 

Magnetometer,  949 

Magnets,  artificial  and  natural,  680 ; 
broken,  685  ;  action  of  earth  on,  689  ; 
equator  of,  68 1  ;  floating,  722  ;  heat 
developed  by,  929  ;  meter,  949  ;  north 
and  south  poles  of,  682  ;  portative  force 
of,  719  ;  saturation  of,  716  ;  influence 
of  heat,  720  ;  induction  by,  904  ;  in- 
ductive action  on  moving  bodies,  905  ; 
action  on  currents,  867  ;  on  solenoids, 
877  ;  rotation  of  induced  currents  by, 
928;  optical  effects  of,  935  ;  total  action 
of  two,  708 

Magnification,  linear  and  superficial,  88  ; 
measure  of,  589  ;  of  a  telescope,  55,  64 

Magnifying  power,  594 

Magnitude,  9  ;  apparent,  of  an  object, 
588  ;  of  images  in  mirrors,  587 

Major  chord,  247  ;  triads,  248 

Malleability,  859 

Mance's  heliograph,  523  ;  method,  957 

Manganese,  magnetic  limit  of,  720 

Manhole,  466 

Manipulator,  888 

Manometer,  97,  183  ;  open-air,  183  ; 
with  compressed  air,  184  ;  Regnault's 
barometric,  186 

Manometric  flames,  288 

Mares'  tails,  981 

Marie-Davy  battery,  812 

Marine  barometer,  165  ;  engines,  466  ; 
galvanometer,  822 

Mariner's  card,  975  ;  compass,  697 


MIC 

Mariotte  and  Boyle's  law,  180 

Mariotte's  tube,  180 

Marloye's  harp,  281 

Maskelyne's  experiment,  67 

Mason's  hygrometer,  398 

Mass,  measure  of,  23  ;  unit  of,  23 

Matter,  2 

Matteucci's  experiment,  903 

Matthiessen's  thermometer,  308  ;  table  of 
electromotive  forces,  940 ;  electrical 
conductivity,  958 

Maxim's  lamp,  838 

Maximum  current,  conditions  of,  826 

Maximum  and  minimum  thermometers, 
310  ;  of  tension,  755 

Maxwell's  electromagnetic  theory  of  light, 
748,  965  ;  colour  discs,  570 

Mayer's  floating  magnets,  722 

Mean  temperature,  1004 

Measure  of  force,  29  ;  of  work,  60 

Measure  of  magnification,  589,  594  ;  of 
mass,  23  ;  of  space,  22  ;  of  time,  21  ; 
of  velocity,  25 

Measurement  of  small  angles  by  reflec- 
tion, 522 

Mechanical  equivalent  of  heat,  497 ; 
effects  of  electrical  discharge,  792 ; 
battery,  839 

Megascope,  606 

Melloni's  researches,  429 ;  thermomul- 
tiplier,  412,  946 

Melting  point,  influence  of  pressure  on, 
339 

Membranes,  vibrations  of,  283 

Memoria  technica,  820 

Meniscus,  132  ;  convex,  131  ;  in  baro- 
meter, 169  ;  Sagitta  of,  169 

Mercury,  frozen,  373,  381,  384  ;  pendu- 
lum, 320 ;  coefficient  of  expansion, 
323  ;  expansion  of,  322  ;  pump,  208  ; 
purification  of,  168 

Meridian,  21  ;  geographical  and  mag- 
netic, 691 

Meriten's  machine,  913 

Metacentre,  115 

Metal,  Rose's  and  Wood's  fusible, 
340 

Metals,  conductivity  of,  955 

Meteoric  stones,  480 

Meteorograph,  974 

Meteorology,  973 

Meteors,  aerial,  964 

Metre,  22,  125 

Mica,  664 

Microfarad,  964 
'    Micrometer  lines,  594  ;  screw,  1 1 
I   Microphone,  931 


1076 


Index. 


Microscope,  12 ;  achromatism  of,  592  ; 
Duboscq's,  606  ;  compound,  591  ;  field 
of,  591  ;  focussing,  587  ;  magnifying 
powers  of,  594  ;  photo-electric,  606  ; 
simple,  586  ;  solar,  605 

Microspectroscope,  580 

Mill,  Barker's,  194 

Milliampere,  964 

Millimetre,  125 

Mineral  waters,  1000 

Mines,  firing  by  electricity,  795,  829 

Minimum  thermometer,  310  ;  deviation, 

547 

Minor  chord,  247 

Minotto's  battery,  812 

Minute,  21 

Mirage,  541 

Mirrors,  512  ;  applications  of,  534;  burn- 
ing, 420;  concave,  419,  528;  conju- 
gate, 420;  convex,  526-529;  glass, 
515;  parabolic,  535;  rotating,  520, 
795  ;  spherical,  524 

Mists,  980 

Mixture  of  gases,  188 ;  of  gases  and 
liquids,  189  ;  laws  of,  383 

Mixtures,  freezing,  347  ;  method  of,  452 

Mobile  equilibrium,  415 

Mobility,  7,  18 

Modulus  of  elasticity,  88 

Moisture  of  the  atmosphere,  400 

Molecular  forces,  3  ;  attraction,  83  ; 
state  of  bodies,  4;  velocity,  294 

Molecular  state,  relation  of  absorption  to, 

443 

Molecules,  3 

Moments  of  forces,  38 

Momentum,  28 

Monochord,  266 

Monochromatic  light,  569 

Monosyllabic  echo,  237 

Montgolfier's  balloon,  196;  ram,  150 

Moon,  510 

Morgagni's  humour,  610 

Morin's  apparatus,  78 

Morrcn's  mercury  pump,  208 

Morse's  telegraph,  889 

Moscr's  images,  193 

Motion,  18;  on  an  inclined  i)lane,  50; 
curvilinear,  25  ;  in  a  circle,  53,  54  ; 
rectilinear,  25 ;  resistance  to,  in  a 
iluid,  48  ;  uniformly  accelerated  rec- 
tilinear, 48 ;  cjuantity  of,  29 ;  of  a 
pendulum,  55;  of  ])rojectilc,  51 

Mouth  instrument,  271 

Multiple  battery,  826 

Multiple  echoes,  237;  images  formeil  by 
mirrors,  515,  516,  517 


OBS 

Multiplication,  method  of,  906 
Multiplier,  821 

Muscular  currents,  966,  967,  968 
Music,  220  ;  physical  theory  of,  246-264 
Musical     boxes,     279  ;     comnia,     248  ; 
intervals,  247  ;    scale,  248  ;  tempera- 
ment, 250  ;  tones,  properties  of,  246  , 
intensity,    notation,    252  ;    pitch    and 
timbre,   246 ;  sound,  223 ;  range,  252 
Myopy,  619,  629 


NAIRNE'S  electrical  machine,  757 
Nascent  state,  84 
Natterer's  apparatus,  381 
Natural  magnets,  680 
Naumann's  law,  458 
Needle,   declination   of,    691  ;    dipping, 

698  ;  astatic,  700 ;  magnetic,  691 
Negative  plate,  801 
Negatives  on  glass,  609 
Nerve-currents,  970 
Neutral     line,     744;     equilibrium,     70; 

point,  744  ;  temperature,  940 
Newtonian  telescope,  600 
Newton's  disc,  567  ;  law  of  cooling,  416 

rings,  650,  651;  theory  of  light,  568 
Niaudet's  element,  812 
Nicholson's  hydrometer,  120 
Nickel,    electrical    deposition    of,    857  ; 

magnetic  limit  of,  720 
Nicol's  prism,  660 
Nimbus,  981 
Nobert's  lines,  594 
Nobili's  battery,  943  ;  rings,  852  ;  ther- 

momultipliers,     945  ;    thermo-electric 

pile,  428,  431,  943 
Nocturnal  radiation,  495 
Nodal  points,  271,  645 
Nodes  and  loops,  269  ;  of  an  organ  pipe, 

274  ;  explanation  of,  276 
Noises,  221 
Nonconductors,  725 
Norremberg's  apparatus,  657 
Northern  light,  1003 
Norwegian  stove,  410 
Notation,  musical,  252 
Notes  in  music,  247  ;  musical,  of  women 

and  l)oys,  259  ;  wave-length  of,  253 
Nut  of  a  screw,  45 


OBJECT-GLASS,  590 
Objective,  590 
Oboe,  272 

Obscure     radiation,     432  ;     rays,    433 
transmutation  of,  433 


Index. 


1077 


OBS 

Observatories,  magnetic,  702 

Occlusion  of  gases,  194 

Occultation,  505 

Octave,  249 

Oersted's  experiment,  S20 

Ohms,  987 

Ohm's  law,  825 

Opaque  bodies,  500 

Opera-glasses,  597 

Ophthalmoscope,  633 

Optic  axis,  617  ;  axis  of  biaxial  crystals, 
644;  angle,  607;  nerve,  612 

Optical  centre,  555  ;  effects  of  magnets, 
926  ;  instruments,  585  ;  electrical  ex- 
periments, 937 

Optics,  499 

Optometer,  619 

Organ,  280  ;  pipes,  274 ;  nodes  and  loops 
of,  274 

Orrery,  electrical,  764 

Orthochromatic  plates,  611 

Oscillations,  55;  axis  of,  79;  method  of, 
705 

Oscillating  discharges,  783 

Otto's  gas  engine,  476 

Otto  von  Guericke's  air-pump,  200 

Outcrop,  III 

Overshot  wheels,  150 

Oxyhydrogen  light,  606 

Ozone,  793,  999 


PACINOTTI'S  ring,  917 
Paddles  of  steam  vessels,  150 
Paint,  luminous,  636 
Pallet,  81 

Pane,  fulminating,  769 ;  luminous,  790 
Papin's  digester,  371 
Parabola,  51,  143 

Paraliolic  mirrors,  535  ;  curve,  60,  143 
Parachute,  198 
Paradox,  hydrostatic,  103 
Parallel    of    latitude,     82  ;    forces,     36 ; 

centre  of,  27 
Parallel  rays,  501 
Parallelogram  offerees,  33 
Paramagnetic  bodies,  938 
Partial  current,  961 
Pascal's  law  of  equality  of  pressures,  96  ; 

experiments,  162 
Passage  tint,  677 
Passive  state  of  iron,  851 
Path,  mean  of  molecules,  273 
Pedal,  279 

Peltier's  cross,  950  ;  effect,  950 
Pendulum,    55  ;    application    to   clocks, 

81  ;  ballistic,  81  ;  compensation,  320; 


PLU 

electrical,  724;  gridiron,  320;  mer- 
curial, 320  ;  length  of  compound,  79  ; 
reversible,  79  ;  verification  of  laws  of, 
80 

Penetration  of  a  telescope,  596 

Penumbra,  503 

Percussion,  heat  due  to,  479 

Periscopic  glasses,  629 

Pennanent  gases,  380 

Persistence  of  impression  on  the  retina, 
625 

Perspective,  aerial,  618 

Perturbations,  magnetic,  692,  693 

Phantasmagoria,  606 

Phenakistoscope,  625 

Phenomenon,  5 

Phial  of  four  elements,  106 

Phonautograph,  287 

Phonograph,  Edison's,  291 

Phosphorescence,  635,  636 

Phosphorogenic  rays,  573 

Phosphoroscope,  636 

Photo-electric  microscope,  606 

Photoelectricity,  732 

Photogenic  apparatus,  606 

Photographs  on  paper,  609 ;  on  albu- 
menised  paper  and  glass,  61 1 

Photography,  608-611 

Photometers,  509,  511 

Photophone,  936 

Physical  phenomena,  5  ;  agents,  6 ; 
properties  of  gases,  152;  shadows,  503 

Physics,  object  of,  I 

Physiological  effects  of  the  electric  dis- 
charge, 785  ;  of  the  current,  827  ;  of 
RuhmkorfFs  coil,  923 

Piano,  279 

Piezometer,  97 

Pigment  colours,  570 

Pile,  voltaic,  804-818 

Pincette,  tourmaline,  666 

Pipes,  organ,  274 

Pisa,  tower  of,  69 

Pistol,  electric,  793 

Piston  of  air-pump,  200  ;  rod,  467 

Pitch,  concert,  251  ;  of  a  note,  246  ; 
a  screw,  45 

Plane,  45  ;  electrical  inclined,  764 ; 
mirrors,  513  ;  wave,  642 

Plante's  secondary  battery,  849 

Plants,  absorption  in,  193 

Plate  electrical  machine,  753 

Plates,  colours  of  thin,  650  ;  vibrations 
of,  282  ;  Chladni's,  282  ;  photographic 
dry,  610 

Plumb  line,  67 

Pluviometer,  983 


I078 


Index. 


Pneumatic  syringe,  154,  479 

Poggendorff's  law,  793 

Point,  boiling,  366,  367 

Points,  action  of,  742  ;  nodal,  271,  645 

Poisseuille's  apparatus,  147 

Poisson's  coefficient,  88 

Polar  aurora,  1003 

Polarisation,  848  ;  angle  of,  654  ;  cur- 
rent, 848 ;  of  electrodes,  806  ;  by 
double  refraction,  652  ;  by  reflection, 
653  ;  by  single  refraction,  655  ;  ellip- 
tical and  circular,  669,  670,  672  ;  of 
heat,  679 ;  galvanic,  806,  848  ;  light, 
652  ;  of  the  electric  medium,  747  ; 
plane  of,  654 ;  plate,  804 ;  rotatory, 
674 

Polarised  light,   theory  of,   661  ;  colours 
produced  by  the  interference  of,  662,    j 
668  ;  rays,  662 

Polariser,  656 

Polarising  instruments,  656 

Polarity,  806  ;  boreal,  austral,  689 

Pole,  glacial,  997 

Poles,  803 ;  analogous  and  antilogous, 
842  ;  electric,  732  ;  of  the  earth,  698  ; 
magnetic,  698  ;  of  a  magnet,  681 ; 
mutual  action  of,  682  ;  precise  defini- 
tion of,  684  ;  austral  and  boreal,  689 

Polygon  of  forces,  35 

Polyorama,  606 

Poly  prism,  544 

Ponderable  matter,  6 

Pores,  13 

Porosity,  7,  13  ;  application  of,  15 

Portative  force,  719 

Positive  plate,  801  ;  crystals,  643 

Positives  on  glass,  610 

Postal  battery,  S89 

Potential  energy,  62  ;  of  electricity,  738  ; 
of  a  Leyden  jar,  782  ;  of  a  sphere,  741 

Pound,  125;  avoirdupois,  23,  29;  foot,  59 

Powders,  radiation  from,  443 

Power  of  a  lever,  40 ;  of  a  microscope, 
594;  of  points,  742 

Presbytism,  619,  629 

Press,  hydraulic,  108 

Pressure,  centre  of,  102  ;  on  a  body  in  a 
liquid,  112;  atmospheric,  158  ;  amount 
of,  on  human  body,  163  ;  exi)eriment 
illustrating,  210;  influence  on  melting 
point,  339  ;  heat  produced  by,  479  ; 
electricity  produced  by,  731 
Pressures,  equality  of,  98  ;  vertical  down- 
ward, 99  ;  vertical  upward,  100  ;  in- 
dependent of  form  of  vessel,  lOl  ;  on 
the  sides  of  vessels,  102  ;  rate  of  trans- 
mission of,  99 


Prevost's  theory  of  exchanges,  415 

Primary  coil,  893 

Primitive  current,  961 

Principal  current,  961 

Principle  of  Archimedes,  113 

Prisms,  543-547  ;  double  refracting,  659  ; 

Nicol's,  660  ;  with  variable  angle,  544 
Problems  on  expansion   of  gases,   332  ; 

on  mixtures  of  gases  and  vapours,  384  ; 

on  hygrometry,  401 
Projectile,  motion  of,  51 
Prony's  brake,  42,  473 
Proof  plane,  735 
Propagation  of  light,  502 
Protoplasm,  827 
Protuberances,  579 
Pulley,  41: 
Pump,  air,  200  ;  condensing,  209  ;  filter, 

206 
Pumping  engine,  467 
Pumps,  different  kinds  of,  215  ;  suction, 

216  ;  suction  and  force,  217 
Punctum  CKCum,  612 
Pupil,  612 

Psychrometer,  398,  974 
Pyroelectricity,  732 
Pyroheliometer,  480 
Pyrometers,  311  ;  electric,  949 


Q 


UADRANTAL  deviation,  715 
Quadrant  electrometer,  756 


RADIANT  heat,  411  ;  detection  and 
^  measurement  of,  412 ;  causes 
which  modify  the  intensity  of,  414 ; 
Melloni's  researches  on,  428  ;  relation 
of  gases  and  vapours  to,  43S;  relation 
to  sound,  446a 

Radiated  heat,  403,  411 

Radiating  power,  425  ;  identity  of  ab- 
sorbing and  radiating,  426 ;  causes 
which  modify,  &c.,  427  ;  of  gases,  441 

Radiation,  cold  produced  by,  495  ;  from 
powders,  443  ;  of  gases,  luminous,  and 
ol)scure,  432;  laws  of,  413;  solar, 
480 

Radiative  power,  9S5 

Radiometer,  445 

Railway,  electrical,  917  ;  friction  on 
centrifugal,  53 

Rain,  983 ;  clouds,  983  ;  bow,  1002 ;  fall, 
974)  9^3  ;  g^"ge,  983  ;  drop,  veloctty 
of,  48 

Ram,  hydraulic,  150;  powder,  479 

Ramsden's  electrical  machine,  753    • 


Index. 


1079 


RAO 

Raoult's  researches,  343 

Rarefaction  in  air-pump,  200  ;  by  Spren- 
gel's  pump,  205 

Ray,  incident,  536 ;  luminous,  501  ; 
ordinary  and  extraordinary,  641 

Rays,  actinic,  or  Ritteric,  433 ;  diver- 
gent and  convergent,  501  ;  frigorific, 
422;  of  heat,  411,  429  ;  Herschelian, 
430 ;  invisible,  429 ;  obscure,  433  ; 
path  of,  in  eye,  615;  phosphorogenic, 
573  ;  polarised,  662  ;  transmutation  of 
thermal,  434 

Reaction  and  action,  39 

Real  volume,  14  ;  foci,  552  ;  focus,  525  ; 
image,  528,  556 

Reaumur  scale,  303 

Receiver  of  air-pump,  200 

Recomposition  of  white  light,  567 

Reed  instruments,  272 

Reeds,  free  and  beating,  272 

Reflected  light,  intensity  of,  519 

Reflecting  power,  423 ;  goniometer, 
534  ;  sextant,  521  ;  stereoscope,  623  ; 
telescope,  598 

Reflection,  apparent,  of  cold,  422 ;  of 
heat,  418  ;  from  concave  mirrors,  419  ; 
irregular,  518  ;  laws  of,  417  ;  verifi- 
cation of  laws  of,  420 ;  in  a  vacuum, 
421  ;  of  light,  511-541;  of  sound, 
236 

Refracting  crystals,  639,  652,  663  ;  stereo 
scope,  624  ;  telescope,  598 

Refraction,  536-545  ;  double,  639  ;  po- 
larisation by,  652  ;  explanation  of 
single,  638  ;  of  sound,  238 

Refractive  index,  538  ;  determination  of, 
562  ;  of  gases,  550  ;  of  liquids,  549  ; 
of  solids,  548  ;  table  of,  550 ;  indices 
of  media  of  eye,  6 1 3 

Refractory  substances,  338 

Refrangibility  of  light,  alteration  of,  5S2 

Regelation,  990 

Regnault's  experiments,  229  ;  determi- 
nation of  density  of  gases,  336  ;  mano- 
meter, 186  ;  methods  of  determining 
the  expansion  of  gases,  333  ;  of  specific 
heat,  454  ;  of  tension  of  aqueous  va- 
pour, 356,  358  ;  hygrometer,  397 

Regnier's  electric  lamp,  838 

Regulator  of  the  electric  light,  835,  836 

Reis's  telephone,  885 

Relay,  889 

Remanent  magnetism,  883 

Repulsions,  magnetic,  705  ;  electrical 
laws  of,  731 

Reservoir,  common,  726 

Residual  charge,  748,  773 


RUH 

Residue,  electric,  773 

Resilience,  773 

Resinous  electricity,  727,  728 

Resistance,    limiting  angle  of,   43  ;  of  a 

conductor,  825  ;    boxes,    953  ;    of   an 

element,  957 
Resonance,  237  ;  box,  251  ;  globe,  255 
Rest,  18 

Resultant  of  forces,  32-34 
Retina,  612  ;  persistence   of  impression 

on,  625 
Return  shock,  1000 
Reversible  pendulum,  79 
Reversibility  of  Holtz's  machine,  759 
Reversion,  method  of,  696 ;  spectroscope, 

577 
Rheometer,  821 
Rheoscope,  821 
Rheoscopic  frog,  968 
Rheostat,  951 
Rhomb,  Fresnel's,  671 
Rhumbs,  697,  975 
Richness,  hygrometric,  392 
Right  ascension,  600 
Rime,  987 
Ring  inductor,  919 
Rings,  coloured,  666 ;  Gravesand's,  295  ; 

in  biaxial  crystals,  667  ;  Newton's,  650, 

651  ;  Nobili's,  852 
Ritchie's  experiment,  426 
Ritteric  rays,  433 
Robinson's  anemometer,  974 
Rock    salt,    heat    transmitted    through, 

437 

Rods,  vibrations  of,  281 

Roget's  vibrating  spiral,  859 

Rose's  fusible  metal,  340 

Rotary  engine,  471 

Rotating  mirror,  520,  795 

Rotation,  electrodynamic  and  electro- 
magnetic, of  liquids,  869  ;  winds,  978 

Rotation  of  the  earth,  80 ;  of  magnets 
by  currents,  912  ;  of  currents  by  mag- 
nets, 868 ;  of  induced  currents  by 
magnets,  928 

Rotatory  power  of  liquids,  676  ;  polari- 
sation, 673,  674;  coloration  produced 
by,  675 

Rousseau's  densimeter,  130 

Roy  and  Ramsden's  measurement  of 
linear  expansion,  361 

Rubbers,  753 

Rubidium,  578 

Ruhlmann's  barometric  and  thermome- 
tric  observations,  179 

Ruhmkorffs  coil,  921  ;  effects  produced 
by,  923 


io8o 


Index. 


Rumford's  photometer,  509 
Rutherford's  thermometers,  310 


SACCHARIMETER,  677 
Saccharometer,  126 

Safety-catch,  829  ;  tuljc,  379  ;  valve,  108, 
371  ;  whistle,  466 

Sagitta  of  meniscus,  169 

Salimeters,  129 

Salts,  decomposition  of,  843 

Saturation,  degree  of,  392 ;  magnetic, 
716  ;  of  colours,  570 

Saussure's  hygrometer,  399 

Savart's  toothed  wheel,  241 

Scale  of  hardness,  93 

Scales  in  music,  248  ;  chromatic,  250  ; 
of  a  thermometer,  303  ;  conversion  of, 
into  one  another,  303 

Scattered  heat,  424;  light,  518 

Schehallien  experiment,  67 

Scheiner's  experinient,  619 

Schwendler's  platinum  light  standard,  838 

Scintillation  of  stars,  541 

Sciopticon,  604 

Sclerotica,  612 

Scott's  phonautograph,  2S7 

Scraping  sound,  281 

Scratching  sound,  281 

Screen,  magnetic,  82 2 

Screw,  II,  45 

Screw,  magnetic,  822 

Secchi's  meteorograph,  974 

Secondary  axis,  555  ;  batteries,  849  ; 
currents,  806;  coil,  893 

Second  of  time,  21,  25 

Seconds  pendulum,  79 

Secular  magnetic  variations,  692 

Segments,  ventral  and  nodal,  269 

Segner's  water-wheel,  149 

Selenite,  664 

Selenium,  951 

Self-induction,  905 

Semicircular  deviation,  715 

Semi-conductors,  725 

Semiprism,  526 

Semitones,  249 

Senarmont's  experiment,  406 

Sensitive  membrane,  229  ;  -wound  ma- 
chine, 919a 

Serein,  985 

Series,  thermo-electric,  940 

Serum,  12 

Sextant,  521 

Shadows,  503 

Shaft,  467 

Shock,  electiic,  770-785  ;  return,  1000 


SOU 

Shooting  stars,  480 

Short  circuit,  810  ;  sight,  629 

Shunt,  961  a  ;  -wound  machine,  919  a 

Siemens'  armature,  914;  dynamo-elec- 
trical machine,  918  ;  unit,  952  ;  elec- 
trical thermometer,  960 

Sight,  line  of,  595 

Silent  discharge,  793 

Silver,  voltameter,  846 

Simoom,  977 

Sine  compass,  824 

Singing  of  liquids,  363 

Sinuous  currents,  861 

Sirocco,  977 

Size,  estimation  of,  618 

Sky,  969 

Sleet,  988 

Slide  valve,  469 

Sling,  53 

Smee's  battery,  811 

Snow,  988  ;  line,  991 

Soap-bubble,  colours  of,  650 

Solar  microscope,  605  ;  light,  thermal 
analysis  of,  430 ;  radiation,  480 ; 
spectrum,  564  ;  properties  of  the,  573  ; 
dark  lines  of,  574,  579  ;  time,  21  ; 
day,  21 

Soleil's  saccharimeter,  677 

Solenoids,  874-878  ;  action  of  currents 
on,  875  ;  of  magnets  and  of  earth  on, 
876,  877  ;  on  solenoids,  878 

Solidification,  343 ;  change  of  volume 
on,  343,  346  ;  retardation  of,  345 

Solidity,  4,  7 

Solids,  conductivity  of,  404  ;  index  of 
refraction  in,  54S ;  diamagnetism  of, 
938  ;  linear  and  cubical  expansion  of, 

3;4>  319 

Solids,  formula;  of  expansion,  31S 

Solution,  342 

Sondhauss's  experiments,  23S 

Sonometer,  266,  932 

Sonorous  body,  222 

Sound,  221  ;  cause  of,  223  ;  not  propa- 
gated in  vacuo,  222  ;  propagated  in  all 
clastic  bodies,  224  ;  propagation  of,  in 
air,  225  ;  causes  which  influence  inten- 
sity of,  226  ;  apparatus  to  strengthen, 
227  ;  interference  of,  261 ;  velocityof,  in 
air,  230  ;  in  gases,  231 -232  ;  in  liquids, 
234 ;  solids,  235  ;  reflection  of,  236 ; 
refraction  of,  237  ;  relation  of  radiant 
heat  to,  446^  ;  transmission  of,  228  ; 
waves,  229 

Sound,  ilelmholtz's  analysis  of,  255 

Sound,  Kiinig's  apparatus,  255;  Kundt's, 
277 


Index. 


io8i 


sou 

Sounder,  896 

Sounds,  intensity  of,  289  ;  limit  of  per- 
ceptible, 244  ;  synthesis  of,  257  ;  per- 
ceptions of,  260 ;  produced  by  currents, 
865 

Space,  meaSire  of,  22 

Spar,  Iceland,  659 

Spark  and  brush  discharge,  7S7  ;  elec- 
trical, 762,  787  ;  duration  and  velocity 
of,  795 

Speaking  trumpet,  239;  tubes,  228 

Specific  gravity,  24,  119,  124;  bottle 
hydrometer,  120,  121;  of  solids,  120; 
of  gases,  335  ;  of  liquids,  123  ;  tables 
of,  124,  125 

Specific  heat,  448-460;  compound  bo- 
dies, 564  ;  detei-mination  of,  by  fusion 
of  ice,  450 ;  by  method  of  mixtures, 
452  ;  by  Regnault's  apparatus,  454  ; 
of  solids  and  liquids,  456,  457 ;  of 
gases,  460 

Specific  inductive  capacity,  748 

Spectacles,  630 

Spectra,  648 

Spectral  analysis,  575  ;  colours  and  pig- 
ment, 571 

Spectroscope,  576  ;  direct  vision,  577  ; 
experiments  with,  578  ;  uses  of  the, 
580 

Spectrum,  calorific,  573  ;  chemical,  573 

Spectrum,  430;  colours  of,  566;  pure, 
565  ;  solar,  564,  577 

Spectrum,  dark  lines  of,  574 

Spectrum,  diffraction,  648 

Spectrum,  luminous  properties  of,  573 

Spectmm  of  aurora  boreahs,  1003  ;  pro- 
perties of,  573 

Specular  reflection,  518 

Spherical  aberration,  533,  558  ;  mirrors, 
524  ;  focus  of,  525  ;  formulae  for,  530, 

Spheroidal  form  of  liquids,    84 ;    state, 

385 
Spherometer,  11 

Spiral,  882  ;  Roget's  vibrating,  859 
Spirit-level,  no 
Sprains,  17 
Spray  producer,  207 
Sprengel's  air-piimp,  205 
Spring  balance,  26 
Springs,  loio  ;  intermittent,  214 
Stable  equilibrium,  70 
Stars,  declination  of,  600;  spectral  analysis 

of,  582 
Staubbach,  76 
Stave,  252 
VSteam-engines,  465  ;  boiler,  466  ;  double 


TEL 

action,  or  Watt's,  467 ;  horn,  242 ; 
pipe,  207 ;  various  kinds  of,  472 ; 
work  of,  473 ;  heating  by,  490 ;  vessels, 

150 
Steel,  467 
Steeling,  857 
Stereoscopes,  622-624 
Sterometer,  185 
Stethoscope,  240 
Stills,  376 

Stool,  insulating,  762 
Stopcock,  doubly  exhausting,  202  ;  Gay- 

Lussac's,  382 
Storage  batteries,  849 
Storms,  magnetic,  694 
Stoves,  489  ;  Norwegian,  410 
Stowage,  115 

Stratification  of  electric  light,  924 
Stratus,  981 

Stringed  instruments,  279 
Strings,    265 ;    transverse    vibration  of, 

26s 
Subdominant  chords,  248 
Substance,  i 
Suction  pump,    216  ;   and   force   pump, 

217;     load    which    piston     supports, 

218 
Sulphate  of  mercury  battery,  812 
Sun,  510  ;  analysis  of,  579;  constitution 

of,  579 
Sun-spots,  701 
Superfusion,  345 
Surface      level,      67  ;      tension,      137  ; 

coloured,  581 
Suspension,  axis  of,  71  ;  Cardan's,  160 
Suspensory  ligament,  612 
Swan  lamps,  838 

Swimming,  118  ; -bladder  of  fishes,  117 
Swing  of  a  needle,  821 
Switch,  932 

Symmer's  theory  of  electricity,  728 
Synthesis  of  sounds,  257 
Syphon,    213;    barometer,    1 67  ;    inter- 
mittent, 214;  recorder,  892 
Syren,  242 
Syringe,  pneumatic,  154,  479 


TAMTAM  rnetal,  94 
Tangent  compass,  or  galvanometer, 
823,  847 
Tasimeter,  933 
Tears  of  wine,  136 

Telegraph,  cables,  Covvper's  writing, 
890;  induction  in,  891  ;  electric,  886- 
890 ;  electrochemical,  892  ;  dial, 
888  ;  Morse's,  889 

4  A 


io82 


Index. 


Telegraphy,  duplex,  893 

Telephone,  885,  930  ;  Edison's,  934  ; 
Reis's,  882  ;  toy,  235 

Telescopes,  595-601  ;  astronomical,  595; 
Galilean,  597  ;  Gregorian,  599  ;  Her- 
schelian,  601  ;  Newtonian,  600  ;'  re- 
flecting, Rosse's,  601 

Telluric  lines,  573 

Telpherage,  920^ 

Temper,  94 

Temperature,  297,  448  ;  correction  for, 
in  barometer,  170  ;  critical,  370  ;  of 
a  body,  297  ;  determined  by  specific 
heat,  457 

Temperature,  absolute  zero  of,  496  ;  in- 
fluence of,  on  specific  gravity,  123  ; 
mean,  1004  ;  how  modified,  1005 ; 
distribution  of,  1009  ;  of  lakes,  seas, 
and  springs,  loio 

Temperatures,  diff"erent  remarkable,  312  ; 
influence  on  expansion,  318 

Tempering,  90,  94 

Tenacity,  7,  91 

Tension,  117,  736,  922  ;  maximum  of, 
electrical  machine,  755  ;  maximum  of, 
vapours,  353  ;  of  aqueous  vapour  at 
various  temperatures,  355-361  ;  of 
vapours  of  different  liquids,  359  ;  of 
mixed  liquids  in.  two  communicating 
vessels,  361  ;  free  surface,  137 

Terquem's  experiment,  735 

Terrestrial  currents,  901  ;  heat,  481  ; 
magnetic  couple,  690  ;  magnetism,  721  ; 
telescope,  596 

Terrestrial  gravitation,  67,  82 

Terrestrial  magnetic  couple,  690 

Tetanus,  827 

Thallium,  578 

Thaumatropc,  625 

Theodolite,  10 

Theory,  5  ;  of  induction,  747 

Thermal  analysis,  430 ;  unit,  447,  484  ; 
springs,  lOio 

Thermal  effects  of  the  current,  829,  830 

Thermal  rays,  transmutation  of,  434  ;: 
unit,  447 

Thermobarometer,  369 

Thermochrose,  436 

Thermo-dynamic  efficiency,  454 

Thermo-electric  battery,  412,  944 ; 
couples,  942  ;  currents,  941,  943,  947, 
pile,  412,  431,  943  ;  series,  940 

Thermo-electricity,  939 

Thermo-element,  940 

Thennometcr,  electric,  792 

Thermometers,  298 ;  liecquerel's  elec- 
trical, 948  ;  correction  of  readings,  328  ; 


TUB 

differential,  308  ;  division  tubes  of  in, 
299  ;  filling,  300  ;  graduation  of,  30X  ; 
determ.ination  of  fixed  points  of,  302  ; 
scale  of,  303  ;  displacement  of  zero, 
304  ;  limits  to  use  of,  305  ;  alcohol, 
306  ;  conditions  of  delicacy  of,  307  ; 
Kinnersley's,  792 ;  Leslie's,  308 ; 
Matthiessen's,  308  ;  Breguet's,  309  ; 
rnaximumand minimum, 310  ;  Siemens' 
electrical,  960  ;  weight,  323  ;  air,  331, 
334 

Thermometry,  297-300 

Thermo-multiplier,  Melloni's,  412,  946 

Thermomotive  wheel,  476 

Thennoscope,  308 

Thomson's  electrometers,  780,  781  ;  gal- 
vanometer, 822  ;  apparatus  for  atmo- 
spheric electricity,  993  » 

Thread  of  a  screw,  45 

Threads,  fine,  89 

Throw  of  a  needle,  82 1 

Thunder,  998 

Timbre,  246 

Time,  measure  of,  21  ,  mean  solar,  21 

Tint,  570  ;  transition,  677 

Tones,  combinational,  263  ;  differential, 
263 

Tonic,  248 

Toothed  wheel,  241 

Torricelli's  experiment,  161  ;  theorem, 
142  ;  vacuum,  168 

Torsion,  angle  of  89  ;  balance,  89,  704, 
734  ;  force  of,  89 

Total  reflection,  540 

Tourmaline,  658,  732 ;  pincette.  666 

Tourniquet,  hydraulic,  149 

Tower  of  Pisa,  69 

Toy  telephone,  235 

Traction,  elasticity  of,  88 

Trajectory,  25 

Transformation  of  energ}-,  64 

Transit,  21 

Transition  tint,  677 

Translucent  bodies,  500 

Transmission  of  heat,  403  ;  of  light,  499, 
542  ;  by  the  current,  844 

Transmission  of  sound,  228 

Transmitter  of  photophone,  936 

Transparency,  7,  500 

Transparent  media,  542-549 

Transpiration  of  gases,  192 

Triad,  harmonic,  247  1 

Triangle,  281  i 

Triangle  of  forces,  35  '  ( 

Trumpet,  speaking,  car,  239  ,' 

Tubes,  Gcissler's,  205,  925  ;  luminous.  ♦ 
789  ;  safety,  379  ;  speaking,  22S 


I 


Inde 


1083 


TUN 


Tuning-fork,  251,  281,  290 
Turbines,  150 
Twilight,  51S 
Twinkling  of  stars,  541 
Tympanum,  260 

Tyndall's    res(Sirches,    431,    446^,    986, 
00 1 


ULTRAGASEOUS  state,  927 
Unannealed  glass,    colours    pro- 
duced by,  668 

Undershot  wheels,  150 

Undulation,  length  of,  225,  637 

Undulatory  theoiy,  499,  637 

Uniaxial  crj'stals,  640-643  ;  double 
refraction  in,  642  ;  positive  and  nega- 
tive, 643 

Unit  jar,  Harris's,  778  ;  Jacobi's,  952  ; 
Siemens',  952  ;  thermal,  447 

Unit  of  length,  area  and  volume,  22  ; 
heat,  447  ;  of  work,  61 

Units,  fundamental,  6irt 

Unstable  equilibrium,  70 

Urinometer,  129 


VACUUM,  application  of,  to  con- 
struction of  air-pump,  200 ;  extent 
of,  produced  by  air-pump,  201  ; 
Crookes's,  446;  fall  of  bodies  in  a, 
76  ;  formation  of  vapour  in,  352  ;  heat 
radiated  in,  413  ;  reflection  in  a,  421  ; 
Torricellian,  168 

Valency,  change  of,  458 

Valve,  safety,  108,  371  ;  chest,  466 

Vane,  electrical,  764 

Vaporisation,  350  ;  latent  heat  of,  372, 
462 

Vapour,  aqueous,  tension  of,  at  various 
temperatures,  357-361  ;  formation  of, 
in  closed  tube,  370  ;  latent  heat  of, 
372 

Vapours,  349  ;  absorption  of  heat  by, 
435  ;  absoqjtive  powers  of,  440  ; 
density  of,  Gay-Lussac's  method,  386  ; 
Hofinann's,  387  ;  densities  of,  389  ; 
determination  of  latent  heat  of,  372, 
462  ;  Dumas's  method,  388  ;  elastic 
force  of,  351  ;  formation  of,  in  vacuo, 
352 ;  saturated,  353  ;  unsaturated, 
354  ;  tension  of  different  liquids,  359 ; 
of  mixed  liquids,  360  ;  in  communicat- 
ing vessels,  361 

Variations,  annual,  693 ;  accidental, 
694 ;  barometric,  171;  causes  of, 
172;     diurnal,    693;    relation   of,    to 


weather,  173  ;  in  magnetic  declination, 
691,   695 

Varley  unit,  952 

Velocity,  25,  6ia,  153  ;  direction  of,  56  ; 
of  efflux,  142  ;  of  electricity,  795  ;  of 
light,  505-507  ;  graphic  representation 
of  changes  of,  56 ;  Kundt's  method, 
277;  molecular,  294;  of  sound  in  air, 
230 ;  gases,  231,  232  ;  formula  for  cal- 
culating, 232;  of  winds,  975 

Velocities,  composition  of,  52  ;  examples 
of,  25 

Vena  contracta,  145 

Ventral  and  nodal  segment,  269,  274 

Verdel's  constant,  935 

Vernier,  10 

Vertical  line,  67 

Vestibule  of  the  ear,  260 

Vibrating  spiral,  Roget's,  859 

Vibration,  222;  arc  of,  55  ;  produced  by 

currents,  884;  of  tuning-forks,  290 
Vibrations,  262 ;  formulje,  275  ;  of 
membranes,  283  ;  laws  of,  267  ;  mea- 
surement of  number  of,  241 ;  number 
of,  producing  each  note,  251  ;  of  mu- 
sical pipe,  275  ;  of  rods,  281  ;  of 
plates,  282 ;  of  strings,  265,  267,  270 

Victoria  Regia,  485 

View,  field  of,  593 

Vinometers,  129 

Violin,  279 

Virtual  and  real  images,  514;  focus, 
525  ;  velocity,  46 

Viscosity,  96,  146,  147 ;  of  gases,  446 

Vision,  distance  of  distinct,  619;  bino- 
cular, 621 

Visual  angle,  617 

Vis  viva,  59,  448,  477  ' 

Vital  fluid,  797 

Vitreous  body,  612;  electricity,  727; 
fusion,  338  ;  humour,  612 

Vocal  chords,  259 

Volatile  liquids,  349 

Volta's    condensing    electroscope,    779 
.  electi-ophoinis,    752;    fundamental   ex- 
periment, 798 

Voltaic  arc,  833  ;  couple,  801  ;  currents, 
819  ;  induction,  900  ;  pile  and  battery, 
804,  805,  815,  832 

Voltameter,  silver,  846;  Faraday's,  846 

Volume,  22  ;  unit  of,  22,  24  ;  determi- 
nation of,  114;  change  of,  on  solidi- 
fication, 346  ;  of  a  liquid  and  that  of 
its  vapour,  relation  between,  390 

Volumometer,  185 

Von  Ebner's  electrical  machine,  794^ 

Voss's  electrical  machine,  759 


io"4 


Index. 


WAL 


ZON 


WALKER'S  battery,  8ii,  886 
Water  barometer,  1 76  ;  bellows, 
207  ;  decomposition  of,  123  ;  hammer, 
76  ;    hot,     heating  by,     492 ;     level, 
109 

Water,  maximum  density  of,  330;  spouts, 
984  ;  wheels,  150 

Watt's  engine,  467 

Wave,  condensed,-  225  ;  expanded,  225  ; 
lengths,  637,  649  ;  plane,  642 ;  of  a 
note,  253 

W' eather,  its  influence  on  barometric  ya- 
riations,  171,  172;  glasses,  174;  charts, 
979 ;  forecasts,  979 

Wedge,  44 

Wedgwood's  pyromete.r,  311 

W^eighing,  method  of  double,  75 

Weight,  23,  82  ;  relative,  43 ;  of  bodies 
weighed  in  air,  correction  for  loss 
of,  402;  of  gases,  155;  thermometer, 
324 

Weights  and  measures,  125 

Wells,  artesian,  iii 

Wells's  theory  of  dew,  987 

Werdermann"s  electric  lamp,  838 

Wet-bulb  hygrometer,  398 

Wheatstone's  bridge,  955  ;  photometer, 
509 ;  rheostat,  95 1  ;  rotating  mirror, 
795  ;  and  Cooke's  telegraph,  887 

Wlieel  and  axle,  42 

Wheel  barometer,  174;  thermomotive, 
476 

Wheels,  friction,  77;  escapement,  81 ; 
water,  150 

Whirl,  electrical,  764 

Whispering  galleries,  237 

Whistle,  safety,  466 

White  light,  deoomposition  of,  564  ;  re- 
composition  of,  567 

W^hite's  pulley,  41 

Wiedemann  and  Franz's  tables  of  con- 
ductivity, 404 


Wiedemann's  determination  of  electro- 
motive force,  959 

Wild's  magneto-electrical  machine,  915 

Wimshurst's  machine,  760 

Winckler's  cushions,  753 

Wind  chest,  272 ;  instruments,  270,  280 

Windhausen's  ice  machine,  494 

Winds,  causes  of,  976 ;  direction  and 
velocity  of,  974,  975,  1005  ;  law- of  ro- 
tation of,  978  ;  periodical,  regular,  and 
variable,  977 

Wine,  alcoholic  value  of,  378  ;  tears  of, 
136 

Wire  telegraph,  886 

Wollaston's  battery,  805  ;  camera  lucida, 
603  ;    cryophorus,  373  ;    doublet,  586 

Wood,  conductivity  of,  404 

Wood's  fusible  metal,  340 

Work,  34,  59  ;  measure  of,  60  ;  of  an 
engine,  472  ;  rate  of,  473  ;  unit  of,  61 ; 
internal  and  external,  of  bodies,  295  ; 
of  a  voltaic  battery,  832  ;  required  for 
the  production  of  electricity,  761 

Writing  telegraphs,  8S9,  890 


YARD,  British,  22,  125 
Yellow  spot,  612 
Young  and  Fresnel's  experiment,  645 
Young's  modukis,  88 


ZAMBONI'S  pile,  817 
Zero,   absolute,  496  ;  aqueous  va- 
pours below,  355  ;  displacement  of,  304 
Zigzag  lightning,  985 
Zinc,  amalgamated,  816  ;  carbon  battery, 

810 
Zither,  279 
Zoetrope,  625 
Zone,  isothermal,    1007 


Spottiswoolic  &"  Co.  Printers,  New-sirect  Sgiiarc,  Loudon. 


